From 122cdde905e56c08e5f0034b8e0d433fc1a7c88c Mon Sep 17 00:00:00 2001 From: Natalia Clementi Date: Wed, 6 May 2015 21:01:59 -0400 Subject: [PATCH 1/7] Clean math explained --- ...inear_vortex_Panel_Method-checkpoint.ipynb | 226 ++++ clementi/Linear_vortex_Panel_Method.ipynb | 248 ++++ clementi/resources/linear_el.svg | 1083 +++++++++++++++++ clementi/resources/linear_element.svg | 1083 +++++++++++++++++ 4 files changed, 2640 insertions(+) create mode 100644 clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb create mode 100644 clementi/Linear_vortex_Panel_Method.ipynb create mode 100644 clementi/resources/linear_el.svg create mode 100644 clementi/resources/linear_element.svg diff --git a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb new file mode 100644 index 0000000..b7b9804 --- /dev/null +++ b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb @@ -0,0 +1,226 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:0366b6a582b68692b0df4e3e38d4a41bed0a37df2acf15069a36c9ce96e32a1b" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "Content provided under a Creative Commons Attribution license, CC-BY 4.0; code under MIT license. (c)2015 Natalia C. Clementi\n", + "\n", + "Some pieces of code are based on the Aeropython course provided Lorena A. Barba " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#Linear vortex panel method" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the last lessons of _AeroPython_, we have been learning (we hope so!) how to apply panel method to represent a cylinder and different airfoils.\n", + "\n", + "We started with a simple source panel method ([Lesson10](http://nbviewer.ipython.org/urls/github.com/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb)) but we realized that if we want to generate lift this method was not able to provide it. Do you remember why?...**Source panel method gives as a solution with no circulation** and we need *circulation* so we can have lift. \n", + "\n", + "Then, to get a solution with circulation we add, to the constant source panel method, vortices to our panels and that allows us to may have lift force.([Lesson11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb))\n", + "\n", + "There are other ways to generate a solution with circulation. One of them is to use only vortices. However, in this case we need to use linear elements instead of use constant ones, as we were doing in the previous lessons. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##What does linear elements mean?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far, we were treating our singularities distribution with constant stregth along the panels. Now we allow the strength to vary linearly.\n", + "\n", + "\\begin{equation}\n", + " \\gamma(x)= \\gamma_0 + \\gamma_1 (x-x_1) \n", + "\\end{equation}\n", + "\n", + "where $\\gamma_0$ is constant and $\\gamma_1$ is the slope. Using the principle of superposition we can separate our problem into a constant-strength elements and linear varying varying elements, to finally add this two solutions. \n", + "\n", + "\n", + "
\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Derivation of the linear vortex panel method" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So now, using the powers of superposition, and remembering that the potential at a location $(x,y)$ in this case is:\n", + "\n", + "\\begin{equation}\n", + " \\phi(x, y) = \\phi_{\\text{free-stream}}(x, y)+ \\phi_{\\text{vortex-sheet}}(x, y)\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Explicitly" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{equation}\n", + " \\phi(x, y) = xU_{\\infty}\\cos(\\alpha) + yU_{\\infty}\\sin(\\alpha) -\n", + " \\frac{1}{2\\pi} \\int_{sheet} \\gamma(s)\\tan^{-1} \\frac{y-\\eta(s)}{x-\\xi(s)}ds\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we discretize into $N$ panels, as we were doing in the preious lessons. Then we can write the potential at a point $(x,y)$ as:\n", + "\n", + "\\begin{equation}\n", + " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha - \\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where:\n", + "\n", + "\\begin{equation}\n", + "\\left\\{\n", + "\\begin{array}{l}\n", + "\\xi_j(s)=x_j-s\\sin\\beta_j \\\\\n", + "\\eta_j(s)=y_j+s\\cos\\beta_j\n", + "\\end{array}\n", + ",\\ \\ \\ \n", + "0\\le s \\le l_j\n", + "\\right.\n", + "\\end{equation}\n", + "\n", + "and $\\gamma_j (s)$ can be written as:\n", + "\\begin{equation}\n", + " \\gamma_j (s) = \\gamma_j + \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right)\\; s\n", + "\\end{equation}\n", + "\n", + "with $l_j$ the length of the panel $j$ and $\\beta_j$ is the angle between the panel's normal and the $x$-axis. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, replacing what we know for $\\gamma_j (s)$ we can write the potential as:\n", + "\n", + "\\begin{equation}\n", + " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha - \\sum_{j=1}^N \\frac{\\gamma_j}{2\\pi} \\int_j \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j \\\\ \n", + " -\\sum_{j=1}^N \\frac{1}{2\\pi} \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right) \\int_j s\\; \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first three terms of the potential should be familiar, we already fight with the math that those terms involve in the previous lessons. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Normal and tangential velocity\n", + "\n", + "We know that we can write the normal and tangential components of the velocity using:\n", + "\n", + "\\begin{equation}\n", + " \\left\\{\n", + " \\begin{array}{l}\n", + " U_{\\text{n}}(x, y)=\\frac{\\partial \\phi}{\\partial x}(x, y) \\,n_x+\\frac{\\partial \\phi}{\\partial y}(x, y) \\,n_y \\\\\n", + " U_{\\text{t}}(x, y)=\\frac{\\partial \\phi}{\\partial x}(x, y) \\,t_x+\\frac{\\partial \\phi}{\\partial y}(x, y) \\,t_y\n", + " \\end{array}\n", + " \\right.\n", + "\\end{equation}\n", + "\n", + "where $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$. Then in order to get the different components of the velocity we need to take some derivatives. We know that you don't like to do a lot of math, but if you completed the exercise of lesson 11 ([11_Lesson11_Exercise](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_Exercise.ipynb)) then you have all the derivatives done!!! " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, the components of the gradient should look like this:\n", + "\n", + "\\begin{align}\n", + " \\frac{\\partial \\phi}{\\partial x}(x,y) &= U_\\infty \\cos \\alpha \\\\\n", + " &+ \\frac{1}{{2\\pi}} \\sum_{j=1}^N \\gamma_j \\int_j \\frac{(y-\\eta_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j \\\\ \n", + " &+ \\frac{1}{2\\pi}\\sum_{j=1}^N \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right) \\int_j \\frac{s\\;(y-\\eta_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j\n", + "\\end{align}\n", + "\n", + "\\begin{align}\n", + " \\frac{\\partial \\phi}{\\partial y}(x,y) &= U_\\infty \\sin \\alpha \\\\\n", + " &- \\frac{1}{{2\\pi}} \\sum_{j=1}^N \\gamma_j \\int_j \\frac{(x-\\xi_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j \\\\ \n", + " &- \\frac{1}{2\\pi}\\sum_{j=1}^N \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right) \\int_j \\frac{s\\;(x-\\xi_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j\n", + "\\end{align}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, rearranging some terms we can write $U_{\\text{n}}(x, y)$ and $U_{\\text{t}}(x, y)$ as:\n", + "\n", + "\\begin{align}\n", + " U_{\\text{n}}(x, y) & = U_\\infty \\cos(\\alpha - \\beta_i) \\\\\n", + " &+\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\gamma_j \\left[ \\int_j f_j(s) {\\rm d}s \\cos(\\beta_i) - \\int_j g_j(s) {\\rm d}s \\sin(\\beta_i) \\right] \\\\\n", + " &-\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_j}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s \\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s \\sin(\\beta_i) \\right] \\\\\n", + " &+ \\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_{j+1}}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s \\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s \\sin(\\beta_i) \\right] \n", + "\\end{align}\n", + "\n", + "\\begin{align}\n", + " U_{\\text{t}}(x, y) & = U_\\infty \\sin(\\alpha - \\beta_i) \\\\\n", + " &+\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\gamma_j \\left[ \\int_j f_j(s) {\\rm d}s (-\\sin(\\beta_i)) - \\int_j g_j(s) {\\rm d}s (\\cos(\\beta_i)) \\right] \\\\\n", + " &-\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_j}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s (-\\sin(\\beta_i)) - \\int_j s\\,g_j(s) {\\rm d}s (\\cos(\\beta_i)) \\right] \\\\\n", + " &+ \\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_{j+1}}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s (-\\sin(\\beta_i)) - \\int_j s\\,g_j(s) {\\rm d}s (\\cos(\\beta_i)) \\right] \n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $f_j(s)$ and $g_j(s)$" + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/clementi/Linear_vortex_Panel_Method.ipynb b/clementi/Linear_vortex_Panel_Method.ipynb new file mode 100644 index 0000000..1e51916 --- /dev/null +++ b/clementi/Linear_vortex_Panel_Method.ipynb @@ -0,0 +1,248 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:38d540e7c4bd7a6fb8eb65ab4e0a69c7b9564eed3d5e60b99776224bfecacbb1" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "Content provided under a Creative Commons Attribution license, CC-BY 4.0; code under MIT license. (c)2015 Natalia C. Clementi\n", + "\n", + "Some pieces of code are based on the Aeropython course provided Lorena A. Barba " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#Linear vortex panel method" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the last lessons of _AeroPython_, we have been learning (we hope so!) how to apply panel method to represent a cylinder and different airfoils.\n", + "\n", + "We started with a simple source panel method ([Lesson10](http://nbviewer.ipython.org/urls/github.com/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb)) but we realized that if we want to generate lift this method was not able to provide it. Do you remember why?...**Source panel method gives as a solution with no circulation** and we need *circulation* so we can have lift. \n", + "\n", + "Then, to get a solution with circulation we add, to the constant source panel method, vortices to our panels and that allows us to may have lift force.([Lesson11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb))\n", + "\n", + "There are other ways to generate a solution with circulation. One of them is to use only vortices. However, in this case we need to use linear elements instead of use constant ones, as we were doing in the previous lessons. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##What does linear elements mean?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far, we were treating our singularities distribution with constant stregth along the panels. Now we allow the strength to vary linearly.\n", + "\n", + "\\begin{equation}\n", + " \\gamma(x)= \\gamma_0 + \\gamma_1 (x-x_1) \n", + "\\end{equation}\n", + "\n", + "where $\\gamma_0$ is constant and $\\gamma_1$ is the slope. Using the principle of superposition we can separate our problem into a constant-strength elements and linear varying varying elements, to finally add this two solutions. \n", + "\n", + "\n", + "
\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Derivation of the linear vortex panel method" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So now, using the powers of superposition, and remembering that the potential at a location $(x,y)$ in this case is:\n", + "\n", + "\\begin{equation}\n", + " \\phi(x, y) = \\phi_{\\text{free-stream}}(x, y)+ \\phi_{\\text{vortex-sheet}}(x, y)\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Explicitly" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{equation}\n", + " \\phi(x, y) = xU_{\\infty}\\cos(\\alpha) + yU_{\\infty}\\sin(\\alpha) -\n", + " \\frac{1}{2\\pi} \\int_{sheet} \\gamma(s)\\tan^{-1} \\frac{y-\\eta(s)}{x-\\xi(s)}ds\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we discretize into $N$ panels, as we were doing in the preious lessons. Then we can write the potential at a point $(x,y)$ as:\n", + "\n", + "\\begin{equation}\n", + " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha - \\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where:\n", + "\n", + "\\begin{equation}\n", + "\\left\\{\n", + "\\begin{array}{l}\n", + "\\xi_j(s)=x_j-s\\sin\\beta_j \\\\\n", + "\\eta_j(s)=y_j+s\\cos\\beta_j\n", + "\\end{array}\n", + ",\\ \\ \\ \n", + "0\\le s \\le l_j\n", + "\\right.\n", + "\\end{equation}\n", + "\n", + "and $\\gamma_j (s)$ can be written as:\n", + "\\begin{equation}\n", + " \\gamma_j (s) = \\gamma_j + \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right)\\; s\n", + "\\end{equation}\n", + "\n", + "with $l_j$ the length of the panel $j$ and $\\beta_j$ is the angle between the panel's normal and the $x$-axis. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, replacing what we know for $\\gamma_j (s)$ we can write the potential as:\n", + "\n", + "\\begin{equation}\n", + " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha - \\sum_{j=1}^N \\frac{\\gamma_j}{2\\pi} \\int_j \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j \\\\ \n", + " -\\sum_{j=1}^N \\frac{1}{2\\pi} \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right) \\int_j s\\; \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first three terms of the potential should be familiar, we already fight with the math that those terms involve in the previous lessons. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Normal and tangential velocity\n", + "\n", + "We know that we can write the normal and tangential components of the velocity using:\n", + "\n", + "\\begin{equation}\n", + " \\left\\{\n", + " \\begin{array}{l}\n", + " U_{\\text{n}}(x, y)=\\frac{\\partial \\phi}{\\partial x}(x, y) \\,n_x+\\frac{\\partial \\phi}{\\partial y}(x, y) \\,n_y \\\\\n", + " U_{\\text{t}}(x, y)=\\frac{\\partial \\phi}{\\partial x}(x, y) \\,t_x+\\frac{\\partial \\phi}{\\partial y}(x, y) \\,t_y\n", + " \\end{array}\n", + " \\right.\n", + "\\end{equation}\n", + "\n", + "where $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$. Then in order to get the different components of the velocity we need to take some derivatives. We know that you don't like to do a lot of math, but if you completed the exercise of lesson 11 ([11_Lesson11_Exercise](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_Exercise.ipynb)) then you have all the derivatives done!!! " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, the components of the gradient should look like this:\n", + "\n", + "\\begin{align}\n", + " \\frac{\\partial \\phi}{\\partial x}(x,y) &= U_\\infty \\cos \\alpha \\\\\n", + " &+ \\frac{1}{{2\\pi}} \\sum_{j=1}^N \\gamma_j \\int_j \\frac{(y-\\eta_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j \\\\ \n", + " &+ \\frac{1}{2\\pi}\\sum_{j=1}^N \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right) \\int_j \\frac{s\\;(y-\\eta_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j\n", + "\\end{align}\n", + "\n", + "\\begin{align}\n", + " \\frac{\\partial \\phi}{\\partial y}(x,y) &= U_\\infty \\sin \\alpha \\\\\n", + " &- \\frac{1}{{2\\pi}} \\sum_{j=1}^N \\gamma_j \\int_j \\frac{(x-\\xi_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j \\\\ \n", + " &- \\frac{1}{2\\pi}\\sum_{j=1}^N \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right) \\int_j \\frac{s\\;(x-\\xi_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2} {\\rm d}s_j\n", + "\\end{align}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, rearranging some terms we can write $U_{\\text{n}}(x, y)$ and $U_{\\text{t}}(x, y)$ as:\n", + "\n", + "\\begin{align}\n", + " U_{\\text{n}}(x, y) & = U_\\infty \\cos(\\alpha - \\beta_i) \\\\\n", + " &+\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\gamma_j \\left[ \\int_j f_j(s) {\\rm d}s \\cos(\\beta_i) - \\int_j g_j(s) {\\rm d}s \\sin(\\beta_i) \\right] \\\\\n", + " &-\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_j}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s \\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s \\sin(\\beta_i) \\right] \\\\\n", + " &+ \\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_{j+1}}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s \\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s \\sin(\\beta_i) \\right] \n", + "\\end{align}\n", + "\n", + "\\begin{align}\n", + " U_{\\text{t}}(x, y) & = U_\\infty \\sin(\\alpha - \\beta_i) \\\\\n", + " &+\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\gamma_j \\left[ \\int_j f_j(s) {\\rm d}s (-\\sin(\\beta_i)) - \\int_j g_j(s) {\\rm d}s (\\cos(\\beta_i)) \\right] \\\\\n", + " &-\\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_j}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s (-\\sin(\\beta_i)) - \\int_j s\\,g_j(s) {\\rm d}s (\\cos(\\beta_i)) \\right] \\\\\n", + " &+ \\frac{1}{{2\\pi}}\\sum_{j=1}^N \\frac{\\gamma_{j+1}}{l_j} \\left[ \\int_j s\\,f_j(s) {\\rm d}s (-\\sin(\\beta_i)) - \\int_j s\\,g_j(s) {\\rm d}s (\\cos(\\beta_i)) \\right] \n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $f_j(s)$ and $g_j(s)$ are:\n", + "\n", + "\\begin{equation}\n", + " f_j(s) = \\frac{(y-\\eta_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " g_j(s) = \\frac{(x-\\xi_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have all the expressions that we need to solve our problem, so let's start coding!!!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Discretization into panels" + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/clementi/resources/linear_el.svg b/clementi/resources/linear_el.svg new file mode 100644 index 0000000..6e6b48c --- /dev/null +++ b/clementi/resources/linear_el.svg @@ -0,0 +1,1083 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/clementi/resources/linear_element.svg b/clementi/resources/linear_element.svg new file mode 100644 index 0000000..6e6b48c --- /dev/null +++ b/clementi/resources/linear_element.svg @@ -0,0 +1,1083 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From 409049953e3ad3fe57d1797d5a86ad8de46cbe33 Mon Sep 17 00:00:00 2001 From: Natalia Clementi Date: Wed, 6 May 2015 21:36:19 -0400 Subject: [PATCH 2/7] Add naca0012 date and generate panels done --- ...inear_vortex_Panel_Method-checkpoint.ipynb | 272 ++++- clementi/Linear_vortex_Panel_Method.ipynb | 248 +++- clementi/resources/linear_element.svg | 1083 ----------------- clementi/resources/naca0012.dat | 130 ++ 4 files changed, 647 insertions(+), 1086 deletions(-) delete mode 100644 clementi/resources/linear_element.svg create mode 100644 clementi/resources/naca0012.dat diff --git a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb index b7b9804..1dfc597 100644 --- a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb +++ b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:0366b6a582b68692b0df4e3e38d4a41bed0a37df2acf15069a36c9ce96e32a1b" + "signature": "sha256:f7e3dc09316a32859999aa1a5fbb18a0422b6d75a49275ac14dbd9b93b850b9f" }, "nbformat": 3, "nbformat_minor": 0, @@ -216,8 +216,276 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "where $f_j(s)$ and $g_j(s)$" + "where $f_j(s)$ and $g_j(s)$ are:\n", + "\n", + "\\begin{equation}\n", + " f_j(s) = \\frac{(y-\\eta_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " g_j(s) = \\frac{(x-\\xi_j(s))}{(x-\\xi_j(s))^2 + (y-\\eta_j(s))^2}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have all the expressions that we need to solve our problem, so let's start coding!!!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Discretization into panels" ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Importing the libraries and modules we need.\n", + "import numpy\n", + "from scipy import integrate, linalg\n", + "from matplotlib import pyplot\n", + "#The next line allows as to plot directly in the notebook.\n", + "%matplotlib inline" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Loading the geometry from a data file\n", + "\n", + "x, y = numpy.loadtxt('./resources/naca0012.dat', dtype=float, delimiter='\\t', unpack=True)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `Panel` class is going to be similar to the one that we were using in the previous lessons. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Panel:\n", + " \"\"\"Contains information related to a panel.\"\"\"\n", + " def __init__(self, xa, ya, xb, yb):\n", + " \"\"\"Creates a panel.\n", + " \n", + " Arguments\n", + " ---------\n", + " xa, ya: Cartesian coordinates of the first end-point.\n", + " xb, yb: Cartesian coordinates of the second end-point.\n", + " \"\"\"\n", + " self.xa, self.ya = xa, ya\n", + " self.xb, self.yb = xb, yb\n", + " \n", + " self.xc, self.yc = (xa+xb)/2, (ya+yb)/2 # control-point (center-point)\n", + " self.length = numpy.sqrt((xb-xa)**2+(yb-ya)**2) # length of the panel\n", + " \n", + " # orientation of the panel (angle between x-axis and panel's normal)\n", + " if xb-xa <= 0.:\n", + " self.beta = numpy.arccos((yb-ya)/self.length)\n", + " elif xb-xa > 0.:\n", + " self.beta = numpy.pi + numpy.arccos(-(yb-ya)/self.length)\n", + " \n", + " # location of the panel\n", + " if self.beta <= numpy.pi:\n", + " self.loc = 'upper face' #upper face\n", + " else:\n", + " self.loc = 'lower face' #lower face\n", + " \n", + " self.vt = 0. # tangential velocity\n", + " self.cp = 0. # pressure coefficient" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def define_panels(x ,y ,N):\n", + " \"\"\"Discretizes the geometry into panels using 'cosine' method.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y : Cartesian coordinates of the geometry (1d arrays).\n", + " N: number of panels (40 by default)\n", + " \n", + " Returns\n", + " -------\n", + " panels: Numpy array of panels\n", + " \"\"\"\n", + " \n", + " R = (x.max()-x.min())/2. #radius of the circle\n", + " x_center = (x.max()+x.min())/2. #x_coord of the center of the circle\n", + " \n", + " theta = numpy.linspace(0, 2*numpy.pi, N+1) #array of angles\n", + " x_circle = x_center + R*numpy.cos(theta) #x_coord of the circle\n", + " \n", + " x_ends = numpy.copy(x_circle) #x_ends of the geometry panels (idem circle)\n", + " y_ends = numpy.empty_like(x_ends) #initializing the y_ends array\n", + " y_t = numpy.empty_like(x_ends) #half thickness at a given value of x (centerline to surface)\n", + " \n", + " \n", + " t=0.12 #the maximum thickness as a fraction of the chord \n", + " #(so 100 t gives the last two digits in the NACA 4-digit denomination).\n", + " c=1. #coord length\n", + " \n", + " y_t = 5.*t*c*(0.2969*numpy.sqrt(x_ends/c) + (-0.1260)*(x_ends/c)+\\\n", + " (-0.3516)*(x_ends/c)**2 + (0.2843)*(x_ends/c)**3 +\\\n", + " (-0.1036)*(x_ends/c)**4)\n", + " \n", + " # computes the y_end\n", + " y_ends[0:N/2] = y_t[0:N/2]\n", + " y_ends[N/2:N] = -y_t[N/2:N]\n", + " \n", + " \n", + " panels = numpy.empty(N, dtype=object)\n", + " for i in range(N):\n", + " panels[i] = Panel(x_ends[i], y_ends[i], x_ends[i+1], y_ends[i+1])\n", + " \n", + " return panels " + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "##Create the panels\n", + "N = 40 # number of panels\n", + "panels = define_panels(x, y, N) # discretizes of the geometry into panels" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Plotting the geometry\n", + "\n", + "#First we'll set some parameters to have a nice plot\n", + "val_x, val_y = 0.1, 0.2 \n", + "\n", + "xp_min, xp_max = min(panel.xa for panel in panels) , max(panel.xa for panel in panels) \n", + "yp_min, yp_max = min(panel.ya for panel in panels) , max(panel.ya for panel in panels) \n", + "\n", + "#limits of the plot\n", + "xp_start, xp_end = xp_min-val_x*(xp_max-xp_min), xp_max+val_x*(xp_max-xp_min)\n", + "yp_start, yp_end = yp_min-val_y*(yp_max-yp_min), yp_max+val_y*(yp_max-yp_min)\n", + "\n", + "#Plot\n", + "size = 10\n", + "pyplot.figure(figsize=(size, (yp_end-yp_start)/(xp_end-xp_start)*size))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=15)\n", + "pyplot.ylabel('y', fontsize=15)\n", + "pyplot.xlim(xp_start, xp_end)\n", + "pyplot.ylim(yp_start, yp_end)\n", + "\n", + "pyplot.plot(x, y, color='deeppink', linestyle='-', linewidth=2);\n", + "\n", + "pyplot.plot(numpy.append([panel.xa for panel in panels], panels[0].xa), \n", + " numpy.append([panel.ya for panel in panels], panels[0].ya), \n", + " linestyle='-', linewidth=1, marker='o', markersize=6, color='#483D8B');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Free stream conditions\n", + "\n", + "The airfoil is immersed in a free-stream ($U_\\infty$,$\\alpha$) where $U_\\infty$ and $\\alpha$ are the velocity magnitude and angle of attack, respectively." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Freestream:\n", + " \"\"\"Freestream conditions.\"\"\"\n", + " def __init__(self, U_inf=1.0, alpha=0.0):\n", + " \"\"\"Sets the freestream conditions.\n", + " \n", + " Arguments\n", + " ---------\n", + " U_inf: Farfield speed (default 1.0).\n", + " alpha: Angle of attack in degrees (default 0.0).\n", + " \"\"\"\n", + " self.U_inf = U_inf\n", + " self.alpha = alpha*numpy.pi/180 # degrees to radians" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "U_inf = 1.0 # freestream speed\n", + "alpha = 0.0 # angle of attack (in degrees)\n", + "freestream = Freestream(U_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] } ], "metadata": {} diff --git a/clementi/Linear_vortex_Panel_Method.ipynb b/clementi/Linear_vortex_Panel_Method.ipynb index 1e51916..1dfc597 100644 --- a/clementi/Linear_vortex_Panel_Method.ipynb +++ b/clementi/Linear_vortex_Panel_Method.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:38d540e7c4bd7a6fb8eb65ab4e0a69c7b9564eed3d5e60b99776224bfecacbb1" + "signature": "sha256:f7e3dc09316a32859999aa1a5fbb18a0422b6d75a49275ac14dbd9b93b850b9f" }, "nbformat": 3, "nbformat_minor": 0, @@ -240,6 +240,252 @@ "source": [ "##Discretization into panels" ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Importing the libraries and modules we need.\n", + "import numpy\n", + "from scipy import integrate, linalg\n", + "from matplotlib import pyplot\n", + "#The next line allows as to plot directly in the notebook.\n", + "%matplotlib inline" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Loading the geometry from a data file\n", + "\n", + "x, y = numpy.loadtxt('./resources/naca0012.dat', dtype=float, delimiter='\\t', unpack=True)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `Panel` class is going to be similar to the one that we were using in the previous lessons. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Panel:\n", + " \"\"\"Contains information related to a panel.\"\"\"\n", + " def __init__(self, xa, ya, xb, yb):\n", + " \"\"\"Creates a panel.\n", + " \n", + " Arguments\n", + " ---------\n", + " xa, ya: Cartesian coordinates of the first end-point.\n", + " xb, yb: Cartesian coordinates of the second end-point.\n", + " \"\"\"\n", + " self.xa, self.ya = xa, ya\n", + " self.xb, self.yb = xb, yb\n", + " \n", + " self.xc, self.yc = (xa+xb)/2, (ya+yb)/2 # control-point (center-point)\n", + " self.length = numpy.sqrt((xb-xa)**2+(yb-ya)**2) # length of the panel\n", + " \n", + " # orientation of the panel (angle between x-axis and panel's normal)\n", + " if xb-xa <= 0.:\n", + " self.beta = numpy.arccos((yb-ya)/self.length)\n", + " elif xb-xa > 0.:\n", + " self.beta = numpy.pi + numpy.arccos(-(yb-ya)/self.length)\n", + " \n", + " # location of the panel\n", + " if self.beta <= numpy.pi:\n", + " self.loc = 'upper face' #upper face\n", + " else:\n", + " self.loc = 'lower face' #lower face\n", + " \n", + " self.vt = 0. # tangential velocity\n", + " self.cp = 0. # pressure coefficient" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def define_panels(x ,y ,N):\n", + " \"\"\"Discretizes the geometry into panels using 'cosine' method.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y : Cartesian coordinates of the geometry (1d arrays).\n", + " N: number of panels (40 by default)\n", + " \n", + " Returns\n", + " -------\n", + " panels: Numpy array of panels\n", + " \"\"\"\n", + " \n", + " R = (x.max()-x.min())/2. #radius of the circle\n", + " x_center = (x.max()+x.min())/2. #x_coord of the center of the circle\n", + " \n", + " theta = numpy.linspace(0, 2*numpy.pi, N+1) #array of angles\n", + " x_circle = x_center + R*numpy.cos(theta) #x_coord of the circle\n", + " \n", + " x_ends = numpy.copy(x_circle) #x_ends of the geometry panels (idem circle)\n", + " y_ends = numpy.empty_like(x_ends) #initializing the y_ends array\n", + " y_t = numpy.empty_like(x_ends) #half thickness at a given value of x (centerline to surface)\n", + " \n", + " \n", + " t=0.12 #the maximum thickness as a fraction of the chord \n", + " #(so 100 t gives the last two digits in the NACA 4-digit denomination).\n", + " c=1. #coord length\n", + " \n", + " y_t = 5.*t*c*(0.2969*numpy.sqrt(x_ends/c) + (-0.1260)*(x_ends/c)+\\\n", + " (-0.3516)*(x_ends/c)**2 + (0.2843)*(x_ends/c)**3 +\\\n", + " (-0.1036)*(x_ends/c)**4)\n", + " \n", + " # computes the y_end\n", + " y_ends[0:N/2] = y_t[0:N/2]\n", + " y_ends[N/2:N] = -y_t[N/2:N]\n", + " \n", + " \n", + " panels = numpy.empty(N, dtype=object)\n", + " for i in range(N):\n", + " panels[i] = Panel(x_ends[i], y_ends[i], x_ends[i+1], y_ends[i+1])\n", + " \n", + " return panels " + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "##Create the panels\n", + "N = 40 # number of panels\n", + "panels = define_panels(x, y, N) # discretizes of the geometry into panels" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Plotting the geometry\n", + "\n", + "#First we'll set some parameters to have a nice plot\n", + "val_x, val_y = 0.1, 0.2 \n", + "\n", + "xp_min, xp_max = min(panel.xa for panel in panels) , max(panel.xa for panel in panels) \n", + "yp_min, yp_max = min(panel.ya for panel in panels) , max(panel.ya for panel in panels) \n", + "\n", + "#limits of the plot\n", + "xp_start, xp_end = xp_min-val_x*(xp_max-xp_min), xp_max+val_x*(xp_max-xp_min)\n", + "yp_start, yp_end = yp_min-val_y*(yp_max-yp_min), yp_max+val_y*(yp_max-yp_min)\n", + "\n", + "#Plot\n", + "size = 10\n", + "pyplot.figure(figsize=(size, (yp_end-yp_start)/(xp_end-xp_start)*size))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=15)\n", + "pyplot.ylabel('y', fontsize=15)\n", + "pyplot.xlim(xp_start, xp_end)\n", + "pyplot.ylim(yp_start, yp_end)\n", + "\n", + "pyplot.plot(x, y, color='deeppink', linestyle='-', linewidth=2);\n", + "\n", + "pyplot.plot(numpy.append([panel.xa for panel in panels], panels[0].xa), \n", + " numpy.append([panel.ya for panel in panels], panels[0].ya), \n", + " linestyle='-', linewidth=1, marker='o', markersize=6, color='#483D8B');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Free stream conditions\n", + "\n", + "The airfoil is immersed in a free-stream ($U_\\infty$,$\\alpha$) where $U_\\infty$ and $\\alpha$ are the velocity magnitude and angle of attack, respectively." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Freestream:\n", + " \"\"\"Freestream conditions.\"\"\"\n", + " def __init__(self, U_inf=1.0, alpha=0.0):\n", + " \"\"\"Sets the freestream conditions.\n", + " \n", + " Arguments\n", + " ---------\n", + " U_inf: Farfield speed (default 1.0).\n", + " alpha: Angle of attack in degrees (default 0.0).\n", + " \"\"\"\n", + " self.U_inf = U_inf\n", + " self.alpha = alpha*numpy.pi/180 # degrees to radians" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "U_inf = 1.0 # freestream speed\n", + "alpha = 0.0 # angle of attack (in degrees)\n", + "freestream = Freestream(U_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] } ], "metadata": {} diff --git a/clementi/resources/linear_element.svg b/clementi/resources/linear_element.svg deleted file mode 100644 index 6e6b48c..0000000 --- a/clementi/resources/linear_element.svg +++ /dev/null @@ -1,1083 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - image/svg+xml - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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-0.0032804 +0.990685 -0.0025595 +0.9947532 -0.0019938 +0.9976658 -0.001587 +0.9994161 -0.0013419 From 3d20402c6454ce70393449bea6cf51bc2cba24f6 Mon Sep 17 00:00:00 2001 From: Natalia Clementi Date: Thu, 7 May 2015 01:27:05 -0400 Subject: [PATCH 3/7] Fixing panels and getting gammas --- ...inear_vortex_Panel_Method-checkpoint.ipynb | 807 +++++++++++++++++- clementi/Linear_vortex_Panel_Method.ipynb | 769 ++++++++++++++++- clementi/resources/A_matrix.png | Bin 0 -> 29608 bytes 3 files changed, 1551 insertions(+), 25 deletions(-) create mode 100644 clementi/resources/A_matrix.png diff --git a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb index 1dfc597..ccdc9fe 100644 --- a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb +++ b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:f7e3dc09316a32859999aa1a5fbb18a0422b6d75a49275ac14dbd9b93b850b9f" + "signature": "sha256:729897b4ac8408749687ffaa1e77b2ca4760277f125ac2d7cbe8373f2eb0f49a" }, "nbformat": 3, "nbformat_minor": 0, @@ -351,7 +351,8 @@ " y_ends = numpy.empty_like(x_ends) #initializing the y_ends array\n", " y_t = numpy.empty_like(x_ends) #half thickness at a given value of x (centerline to surface)\n", " \n", - " \n", + " x_ends = numpy.append(x_ends, x_ends[0])\n", + " \n", " t=0.12 #the maximum thickness as a fraction of the chord \n", " #(so 100 t gives the last two digits in the NACA 4-digit denomination).\n", " c=1. #coord length\n", @@ -361,20 +362,42 @@ " (-0.1036)*(x_ends/c)**4)\n", " \n", " # computes the y_end\n", + " \n", " y_ends[0:N/2] = y_t[0:N/2]\n", - " y_ends[N/2:N] = -y_t[N/2:N]\n", + " y_ends[N/2:N+1] = -y_t[N/2:N+1]\n", " \n", " \n", " panels = numpy.empty(N, dtype=object)\n", " for i in range(N):\n", " panels[i] = Panel(x_ends[i], y_ends[i], x_ends[i+1], y_ends[i+1])\n", " \n", - " return panels " + " return panels , x_ends, y_ends " ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 4 + "prompt_number": 70 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print panels[0].xa , panels[0].ya\n", + "print panels[-1].xb , panels[-1].yb" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1.0 -1.66533453694e-17\n", + "1.0 6.28318530718\n" + ] + } + ], + "prompt_number": 50 }, { "cell_type": "code", @@ -382,12 +405,43 @@ "input": [ "##Create the panels\n", "N = 40 # number of panels\n", - "panels = define_panels(x, y, N) # discretizes of the geometry into panels" + "panels, x_ends, y_ends = define_panels(x, y, N)" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 13 + "prompt_number": 71 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print y_ends\n", + "#print panels[0].xa , panels[0].ya\n", + "#print panels[-1].xb , panels[-1].yb" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ -1.66533454e-17 8.91186344e-04 3.50136226e-03 7.65082165e-03\n", + " 1.30709457e-02 1.94384764e-02 2.64046500e-02 3.36104300e-02\n", + " 4.06861839e-02 4.72421489e-02 5.28615020e-02 5.71082323e-02\n", + " 5.95567645e-02 5.98411270e-02 5.77118565e-02 5.30826501e-02\n", + " 4.60488284e-02 3.68665348e-02 2.58933127e-02 1.35033681e-02\n", + " -0.00000000e+00 -1.35033681e-02 -2.58933127e-02 -3.68665348e-02\n", + " -4.60488284e-02 -5.30826501e-02 -5.77118565e-02 -5.98411270e-02\n", + " -5.95567645e-02 -5.71082323e-02 -5.28615020e-02 -4.72421489e-02\n", + " -4.06861839e-02 -3.36104300e-02 -2.64046500e-02 -1.94384764e-02\n", + " -1.30709457e-02 -7.65082165e-03 -3.50136226e-03 -8.91186344e-04\n", + " 1.66533454e-17]\n" + ] + } + ], + "prompt_number": 72 }, { "cell_type": "code", @@ -428,11 +482,11 @@ "output_type": 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U1KTMVHtd1NR7cDd6+HTkhbwzOj0nzqTiwX29zPiuyYzP6WU6NsuUZEtcIf35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\nICGEEEKIKeAZYPFkV0IIIYQ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"text": [ - "" + "" ] } ], - "prompt_number": 14 + "prompt_number": 73 }, { "cell_type": "markdown", @@ -463,7 +517,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 15 + "prompt_number": 74 }, { "cell_type": "code", @@ -477,15 +531,742 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 16 + "prompt_number": 75 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Flow-tangency boundary condition\n", + "\n", + "As we already know, to solve our problem, we need to require $U_{\\text{n}}(x, y)=0$ at the center (collocation point) of each panel. However we have to be careful, because at $(x_{c_i}, y_{c_i})$ all our integrals have a singularity. To skip that singularity, for $i=j$ we have to solve them analytically in the local coordinates of the panel.\n", + "\n", + "So for the flow-tangency boundary condition, the integrals (in local coordinates) that we have to solve analytically are:\n", + "\n", + "\\begin{equation}\n", + " I_1=\\frac{1}{2\\pi} \\int^l_0 \\frac{(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " I_2=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "\n", + "\n", + "\\begin{equation}\n", + " I_1=0 \\qquad ; \\qquad I_2=-\\frac{1}{2\\pi}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For all the integrals that appear in our equations, we are gonna use the function `integrate.quad()` from SciPy. So following the same idea we use in the previous lessons, we are going to define two integrate functions on to solve the terms of the form:\n", + "\n", + "`integral`:\n", + "\n", + "\\begin{equation}\n", + " \\int_j f_j(s) {\\rm d}s\\;a - \\int_j g_j(s) {\\rm d}s\\;b\n", + "\\end{equation}\n", + "\n", + "`integral_s`:\n", + "\n", + "\\begin{equation}\n", + " \\int_j s\\,f_j(s) {\\rm d}s\\;a - \\int_j s\\,g_j(s) {\\rm d}s\\;b\n", + "\\end{equation}\n", + "\n", + "where $a$ and $b$ can be $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$ depending the case. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral(x, y, panel, dxdk, dydk):\n", + " \"\"\"\n", + " Arguments\n", + " ---------\n", + " x, y: Cartesian coordinates of the point.\n", + " panel: panel which contribution is evaluated.\n", + " dxdk: derivative of x in the z-direction.\n", + " dydk: derivative of y in the z-direction.\n", + " \n", + " Returns\n", + " -------\n", + " Integral over the panel of the influence at one point.\n", + " \"\"\"\n", + " def func(s):\n", + " return ( ((x - (panel.xa - numpy.sin(panel.beta)*s))*dxdk\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))*dydk)\n", + " / ((x - (panel.xa - numpy.sin(panel.beta)*s))**2\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 76 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral_s(x, y, panel, dxdk, dydk):\n", + " \"\"\"\n", + " Arguments\n", + " ---------\n", + " x, y: Cartesian coordinates of the point.\n", + " panel: panel which contribution is evaluated.\n", + " dxdk: derivative of x in the z-direction.\n", + " dydk: derivative of y in the z-direction.\n", + " \n", + " Returns\n", + " -------\n", + " Integral over the panel of the influence at one point.\n", + " \"\"\"\n", + " def func(s):\n", + " return ( s*((x - (panel.xa - numpy.sin(panel.beta)*s))*dxdk\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))*dydk)\n", + " / ((x - (panel.xa - numpy.sin(panel.beta)*s))**2\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 77 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use this functions to calculate the coefficients of the matrices corresponding to each term in the equation for $U_{\\text{n}}(x, y)$ to finally solve the linear system $$[A][\\gamma] = [b]$$.\n", + "\n", + "So we will call:\n", + "\n", + "$A_1$ the term related to the first integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $A_2$ the term related to the second integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j s\\,f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ correspond to $\\gamma_j$ and $A_3$ correspond to $\\gamma_{j+1}$.\n", + "\n", + "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build Thre different functions that return these coefficients." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_1_normal(panels):\n", + " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_n ---> (A_1)\n", + " \"\"\"\n", + " N = len(panels)\n", + " A1 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(A1, 0.) #value of I_1\n", + "\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " A1[i,j] = 0.5/numpy.pi*(integral(p_i.xc, p_i.yc, p_j, -numpy.sin(p_i.beta),numpy.cos(p_i.beta)))\n", + " \n", + " return A1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 78 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_2_normal(panels):\n", + " \"\"\"\n", + " Build matrix coefficients associated with the second\n", + " integral in U_n ---> (A_2)\n", + " \"\"\"\n", + " N = len(panels)\n", + " A2 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(A2, -0.5/numpy.pi) #value of I_2\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " A2[i,j] = (0.5/numpy.pi)*(1./p_j.length)*(integral_s(p_i.xc, p_i.yc, p_j, -numpy.sin(p_i.beta),numpy.cos(p_i.beta)))\n", + " \n", + " return A2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 79 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_3_normal(panels, A2):\n", + " \"\"\"\n", + " Build matrix coefficients associated with the third\n", + " integral in U_n ---> (A_3)\n", + " \"\"\"\n", + " N = len(panels)\n", + " A3 = A2\n", + " \n", + " return A3" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 80 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Let's call this functions to get A1,A2,A3.\n", + "\n", + "A1 = coeff_1_normal(panels)\n", + "A2 = coeff_2_normal(panels)\n", + "A3 = coeff_3_normal(panels,A2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 81 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We got our coefficintes, but how are these guys related with the matrix $A$ that we need to build in order to solve our system?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##How to build the A matrix\n", + "\n", + "This is the moment, where you should grab a piece of paper and write some terms of the $U_n$ for a panel $i$. After writing couple of $j$-terms, you should notice that. (tip: write the terms counting from zero, so then you match this with the code)\n", + "\n", + "* For $j=0$ you only have contribution from the first and second integral ($A_1$ and $A_2$), which are the coefficients related with $\\gamma_j$. \n", + "\n", + "\n", + "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", + "\n", + "\n", + "* For $ 0
\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#In code, except for the kutta condition (in cell after)...\n", + "\n", + "def A_normal(panels,A1,A2,A3):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " A_n = numpy.zeros((N, N+1), dtype=float) \n", + " \n", + " for i in range(N):\n", + " \n", + " A_n[i,0] = A1[i,0] - A2[i,0]\n", + " A_n[i,-1] = A3[i,-1]\n", + " \n", + " for j in range(N-1):\n", + " \n", + " A_n[i,j+1] = A1[i,j+1] - A2[i,j+1] + A3[i,j]\n", + " \n", + " return A_n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 82 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Kutta condition\n", + "\n", + "In this case the _kutta condition_ is easy, we just need to ask $\\gamma_0 + \\gamma_{N}=0$ then:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Kutta array\n", + "\n", + "def kutta_array(N):\n", + " \"\"\"Builds the kutta array.\n", + " \n", + " Arguments\n", + " ---------\n", + " N: number of panels\n", + " \n", + " Returns\n", + " -------\n", + " k_a -- 1D array ((N+1)x1, N is the number of panels). kutta array\n", + " \"\"\"\n", + " k_a = numpy.zeros(N+1,dtype=float)\n", + "\n", + " k_a[0] = 1.\n", + " k_a[-1] = 1.\n", + " \n", + " return k_a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 83 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Building the A matrix and the RHS" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_matrix(A_n, k_a, N):\n", + " \"\"\"Builds the A matrix to solve the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: array of panels.\n", + " A_n: Nx(N+1) matrix (N is the number of panels).\n", + " k_a -- 1D array ((N+1)x1, N is the number of panels).\n", + " Returns\n", + " -------\n", + " A_solve: (N+1)x(N+1) matrix (N is the number of panels).\n", + " \"\"\"\n", + "\n", + " #Matrix A_normal (Nx(N+2))\n", + "\n", + " A_solve = numpy.empty((N+1, N+1), dtype=float)\n", + " \n", + " A_solve[0:N,:] = A_n[:,:]\n", + " A_solve[-1,:] = k_a[:]\n", + "\n", + " return A_solve" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 84 }, { "cell_type": "code", "collapsed": false, - "input": [], + "input": [ + "def build_rhs(panels, freestream):\n", + " \"\"\"Builds the RHS of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: array of panels.\n", + " freestream: farfield conditions.\n", + " \n", + " Returns\n", + " -------\n", + " b: 1D array ((N+1)x1, N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " b = numpy.empty(N+1,dtype=float)\n", + " \n", + " for i, panel in enumerate(panels):\n", + " b[i] = -freestream.U_inf * numpy.cos(freestream.alpha - panel.beta)\n", + " b[-1] = 0.\n", + " \n", + " return b" + ], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 85 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's call all the functions we need to solve the system" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "N=len(panels)\n", + "#To build A\n", + "A_n =A_normal(panels,A1,A2,A3)\n", + "k_a = kutta_array(N)\n", + "\n", + "#Putting all together to get A\n", + "A = build_matrix(A_n, k_a, N)\n", + "\n", + "#RHS\n", + "b = build_rhs(panels, freestream)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 86 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To solve the linear system we use `linalg.solve` from SciPy. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "gammas = linalg.solve(A, b)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 87 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print gammas" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ -4.21662619e-01 7.85345134e-01 8.88452244e-01 9.38163042e-01\n", + " 9.72623608e-01 9.99984608e-01 1.02340817e+00 1.04467929e+00\n", + " 1.06499834e+00 1.08514099e+00 1.10544154e+00 1.12574662e+00\n", + " 1.14539977e+00 1.16327415e+00 1.17781875e+00 1.18696629e+00\n", + " 1.18740033e+00 1.17128091e+00 1.11213209e+00 8.73968399e-01\n", + " 4.89980063e-14 -8.73968399e-01 -1.11213209e+00 -1.17128091e+00\n", + " -1.18740033e+00 -1.18696629e+00 -1.17781875e+00 -1.16327415e+00\n", + " -1.14539977e+00 -1.12574662e+00 -1.10544154e+00 -1.08514099e+00\n", + " -1.06499834e+00 -1.04467929e+00 -1.02340817e+00 -9.99984608e-01\n", + " -9.72623608e-01 -9.38163042e-01 -8.88452244e-01 -7.85345134e-01\n", + " 4.21662619e-01]\n" + ] + } + ], + "prompt_number": 88 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_1_tangential(panels):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " B1 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(B1, -0.5)\n", + "\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " B1[i,j] = 0.5/numpy.pi*(integral(p_i.xc, p_i.yc, p_j,-numpy.cos(p_i.beta), -numpy.sin(p_i.beta)))\n", + " \n", + " return B1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 89 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_2_tangential(panels):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " B2 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(B2, -0.25)\n", + "\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " B2[i,j] = 0.5/numpy.pi*(1./p_j.length)*(integral_s(p_i.xc, p_i.yc, p_j,-numpy.cos(p_i.beta), -numpy.sin(p_i.beta)))\n", + " \n", + " return B2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 90 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_3_tangential(panels, B2):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " B3 = B2\n", + " \n", + " return B3" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 91 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def A_tangential(panels,B1,B2,B3):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " A_t = numpy.zeros((N, N+1), dtype=float) \n", + " \n", + " for i in range(N):\n", + " \n", + " A_t[i,0] = B1[i,0] - B2[i,0]\n", + " A_t[i,-1] = B3[i,-1]\n", + " \n", + " for j in range(N-1):\n", + " \n", + " A_t[i,j+1] = B1[i,j+1] - B2[i,j+1] + B3[i,j]\n", + " \n", + " return A_t" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 92 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "B1 = coeff_1_tangential(panels)\n", + "B2 = coeff_2_tangential(panels)\n", + "B3 = coeff_3_tangential(panels,B2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 93 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "A_t = A_tangential(panels,B1,B2,B3)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 94 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 95 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " vt = numpy.dot(A_t, gammas) + b_t" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 96 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i, panel in enumerate(panels):\n", + " panel.vt = vt[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 97 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_pressure_coefficient(panels, freestream):\n", + " \"\"\"Computes the surface pressure coefficients.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \"\"\"\n", + " for panel in panels:\n", + " panel.cp = 1.0 - (panel.vt/freestream.U_inf)**2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 98 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "get_pressure_coefficient(panels, freestream)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 99 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "voverVsquared=numpy.array([0, 0.64, 1.01, 1.241, 1.378, 1.402, 1.411, 1.411, 1.399, 1.378, 1.35, 1.288, 1.228, 1.166, 1.109, 1.044, 0.956, 0.906, 0])\n", + "print voverVsquared" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 0. 0.64 1.01 1.241 1.378 1.402 1.411 1.411 1.399 1.378\n", + " 1.35 1.288 1.228 1.166 1.109 1.044 0.956 0.906 0. ]\n" + ] + } + ], + "prompt_number": 100 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xtheo=numpy.array([0, 0.5, 1.25, 2.5, 5.0, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, 90, 95, 100])\n", + "xtheo = xtheo/100\n", + "print xtheo" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 0. 0.005 0.0125 0.025 0.05 0.075 0.1 0.15 0.2 0.25\n", + " 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 1. ]\n" + ] + } + ], + "prompt_number": 101 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# plots the surface pressure coefficient\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = cp_min-val_y*(cp_max-cp_min), cp_max+val_y*(cp_max-cp_min)\n", + "\n", + "pyplot.figure(figsize=(10, 6))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('$C_p$', fontsize=16)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'upper face'], \n", + " [panel.cp for panel in panels if panel.loc == 'upper face'], \n", + " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'lower face'], \n", + " [panel.cp for panel in panels if panel.loc == 'lower face'], \n", + " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + "pyplot.plot(xtheo, 1-voverVsquared, color='k', linestyle='--',linewidth=2)\n", + "pyplot.legend(['extrados', 'intrados'], loc='best', prop={'size':14})\n", + "\n", + "#pyplot.ylim(-0.6, 1.)\n", + "\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Number of panels : %d' % N);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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iz8/PZ+zYsSQnJ2NhYYGPjw/+/v4EBATg4eGBupwxiEIIIfSX3IET95W9cAkB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\nTaGnMWyvclwDY1hK6+tZjixOWSXHLfwTIj9/P3v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+ "text": [ + "" + ] + } + ], + "prompt_number": 102 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##References" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Katz, J. & Plotkin, A. _Low speed aerodynamics. 1947-Second Edition \n", + "2. http://en.wikipedia.org/wiki/NACA_airfoil\n", + "3. http://turbmodels.larc.nasa.gov/naca0012_val.html\n" + ] } ], "metadata": {} diff --git a/clementi/Linear_vortex_Panel_Method.ipynb b/clementi/Linear_vortex_Panel_Method.ipynb index 1dfc597..e7b70e1 100644 --- a/clementi/Linear_vortex_Panel_Method.ipynb +++ b/clementi/Linear_vortex_Panel_Method.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:f7e3dc09316a32859999aa1a5fbb18a0422b6d75a49275ac14dbd9b93b850b9f" + "signature": "sha256:ed2ae6e256b68108a49a71903b890febff8656e49d039a6c97b07b673cb594c2" }, "nbformat": 3, "nbformat_minor": 0, @@ -261,7 +261,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel." + "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel.\n", + "\n", + "The data we are loading is just to plot the airfoil and to be ensure panels follow the shape of the airfoil. However, we are not going to use this data to build the panels, instead we will use the equation we mention before." ] }, { @@ -351,7 +353,8 @@ " y_ends = numpy.empty_like(x_ends) #initializing the y_ends array\n", " y_t = numpy.empty_like(x_ends) #half thickness at a given value of x (centerline to surface)\n", " \n", - " \n", + " x_ends = numpy.append(x_ends, x_ends[0]) # extend array with the last element using numpy.append \n", + " \n", " t=0.12 #the maximum thickness as a fraction of the chord \n", " #(so 100 t gives the last two digits in the NACA 4-digit denomination).\n", " c=1. #coord length\n", @@ -361,20 +364,21 @@ " (-0.1036)*(x_ends/c)**4)\n", " \n", " # computes the y_end\n", + " \n", " y_ends[0:N/2] = y_t[0:N/2]\n", - " y_ends[N/2:N] = -y_t[N/2:N]\n", + " y_ends[N/2:N+1] = -y_t[N/2:N+1]\n", " \n", " \n", " panels = numpy.empty(N, dtype=object)\n", " for i in range(N):\n", " panels[i] = Panel(x_ends[i], y_ends[i], x_ends[i+1], y_ends[i+1])\n", " \n", - " return panels " + " return panels " ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 4 + "prompt_number": 103 }, { "cell_type": "code", @@ -382,12 +386,12 @@ "input": [ "##Create the panels\n", "N = 40 # number of panels\n", - "panels = define_panels(x, y, N) # discretizes of the geometry into panels" + "panels = define_panels(x, y, N)" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 13 + "prompt_number": 104 }, { "cell_type": "code", @@ -428,11 +432,11 @@ "output_type": "display_data", "png": 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U1KTMVHtd1NR7cDd6+HTkhbwzOj0nzqTiwX29zPiuyYzP6WU6NsuUZEtcIf35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\nICGEEEKIKeAZYPFkV0IIIYQ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"text": [ - "" + "" ] } ], - "prompt_number": 14 + "prompt_number": 73 }, { "cell_type": "markdown", @@ -463,7 +467,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 15 + "prompt_number": 74 }, { "cell_type": "code", @@ -477,7 +481,466 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 16 + "prompt_number": 75 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Flow-tangency boundary condition\n", + "\n", + "As we already know, to solve our problem, we need to require $U_{\\text{n}}(x, y)=0$ at the center (collocation point) of each panel. However we have to be careful, because at $(x_{c_i}, y_{c_i})$ all our integrals have a singularity. To skip that singularity, for $i=j$ we have to solve them analytically in the local coordinates of the panel.\n", + "\n", + "So for the flow-tangency boundary condition, the integrals (in local coordinates) that we have to solve analytically are:\n", + "\n", + "\\begin{equation}\n", + " I_1=\\frac{1}{2\\pi} \\int^l_0 \\frac{(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " I_2=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "\n", + "\n", + "\\begin{equation}\n", + " I_1=0 \\qquad ; \\qquad I_2=-\\frac{1}{2\\pi}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For all the integrals that appear in our equations, we are gonna use the function `integrate.quad()` from SciPy. So following the same idea we use in the previous lessons, we are going to define two integrate functions on to solve the terms of the form:\n", + "\n", + "`integral`:\n", + "\n", + "\\begin{equation}\n", + " \\int_j f_j(s) {\\rm d}s\\;a - \\int_j g_j(s) {\\rm d}s\\;b\n", + "\\end{equation}\n", + "\n", + "`integral_s`:\n", + "\n", + "\\begin{equation}\n", + " \\int_j s\\,f_j(s) {\\rm d}s\\;a - \\int_j s\\,g_j(s) {\\rm d}s\\;b\n", + "\\end{equation}\n", + "\n", + "where $a$ and $b$ can be $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$ depending the case. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral(x, y, panel, dxdk, dydk):\n", + " \"\"\"\n", + " Arguments\n", + " ---------\n", + " x, y: Cartesian coordinates of the point.\n", + " panel: panel which contribution is evaluated.\n", + " dxdk: derivative of x in the z-direction.\n", + " dydk: derivative of y in the z-direction.\n", + " \n", + " Returns\n", + " -------\n", + " Integral over the panel of the influence at one point.\n", + " \"\"\"\n", + " def func(s):\n", + " return ( ((x - (panel.xa - numpy.sin(panel.beta)*s))*dxdk\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))*dydk)\n", + " / ((x - (panel.xa - numpy.sin(panel.beta)*s))**2\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 76 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral_s(x, y, panel, dxdk, dydk):\n", + " \"\"\"\n", + " Arguments\n", + " ---------\n", + " x, y: Cartesian coordinates of the point.\n", + " panel: panel which contribution is evaluated.\n", + " dxdk: derivative of x in the z-direction.\n", + " dydk: derivative of y in the z-direction.\n", + " \n", + " Returns\n", + " -------\n", + " Integral over the panel of the influence at one point.\n", + " \"\"\"\n", + " def func(s):\n", + " return ( s*((x - (panel.xa - numpy.sin(panel.beta)*s))*dxdk\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))*dydk)\n", + " / ((x - (panel.xa - numpy.sin(panel.beta)*s))**2\n", + " +(y - (panel.ya + numpy.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 77 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use this functions to calculate the coefficients of the matrices corresponding to each term in the equation for $U_{\\text{n}}(x, y)$ to finally solve the linear system $$[A][\\gamma] = [b]$$.\n", + "\n", + "So we will call:\n", + "\n", + "$A_1$ the term related to the first integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $A_2$ the term related to the second integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j s\\,f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ correspond to $\\gamma_j$ and $A_3$ correspond to $\\gamma_{j+1}$.\n", + "\n", + "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build Thre different functions that return these coefficients." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_1_normal(panels):\n", + " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_n ---> (A_1)\n", + " \"\"\"\n", + " N = len(panels)\n", + " A1 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(A1, 0.) #value of I_1\n", + "\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " A1[i,j] = 0.5/numpy.pi*(integral(p_i.xc, p_i.yc, p_j, -numpy.sin(p_i.beta),numpy.cos(p_i.beta)))\n", + " \n", + " return A1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 78 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_2_normal(panels):\n", + " \"\"\"\n", + " Build matrix coefficients associated with the second\n", + " integral in U_n ---> (A_2)\n", + " \"\"\"\n", + " N = len(panels)\n", + " A2 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(A2, -0.5/numpy.pi) #value of I_2\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " A2[i,j] = (0.5/numpy.pi)*(1./p_j.length)*(integral_s(p_i.xc, p_i.yc, p_j, -numpy.sin(p_i.beta),numpy.cos(p_i.beta)))\n", + " \n", + " return A2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 79 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_3_normal(panels, A2):\n", + " \"\"\"\n", + " Build matrix coefficients associated with the third\n", + " integral in U_n ---> (A_3)\n", + " \"\"\"\n", + " N = len(panels)\n", + " A3 = A2\n", + " \n", + " return A3" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 80 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Let's call this functions to get A1,A2,A3.\n", + "\n", + "A1 = coeff_1_normal(panels)\n", + "A2 = coeff_2_normal(panels)\n", + "A3 = coeff_3_normal(panels,A2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 81 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We got our coefficintes, but how are these guys related with the matrix $A$ that we need to build in order to solve our system?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##How to build the A matrix\n", + "\n", + "This is the moment, where you should grab a piece of paper and write some terms of the $U_n$ for a panel $i$. After writing couple of $j$-terms, you should notice that. (tip: write the terms counting from zero, so then you match this with the code)\n", + "\n", + "* For $j=0$ you only have contribution from the first and second integral ($A_1$ and $A_2$), which are the coefficients related with $\\gamma_j$. \n", + "\n", + "\n", + "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", + "\n", + "\n", + "* For $ 0
\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#In code, except for the kutta condition (in cell after)...\n", + "\n", + "def A_normal(panels,A1,A2,A3):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " A_n = numpy.zeros((N, N+1), dtype=float) \n", + " \n", + " for i in range(N):\n", + " \n", + " A_n[i,0] = A1[i,0] - A2[i,0]\n", + " A_n[i,-1] = A3[i,-1]\n", + " \n", + " for j in range(N-1):\n", + " \n", + " A_n[i,j+1] = A1[i,j+1] - A2[i,j+1] + A3[i,j]\n", + " \n", + " return A_n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 82 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Kutta condition\n", + "\n", + "In this case the _kutta condition_ is easy, we just need to ask $\\gamma_0 + \\gamma_{N}=0$ then:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Kutta array\n", + "\n", + "def kutta_array(N):\n", + " \"\"\"Builds the kutta array.\n", + " \n", + " Arguments\n", + " ---------\n", + " N: number of panels\n", + " \n", + " Returns\n", + " -------\n", + " k_a -- 1D array ((N+1)x1, N is the number of panels). kutta array\n", + " \"\"\"\n", + " k_a = numpy.zeros(N+1,dtype=float)\n", + "\n", + " k_a[0] = 1.\n", + " k_a[-1] = 1.\n", + " \n", + " return k_a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 83 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Building the A matrix and the RHS" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_matrix(A_n, k_a, N):\n", + " \"\"\"Builds the A matrix to solve the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: array of panels.\n", + " A_n: Nx(N+1) matrix (N is the number of panels).\n", + " k_a -- 1D array ((N+1)x1, N is the number of panels).\n", + " Returns\n", + " -------\n", + " A_solve: (N+1)x(N+1) matrix (N is the number of panels).\n", + " \"\"\"\n", + "\n", + " #Matrix A_normal (Nx(N+2))\n", + "\n", + " A_solve = numpy.empty((N+1, N+1), dtype=float)\n", + " \n", + " A_solve[0:N,:] = A_n[:,:]\n", + " A_solve[-1,:] = k_a[:]\n", + "\n", + " return A_solve" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 84 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_rhs(panels, freestream):\n", + " \"\"\"Builds the RHS of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: array of panels.\n", + " freestream: farfield conditions.\n", + " \n", + " Returns\n", + " -------\n", + " b: 1D array ((N+1)x1, N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " b = numpy.empty(N+1,dtype=float)\n", + " \n", + " for i, panel in enumerate(panels):\n", + " b[i] = -freestream.U_inf * numpy.cos(freestream.alpha - panel.beta)\n", + " b[-1] = 0.\n", + " \n", + " return b" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 85 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's call all the functions we need to solve the system" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "N=len(panels)\n", + "#To build A\n", + "A_n =A_normal(panels,A1,A2,A3)\n", + "k_a = kutta_array(N)\n", + "\n", + "#Putting all together to get A\n", + "A = build_matrix(A_n, k_a, N)\n", + "\n", + "#RHS\n", + "b = build_rhs(panels, freestream)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 86 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To solve the linear system we use `linalg.solve` from SciPy. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "gammas = linalg.solve(A, b)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 87 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have the solution of our system we can get the surface pressure coefficient by calculating the tangential velocity. So let's keep coding (and doing a little bit more of math)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Surface pressure coefficient" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] }, { "cell_type": "code", @@ -486,6 +949,288 @@ "language": "python", "metadata": {}, "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_1_tangential(panels):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " B1 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(B1, -0.5)\n", + "\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " B1[i,j] = 0.5/numpy.pi*(integral(p_i.xc, p_i.yc, p_j,-numpy.cos(p_i.beta), -numpy.sin(p_i.beta)))\n", + " \n", + " return B1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 89 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_2_tangential(panels):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " B2 = numpy.empty((N, N), dtype=float) \n", + " numpy.fill_diagonal(B2, -0.25)\n", + "\n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels): \n", + " if i != j:\n", + " B2[i,j] = 0.5/numpy.pi*(1./p_j.length)*(integral_s(p_i.xc, p_i.yc, p_j,-numpy.cos(p_i.beta), -numpy.sin(p_i.beta)))\n", + " \n", + " return B2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 90 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def coeff_3_tangential(panels, B2):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " B3 = B2\n", + " \n", + " return B3" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 91 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def A_tangential(panels,B1,B2,B3):\n", + " \"\"\"\n", + " \"\"\"\n", + " N = len(panels)\n", + " A_t = numpy.zeros((N, N+1), dtype=float) \n", + " \n", + " for i in range(N):\n", + " \n", + " A_t[i,0] = B1[i,0] - B2[i,0]\n", + " A_t[i,-1] = B3[i,-1]\n", + " \n", + " for j in range(N-1):\n", + " \n", + " A_t[i,j+1] = B1[i,j+1] - B2[i,j+1] + B3[i,j]\n", + " \n", + " return A_t" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 92 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "B1 = coeff_1_tangential(panels)\n", + "B2 = coeff_2_tangential(panels)\n", + "B3 = coeff_3_tangential(panels,B2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 93 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "A_t = A_tangential(panels,B1,B2,B3)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 94 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 95 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " vt = numpy.dot(A_t, gammas) + b_t" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 96 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i, panel in enumerate(panels):\n", + " panel.vt = vt[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 97 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_pressure_coefficient(panels, freestream):\n", + " \"\"\"Computes the surface pressure coefficients.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \"\"\"\n", + " for panel in panels:\n", + " panel.cp = 1.0 - (panel.vt/freestream.U_inf)**2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 98 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "get_pressure_coefficient(panels, freestream)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 99 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "voverVsquared=numpy.array([0, 0.64, 1.01, 1.241, 1.378, 1.402, 1.411, 1.411, 1.399, 1.378, 1.35, 1.288, 1.228, 1.166, 1.109, 1.044, 0.956, 0.906, 0])\n", + "print voverVsquared" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 0. 0.64 1.01 1.241 1.378 1.402 1.411 1.411 1.399 1.378\n", + " 1.35 1.288 1.228 1.166 1.109 1.044 0.956 0.906 0. ]\n" + ] + } + ], + "prompt_number": 100 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xtheo=numpy.array([0, 0.5, 1.25, 2.5, 5.0, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, 90, 95, 100])\n", + "xtheo = xtheo/100\n", + "print xtheo" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 0. 0.005 0.0125 0.025 0.05 0.075 0.1 0.15 0.2 0.25\n", + " 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 1. ]\n" + ] + } + ], + "prompt_number": 101 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# plots the surface pressure coefficient\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = cp_min-val_y*(cp_max-cp_min), cp_max+val_y*(cp_max-cp_min)\n", + "\n", + "pyplot.figure(figsize=(10, 6))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('$C_p$', fontsize=16)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'upper face'], \n", + " [panel.cp for panel in panels if panel.loc == 'upper face'], \n", + " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'lower face'], \n", + " [panel.cp for panel in panels if panel.loc == 'lower face'], \n", + " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + "pyplot.plot(xtheo, 1-voverVsquared, color='k', linestyle='--',linewidth=2)\n", + "pyplot.legend(['extrados', 'intrados'], loc='best', prop={'size':14})\n", + "\n", + "#pyplot.ylim(-0.6, 1.)\n", + "\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Number of panels : %d' % N);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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iz8/PZ+zYsSQnJ2NhYYGPjw/+/v4EBATg4eGBupwxiEIIIfSX3IET95W9cAkB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\nTaGnMWyvclwDY1hK6+tZjixOWSXHLfwTIj9/P3v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+ "text": [ + "" + ] + } + ], + "prompt_number": 102 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##References" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Katz, J. & Plotkin, A. _Low speed aerodynamics. 1947-Second Edition \n", + "2. http://en.wikipedia.org/wiki/NACA_airfoil\n", + "3. http://turbmodels.larc.nasa.gov/naca0012_val.html\n" + ] } ], "metadata": {} diff --git a/clementi/resources/A_matrix.png b/clementi/resources/A_matrix.png new file mode 100644 index 0000000000000000000000000000000000000000..cf6791286369d425e2e8d5229f9b4db8540616f7 GIT binary patch literal 29608 zcmce;by$>Z`}cbfASor%4GKu7gp^81gNPs%OitzTeMjkgBpQE;a==1VOlRFQi^V5Xw9R!6-4& z!6QyTwe7$k=*9}NQqaxqe<}4@5fDTN$w@tZ<(9BH-=PoqSkV(hOqC$l<;Pb>_9CEIhfVJiuW zFP7OhW+Q>)h=r%SsEIJkJ z=O;U1xtfI{H3GGdR;LUPR|gz+*|p19wx_EZ$7sa8SjM!=%;yoD2PCtZ?2W}^{Z39! z{Lh|0SId3PQB_mZ6-G%;9y?_FAqOl98$nZ3)3@*6KSoC0KRrFwx)N#+qm{inKPonE z#cpYB{iztsTjhHr{)1ERi^tLWeA6eK$D1OqC1a0;>=)3Ew`by)yx$+yXzwSSCy9H1 zQIWXfZ|_gkoH!SN+~P|v+b5IPLMa8CnwwGQd@k}kFIw8#jL-I$0)vD73JYzOC*R)Q z4`NL3^TVep|`LOSD; z*Fr+>*17GWSXfvv?Wlvbm~Ql?J=valo-FR|Fv(QPh&P{y(609=zcj1Oy9QT{2ie_R 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zvx&uM{G^zc`|H^*qZdj3{#E6aJb;_8O!g<$WVLQwm=<+xP3bFLkc7MU_t1*bu;~76A{guX@i5p3nI>X77$K z%*`L-gn}U(%NKH6Yh|nCyT|O62neK5_RFt8&5;(F+*Yt+qvu|1FL-BA0l|Pgiml52pBF`%eD%Wr&K7~?G$RYk4i1J*DUW`b0-6NYyr_tfh zY!FJu2|tvlA!6-u?}w-b_=U0tO3fnM6U9jp*Z~HE7ezxYq*dNMg*-!klziZUqL^td zg46<{5m|JCU&!SD+#0jco_r9Zz39MTB@c0+ Date: Thu, 7 May 2015 05:22:06 -0400 Subject: [PATCH 4/7] Final version done, let's wait for comments --- ...inear_vortex_Panel_Method-checkpoint.ipynb | 869 +++++++++++++++--- clementi/Linear_vortex_Panel_Method.ipynb | 787 ++++++++++++++-- .../resources/CP_Gregory_expdata_alpha_10.dat | 32 + clementi/styles/custom.css | 143 +++ 4 files changed, 1602 insertions(+), 229 deletions(-) create mode 100644 clementi/resources/CP_Gregory_expdata_alpha_10.dat create mode 100755 clementi/styles/custom.css diff --git a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb index ccdc9fe..031c3f9 100644 --- a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb +++ b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:729897b4ac8408749687ffaa1e77b2ca4760277f125ac2d7cbe8373f2eb0f49a" + "signature": "sha256:0f9d5fc56ace7b95d542a47f14a3414137e15233d5c9fb9b74bb33b56cb0eb2b" }, "nbformat": 3, "nbformat_minor": 0, @@ -261,7 +261,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel." + "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel.\n", + "\n", + "The data we are loading is just to plot the airfoil and to be ensure panels follow the shape of the airfoil. However, we are not going to use this data to build the panels, instead we will use the equation we mention before." ] }, { @@ -328,13 +330,12 @@ "cell_type": "code", "collapsed": false, "input": [ - "def define_panels(x ,y ,N):\n", + "def define_panels(N):\n", " \"\"\"Discretizes the geometry into panels using 'cosine' method.\n", " \n", " Arguments\n", " ---------\n", - " x, y : Cartesian coordinates of the geometry (1d arrays).\n", - " N: number of panels (40 by default)\n", + " N: number of panels \n", " \n", " Returns\n", " -------\n", @@ -351,7 +352,7 @@ " y_ends = numpy.empty_like(x_ends) #initializing the y_ends array\n", " y_t = numpy.empty_like(x_ends) #half thickness at a given value of x (centerline to surface)\n", " \n", - " x_ends = numpy.append(x_ends, x_ends[0])\n", + " x_ends = numpy.append(x_ends, x_ends[0]) # extend array with the last element using numpy.append \n", " \n", " t=0.12 #the maximum thickness as a fraction of the chord \n", " #(so 100 t gives the last two digits in the NACA 4-digit denomination).\n", @@ -371,77 +372,25 @@ " for i in range(N):\n", " panels[i] = Panel(x_ends[i], y_ends[i], x_ends[i+1], y_ends[i+1])\n", " \n", - " return panels , x_ends, y_ends " + " return panels " ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 70 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print panels[0].xa , panels[0].ya\n", - "print panels[-1].xb , panels[-1].yb" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "1.0 -1.66533453694e-17\n", - "1.0 6.28318530718\n" - ] - } - ], - "prompt_number": 50 + "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "##Create the panels\n", - "N = 40 # number of panels\n", - "panels, x_ends, y_ends = define_panels(x, y, N)" + "N = 100 # number of panels\n", + "panels = define_panels(N)" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 71 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print y_ends\n", - "#print panels[0].xa , panels[0].ya\n", - "#print panels[-1].xb , panels[-1].yb" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ -1.66533454e-17 8.91186344e-04 3.50136226e-03 7.65082165e-03\n", - " 1.30709457e-02 1.94384764e-02 2.64046500e-02 3.36104300e-02\n", - " 4.06861839e-02 4.72421489e-02 5.28615020e-02 5.71082323e-02\n", - " 5.95567645e-02 5.98411270e-02 5.77118565e-02 5.30826501e-02\n", - " 4.60488284e-02 3.68665348e-02 2.58933127e-02 1.35033681e-02\n", - " -0.00000000e+00 -1.35033681e-02 -2.58933127e-02 -3.68665348e-02\n", - " -4.60488284e-02 -5.30826501e-02 -5.77118565e-02 -5.98411270e-02\n", - " -5.95567645e-02 -5.71082323e-02 -5.28615020e-02 -4.72421489e-02\n", - " -4.06861839e-02 -3.36104300e-02 -2.64046500e-02 -1.94384764e-02\n", - " -1.30709457e-02 -7.65082165e-03 -3.50136226e-03 -8.91186344e-04\n", - " 1.66533454e-17]\n" - ] - } - ], - "prompt_number": 72 + "prompt_number": 5 }, { "cell_type": "code", @@ -480,13 +429,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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KdZtMeui+WB1D0ZtJm0eetHnXhRuUNe3bNjj6029vhxuqOPeY8ZTtKqP0+0pK\nDtVw1ycvYD1mSkh5W+pZPLDqLS7JCgZmHoVcj0JBg34yYvCx/Zj2+OUw2Aq2eOY7Rul3cV67oDmA\ng867OlvvF43fJ7H6PpcgLgo1fYjmzJ6Ps6Rle3uTHu67+5GwDzhCCCHa1+FYtAumQGk9HKzFs9dJ\nRWE5jyx5HGt6aDdlQtxx3HD304waYifTq5DpgX5eBW+j9rxoAKNSbdx5+VkwKBkGWWGQlcavR5N/\n17Pa4GzRAhiX2bwt3OCsaV/5bogu0p0axdoeTNpejgSC2bnSrxg1YmbzNhk3J4QQqrCzah4flNQz\nZ+4CnA0naB6u/u49pvazU2r0U2YO4DRCqhc27V2j2+1p+v4D3pp4DYaByTBAXeYsuQun90TNvu1d\nZlG6NvsG6U6NUW1/YRkPaOcNlVXuCAngoOWUJIBk6IQQMaMr3ZxN++cvegprXKsrDPzhYUpe2sQ4\ny3DKymopr66nvM5Nmc9LmSnA14eKGZqrfS6jN8DkKgOZiQn0S7KSNsCGcaCVOR98pjujM/HU/hhW\nTA/Zlpd+VYezO9uSzJmQTFyUCKc/Xy/Nv233a4we9hPNvsU73yQhJRVb1jnN2yRDFypWx1D0ZtLm\nkddb27xbAVnbAMj9CQvn/Rz7iFNo3F9D5fdVlB+oprzESXllHQ/seBWbTpZsz24H07OnkeFB7e70\nKmT4DGQkW7ip6p+4h+hMFLB+q2bLEkJzI3r12lf2Fg88dFu7kxsku3bk9db3eTgkE9dH6I19GKoM\nAJ2YtcRTx/FZl4Rss5onsew5ydAJIXpWh+POLpwClW4odcGhOrz7nVR+X8ljf38Ma0abqwlYTudP\ndz7FsmPs1Ae7NzO8ChkehQyvgqI/BI1j+6Vxz/UXQE4S5CSqt5mJYDJwjWOYfrbs+gWaAA70j8tX\nXPTjdo+pkl0TXSGZuBin++u04RNMDY0k2CZr9t+37XWSkmykDT6/ZX/J0AkhuimsjFogAM5GKKlX\nx53d9Eecysma53Lufo9ZmXYqDAEqTOriNILNB9/sWcMgnawaRe/zyinzSOlvw9A/ORiYqcucRTfj\nrDlOU6S9MWit/ybJlolIkUxcH9bezKSlS5aHzGxtUu1zMWjwrJBtVvMklt2xBHvuiTAqHcea/0im\nTog+pqvdmwCON1epMygTz2jedscNiyke9TnHxw+jsqqeSqebSlcDFYqfShNUmAJsOljOsFzt8wV8\nAUbXKaQdJLmuAAARSElEQVTHxZMRn0B6v2RS+tsw9k9mzrvrdcee2SYMIG3lLJ1HIO+6y7s0Bq2J\nZMtEb9Gbgrh0YAUwBCgC5gBVOvvZgYcBI7AEuC+4fREwHygNrt8COI5abSPscPrz2zvg6B28ho0Y\novscX+2r4I7LXsRTU8Qa33bSj2nJ1LU9F113Dva9UTSPoYhW0uZHX9vP5ykTxnDjjX/otIyme/OW\nx+Hzg1xwzHhq9lVTddBJZamTqop6qpxuKl2NPF3yNhkjQ09InpJ9Dg9sdHBxdjxpXkjzKqR5FYYb\n40hLsJCemkRZlQVX20oAg04ZyNTXrgOL9qsr7zRXlwOyrpx+40iS93nkxWqb96Yg7mbgPeB+4Kbg\n+s1t9jECjwPnAfuBz4G3ga2oI78eCi6iE13N0I1NsHCWMYlb6reQ3uagbDVP4onfPMKU+cn8x7OL\n/H++gTXh9ObH5YTDQhxZ3f2hpBeMvbTsn/wgawT2406DcheUumgoqaXqkJPq0lqqKup4YONLWHND\nT0Jrtf6Q3z77IiNyi0n0QapPDcZSvZDmU0j1KiRi1K3HqIEZ3PN/M6BfImQlqrdJ5ubHf+no1/4J\nanUCOOh+QCZZNRHNetOYuG3A2UAxkAMUAKPb7DMJuA01GwctQd69we21wF87eZ0+NSauqzq79MrM\nqVfiqjteU27vd2sYMeQCCr9zMGi4XfO4LW4TK/7xDGQmgKLETLZOiMPRrS5Kvc9o07jVKedAZYM6\n8L/Crd6Wu3CX1FFT7CTv7UfwZZ2lec6SXas5c6CdaiNUGwN4FUj1QYpXIdWn4Ch2kDlc51xnBz7k\nzR/dgCkrGIxlJUG/BMhWA7M5Vy3AWaq9vmdnY86a/k4ZdyZE9IyJy0YN4AjeZuvsMxDY22p9H3Ba\nq/XrgV8AG4A/oN8dKzrQ2a9ZU5IZ6rTlxg3J5MXJpzLjQIHu827bVsxj5z7DYGMc+8z7eaVyIykD\nWn7Z59/2ZMjrQ+x0y4rYdiSzYiFZa5cXKlwtwViFujz/xNNYkyaFPJfVPIm78+6nKP0baowBaoLB\nWI0pQLUR/ECKD4rq3AzWqUuqwcQ1tixS0hNJyUwmMSsJpV8iZCRARgLbH9yI060tlzg+C9MjU7QP\nBOVdfVm3xpw1tYF83oXoWKSDuPdQs2xt/aXNegDdE2PobmvyFHBH8P6dqBm5eV2tYG8Vyf78jg6e\nefMv1T8oL1qAxX42Kdte0u2OHWAyMQQTe72NLCldT/822Tpr/OncN+8BMo47SP/BqXzlLeLeDWuw\npp/dvE9H3bJHI+CL1TEUvVlPtflRC8Q8PqhuhOoGdalyB28beP6JZ7AmaoOxe+c9QEnGZpx+PzVG\ndfal0xhovv9NaQ0jkrR18QLZHoWRxnhs8fGk2CykpCVgS0/C0i8JJTOROcs3aAb/l1cVMnTiQMas\nvKLdvzPPf2W3JwBA5Mec9XZybIm8WG3zSAdx53fwWFM36iGgP6ATCrAfQn5IDkbNxtFm/yXAv9p7\noblz55KbmwtAamoq48ePb/7nFhQUAPS69SY9XR+LxcT0S07ni/Vb8Xj8VFYVM33muc0H5VMmjOGl\nF95iUKZ6JvLyqkJc3m954OnbsF84hYLXHVjvfKf57ymvKgQgI3U4dYEAj+z+lIq9AXY4dzJyqD3k\ncat5Erde+RdKxn7Mj06YROqgVD6q3ML60l28/cVmrElnNO/f9EVqCY6faf33rF//BRvWb8Xr8VNR\nVcy0H53bPLC7p9u3r69/9dVXh1X+/vv/yrvvvE96anbzoP0JE07usPz69V/w9pufYDVP0r5/zAao\n9zL5hIngbKRg3Tqo9zA590SoauCe+++k0TIWUgGa3s9Z3D/vAWoytvB5zXZcCuSkDKfWCNvrdlJv\ngOS04WwqqSY9teX93VTe6S7H4PEzCAO7G4pITzBzzoATsaUmstG1i/uKG2jS+vMxeMIg0n5zAhgU\nTtX8veq1O09xnar5fJZW/5c75i/usH2bPt/33bMYr9fPgP4DuWH+AiwWU8iXo155i8XU3HXa245n\nff14Luu9c73pflFREZ3pTWPi7gfKUWeb3ox6WGw7scEEbAemAAeA9cBlqBMb+gMHg/v9DjgV+JnO\n68iYuKOss7Esc2bPx1nSdrgj2FI2s+JPd8AeJ5f89f9wWydq9ikuXMMZAy6kPHhtwhQvfL3HwUCd\ncXiG/QU8c/YvScmykpSdjKFfEo6iL8l/fSVWa8sFqTs6D153zhrfnTFOvbnb+HCyVJEup8kW1X/M\nwryfYz9hIjg96rnInI0EahrwVDdQX+3iyncfpVFnnFjdzjVcmTaVeiPUGgLNt3VGqDcEqDXCt3vW\nMDJXO1asfNcarkmdijWgkBxnIjkhjuTEeKxWC8kpCSSnJZC37mlqbZM0ZW22b1mx/Fl1oL+iPUR3\nNm41nHaSsWZCRI9oGRN3L/AqahdoEeopRgAGAM8BP0LtMbgOWI06U/V51AAO1OBvPGqX63fANRGq\nt2ijs7Es7XbJXrsAzlITreZ/puLWycWOHJfDY9fPUM/UfsBJxb5qrigp0H2dvQ2N3LZlJ9XbAzQY\nwOpTA77Bw7Sza++f9wCJw78nKSmeZJuFJKuF/1Vu5eFvC7Bmt1yaLP+mR2FzmTqAPClOPUN7ogkS\nzDgKPiD/jqfb71rT0Wl3XDsiFSweTv10y/n82M85Bxp90OBTb11edanz4Fi3jvx/LMea2hJU5f92\nMd5TN3N2v+Nw1zXgqm/E7fKoS4MXd4MHd6OXe/e+jnVEaEBlTTyDP9/1DO/1/556gxp8uQxQbwQl\nAIl+2FnnRu/EOh4FrAGFHMVEUpyZxAQzyQlxJCXGk5iaQHJ6AlfW/U/33GRDTxrAvFcWQHIcGPR/\nK89zKPqfg+uC5dpxuF2UMtZMiNjRmzJxkRKVmbjWXRaxoLNsQFeyDe1m9oxfseJXC6GsHk9pPTWH\nnFy+9kkYcLZm3/Jda5iRZafOALVGNduypvAVjhtzmWbfA4UOfpQ9jQQ/WAJg8StY/PBi+TtYR2kz\ngoE973PPuJ8TZzZhjjNijjNhjlfv/+qjZ3Gnn6EpY6v/jBWX3agGAMbgYlDAYMCx9TPy3/sX1oyW\nv8NZsY6F02diP/l0MBiCLxwAXwD8ARwbPyH/32+GjDF0lq9j4ZSLsI+eAP6WfZuWgNfPnFcfpFYn\nIxpf+hGPnZqHt9FLY4MPr8eLt9GHx+vD6/Vz63evYhqqDRScO1ZzZcY0GhVoMECjEqDRgLquBFj5\n/SuMHqtt811FDsYPthPvV9u7ddur2+C1MgfpI7RZMc/37/PwcZeTmBhHotVCgi2ehNQE4mwWsJqZ\n88I9OI2naP8HGVtZ8cYS3WxYk1jIisXasSUaSJtHXjS3ebRk4kQf0lk2oCvZho4mW2BXgzszkAFY\nZ7+uO/Fi6MkD+cvdV6iDzivd4GzkzNv/rVu3nHgLM23pahbIE1wCPgKKQXf/Yq+XFYeKaVQCeBQ1\nw+MxgEcJsLWmjqHp2jJfllQz4811GABDAAyAMXj75V4HQ4e2ySamn83v//YyK96v0K3DZ/tWMaRt\nBjLjbH775mv8YLATv6LOYPQ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"text": [ - "" + "" ] } ], - "prompt_number": 73 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -517,7 +466,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 74 + "prompt_number": 7 }, { "cell_type": "code", @@ -531,7 +480,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 75 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -556,6 +505,11 @@ "\n", "\\begin{equation}\n", " I_1=0 \\qquad ; \\qquad I_2=-\\frac{1}{2\\pi}\n", + "\\end{equation}\n", + "\n", + "Tip:\n", + "\\begin{equation}\n", + " \\tan^{-1} \\left(\\frac{s-x}{y}\\right)=\\tan^{-1} \\left(\\frac{y}{x-s}\\right) \\;-\\; \\frac{\\pi}{2}\n", "\\end{equation}" ] }, @@ -607,7 +561,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 76 + "prompt_number": 9 }, { "cell_type": "code", @@ -636,7 +590,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 77 + "prompt_number": 10 }, { "cell_type": "markdown", @@ -660,7 +614,7 @@ "\n", "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ correspond to $\\gamma_j$ and $A_3$ correspond to $\\gamma_{j+1}$.\n", "\n", - "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build Thre different functions that return these coefficients." + "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." ] }, { @@ -686,7 +640,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 78 + "prompt_number": 11 }, { "cell_type": "code", @@ -710,7 +664,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 79 + "prompt_number": 12 }, { "cell_type": "code", @@ -729,7 +683,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 80 + "prompt_number": 13 }, { "cell_type": "code", @@ -744,7 +698,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 81 + "prompt_number": 14 }, { "cell_type": "markdown", @@ -803,7 +757,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 82 + "prompt_number": 15 }, { "cell_type": "markdown", @@ -841,7 +795,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 83 + "prompt_number": 16 }, { "cell_type": "markdown", @@ -867,7 +821,7 @@ " A_solve: (N+1)x(N+1) matrix (N is the number of panels).\n", " \"\"\"\n", "\n", - " #Matrix A_normal (Nx(N+2))\n", + " #Matrix A_solve (N+1)x(N+1)\n", "\n", " A_solve = numpy.empty((N+1, N+1), dtype=float)\n", " \n", @@ -879,7 +833,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 84 + "prompt_number": 17 }, { "cell_type": "code", @@ -909,7 +863,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 85 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -936,7 +890,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 86 + "prompt_number": 19 }, { "cell_type": "markdown", @@ -955,44 +909,87 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 87 + "prompt_number": 20 }, { - "cell_type": "code", - "collapsed": false, - "input": [ - "print gammas" - ], - "language": "python", + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ -4.21662619e-01 7.85345134e-01 8.88452244e-01 9.38163042e-01\n", - " 9.72623608e-01 9.99984608e-01 1.02340817e+00 1.04467929e+00\n", - " 1.06499834e+00 1.08514099e+00 1.10544154e+00 1.12574662e+00\n", - " 1.14539977e+00 1.16327415e+00 1.17781875e+00 1.18696629e+00\n", - " 1.18740033e+00 1.17128091e+00 1.11213209e+00 8.73968399e-01\n", - " 4.89980063e-14 -8.73968399e-01 -1.11213209e+00 -1.17128091e+00\n", - " -1.18740033e+00 -1.18696629e+00 -1.17781875e+00 -1.16327415e+00\n", - " -1.14539977e+00 -1.12574662e+00 -1.10544154e+00 -1.08514099e+00\n", - " -1.06499834e+00 -1.04467929e+00 -1.02340817e+00 -9.99984608e-01\n", - " -9.72623608e-01 -9.38163042e-01 -8.88452244e-01 -7.85345134e-01\n", - " 4.21662619e-01]\n" - ] - } - ], - "prompt_number": 88 + "source": [ + "Now we have the solution of our system we can get the surface pressure coefficient by calculating the tangential velocity. So let's keep coding (and doing a little bit more of math)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Surface pressure coefficient" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The pressure coefficient at the center of the $i$-th panel is:\n", + "\n", + "$$C_{p_i} = 1 - (\\frac{U_{t_i}}{U_\\infty})^2$$\n", + "\n", + "So, we have to compute the tangential velocity. However, we can not escape from the math. To calculate $U_t$, we have to do some integral, do you remember?. Guess what, yes! we have the singularities issue again. In this case, the integrals we have to solve analytically are:\n", + "\n", + "\\begin{equation}\n", + " I_3=\\frac{1}{2\\pi} \\int^l_0 \\frac{y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " I_4=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "\n", + "\n", + "\\begin{equation}\n", + " I_3=-\\frac{1}{2} \\qquad ; \\qquad I_4=-\\frac{1}{4}\n", + "\\end{equation}\n", + "\n", + "Tip:\n", + "\\begin{equation}\n", + " \\tan^{-1} \\left(\\frac{s-x}{y}\\right)=\\tan^{-1} \\left(\\frac{y}{x-s}\\right) \\;-\\; \\frac{\\pi}{2}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, following the same idea that we use to build the **A** matrix, we define:\n", + "\n", + "$B_1$ the term related to the first integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $B_2$ the term related to the second integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j s\\,f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j s\\,g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $B_3=B_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $B_2$ correspond to $\\gamma_j$ and $B_3$ correspond to $\\gamma_{j+1}$.\n", + "\n", + "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." + ] }, { "cell_type": "code", "collapsed": false, "input": [ "def coeff_1_tangential(panels):\n", + " \n", " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_t ---> (B_1)\n", " \"\"\"\n", + "\n", " N = len(panels)\n", " B1 = numpy.empty((N, N), dtype=float) \n", " numpy.fill_diagonal(B1, -0.5)\n", @@ -1007,7 +1004,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 89 + "prompt_number": 21 }, { "cell_type": "code", @@ -1015,6 +1012,8 @@ "input": [ "def coeff_2_tangential(panels):\n", " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_t ---> (B_2)\n", " \"\"\"\n", " N = len(panels)\n", " B2 = numpy.empty((N, N), dtype=float) \n", @@ -1030,7 +1029,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 90 + "prompt_number": 22 }, { "cell_type": "code", @@ -1038,6 +1037,8 @@ "input": [ "def coeff_3_tangential(panels, B2):\n", " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_t ---> (B_3)\n", " \"\"\"\n", " N = len(panels)\n", " B3 = B2\n", @@ -1047,7 +1048,28 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 91 + "prompt_number": 23 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Let's call this functions to get B1,B2,B3.\n", + "B1 = coeff_1_tangential(panels)\n", + "B2 = coeff_2_tangential(panels)\n", + "B3 = coeff_3_tangential(panels,B2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the same logic we used to build the **A** matrix, excepting that now we don't need the kutta condition, we can get the **A_tangential**." + ] }, { "cell_type": "code", @@ -1073,65 +1095,68 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 92 + "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ - "B1 = coeff_1_tangential(panels)\n", - "B2 = coeff_2_tangential(panels)\n", - "B3 = coeff_3_tangential(panels,B2)" + "A_t = A_tangential(panels,B1,B2,B3)" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 93 + "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ - "A_t = A_tangential(panels,B1,B2,B3)" + "#The vector associated with the free-stream for U_t\n", + "\n", + "b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 94 + "prompt_number": 27 }, { - "cell_type": "code", - "collapsed": false, - "input": [ - "b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n" - ], - "language": "python", + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "prompt_number": 95 + "source": [ + "###The tangential velocity:" + ] }, { "cell_type": "code", "collapsed": false, "input": [ - " vt = numpy.dot(A_t, gammas) + b_t" + " U_t = numpy.dot(A_t, gammas) + b_t" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 96 + "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "for i, panel in enumerate(panels):\n", - " panel.vt = vt[i]" + " panel.vt = U_t[i]" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 97 + "prompt_number": 29 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Pressure coefficient:" + ] }, { "cell_type": "code", @@ -1142,8 +1167,8 @@ " \n", " Arguments\n", " ---------\n", - " panels -- array of panels.\n", - " freestream -- farfield conditions.\n", + " panels: array of panels.\n", + " freestream: farfield conditions.\n", " \"\"\"\n", " for panel in panels:\n", " panel.cp = 1.0 - (panel.vt/freestream.U_inf)**2" @@ -1151,7 +1176,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 98 + "prompt_number": 30 }, { "cell_type": "code", @@ -1162,7 +1187,14 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 99 + "prompt_number": 31 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From [Lesson 10](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb) we kow the exact solution for zero angle of attack, so let copy that solution, to compare with our result." + ] }, { "cell_type": "code", @@ -1183,7 +1215,7 @@ ] } ], - "prompt_number": 100 + "prompt_number": 32 }, { "cell_type": "code", @@ -1205,13 +1237,14 @@ ] } ], - "prompt_number": 101 + "prompt_number": 33 }, { "cell_type": "code", "collapsed": false, "input": [ "# plots the surface pressure coefficient\n", + "\n", "val_x, val_y = 0.1, 0.2\n", "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", @@ -1224,15 +1257,177 @@ "pyplot.ylabel('$C_p$', fontsize=16)\n", "pyplot.plot([panel.xc for panel in panels if panel.loc == 'upper face'], \n", " [panel.cp for panel in panels if panel.loc == 'upper face'], \n", - " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + " color='r', linewidth=1, marker='x', markersize=8)\n", "pyplot.plot([panel.xc for panel in panels if panel.loc == 'lower face'], \n", " [panel.cp for panel in panels if panel.loc == 'lower face'], \n", - " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + " color='b', linewidth=0, marker='d', markersize=6)\n", "pyplot.plot(xtheo, 1-voverVsquared, color='k', linestyle='--',linewidth=2)\n", - "pyplot.legend(['extrados', 'intrados'], loc='best', prop={'size':14})\n", + "pyplot.legend(['upper face', 'lower face', 'analytical'], loc='best', prop={'size':14})\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(-0.65, 1.)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Number of panels : %d' % N);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Vqk0bFew1SLkXH2NyfuVKE9SRI+ZnCv/8rbdS9dpVr15dzZ8/37Tdwmrf87xM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\nkiUsWrSIcePG2f/g7t3Qty8UFMSuuBjzw0icROjYLRERiTM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+ "text": [ + "" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nice!! our solution match with the theoretical one. However the purpouse of use vortices as our singularities is to get some lift and see how our model behaves. So let's calculate solve the problem for an angle of attack $\\alpha=10$ degrees. We pick $10\u00b0$ because we have some experimental data for the coefficient of pressure of the upper face, to compare. [Gregory & O'Reilly pressure data.](http://turbmodels.larc.nasa.gov/naca0012_val.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Let's solve for $\\alpha=10\u00b0$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "U_inf = 1.0 # freestream speed\n", + "alpha = 10.0 # angle of attack (in degrees)\n", + "freestream_10 = Freestream(U_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 35 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#We need to recalculate the RHS\n", + "\n", + "b_10 = build_rhs(panels, freestream_10)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 36 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "gammas_10 = linalg.solve(A, b_10)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 37 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#The vector associated with the free-stream for U_t\n", + "\n", + "b_t_10 = freestream.U_inf * numpy.sin([freestream_10.alpha - panel.beta for panel in panels])\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 38 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Getting the tangential velocity\n", + "U_t_10 = numpy.dot(A_t, gammas_10) + b_t_10" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 39 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i, panel in enumerate(panels):\n", + " panel.vt = U_t_10[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 40 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "get_pressure_coefficient(panels, freestream_10)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 41 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we mention before we have some experimental data for the upper face, so let's import that data to compare with our results. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_exp , Cp_exp = numpy.loadtxt('./resources/CP_Gregory_expdata_alpha_10.dat', dtype=float, delimiter=' ', unpack=True)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 42 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# plots the surface pressure coefficient\n", "\n", - "#pyplot.ylim(-0.6, 1.)\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = cp_min-val_y*(cp_max-cp_min), cp_max+val_y*(cp_max-cp_min)\n", + "\n", + "pyplot.figure(figsize=(10, 6))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('$C_p$', fontsize=16)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'upper face'], \n", + " [panel.cp for panel in panels if panel.loc == 'upper face'], \n", + " color='r', linewidth=1, marker='d', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'lower face'], \n", + " [panel.cp for panel in panels if panel.loc == 'lower face'], \n", + " color='b', linewidth=1, marker='d', markersize=6)\n", "\n", + "pyplot.plot(x_exp,Cp_exp,color='g', linewidth=0, marker='D', markersize=8, markeredgecolor='g',\n", + "markerfacecolor='None', markeredgewidth=1.5)\n", + "\n", + "pyplot.legend(['upper face', 'lower face', 'Gregory exp_data (upper face)'], loc='best', prop={'size':14})\n", "pyplot.xlim(x_start, x_end)\n", "pyplot.ylim(y_start, y_end)\n", "pyplot.gca().invert_yaxis()\n", @@ -1244,13 +1439,213 @@ { "metadata": {}, "output_type": "display_data", - "png": 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iz8/PZ+zYsSQnJ2NhYYGPjw/+/v4EBATg4eGBupwxiEIIIfSX3IET95W9cAkB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\nd+7cvd6Xxsxt4JKkewTOBk6SJHjllVeYM2cOr732WtylBGc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HD0vVqlXl008/lfz8fOnWrZs88cQThmMsX75c3Nzc5JFHHpFdu3bJgQMH5PHH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\nYdfU8jytrqVF21599TXVx3vz3GqPVXPc7t2l0sOQKoDF7phvvzXL4cM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"text": [ - "" + "" ] } ], - "prompt_number": 102 + "prompt_number": 43 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Great!! Our results seem to match the experimental data. What we can do is calculate the lift coefficient and compare it with the experimental value. Morover, we can see how the error behaves for different number of panels. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's define a function to calculate the lift for different angles of attack:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_lift(freestream, Np):\n", + " \"\"\"\n", + " Get the lift coefficient for a number of panels Np\n", + " \"\"\"\n", + " #define panels\n", + " panels = define_panels(Np)\n", + " \n", + " #coefficients to build A\n", + " A1 = coeff_1_normal(panels)\n", + " A2 = coeff_2_normal(panels)\n", + " A3 = coeff_3_normal(panels,A2)\n", + " \n", + " #To build A\n", + " A_n =A_normal(panels,A1,A2,A3)\n", + " k_a = kutta_array(Np)\n", + "\n", + " #Putting all together to get A\n", + " A = build_matrix(A_n, k_a, Np)\n", + "\n", + " #RHS\n", + " b = build_rhs(panels, freestream)\n", + "\n", + " # solves the linear system\n", + " gammas = linalg.solve(A, b)\n", + " \n", + " #Coefficients to get A_tangential.\n", + " B1 = coeff_1_tangential(panels)\n", + " B2 = coeff_2_tangential(panels)\n", + " B3 = coeff_3_tangential(panels,B2)\n", + " \n", + " #A_tangential\n", + " A_t = A_tangential(panels,B1,B2,B3)\n", + " \n", + " #The vector associated with the free-stream for U_t\n", + " b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n", + "\n", + " #Get tangential velocity\n", + " U_t = numpy.dot(A_t, gammas) + b_t\n", + " \n", + " for i, panel in enumerate(panels):\n", + " panel.vt = U_t[i]\n", + " \n", + " #Get Cp\n", + " get_pressure_coefficient(panels, freestream)\n", + " \n", + " L = 0.\n", + " for panel in panels:\n", + " L -= panel.cp*panel.length*numpy.sin(panel.beta)\n", + " \n", + " return L" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 44 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can calculate the value of the lift coefficients for different number of panels and compare it with the value of the experimental data.\n", + "\n", + "The value of the experimental lift for $\\alpha = 10\u00b0$ was obtain from reference [4](https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises),\n", + "\n", + "$$ L_{exp} = 1.2219 $$\n", + "\n", + "with this value as a reference we can plot de relative error as a function of the number of panels $N_p$ and see how our model behaves." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "L_np=[]\n", + "Np_list=[20,40,60,80,100,120,140,160,180,200, 400]\n", + "for i in Np_list:\n", + " L_np.append(get_lift(freestream_10, i))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 45 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "L_exp = 1.2219\n", + "\n", + "#Relative error\n", + "\n", + "rel_err = []\n", + "for i in L_np:\n", + " rel_err.append(numpy.abs(L_exp - i)/L_exp)\n", + "\n", + "#Percentage error\n", + "\n", + "per_err = []\n", + "for i in rel_err:\n", + " per_err.append(100.*i)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 47 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Plotting\n", + "pyplot.figure(figsize=(10, 6))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('Np', fontsize=16)\n", + "pyplot.ylabel('error $\\%$', fontsize=16)\n", + "pyplot.xlim(10, 210)\n", + "pyplot.ylim(3, 8)\n", + "pyplot.xticks(numpy.linspace(10, 210, 21)) \n", + "pyplot.yticks(numpy.linspace(2, 8, 17))\n", + "\n", + "pyplot.title('Percentage error vs number of panels', fontsize=20)\n", + "\n", + "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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3Ag8Dv6XvyRhPEEXfDOKsW0/GkCRJLalVT8YAmAZ8jxiDtwtwKnBE+gF4L3An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\nIkmStJoiC711iIJtGXEo9u4hbKMd2I0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+ "text": [ + "" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#For Np=400 the precentage error is:\n", + "L_400 = per_err[-1]\n", + "\n", + "print ('L_400 = %.4f' %L_400)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "L_400 = 3.3855\n" + ] + } + ], + "prompt_number": 51 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we expected, when the number of panels increases, the percentage error decreases. For $Np >60$ the percentage error is less than $5\\%$ what is an acceptable value. As $Np$ keeps increasing, the error continues decreasing but slowly. For $Np=400$ the error is around $3.4\\%$, which is close to the value for $Np=200$ ($\\approx 3.5\\%$). Then, it is not worthy to solve for all this panels if we can get a similar performance for a smaller $Np$." + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "Challange task" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Try to do the same analysis we did in the last section, for the vortex-source panel method from [Lesson 11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb) and compare the results." + ] }, { "cell_type": "markdown", @@ -1265,8 +1660,194 @@ "source": [ "1. Katz, J. & Plotkin, A. _Low speed aerodynamics. 1947-Second Edition \n", "2. http://en.wikipedia.org/wiki/NACA_airfoil\n", - "3. http://turbmodels.larc.nasa.gov/naca0012_val.html\n" + "3. http://turbmodels.larc.nasa.gov/naca0012_val.html\n", + "4. https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises\n" ] + }, + { + "cell_type": "heading", + "level": 6, + "metadata": {}, + "source": [ + "Please ignore the cell below. It just loads our style for the notebook." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "def css_styling():\n", + " styles = open('./styles/custom.css', 'r').read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 54, + "text": [ + "" + ] + } + ], + "prompt_number": 54 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] } ], "metadata": {} diff --git a/clementi/Linear_vortex_Panel_Method.ipynb b/clementi/Linear_vortex_Panel_Method.ipynb index e7b70e1..031c3f9 100644 --- a/clementi/Linear_vortex_Panel_Method.ipynb +++ b/clementi/Linear_vortex_Panel_Method.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:ed2ae6e256b68108a49a71903b890febff8656e49d039a6c97b07b673cb594c2" + "signature": "sha256:0f9d5fc56ace7b95d542a47f14a3414137e15233d5c9fb9b74bb33b56cb0eb2b" }, "nbformat": 3, "nbformat_minor": 0, @@ -330,13 +330,12 @@ "cell_type": "code", "collapsed": false, "input": [ - "def define_panels(x ,y ,N):\n", + "def define_panels(N):\n", " \"\"\"Discretizes the geometry into panels using 'cosine' method.\n", " \n", " Arguments\n", " ---------\n", - " x, y : Cartesian coordinates of the geometry (1d arrays).\n", - " N: number of panels (40 by default)\n", + " N: number of panels \n", " \n", " Returns\n", " -------\n", @@ -378,20 +377,20 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 103 + "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "##Create the panels\n", - "N = 40 # number of panels\n", - "panels = define_panels(x, y, N)" + "N = 100 # number of panels\n", + "panels = define_panels(N)" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 104 + "prompt_number": 5 }, { "cell_type": "code", @@ -430,13 +429,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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KdZtMeui+WB1D0ZtJm0eetHnXhRuUNe3bNjj6029vhxuqOPeY8ZTtKqP0+0pK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\nBjLjbH775mv8YLATv6LOYPQ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"text": [ - "" + "" ] } ], - "prompt_number": 73 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -467,7 +466,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 74 + "prompt_number": 7 }, { "cell_type": "code", @@ -481,7 +480,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 75 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -506,6 +505,11 @@ "\n", "\\begin{equation}\n", " I_1=0 \\qquad ; \\qquad I_2=-\\frac{1}{2\\pi}\n", + "\\end{equation}\n", + "\n", + "Tip:\n", + "\\begin{equation}\n", + " \\tan^{-1} \\left(\\frac{s-x}{y}\\right)=\\tan^{-1} \\left(\\frac{y}{x-s}\\right) \\;-\\; \\frac{\\pi}{2}\n", "\\end{equation}" ] }, @@ -557,7 +561,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 76 + "prompt_number": 9 }, { "cell_type": "code", @@ -586,7 +590,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 77 + "prompt_number": 10 }, { "cell_type": "markdown", @@ -610,7 +614,7 @@ "\n", "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ correspond to $\\gamma_j$ and $A_3$ correspond to $\\gamma_{j+1}$.\n", "\n", - "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build Thre different functions that return these coefficients." + "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." ] }, { @@ -636,7 +640,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 78 + "prompt_number": 11 }, { "cell_type": "code", @@ -660,7 +664,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 79 + "prompt_number": 12 }, { "cell_type": "code", @@ -679,7 +683,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 80 + "prompt_number": 13 }, { "cell_type": "code", @@ -694,7 +698,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 81 + "prompt_number": 14 }, { "cell_type": "markdown", @@ -753,7 +757,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 82 + "prompt_number": 15 }, { "cell_type": "markdown", @@ -791,7 +795,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 83 + "prompt_number": 16 }, { "cell_type": "markdown", @@ -817,7 +821,7 @@ " A_solve: (N+1)x(N+1) matrix (N is the number of panels).\n", " \"\"\"\n", "\n", - " #Matrix A_normal (Nx(N+2))\n", + " #Matrix A_solve (N+1)x(N+1)\n", "\n", " A_solve = numpy.empty((N+1, N+1), dtype=float)\n", " \n", @@ -829,7 +833,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 84 + "prompt_number": 17 }, { "cell_type": "code", @@ -859,7 +863,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 85 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -886,7 +890,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 86 + "prompt_number": 19 }, { "cell_type": "markdown", @@ -905,7 +909,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 87 + "prompt_number": 20 }, { "cell_type": "markdown", @@ -924,39 +928,68 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] + "source": [ + "The pressure coefficient at the center of the $i$-th panel is:\n", + "\n", + "$$C_{p_i} = 1 - (\\frac{U_{t_i}}{U_\\infty})^2$$\n", + "\n", + "So, we have to compute the tangential velocity. However, we can not escape from the math. To calculate $U_t$, we have to do some integral, do you remember?. Guess what, yes! we have the singularities issue again. In this case, the integrals we have to solve analytically are:\n", + "\n", + "\\begin{equation}\n", + " I_3=\\frac{1}{2\\pi} \\int^l_0 \\frac{y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " I_4=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", + "\\end{equation}\n", + "\n", + "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "\n", + "\n", + "\\begin{equation}\n", + " I_3=-\\frac{1}{2} \\qquad ; \\qquad I_4=-\\frac{1}{4}\n", + "\\end{equation}\n", + "\n", + "Tip:\n", + "\\begin{equation}\n", + " \\tan^{-1} \\left(\\frac{s-x}{y}\\right)=\\tan^{-1} \\left(\\frac{y}{x-s}\\right) \\;-\\; \\frac{\\pi}{2}\n", + "\\end{equation}" + ] }, { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", + "cell_type": "markdown", "metadata": {}, - "outputs": [] + "source": [ + "So, following the same idea that we use to build the **A** matrix, we define:\n", + "\n", + "$B_1$ the term related to the first integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $B_2$ the term related to the second integral:\n", + "\n", + "\\begin{equation}\n", + " \\int_j s\\,f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j s\\,g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", + "\\end{equation}\n", + "\n", + "and $B_3=B_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $B_2$ correspond to $\\gamma_j$ and $B_3$ correspond to $\\gamma_{j+1}$.\n", + "\n", + "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." + ] }, { "cell_type": "code", "collapsed": false, "input": [ "def coeff_1_tangential(panels):\n", + " \n", " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_t ---> (B_1)\n", " \"\"\"\n", + "\n", " N = len(panels)\n", " B1 = numpy.empty((N, N), dtype=float) \n", " numpy.fill_diagonal(B1, -0.5)\n", @@ -971,7 +1004,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 89 + "prompt_number": 21 }, { "cell_type": "code", @@ -979,6 +1012,8 @@ "input": [ "def coeff_2_tangential(panels):\n", " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_t ---> (B_2)\n", " \"\"\"\n", " N = len(panels)\n", " B2 = numpy.empty((N, N), dtype=float) \n", @@ -994,7 +1029,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 90 + "prompt_number": 22 }, { "cell_type": "code", @@ -1002,6 +1037,8 @@ "input": [ "def coeff_3_tangential(panels, B2):\n", " \"\"\"\n", + " Build matrix coefficients associated with the first\n", + " integral in U_t ---> (B_3)\n", " \"\"\"\n", " N = len(panels)\n", " B3 = B2\n", @@ -1011,7 +1048,28 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 91 + "prompt_number": 23 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Let's call this functions to get B1,B2,B3.\n", + "B1 = coeff_1_tangential(panels)\n", + "B2 = coeff_2_tangential(panels)\n", + "B3 = coeff_3_tangential(panels,B2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the same logic we used to build the **A** matrix, excepting that now we don't need the kutta condition, we can get the **A_tangential**." + ] }, { "cell_type": "code", @@ -1037,65 +1095,68 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 92 + "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ - "B1 = coeff_1_tangential(panels)\n", - "B2 = coeff_2_tangential(panels)\n", - "B3 = coeff_3_tangential(panels,B2)" + "A_t = A_tangential(panels,B1,B2,B3)" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 93 + "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ - "A_t = A_tangential(panels,B1,B2,B3)" + "#The vector associated with the free-stream for U_t\n", + "\n", + "b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 94 + "prompt_number": 27 }, { - "cell_type": "code", - "collapsed": false, - "input": [ - "b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n" - ], - "language": "python", + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "prompt_number": 95 + "source": [ + "###The tangential velocity:" + ] }, { "cell_type": "code", "collapsed": false, "input": [ - " vt = numpy.dot(A_t, gammas) + b_t" + " U_t = numpy.dot(A_t, gammas) + b_t" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 96 + "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "for i, panel in enumerate(panels):\n", - " panel.vt = vt[i]" + " panel.vt = U_t[i]" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 97 + "prompt_number": 29 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Pressure coefficient:" + ] }, { "cell_type": "code", @@ -1106,8 +1167,8 @@ " \n", " Arguments\n", " ---------\n", - " panels -- array of panels.\n", - " freestream -- farfield conditions.\n", + " panels: array of panels.\n", + " freestream: farfield conditions.\n", " \"\"\"\n", " for panel in panels:\n", " panel.cp = 1.0 - (panel.vt/freestream.U_inf)**2" @@ -1115,7 +1176,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 98 + "prompt_number": 30 }, { "cell_type": "code", @@ -1126,7 +1187,14 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 99 + "prompt_number": 31 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From [Lesson 10](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb) we kow the exact solution for zero angle of attack, so let copy that solution, to compare with our result." + ] }, { "cell_type": "code", @@ -1147,7 +1215,7 @@ ] } ], - "prompt_number": 100 + "prompt_number": 32 }, { "cell_type": "code", @@ -1169,13 +1237,14 @@ ] } ], - "prompt_number": 101 + "prompt_number": 33 }, { "cell_type": "code", "collapsed": false, "input": [ "# plots the surface pressure coefficient\n", + "\n", "val_x, val_y = 0.1, 0.2\n", "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", @@ -1188,15 +1257,177 @@ "pyplot.ylabel('$C_p$', fontsize=16)\n", "pyplot.plot([panel.xc for panel in panels if panel.loc == 'upper face'], \n", " [panel.cp for panel in panels if panel.loc == 'upper face'], \n", - " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + " color='r', linewidth=1, marker='x', markersize=8)\n", "pyplot.plot([panel.xc for panel in panels if panel.loc == 'lower face'], \n", " [panel.cp for panel in panels if panel.loc == 'lower face'], \n", - " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + " color='b', linewidth=0, marker='d', markersize=6)\n", "pyplot.plot(xtheo, 1-voverVsquared, color='k', linestyle='--',linewidth=2)\n", - "pyplot.legend(['extrados', 'intrados'], loc='best', prop={'size':14})\n", + "pyplot.legend(['upper face', 'lower face', 'analytical'], loc='best', prop={'size':14})\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(-0.65, 1.)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Number of panels : %d' % N);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Vqk0bFew1SLkXH2NyfuVKE9SRI+ZnCv/8rbdS9dpVr15dzZ8/37Tdwmrf87xM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\nkiUsWrSIcePG2f/g7t3Qty8UFMSuuBjzw0icROjYLRERiTM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+ "text": [ + "" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nice!! our solution match with the theoretical one. However the purpouse of use vortices as our singularities is to get some lift and see how our model behaves. So let's calculate solve the problem for an angle of attack $\\alpha=10$ degrees. We pick $10\u00b0$ because we have some experimental data for the coefficient of pressure of the upper face, to compare. [Gregory & O'Reilly pressure data.](http://turbmodels.larc.nasa.gov/naca0012_val.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Let's solve for $\\alpha=10\u00b0$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "U_inf = 1.0 # freestream speed\n", + "alpha = 10.0 # angle of attack (in degrees)\n", + "freestream_10 = Freestream(U_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 35 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#We need to recalculate the RHS\n", "\n", - "#pyplot.ylim(-0.6, 1.)\n", + "b_10 = build_rhs(panels, freestream_10)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 36 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "gammas_10 = linalg.solve(A, b_10)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 37 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#The vector associated with the free-stream for U_t\n", "\n", + "b_t_10 = freestream.U_inf * numpy.sin([freestream_10.alpha - panel.beta for panel in panels])\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 38 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Getting the tangential velocity\n", + "U_t_10 = numpy.dot(A_t, gammas_10) + b_t_10" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 39 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i, panel in enumerate(panels):\n", + " panel.vt = U_t_10[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 40 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "get_pressure_coefficient(panels, freestream_10)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 41 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we mention before we have some experimental data for the upper face, so let's import that data to compare with our results. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_exp , Cp_exp = numpy.loadtxt('./resources/CP_Gregory_expdata_alpha_10.dat', dtype=float, delimiter=' ', unpack=True)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 42 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# plots the surface pressure coefficient\n", + "\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = cp_min-val_y*(cp_max-cp_min), cp_max+val_y*(cp_max-cp_min)\n", + "\n", + "pyplot.figure(figsize=(10, 6))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('$C_p$', fontsize=16)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'upper face'], \n", + " [panel.cp for panel in panels if panel.loc == 'upper face'], \n", + " color='r', linewidth=1, marker='d', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'lower face'], \n", + " [panel.cp for panel in panels if panel.loc == 'lower face'], \n", + " color='b', linewidth=1, marker='d', markersize=6)\n", + "\n", + "pyplot.plot(x_exp,Cp_exp,color='g', linewidth=0, marker='D', markersize=8, markeredgecolor='g',\n", + "markerfacecolor='None', markeredgewidth=1.5)\n", + "\n", + "pyplot.legend(['upper face', 'lower face', 'Gregory exp_data (upper face)'], loc='best', prop={'size':14})\n", "pyplot.xlim(x_start, x_end)\n", "pyplot.ylim(y_start, y_end)\n", "pyplot.gca().invert_yaxis()\n", @@ -1208,13 +1439,213 @@ { "metadata": {}, "output_type": "display_data", - "png": 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iz8/PZ+zYsSQnJ2NhYYGPjw/+/v4EBATg4eGBupwxiEIIIfSX3IET95W9cAkB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\nd+7cvd6Xxsxt4JKkewTOBk6SJHjllVeYM2cOr732WtylBGc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HD0vVqlXl008/lfz8fOnWrZs88cQThmMsX75c3Nzc5JFHHpFdu3bJgQMH5PHH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\nYdfU8jytrqVF21599TXVx3vz3GqPVXPc7t2l0sOQKoDF7phvvzXL4cM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+ "text": [ + "" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Great!! Our results seem to match the experimental data. What we can do is calculate the lift coefficient and compare it with the experimental value. Morover, we can see how the error behaves for different number of panels. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's define a function to calculate the lift for different angles of attack:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_lift(freestream, Np):\n", + " \"\"\"\n", + " Get the lift coefficient for a number of panels Np\n", + " \"\"\"\n", + " #define panels\n", + " panels = define_panels(Np)\n", + " \n", + " #coefficients to build A\n", + " A1 = coeff_1_normal(panels)\n", + " A2 = coeff_2_normal(panels)\n", + " A3 = coeff_3_normal(panels,A2)\n", + " \n", + " #To build A\n", + " A_n =A_normal(panels,A1,A2,A3)\n", + " k_a = kutta_array(Np)\n", + "\n", + " #Putting all together to get A\n", + " A = build_matrix(A_n, k_a, Np)\n", + "\n", + " #RHS\n", + " b = build_rhs(panels, freestream)\n", + "\n", + " # solves the linear system\n", + " gammas = linalg.solve(A, b)\n", + " \n", + " #Coefficients to get A_tangential.\n", + " B1 = coeff_1_tangential(panels)\n", + " B2 = coeff_2_tangential(panels)\n", + " B3 = coeff_3_tangential(panels,B2)\n", + " \n", + " #A_tangential\n", + " A_t = A_tangential(panels,B1,B2,B3)\n", + " \n", + " #The vector associated with the free-stream for U_t\n", + " b_t = freestream.U_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n", + "\n", + " #Get tangential velocity\n", + " U_t = numpy.dot(A_t, gammas) + b_t\n", + " \n", + " for i, panel in enumerate(panels):\n", + " panel.vt = U_t[i]\n", + " \n", + " #Get Cp\n", + " get_pressure_coefficient(panels, freestream)\n", + " \n", + " L = 0.\n", + " for panel in panels:\n", + " L -= panel.cp*panel.length*numpy.sin(panel.beta)\n", + " \n", + " return L" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 44 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can calculate the value of the lift coefficients for different number of panels and compare it with the value of the experimental data.\n", + "\n", + "The value of the experimental lift for $\\alpha = 10\u00b0$ was obtain from reference [4](https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises),\n", + "\n", + "$$ L_{exp} = 1.2219 $$\n", + "\n", + "with this value as a reference we can plot de relative error as a function of the number of panels $N_p$ and see how our model behaves." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "L_np=[]\n", + "Np_list=[20,40,60,80,100,120,140,160,180,200, 400]\n", + "for i in Np_list:\n", + " L_np.append(get_lift(freestream_10, i))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 45 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "L_exp = 1.2219\n", + "\n", + "#Relative error\n", + "\n", + "rel_err = []\n", + "for i in L_np:\n", + " rel_err.append(numpy.abs(L_exp - i)/L_exp)\n", + "\n", + "#Percentage error\n", + "\n", + "per_err = []\n", + "for i in rel_err:\n", + " per_err.append(100.*i)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 47 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Plotting\n", + "pyplot.figure(figsize=(10, 6))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('Np', fontsize=16)\n", + "pyplot.ylabel('error $\\%$', fontsize=16)\n", + "pyplot.xlim(10, 210)\n", + "pyplot.ylim(3, 8)\n", + "pyplot.xticks(numpy.linspace(10, 210, 21)) \n", + "pyplot.yticks(numpy.linspace(2, 8, 17))\n", + "\n", + "pyplot.title('Percentage error vs number of panels', fontsize=20)\n", + "\n", + "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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3Ag8Dv6XvyRhPEEXfDOKsW0/GkCRJLalVT8YAmAZ8jxiDtwtwKnBE+gF4L3An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\nIkmStJoiC711iIJtGXEo9u4hbKMd2I0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b3U5sq5nrt668bgQeJhoLWetXafv8Y8R2u5LY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\nAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#For Np=400 the precentage error is:\n", + "L_400 = per_err[-1]\n", + "\n", + "print ('L_400 = %.4f' %L_400)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", "text": [ - "" + "L_400 = 3.3855\n" ] } ], - "prompt_number": 102 + "prompt_number": 51 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we expected, when the number of panels increases, the percentage error decreases. For $Np >60$ the percentage error is less than $5\\%$ what is an acceptable value. As $Np$ keeps increasing, the error continues decreasing but slowly. For $Np=400$ the error is around $3.4\\%$, which is close to the value for $Np=200$ ($\\approx 3.5\\%$). Then, it is not worthy to solve for all this panels if we can get a similar performance for a smaller $Np$." + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "Challange task" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Try to do the same analysis we did in the last section, for the vortex-source panel method from [Lesson 11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb) and compare the results." + ] }, { "cell_type": "markdown", @@ -1229,8 +1660,194 @@ "source": [ "1. Katz, J. & Plotkin, A. _Low speed aerodynamics. 1947-Second Edition \n", "2. http://en.wikipedia.org/wiki/NACA_airfoil\n", - "3. http://turbmodels.larc.nasa.gov/naca0012_val.html\n" + "3. http://turbmodels.larc.nasa.gov/naca0012_val.html\n", + "4. https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises\n" ] + }, + { + "cell_type": "heading", + "level": 6, + "metadata": {}, + "source": [ + "Please ignore the cell below. It just loads our style for the notebook." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "def css_styling():\n", + " styles = open('./styles/custom.css', 'r').read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 54, + "text": [ + "" + ] + } + ], + "prompt_number": 54 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] } ], "metadata": {} diff --git a/clementi/resources/CP_Gregory_expdata_alpha_10.dat b/clementi/resources/CP_Gregory_expdata_alpha_10.dat new file mode 100644 index 0000000..53887eb --- /dev/null +++ b/clementi/resources/CP_Gregory_expdata_alpha_10.dat @@ -0,0 +1,32 @@ +# Data from Gregory & O'Reilly, NASA R&M 3726, Jan 1970 +# Re=2.88 million +# Data was digitized from a photocopy - hence is only approximate +# Data for upper airfoil surface only +# variables="x/c","cp" +#alpha=10 + + +0 -3.66423 +0.00218341 -5.04375 +0.00873362 -5.24068 +0.0131004 -4.67125 +0.0174672 -4.32079 +0.0480349 -2.74347 +0.0742358 -2.26115 +0.0982533 -1.95405 +0.124454 -1.7345 +0.146288 -1.55884 +0.176856 -1.36109 +0.28821 -1.00829 +0.320961 -0.941877 +0.384279 -0.787206 +0.447598 -0.654432 +0.515284 -0.543461 +0.576419 -0.432633 +0.637555 -0.343703 +0.700873 -0.254725 +0.766376 -0.1657 +0.831878 -0.098572 +0.893013 -0.00964205 +0.958515 0.0793835 +1 0.124088 diff --git a/clementi/styles/custom.css b/clementi/styles/custom.css new file mode 100755 index 0000000..e47f2d9 --- /dev/null +++ b/clementi/styles/custom.css @@ -0,0 +1,143 @@ + + + + + From 9758d4f718f5370f6661c14e5296eb3aa61cd0af Mon Sep 17 00:00:00 2001 From: Natalia Clementi Date: Thu, 7 May 2015 15:10:30 -0400 Subject: [PATCH 5/7] Fixing typos --- ...inear_vortex_Panel_Method-checkpoint.ipynb | 132 +++++++++--------- clementi/Linear_vortex_Panel_Method.ipynb | 132 +++++++++--------- 2 files changed, 128 insertions(+), 136 deletions(-) diff --git a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb index 031c3f9..673dc65 100644 --- a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb +++ b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb @@ -1,7 +1,8 @@ { "metadata": { + "hide_input": false, "name": "", - "signature": "sha256:0f9d5fc56ace7b95d542a47f14a3414137e15233d5c9fb9b74bb33b56cb0eb2b" + "signature": "sha256:bf975f50395233eeb12b96935ffe6939d9e6efbb33e24f131d7a74ce3bbaacc6" }, "nbformat": 3, "nbformat_minor": 0, @@ -103,7 +104,7 @@ "If we discretize into $N$ panels, as we were doing in the preious lessons. Then we can write the potential at a point $(x,y)$ as:\n", "\n", "\\begin{equation}\n", - " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha - \\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", + " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha \\\\-\\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", "\\end{equation}" ] }, @@ -255,7 +256,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 1 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -277,7 +278,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 2 + "prompt_number": 3 }, { "cell_type": "markdown", @@ -324,7 +325,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 4 }, { "cell_type": "code", @@ -377,7 +378,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 4 + "prompt_number": 5 }, { "cell_type": "code", @@ -390,7 +391,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 5 + "prompt_number": 6 }, { "cell_type": "code", @@ -431,11 +432,11 @@ "output_type": "display_data", "png": 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KdZtMeui+WB1D0ZtJm0eetHnXhRuUNe3bNjj6029vhxuqOPeY8ZTtKqP0+0pK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\nBjLjbH775mv8YLATv6LOYPQ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"text": [ - "" + "" ] } ], - "prompt_number": 6 + "prompt_number": 7 }, { "cell_type": "markdown", @@ -466,7 +467,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 7 + "prompt_number": 8 }, { "cell_type": "code", @@ -480,7 +481,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 8 + "prompt_number": 9 }, { "cell_type": "markdown", @@ -561,7 +562,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 9 + "prompt_number": 10 }, { "cell_type": "code", @@ -590,7 +591,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 10 + "prompt_number": 11 }, { "cell_type": "markdown", @@ -640,7 +641,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 11 + "prompt_number": 12 }, { "cell_type": "code", @@ -664,7 +665,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 12 + "prompt_number": 13 }, { "cell_type": "code", @@ -683,7 +684,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 13 + "prompt_number": 14 }, { "cell_type": "code", @@ -698,7 +699,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 14 + "prompt_number": 15 }, { "cell_type": "markdown", @@ -718,7 +719,7 @@ "* For $j=0$ you only have contribution from the first and second integral ($A_1$ and $A_2$), which are the coefficients related with $\\gamma_j$. \n", "\n", "\n", - "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", + "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", "\n", "\n", "* For $ 0 " + "" ] } ], - "prompt_number": 34 + "prompt_number": 35 }, { "cell_type": "markdown", @@ -1308,7 +1310,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 35 + "prompt_number": 36 }, { "cell_type": "code", @@ -1321,7 +1323,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 36 + "prompt_number": 37 }, { "cell_type": "code", @@ -1333,7 +1335,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 37 + "prompt_number": 38 }, { "cell_type": "code", @@ -1346,7 +1348,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 38 + "prompt_number": 39 }, { "cell_type": "code", @@ -1358,7 +1360,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 39 + "prompt_number": 40 }, { "cell_type": "code", @@ -1370,7 +1372,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 40 + "prompt_number": 41 }, { "cell_type": "code", @@ -1381,7 +1383,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 41 + "prompt_number": 42 }, { "cell_type": "markdown", @@ -1399,7 +1401,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 42 + "prompt_number": 43 }, { "cell_type": "code", @@ -1431,7 +1433,8 @@ "pyplot.xlim(x_start, x_end)\n", "pyplot.ylim(y_start, y_end)\n", "pyplot.gca().invert_yaxis()\n", - "pyplot.title('Number of panels : %d' % N);" + "pyplot.title('Angle of attack 10 deg, Number of panels : %d' % N, fontsize=20)\n", + "#pyplot.savefig('CP_10.pdf'); add this line to save fig" ], "language": "python", "metadata": {}, @@ -1439,13 +1442,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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HD0vVqlXl008/lfz8fOnWrZs88cQThmMsX75c3Nzc5JFHHpFdu3bJgQMH5PHH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q0LRpU6ZPn+53Casou/ylWfN/QC0n00ehy1gFaAPcBnwMNHK2kv79+xMbGwtA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"text": [ - "" + "" ] } ], - "prompt_number": 43 + "prompt_number": 53 }, { "cell_type": "markdown", @@ -1519,7 +1522,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 44 + "prompt_number": 55 }, { "cell_type": "markdown", @@ -1546,7 +1549,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 45 + "prompt_number": 56 }, { "cell_type": "code", @@ -1569,7 +1572,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 47 + "prompt_number": 57 }, { "cell_type": "code", @@ -1587,7 +1590,8 @@ "\n", "pyplot.title('Percentage error vs number of panels', fontsize=20)\n", "\n", - "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);" + "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);\n", + "#pyplot.savefig('error.pdf'); add this line to save fig" ], "language": "python", "metadata": {}, @@ -1597,11 +1601,11 @@ "output_type": "display_data", "png": 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3Ag8Dv6XvyRhPEEXfDOKsW0/GkCRJLalVT8YAmAZ8jxiDtwtwKnBE+gF4L3An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\nIkmStJoiC711iIJtGXEo9u4hbKMd2I0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"text": [ - "" + "" ] } ], - "prompt_number": 50 + "prompt_number": 58 }, { "cell_type": "code", @@ -1623,7 +1627,7 @@ ] } ], - "prompt_number": 51 + "prompt_number": 59 }, { "cell_type": "markdown", @@ -1840,14 +1844,6 @@ } ], "prompt_number": 54 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] } ], "metadata": {} diff --git a/clementi/Linear_vortex_Panel_Method.ipynb b/clementi/Linear_vortex_Panel_Method.ipynb index 031c3f9..673dc65 100644 --- a/clementi/Linear_vortex_Panel_Method.ipynb +++ b/clementi/Linear_vortex_Panel_Method.ipynb @@ -1,7 +1,8 @@ { "metadata": { + "hide_input": false, "name": "", - "signature": "sha256:0f9d5fc56ace7b95d542a47f14a3414137e15233d5c9fb9b74bb33b56cb0eb2b" + "signature": "sha256:bf975f50395233eeb12b96935ffe6939d9e6efbb33e24f131d7a74ce3bbaacc6" }, "nbformat": 3, "nbformat_minor": 0, @@ -103,7 +104,7 @@ "If we discretize into $N$ panels, as we were doing in the preious lessons. Then we can write the potential at a point $(x,y)$ as:\n", "\n", "\\begin{equation}\n", - " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha - \\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", + " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha \\\\-\\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", "\\end{equation}" ] }, @@ -255,7 +256,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 1 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -277,7 +278,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 2 + "prompt_number": 3 }, { "cell_type": "markdown", @@ -324,7 +325,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 4 }, { "cell_type": "code", @@ -377,7 +378,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 4 + "prompt_number": 5 }, { "cell_type": "code", @@ -390,7 +391,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 5 + "prompt_number": 6 }, { "cell_type": "code", @@ -431,11 +432,11 @@ "output_type": "display_data", "png": 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KdZtMeui+WB1D0ZtJm0eetHnXhRuUNe3bNjj6029vhxuqOPeY8ZTtKqP0+0pK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\nBjLjbH775mv8YLATv6LOYPQ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"text": [ - "" + "" ] } ], - "prompt_number": 6 + "prompt_number": 7 }, { "cell_type": "markdown", @@ -466,7 +467,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 7 + "prompt_number": 8 }, { "cell_type": "code", @@ -480,7 +481,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 8 + "prompt_number": 9 }, { "cell_type": "markdown", @@ -561,7 +562,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 9 + "prompt_number": 10 }, { "cell_type": "code", @@ -590,7 +591,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 10 + "prompt_number": 11 }, { "cell_type": "markdown", @@ -640,7 +641,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 11 + "prompt_number": 12 }, { "cell_type": "code", @@ -664,7 +665,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 12 + "prompt_number": 13 }, { "cell_type": "code", @@ -683,7 +684,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 13 + "prompt_number": 14 }, { "cell_type": "code", @@ -698,7 +699,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 14 + "prompt_number": 15 }, { "cell_type": "markdown", @@ -718,7 +719,7 @@ "* For $j=0$ you only have contribution from the first and second integral ($A_1$ and $A_2$), which are the coefficients related with $\\gamma_j$. \n", "\n", "\n", - "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", + "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", "\n", "\n", "* For $ 0 " + "" ] } ], - "prompt_number": 34 + "prompt_number": 35 }, { "cell_type": "markdown", @@ -1308,7 +1310,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 35 + "prompt_number": 36 }, { "cell_type": "code", @@ -1321,7 +1323,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 36 + "prompt_number": 37 }, { "cell_type": "code", @@ -1333,7 +1335,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 37 + "prompt_number": 38 }, { "cell_type": "code", @@ -1346,7 +1348,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 38 + "prompt_number": 39 }, { "cell_type": "code", @@ -1358,7 +1360,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 39 + "prompt_number": 40 }, { "cell_type": "code", @@ -1370,7 +1372,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 40 + "prompt_number": 41 }, { "cell_type": "code", @@ -1381,7 +1383,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 41 + "prompt_number": 42 }, { "cell_type": "markdown", @@ -1399,7 +1401,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 42 + "prompt_number": 43 }, { "cell_type": "code", @@ -1431,7 +1433,8 @@ "pyplot.xlim(x_start, x_end)\n", "pyplot.ylim(y_start, y_end)\n", "pyplot.gca().invert_yaxis()\n", - "pyplot.title('Number of panels : %d' % N);" + "pyplot.title('Angle of attack 10 deg, Number of panels : %d' % N, fontsize=20)\n", + "#pyplot.savefig('CP_10.pdf'); add this line to save fig" ], "language": "python", "metadata": {}, @@ -1439,13 +1442,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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HD0vVqlXl008/lfz8fOnWrZs88cQThmMsX75c3Nzc5JFHHpFdu3bJgQMH5PHH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q0LRpU6ZPn+53Casou/ylWfN/QC0n00ehy1gFaAPcBnwMNHK2kv79+xMbGwtA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"text": [ - "" + "" ] } ], - "prompt_number": 43 + "prompt_number": 53 }, { "cell_type": "markdown", @@ -1519,7 +1522,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 44 + "prompt_number": 55 }, { "cell_type": "markdown", @@ -1546,7 +1549,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 45 + "prompt_number": 56 }, { "cell_type": "code", @@ -1569,7 +1572,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 47 + "prompt_number": 57 }, { "cell_type": "code", @@ -1587,7 +1590,8 @@ "\n", "pyplot.title('Percentage error vs number of panels', fontsize=20)\n", "\n", - "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);" + "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);\n", + "#pyplot.savefig('error.pdf'); add this line to save fig" ], "language": "python", "metadata": {}, @@ -1597,11 +1601,11 @@ "output_type": "display_data", "png": 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3Ag8Dv6XvyRhPEEXfDOKsW0/GkCRJLalVT8YAmAZ8jxiDtwtwKnBE+gF4L3An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\nAABJRU5ErkJggg==\n", "text": [ - "" + "" ] } ], - "prompt_number": 50 + "prompt_number": 58 }, { "cell_type": "code", @@ -1623,7 +1627,7 @@ ] } ], - "prompt_number": 51 + "prompt_number": 59 }, { "cell_type": "markdown", @@ -1840,14 +1844,6 @@ } ], "prompt_number": 54 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] } ], "metadata": {} From a400cb84f8023c896d0d40d3d94c2ee2a5d77905 Mon Sep 17 00:00:00 2001 From: Natalia Clementi Date: Wed, 27 May 2015 18:08:31 -0400 Subject: [PATCH 6/7] Fixing typos and grammar --- ...inear_vortex_Panel_Method-checkpoint.ipynb | 126 +++--- clementi/Linear_vortex_Panel_Method.ipynb | 413 ++++++------------ 2 files changed, 203 insertions(+), 336 deletions(-) diff --git a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb index 673dc65..7971bb3 100644 --- a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb +++ b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb @@ -2,7 +2,7 @@ "metadata": { "hide_input": false, "name": "", - "signature": "sha256:bf975f50395233eeb12b96935ffe6939d9e6efbb33e24f131d7a74ce3bbaacc6" + "signature": "sha256:5d8e6960e66497e40f7e396fcb6e5f0c1fcfc5cd53c6b4489da6a310491cfc58" }, "nbformat": 3, "nbformat_minor": 0, @@ -29,33 +29,33 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the last lessons of _AeroPython_, we have been learning (we hope so!) how to apply panel method to represent a cylinder and different airfoils.\n", + "In the last lessons of _AeroPython_, we have been learning (we hope so!) how to apply panel methods to represent a cylinder and different airfoils.\n", "\n", - "We started with a simple source panel method ([Lesson10](http://nbviewer.ipython.org/urls/github.com/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb)) but we realized that if we want to generate lift this method was not able to provide it. Do you remember why?...**Source panel method gives as a solution with no circulation** and we need *circulation* so we can have lift. \n", + "We started with a simple source panel method ([Lesson 10](http://nbviewer.ipython.org/urls/github.com/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb)) but we realized that if we want to generate lift this method was not able to provide it. Do you remember why?...**The source panel method gives as a solution with no circulation** and we need *circulation* so we can have lift. \n", "\n", - "Then, to get a solution with circulation we add, to the constant source panel method, vortices to our panels and that allows us to may have lift force.([Lesson11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb))\n", + "Then, to get a solution with circulation, we add vortices to the constant-source panel method, allowing us to obtain an lift force.([Lesson 11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb))\n", "\n", - "There are other ways to generate a solution with circulation. One of them is to use only vortices. However, in this case we need to use linear elements instead of use constant ones, as we were doing in the previous lessons. " + "There are other ways to generate a solution with circulation. One of them is to use linearly varying strength vortices." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "##What does linear elements mean?" + "##What does \"linearly varying strength\" mean?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "So far, we were treating our singularities distribution with constant stregth along the panels. Now we allow the strength to vary linearly.\n", + "So far, we were treating our singularity distribution with constant strength along the panels. Now we allow the strength to vary linearly.\n", "\n", "\\begin{equation}\n", " \\gamma(x)= \\gamma_0 + \\gamma_1 (x-x_1) \n", "\\end{equation}\n", "\n", - "where $\\gamma_0$ is constant and $\\gamma_1$ is the slope. Using the principle of superposition we can separate our problem into a constant-strength elements and linear varying varying elements, to finally add this two solutions. \n", + "where $\\gamma_0$ is constant and $\\gamma_1$ is the slope. Using the principle of superposition we can separate our problem into a constant-strength part and other where the strength varies linearly, to finally add these two solutions. \n", "\n", "\n", "
\n", @@ -73,7 +73,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So now, using the powers of superposition, and remembering that the potential at a location $(x,y)$ in this case is:\n", + "Using the powers of superposition, and remembering that the potential at a location $(x,y)$ in this case is,\n", "\n", "\\begin{equation}\n", " \\phi(x, y) = \\phi_{\\text{free-stream}}(x, y)+ \\phi_{\\text{vortex-sheet}}(x, y)\n", @@ -84,7 +84,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Explicitly" + "we explicitly write the potentitial function as," ] }, { @@ -101,7 +101,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "If we discretize into $N$ panels, as we were doing in the preious lessons. Then we can write the potential at a point $(x,y)$ as:\n", + "If we discretize the geometry into $N$ panels, as we were doing in the previous lessons, then we can write the potential at a point $(x,y)$ as,\n", "\n", "\\begin{equation}\n", " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha \\\\-\\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", @@ -112,7 +112,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "where:\n", + "where, \n", "\n", "\\begin{equation}\n", "\\left\\{\n", @@ -125,12 +125,13 @@ "\\right.\n", "\\end{equation}\n", "\n", - "and $\\gamma_j (s)$ can be written as:\n", + "and $\\gamma_j (s)$ can be written as,\n", + "\n", "\\begin{equation}\n", " \\gamma_j (s) = \\gamma_j + \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right)\\; s\n", "\\end{equation}\n", "\n", - "with $l_j$ the length of the panel $j$ and $\\beta_j$ is the angle between the panel's normal and the $x$-axis. " + "with $l_j$ the length of panel $j$ and $\\beta_j$ the angle between the panel's normal and the $x$-axis. " ] }, { @@ -149,7 +150,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The first three terms of the potential should be familiar, we already fight with the math that those terms involve in the previous lessons. " + "The first three terms of the potential should be familiar, we already had to fight with the math that those terms involve in the previous lessons. " ] }, { @@ -169,14 +170,14 @@ " \\right.\n", "\\end{equation}\n", "\n", - "where $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$. Then in order to get the different components of the velocity we need to take some derivatives. We know that you don't like to do a lot of math, but if you completed the exercise of lesson 11 ([11_Lesson11_Exercise](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_Exercise.ipynb)) then you have all the derivatives done!!! " + "where $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$. In order to get the different components of the velocity we need to take some derivatives. We know that you don't like to do a lot of math, but if you completed the exercise of lesson 11 ([11_Lesson11_Exercise](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_Exercise.ipynb)) then you have all the derivatives done!!! " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Then, the components of the gradient should look like this:\n", + "The components of the gradient should look like this:\n", "\n", "\\begin{align}\n", " \\frac{\\partial \\phi}{\\partial x}(x,y) &= U_\\infty \\cos \\alpha \\\\\n", @@ -262,9 +263,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel.\n", + "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength of the singularities are going to be at the beginning and end of each panel.\n", "\n", - "The data we are loading is just to plot the airfoil and to be ensure panels follow the shape of the airfoil. However, we are not going to use this data to build the panels, instead we will use the equation we mention before." + "The data we are loading is just to plot the airfoil and to ensure that panels follow the shape of the airfoil. However, we are not going to use this data to build the panels, instead we will use the equation we mentioned before." ] }, { @@ -491,7 +492,7 @@ "\n", "As we already know, to solve our problem, we need to require $U_{\\text{n}}(x, y)=0$ at the center (collocation point) of each panel. However we have to be careful, because at $(x_{c_i}, y_{c_i})$ all our integrals have a singularity. To skip that singularity, for $i=j$ we have to solve them analytically in the local coordinates of the panel.\n", "\n", - "So for the flow-tangency boundary condition, the integrals (in local coordinates) that we have to solve analytically are:\n", + "For the flow-tangency boundary condition, the integrals (in local coordinates) that we have to solve analytically are:\n", "\n", "\\begin{equation}\n", " I_1=\\frac{1}{2\\pi} \\int^l_0 \\frac{(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", @@ -501,7 +502,7 @@ " I_2=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", "\\end{equation}\n", "\n", - "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "After we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", "\n", "\n", "\\begin{equation}\n", @@ -518,7 +519,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "For all the integrals that appear in our equations, we are gonna use the function `integrate.quad()` from SciPy. So following the same idea we use in the previous lessons, we are going to define two integrate functions on to solve the terms of the form:\n", + "For all the integrals that appear in our equations, we use the function `integrate.quad()` from SciPy. Following the same idea we use in the previous lessons, we define two integrate functions to compute the terms of the form:\n", "\n", "`integral`:\n", "\n", @@ -532,7 +533,7 @@ " \\int_j s\\,f_j(s) {\\rm d}s\\;a - \\int_j s\\,g_j(s) {\\rm d}s\\;b\n", "\\end{equation}\n", "\n", - "where $a$ and $b$ can be $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$ depending the case. " + "where $a$ and $b$ can be $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$ depending on the case. " ] }, { @@ -597,23 +598,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can use this functions to calculate the coefficients of the matrices corresponding to each term in the equation for $U_{\\text{n}}(x, y)$ to finally solve the linear system $$[A][\\gamma] = [b]$$.\n", - "\n", - "So we will call:\n", + "Now we can use these functions to calculate the coefficients of the matrices corresponding to each term in the equation for $U_{\\text{n}}(x, y)$ to finally solve the linear system $$[A][\\gamma] = [b]$$\n", "\n", - "$A_1$ the term related to the first integral:\n", + "We will call $A_1$ the term related to the first integral,\n", "\n", "\\begin{equation}\n", " \\int_j f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $A_2$ the term related to the second integral:\n", + "$A_2$ the term related to the second integral,\n", "\n", "\\begin{equation}\n", " \\int_j s\\,f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ correspond to $\\gamma_j$ and $A_3$ correspond to $\\gamma_{j+1}$.\n", + "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ corresponds to $\\gamma_j$ and $A_3$ corresponds to $\\gamma_{j+1}$.\n", "\n", "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." ] @@ -705,7 +704,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We got our coefficintes, but how are these guys related with the matrix $A$ that we need to build in order to solve our system?" + "We got our coefficients, but how are these guys related with the matrix $A$ that we need to build in order to solve our system?" ] }, { @@ -714,7 +713,7 @@ "source": [ "##How to build the A matrix\n", "\n", - "This is the moment, where you should grab a piece of paper and write some terms of the $U_n$ for a panel $i$. After writing couple of $j$-terms, you should notice that. (tip: write the terms counting from zero, so then you match this with the code)\n", + "This is the moment when you should grab a piece of paper and write some terms of the $U_n$ for a panel $i$. After writing a couple of $j$-terms, you should notice that. (tip: write the terms counting from zero, so then you match this with the code)\n", "\n", "* For $j=0$ you only have contribution from the first and second integral ($A_1$ and $A_2$), which are the coefficients related with $\\gamma_j$. \n", "\n", @@ -722,12 +721,12 @@ "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", "\n", "\n", - "* For $ 0
\n" ] @@ -739,7 +738,19 @@ "#In code, except for the kutta condition (in cell after)...\n", "\n", "def A_normal(panels,A1,A2,A3):\n", - " \"\"\"\n", + " \"\"\"Builds the normal matrix\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: panels of the geometry\n", + " A1: term related to the first integral in U_n\n", + " A2: term related to the second integral in U_n\n", + " A3: term related to the third integral in U_n\n", + " \n", + " Returns\n", + " -------\n", + " A_n: Nx(N+1) matrix, where N is number of panels. \n", + " \n", " \"\"\"\n", " N = len(panels)\n", " A_n = numpy.zeros((N, N+1), dtype=float) \n", @@ -916,7 +927,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we have the solution of our system we can get the surface pressure coefficient by calculating the tangential velocity. So let's keep coding (and doing a little bit more of math)." + "Now we have the solution of our system, we can get the surface pressure coefficient by calculating the tangential velocity. So let's keep coding (and doing a little bit more of math)." ] }, { @@ -934,7 +945,7 @@ "\n", "$$C_{p_i} = 1 - \\left(\\frac{U_{t_i}}{U_\\infty}\\right)^2$$\n", "\n", - "So, we have to compute the tangential velocity. However, we can not escape from the math. To calculate $U_t$, we have to do some integral, do you remember?. Guess what, yes! we have the singularities issue again. In this case, the integrals we have to solve analytically are:\n", + "We have to compute the tangential velocity. However, we can not escape from the math. To calculate $U_t$, we have to do some integrals, do you remember? Guess what, yes! we have the singularities issue again. In this case, the integrals we have to solve analytically are:\n", "\n", "\\begin{equation}\n", " I_3=\\frac{1}{2\\pi} \\int^l_0 \\frac{y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", @@ -944,7 +955,7 @@ " I_4=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", "\\end{equation}\n", "\n", - "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "After we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", "\n", "\n", "\\begin{equation}\n", @@ -961,21 +972,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So, following the same idea that we use to build the **A** matrix, we define:\n", + "Following the same idea that we use to build the **A** matrix, we define:\n", "\n", - "$B_1$ the term related to the first integral:\n", + "$B_1$, the term related to the first integral:\n", "\n", "\\begin{equation}\n", " \\int_j f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $B_2$ the term related to the second integral:\n", + "$B_2$ the term related to the second integral:\n", "\n", "\\begin{equation}\n", " \\int_j s\\,f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j s\\,g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $B_3=B_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $B_2$ correspond to $\\gamma_j$ and $B_3$ correspond to $\\gamma_{j+1}$.\n", + "and $B_3=B_2$, the term related to the third integral. We want to keep the three terms to avoid confusions. $B_2$ correspond to $\\gamma_j$ and $B_3$ correspond to $\\gamma_{j+1}$.\n", "\n", "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." ] @@ -1077,7 +1088,18 @@ "collapsed": false, "input": [ "def A_tangential(panels,B1,B2,B3):\n", - " \"\"\"\n", + " \"\"\"Builds the tangential matrix\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: panels of the geometry\n", + " B1: term related to the first integral in U_t\n", + " B2: term related to the second integral in U_t\n", + " B3: term related to the third integral in U_t\n", + " \n", + " Returns\n", + " -------\n", + " A_t: Nx(N+1) matrix, where N is number of panels. \n", " \"\"\"\n", " N = len(panels)\n", " A_t = numpy.zeros((N, N+1), dtype=float) \n", @@ -1194,7 +1216,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "From [Lesson 10](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb) we kow the exact solution for zero angle of attack, so let copy that solution, to compare with our result." + "From [Lesson 10](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb) we know the exact solution for zero angle of attack, so let's copy that solution, to compare with our result." ] }, { @@ -1288,7 +1310,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Nice!! our solution match with the theoretical one. However the purpouse of use vortices as our singularities is to get some lift and see how our model behaves. So let's calculate solve the problem for an angle of attack $\\alpha=10$ degrees. We pick $10\u00b0$ because we have some experimental data for the coefficient of pressure of the upper face, to compare. [Gregory & O'Reilly pressure data.](http://turbmodels.larc.nasa.gov/naca0012_val.html)" + "Nice!! Our solution matches with the theoretical one. However, the purpouse of using vortices as our singularities is to get some lift and see how our model behaves. Let's calculate solve the problem for an angle of attack $\\alpha=10$ degrees. We pick $10\u00b0$ because we have some experimental data for the coefficient of pressure of the upper face, to compare. See [Gregory & O'Reilly pressure data.](http://turbmodels.larc.nasa.gov/naca0012_val.html)" ] }, { @@ -1389,7 +1411,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As we mention before we have some experimental data for the upper face, so let's import that data to compare with our results. " + "As we mentioned before, we have some experimental data for the upper face, so let's import that data to compare with our results. " ] }, { @@ -1530,11 +1552,11 @@ "source": [ "We can calculate the value of the lift coefficients for different number of panels and compare it with the value of the experimental data.\n", "\n", - "The value of the experimental lift for $\\alpha = 10\u00b0$ was obtain from reference [4](https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises),\n", + "The value of the experimental lift for $\\alpha = 10\u00b0$ was obtained from reference [4](https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises),\n", "\n", "$$ L_{exp} = 1.2219 $$\n", "\n", - "with this value as a reference we can plot de relative error as a function of the number of panels $N_p$ and see how our model behaves." + "With this value as a reference, we can plot de relative error as a function of the number of panels $N_p$ and see how our model behaves." ] }, { @@ -1612,9 +1634,9 @@ "collapsed": false, "input": [ "#For Np=400 the precentage error is:\n", - "L_400 = per_err[-1]\n", + "L_400_err = per_err[-1]\n", "\n", - "print ('L_400 = %.4f' %L_400)" + "print ('L_400_err = %.4f' %L_400_err)" ], "language": "python", "metadata": {}, @@ -1633,7 +1655,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As we expected, when the number of panels increases, the percentage error decreases. For $Np >60$ the percentage error is less than $5\\%$ what is an acceptable value. As $Np$ keeps increasing, the error continues decreasing but slowly. For $Np=400$ the error is around $3.4\\%$, which is close to the value for $Np=200$ ($\\approx 3.5\\%$). Then, it is not worthy to solve for all this panels if we can get a similar performance for a smaller $Np$." + "As we expected, when the number of panels increases, the percentage error decreases. For $Np >60$ the percentage error is less than $5\\%$ which may be an acceptable value. As $Np$ keeps increasing, the error continues decreasing but slowly. For $Np=400$ the error is around $3.4\\%$, which is close to the value for $Np=200$ ($\\approx 3.5\\%$). Then, it is not worthwhile to solve for all these panels if we can get a similar result with smaller $Np$." ] }, { diff --git a/clementi/Linear_vortex_Panel_Method.ipynb b/clementi/Linear_vortex_Panel_Method.ipynb index 673dc65..4511165 100644 --- a/clementi/Linear_vortex_Panel_Method.ipynb +++ b/clementi/Linear_vortex_Panel_Method.ipynb @@ -2,7 +2,7 @@ "metadata": { "hide_input": false, "name": "", - "signature": "sha256:bf975f50395233eeb12b96935ffe6939d9e6efbb33e24f131d7a74ce3bbaacc6" + "signature": "sha256:d9103dc4ef75113b3ccd3154e57dd4cd2735cb2549e0ea8b71d47d777d18a321" }, "nbformat": 3, "nbformat_minor": 0, @@ -29,33 +29,33 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the last lessons of _AeroPython_, we have been learning (we hope so!) how to apply panel method to represent a cylinder and different airfoils.\n", + "In the last lessons of _AeroPython_, we have been learning (we hope so!) how to apply panel methods to represent a cylinder and different airfoils.\n", "\n", - "We started with a simple source panel method ([Lesson10](http://nbviewer.ipython.org/urls/github.com/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb)) but we realized that if we want to generate lift this method was not able to provide it. Do you remember why?...**Source panel method gives as a solution with no circulation** and we need *circulation* so we can have lift. \n", + "We started with a simple source panel method ([Lesson 10](http://nbviewer.ipython.org/urls/github.com/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb)) but we realized that if we want to generate lift this method was not able to provide it. Do you remember why?...**The source panel method gives as a solution with no circulation** and we need *circulation* so we can have lift. \n", "\n", - "Then, to get a solution with circulation we add, to the constant source panel method, vortices to our panels and that allows us to may have lift force.([Lesson11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb))\n", + "Then, to get a solution with circulation, we add vortices to the constant-source panel method, allowing us to obtain an lift force.([Lesson 11](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_vortexSourcePanelMethod.ipynb))\n", "\n", - "There are other ways to generate a solution with circulation. One of them is to use only vortices. However, in this case we need to use linear elements instead of use constant ones, as we were doing in the previous lessons. " + "There are other ways to generate a solution with circulation. One of them is to use linearly varying strength vortices." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "##What does linear elements mean?" + "##What does \"linearly varying strength\" mean?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "So far, we were treating our singularities distribution with constant stregth along the panels. Now we allow the strength to vary linearly.\n", + "So far, we were treating our singularity distribution with constant strength along the panels. Now we allow the strength to vary linearly.\n", "\n", "\\begin{equation}\n", " \\gamma(x)= \\gamma_0 + \\gamma_1 (x-x_1) \n", "\\end{equation}\n", "\n", - "where $\\gamma_0$ is constant and $\\gamma_1$ is the slope. Using the principle of superposition we can separate our problem into a constant-strength elements and linear varying varying elements, to finally add this two solutions. \n", + "where $\\gamma_0$ is constant and $\\gamma_1$ is the slope. Using the principle of superposition we can separate our problem into a constant-strength part and other where the strength varies linearly, to finally add these two solutions. \n", "\n", "\n", "
\n", @@ -73,7 +73,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So now, using the powers of superposition, and remembering that the potential at a location $(x,y)$ in this case is:\n", + "Using the powers of superposition, and remembering that the potential at a location $(x,y)$ in this case is,\n", "\n", "\\begin{equation}\n", " \\phi(x, y) = \\phi_{\\text{free-stream}}(x, y)+ \\phi_{\\text{vortex-sheet}}(x, y)\n", @@ -84,7 +84,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Explicitly" + "we explicitly write the potentitial function as," ] }, { @@ -101,7 +101,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "If we discretize into $N$ panels, as we were doing in the preious lessons. Then we can write the potential at a point $(x,y)$ as:\n", + "If we discretize the geometry into $N$ panels, as we were doing in the previous lessons, then we can write the potential at a point $(x,y)$ as,\n", "\n", "\\begin{equation}\n", " \\phi\\left(x,y\\right) = xU_\\infty \\cos \\alpha + yU_\\infty \\sin \\alpha \\\\-\\sum_{j=1}^N \\frac{1}{2\\pi} \\int_j \\gamma_j (s) \\tan^{-1} \\left(\\frac{y-\\eta_j(s)}{x-\\xi_j(s)}\\right) {\\rm d}s_j\n", @@ -112,7 +112,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "where:\n", + "where, \n", "\n", "\\begin{equation}\n", "\\left\\{\n", @@ -125,12 +125,13 @@ "\\right.\n", "\\end{equation}\n", "\n", - "and $\\gamma_j (s)$ can be written as:\n", + "and $\\gamma_j (s)$ can be written as,\n", + "\n", "\\begin{equation}\n", " \\gamma_j (s) = \\gamma_j + \\left(\\frac{\\gamma_{j+1}-\\gamma_j}{l_j} \\right)\\; s\n", "\\end{equation}\n", "\n", - "with $l_j$ the length of the panel $j$ and $\\beta_j$ is the angle between the panel's normal and the $x$-axis. " + "with $l_j$ the length of panel $j$ and $\\beta_j$ the angle between the panel's normal and the $x$-axis. " ] }, { @@ -149,7 +150,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The first three terms of the potential should be familiar, we already fight with the math that those terms involve in the previous lessons. " + "The first three terms of the potential should be familiar, we already had to fight with the math that those terms involve in the previous lessons. " ] }, { @@ -169,14 +170,14 @@ " \\right.\n", "\\end{equation}\n", "\n", - "where $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$. Then in order to get the different components of the velocity we need to take some derivatives. We know that you don't like to do a lot of math, but if you completed the exercise of lesson 11 ([11_Lesson11_Exercise](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_Exercise.ipynb)) then you have all the derivatives done!!! " + "where $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$. In order to get the different components of the velocity we need to take some derivatives. We know that you don't like to do a lot of math, but if you completed the exercise of lesson 11 ([11_Lesson11_Exercise](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/11_Lesson11_Exercise.ipynb)) then you have all the derivatives done!!! " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Then, the components of the gradient should look like this:\n", + "The components of the gradient should look like this:\n", "\n", "\\begin{align}\n", " \\frac{\\partial \\phi}{\\partial x}(x,y) &= U_\\infty \\cos \\alpha \\\\\n", @@ -256,15 +257,15 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 2 + "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength singularities are going to be at the beginning and end of each panel.\n", + "We are going to work with the airfoil _NACA0012_, so we are going to load the same data that we were using in previous lessons. We will use the cosine method to get the `x_ends` and we are going to generate the `y_ends` using the [equation for a symmetrical 4-digit _NACA_ airfoil](http://en.wikipedia.org/wiki/NACA_airfoil) with the correction for zero-thickness trailing edge. We need this because now the strength of the singularities are going to be at the beginning and end of each panel.\n", "\n", - "The data we are loading is just to plot the airfoil and to be ensure panels follow the shape of the airfoil. However, we are not going to use this data to build the panels, instead we will use the equation we mention before." + "The data we are loading is just to plot the airfoil and to ensure that panels follow the shape of the airfoil. However, we are not going to use this data to build the panels, instead we will use the equation we mentioned before." ] }, { @@ -278,7 +279,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -325,7 +326,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 4 + "prompt_number": 3 }, { "cell_type": "code", @@ -378,7 +379,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 5 + "prompt_number": 4 }, { "cell_type": "code", @@ -391,7 +392,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 6 + "prompt_number": 5 }, { "cell_type": "code", @@ -432,11 +433,11 @@ "output_type": "display_data", "png": 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KdZtMeui+WB1D0ZtJm0eetHnXhRuUNe3bNjj6029vhxuqOPeY8ZTtKqP0+0pK\nDtVw1ycvYD1mSkh5W+pZPLDqLS7JCgZmHoVcj0JBg34yYvCx/Zj2+OUw2Aq2eOY7Rul3cV67oDmA\ng867OlvvF43fJ7H6PpcgLgo1fYjmzJ6Ps6Rle3uTHu67+5GwDzhCCCHa1+FYtAumQGk9HKzFs9dJ\nRWE5jyx5HGt6aDdlQtxx3HD304waYifTq5DpgX5eBW+j9rxoAKNSbdx5+VkwKBkGWWGQlcavR5N/\n17Pa4GzRAhiX2bwt3OCsaV/5bogu0p0axdoeTNpejgSC2bnSrxg1YmbzNhk3J4QQqrCzah4flNQz\nZ+4CnA0naB6u/u49pvazU2r0U2YO4DRCqhc27V2j2+1p+v4D3pp4DYaByTBAXeYsuQun90TNvu1d\nZlG6NvsG6U6NUW1/YRkPaOcNlVXuCAngoOWUJIBk6IQQMaMr3ZxN++cvegprXKsrDPzhYUpe2sQ4\ny3DKymopr66nvM5Nmc9LmSnA14eKGZqrfS6jN8DkKgOZiQn0S7KSNsCGcaCVOR98pjujM/HU/hhW\nTA/Zlpd+VYezO9uSzJmQTFyUCKc/Xy/Nv233a4we9hPNvsU73yQhJRVb1jnN2yRDFypWx1D0ZtLm\nkddb27xbAVnbAMj9CQvn/Rz7iFNo3F9D5fdVlB+oprzESXllHQ/seBWbTpZsz24H07OnkeFB7e70\nKmT4DGQkW7ip6p+4h+hMFLB+q2bLEkJzI3r12lf2Fg88dFu7kxsku3bk9db3eTgkE9dH6I19GKoM\nAJ2YtcRTx/FZl4Rss5onsew5ydAJIXpWh+POLpwClW4odcGhOrz7nVR+X8ljf38Ma0abqwlYTudP\ndz7FsmPs1Ae7NzO8ChkehQyvgqI/BI1j+6Vxz/UXQE4S5CSqt5mJYDJwjWOYfrbs+gWaAA70j8tX\nXPTjdo+pkl0TXSGZuBin++u04RNMDY0k2CZr9t+37XWSkmykDT6/ZX/J0AkhuimsjFogAM5GKKlX\nx53d9Eecysma53Lufo9ZmXYqDAEqTOriNILNB9/sWcMgnawaRe/zyinzSOlvw9A/ORiYqcucRTfj\nrDlOU6S9MWit/ybJlolIkUxcH9bezKSlS5aHzGxtUu1zMWjwrJBtVvMklt2xBHvuiTAqHcea/0im\nTog+pqvdmwCON1epMygTz2jedscNiyke9TnHxw+jsqqeSqebSlcDFYqfShNUmAJsOljOsFzt8wV8\nAUbXKaQdJLmuAAARSElEQVTHxZMRn0B6v2RS+tsw9k9mzrvrdcee2SYMIG3lLJ1HIO+6y7s0Bq2J\nZMtEb9Gbgrh0YAUwBCgC5gBVOvvZgYcBI7AEuC+4fREwHygNrt8COI5abSPscPrz2zvg6B28ho0Y\novscX+2r4I7LXsRTU8Qa33bSj2nJ1LU9F113Dva9UTSPoYhW0uZHX9vP5ykTxnDjjX/otIyme/OW\nx+Hzg1xwzHhq9lVTddBJZamTqop6qpxuKl2NPF3yNhkjQ09InpJ9Dg9sdHBxdjxpXkjzKqR5FYYb\n40hLsJCemkRZlQVX20oAg04ZyNTXrgOL9qsr7zRXlwOyrpx+40iS93nkxWqb96Yg7mbgPeB+4Kbg\n+s1t9jECjwPnAfuBz4G3ga2oI78eCi6iE13N0I1NsHCWMYlb6reQ3uagbDVP4onfPMKU+cn8x7OL\n/H++gTXh9ObH5YTDQhxZ3f2hpBeMvbTsn/wgawT2406DcheUumgoqaXqkJPq0lqqKup4YONLWHND\nT0Jrtf6Q3z77IiNyi0n0QapPDcZSvZDmU0j1KiRi1K3HqIEZ3PN/M6BfImQlqrdJ5ubHf+no1/4J\nanUCOOh+QCZZNRHNetOYuG3A2UAxkAMUAKPb7DMJuA01GwctQd69we21wF87eZ0+NSauqzq79MrM\nqVfiqjteU27vd2sYMeQCCr9zMGi4XfO4LW4TK/7xDGQmgKLETLZOiMPRrS5Kvc9o07jVKedAZYM6\n8L/Crd6Wu3CX1FFT7CTv7UfwZZ2lec6SXas5c6CdaiNUGwN4FUj1QYpXIdWn4Ch2kDlc51xnBz7k\nzR/dgCkrGIxlJUG/BMhWA7M5Vy3AWaq9vmdnY86a/k4ZdyZE9IyJy0YN4AjeZuvsMxDY22p9H3Ba\nq/XrgV8AG4A/oN8dKzrQ2a9ZU5IZ6rTlxg3J5MXJpzLjQIHu827bVsxj5z7DYGMc+8z7eaVyIykD\nWn7Z59/2ZMjrQ+x0y4rYdiSzYiFZa5cXKlwtwViFujz/xNNYkyaFPJfVPIm78+6nKP0baowBaoLB\nWI0pQLUR/ECKD4rq3AzWqUuqwcQ1tixS0hNJyUwmMSsJpV8iZCRARgLbH9yI060tlzg+C9MjU7QP\nBOVdfVm3xpw1tYF83oXoWKSDuPdQs2xt/aXNegDdE2PobmvyFHBH8P6dqBm5eV2tYG8Vyf78jg6e\nefMv1T8oL1qAxX42Kdte0u2OHWAyMQQTe72NLCldT/822Tpr/OncN+8BMo47SP/BqXzlLeLeDWuw\npp/dvE9H3bJHI+CL1TEUvVlPtflRC8Q8PqhuhOoGdalyB28beP6JZ7AmaoOxe+c9QEnGZpx+PzVG\ndfal0xhovv9NaQ0jkrR18QLZHoWRxnhs8fGk2CykpCVgS0/C0i8JJTOROcs3aAb/l1cVMnTiQMas\nvKLdvzPPf2W3JwBA5Mec9XZybIm8WG3zSAdx53fwWFM36iGgP6ATCrAfQn5IDkbNxtFm/yXAv9p7\noblz55KbmwtAamoq48ePb/7nFhQUAPS69SY9XR+LxcT0S07ni/Vb8Xj8VFYVM33muc0H5VMmjOGl\nF95iUKZ6JvLyqkJc3m954OnbsF84hYLXHVjvfKf57ymvKgQgI3U4dYEAj+z+lIq9AXY4dzJyqD3k\ncat5Erde+RdKxn7Mj06YROqgVD6q3ML60l28/cVmrElnNO/f9EVqCY6faf33rF//BRvWb8Xr8VNR\nVcy0H53bPLC7p9u3r69/9dVXh1X+/vv/yrvvvE96anbzoP0JE07usPz69V/w9pufYDVP0r5/zAao\n9zL5hIngbKRg3Tqo9zA590SoauCe+++k0TIWUgGa3s9Z3D/vAWoytvB5zXZcCuSkDKfWCNvrdlJv\ngOS04WwqqSY9teX93VTe6S7H4PEzCAO7G4pITzBzzoATsaUmstG1i/uKG2jS+vMxeMIg0n5zAhgU\nTtX8veq1O09xnar5fJZW/5c75i/usH2bPt/33bMYr9fPgP4DuWH+AiwWU8iXo155i8XU3HXa245n\nff14Luu9c73pflFREZ3pTWPi7gfKUWeb3ox6WGw7scEEbAemAAeA9cBlqBMb+gMHg/v9DjgV+JnO\n68iYuKOss7Esc2bPx1nSdrgj2FI2s+JPd8AeJ5f89f9wWydq9ikuXMMZAy6kPHhtwhQvfL3HwUCd\ncXiG/QU8c/YvScmykpSdjKFfEo6iL8l/fSVWa8sFqTs6D153zhrfnTFOvbnb+HCyVJEup8kW1X/M\nwryfYz9hIjg96rnInI0EahrwVDdQX+3iyncfpVFnnFjdzjVcmTaVeiPUGgLNt3VGqDcEqDXCt3vW\nMDJXO1asfNcarkmdijWgkBxnIjkhjuTEeKxWC8kpCSSnJZC37mlqbZM0ZW22b1mx/Fl1oL+iPUR3\nNm41nHaSsWZCRI9oGRN3L/AqahdoEeopRgAGAM8BP0LtMbgOWI06U/V51AAO1OBvPGqX63fANRGq\nt2ijs7Es7XbJXrsAzlITreZ/puLWycWOHJfDY9fPUM/UfsBJxb5qrigp0H2dvQ2N3LZlJ9XbAzQY\nwOpTA77Bw7Sza++f9wCJw78nKSmeZJuFJKuF/1Vu5eFvC7Bmt1yaLP+mR2FzmTqAPClOPUN7ogkS\nzDgKPiD/jqfb71rT0Wl3XDsiFSweTv10y/n82M85Bxp90OBTb11edanz4Fi3jvx/LMea2hJU5f92\nMd5TN3N2v+Nw1zXgqm/E7fKoS4MXd4MHd6OXe/e+jnVEaEBlTTyDP9/1DO/1/556gxp8uQxQbwQl\nAIl+2FnnRu/EOh4FrAGFHMVEUpyZxAQzyQlxJCXGk5iaQHJ6AlfW/U/33GRDTxrAvFcWQHIcGPR/\nK89zKPqfg+uC5dpxuF2UMtZMiNjRmzJxkRKVmbjWXRaxoLNsQFeyDe1m9oxfseJXC6GsHk9pPTWH\nnFy+9kkYcLZm3/Jda5iRZafOALVGNduypvAVjhtzmWbfA4UOfpQ9jQQ/WAJg8StY/PBi+TtYR2kz\ngoE973PPuJ8TZzZhjjNijjNhjlfv/+qjZ3Gnn6EpY6v/jBWX3agGAMbgYlDAYMCx9TPy3/sX1oyW\nv8NZsY6F02diP/l0MBiCLxwAXwD8ARwbPyH/32+GjDF0lq9j4ZSLsI+eAP6WfZuWgNfPnFcfpFYn\nIxpf+hGPnZqHt9FLY4MPr8eLt9GHx+vD6/Vz63evYhqqDRScO1ZzZcY0GhVoMECjEqDRgLquBFj5\n/SuMHqtt811FDsYPthPvV9u7ddur2+C1MgfpI7RZMc/37/PwcZeTmBhHotVCgi2ehNQE4mwWsJqZ\n88I9OI2naP8HGVtZ8cYS3WxYk1jIisXasSUaSJtHXjS3ebRk4kQf0lk2oCvZho4mW2BXgzszkAFY\nZ7+uO/Fi6MkD+cvdV6iDzivd4GzkzNv/rVu3nHgLM23pahbIE1wCPgKKQXf/Yq+XFYeKaVQCeBQ1\nw+MxgEcJsLWmjqHp2jJfllQz4811GABDAAyAMXj75V4HQ4e2ySamn83v//YyK96v0K3DZ/tWMaRt\nBjLjbH775mv8YLATv6LOYPQpNN/3K7CzvIaRVu3z7ah1ccf2XZgCYA4upoCCKQCmAFT4/WTp1COg\nKKQpBuIMRuKNBsxGA/FmE3HxJuItJtYd1M9AHd8vndfmng8JZkgyQaJZXZoyoYlm1l//Dc5qbdmM\nUwdw3Eq9kRWqvMHz9d8/1yzoMIADyYoJIXqWBHFRIlp/QRyOcL/gjkjAd+0COL5fyL793xiuG/Cl\nnpTDKSvnara/OutrnKXa/UeNyeHe/5vT0n3YdNvoY84Tn+t2x43PTOGlCyfh9/rx+/z4/X783gA+\nr58rqz9G77rdQ5OSuGv0SDWTFqA5e6cYFeZXfYRfp8zIFBvPnXUSBoMBo8mIwahgMBowmgwYDAo/\nffUz3fodPySD5/5wMcQZ1SU+9HbrHzfh1DkVzaAzjmH2yht0nlGVO7tAt83NQ21w9QntlgPIu/bn\nPTKDMtoDsb54bOlp0uaRF6ttLkGciAkRDfjaCQraPSfWnxfAmYP0y/S7Wr/M3Quw2LXdrACJs/Wv\nqpF8fD8GvDBdt0zS7H/qlkkcnU7KvefqlgHI+8E1HWQ5R7Vf7oYruhVQdbXNWzucYCzaAzEhRN8k\nY+KiRDT350ergoIC3G5vl8YsdWeMU1fLdGcc1uGM3eruuK3ulOtOm4vDI8eWyJM2j7xobvOOxsRJ\nEBclovkNGK16c5tHIljsCb25zWOVtHnkSZtHXjS3uQRxoaIyiBNCCCFE39NREKc/nU4IIYQQQvRq\nEsRFibaXaxFHn7R55EmbR560eeRJm0derLa5BHFRoumakiJypM0jT9o88qTNI0/aPPJitc0liIsS\nVVVVPV2FPkfaPPKkzSNP2jzypM0jL1bbXII4IYQQQogoJEFclCgqKurpKvQ50uaRJ20eedLmkSdt\nHnmx2uZ98RQjBYD2CuhCCCGEEL3POmByT1dCCCGEEEIIIYQQQgghhBBCCCGEOAx2YBuwE7ipnX0e\nDT6+CTgxQvWKZZ21+c9R2/pr4GPgB5GrWswK530OcCrgBWZGolIxLpw2nwxsBL5FHT8sDk9nbZ4J\nOICvUNt8bsRqFpuWAsXANx3sI9+f4qgxAruAXMCM+sEe02afacC7wfunAf+LVOViVDhtPglICd63\nI21+uMJp86b93gf+DcyKVOViVDhtngpsBgYF1zMjVbkYFU6bLwLuCd7PBMoBU2SqF5PORA3M2gvi\nYu77U04x0rtMQP3QFwEeYDkwo80+04EXg/c/Qz3wZkeofrEonDb/FKgO3v+Mli850T3htDnA9cBK\noDRiNYtd4bT5z4DXgX3B9bJIVS5GhdPmBwFb8L4NNYjzRqh+segjoLKDx2Pu+1OCuN5lILC31fq+\n4LbO9pGgovvCafPW5tHyS050T7jv8xnAU8H1QATqFcvCafORQDrwAbABuCIyVYtZ4bT5c8A44ABq\n994NkalanxVz35+Stu1dwv2iant+P/mC676utN05QB5wxlGqS18RTps/DNwc3Fehb57T8kgKp83N\nwEnAFCARNQP9P9TxQ6LrwmnzP6N2s04GhgPvAScAzqNXrT4vpr4/JYjrXfYDg1utD6ala6O9fQYF\nt4nuCafNQZ3M8BzqmLiO0vWic+G0+cmo3U+gjhWaitol9fZRr11sCqfN96J2obqCy4eoAYUEcd0T\nTpufDtwVvF8IfAcci5oJFUeefH+Ko8qE+kHOBeLofGLDRGJgYGYPC6fNj0Ed2zIxojWLXeG0eWvL\nkNmphyucNh8NrEUdkJ+IOjh8bOSqGHPCafOHgNuC97NRg7z0CNUvVuUS3sQG+f4UR8VUYDtq0HBL\ncNs1waXJ48HHN6F2f4jD01mbL0EdcLwxuKyPdAVjUDjv8yYSxB0Z4bT5H1FnqH4D/CaitYtNnbV5\nJvAv1GP5N6iTS0T3/QN1fGEjamY5D/n+FEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEII\nIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYBU1Gtdvthm+9uol1qyRLxGQgghhBAiLBcA\nfmB6cP0qwAuc1mM1EkIIIYQQYXkaOAScCFQB9/RsdYQQQgghRDiSgELABXwNmHu2OkKIvsLQ0xUQ\nQogoVwe8A8QDzwOenq2OEEIIIYQIx6lAI7ABKAOye7Y6QgghhBCiMxZgC+qM1ARgB/BWj9ZICCGE\nEEJ06kFCs2+no85OvbLHaiSEEEIIITp0BmrAdmmb7fcDFcCAiNdICCGEEEIIIYQQQgghhBBCCCGE\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCFi2v8DGr35qHhRPjYA\nAAAASUVORK5CYII=\n", "text": [ - "" + "" ] } ], - "prompt_number": 7 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -467,7 +468,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 8 + "prompt_number": 7 }, { "cell_type": "code", @@ -481,7 +482,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 9 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -491,7 +492,7 @@ "\n", "As we already know, to solve our problem, we need to require $U_{\\text{n}}(x, y)=0$ at the center (collocation point) of each panel. However we have to be careful, because at $(x_{c_i}, y_{c_i})$ all our integrals have a singularity. To skip that singularity, for $i=j$ we have to solve them analytically in the local coordinates of the panel.\n", "\n", - "So for the flow-tangency boundary condition, the integrals (in local coordinates) that we have to solve analytically are:\n", + "For the flow-tangency boundary condition, the integrals (in local coordinates) that we have to solve analytically are:\n", "\n", "\\begin{equation}\n", " I_1=\\frac{1}{2\\pi} \\int^l_0 \\frac{(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", @@ -501,7 +502,7 @@ " I_2=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,(x^*_{i}-s)}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", "\\end{equation}\n", "\n", - "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "After we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", "\n", "\n", "\\begin{equation}\n", @@ -518,7 +519,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "For all the integrals that appear in our equations, we are gonna use the function `integrate.quad()` from SciPy. So following the same idea we use in the previous lessons, we are going to define two integrate functions on to solve the terms of the form:\n", + "For all the integrals that appear in our equations, we use the function `integrate.quad()` from SciPy. Following the same idea we use in the previous lessons, we define two integrate functions to compute the terms of the form:\n", "\n", "`integral`:\n", "\n", @@ -532,7 +533,7 @@ " \\int_j s\\,f_j(s) {\\rm d}s\\;a - \\int_j s\\,g_j(s) {\\rm d}s\\;b\n", "\\end{equation}\n", "\n", - "where $a$ and $b$ can be $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$ depending the case. " + "where $a$ and $b$ can be $n_x=\\cos (\\beta_i)$ , $n_y=\\sin (\\beta_i)$ , $t_x=-\\sin (\\beta_i)$ and $t_y=\\cos (\\beta_i)$ depending on the case. " ] }, { @@ -562,7 +563,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 10 + "prompt_number": 9 }, { "cell_type": "code", @@ -591,29 +592,27 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 11 + "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can use this functions to calculate the coefficients of the matrices corresponding to each term in the equation for $U_{\\text{n}}(x, y)$ to finally solve the linear system $$[A][\\gamma] = [b]$$.\n", + "Now we can use these functions to calculate the coefficients of the matrices corresponding to each term in the equation for $U_{\\text{n}}(x, y)$ to finally solve the linear system $$[A][\\gamma] = [b]$$\n", "\n", - "So we will call:\n", - "\n", - "$A_1$ the term related to the first integral:\n", + "We will call $A_1$ the term related to the first integral,\n", "\n", "\\begin{equation}\n", " \\int_j f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $A_2$ the term related to the second integral:\n", + "$A_2$ the term related to the second integral,\n", "\n", "\\begin{equation}\n", " \\int_j s\\,f_j(s) {\\rm d}s\\;\\cos(\\beta_i) - \\int_j s\\,g_j(s) {\\rm d}s\\;\\sin(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ correspond to $\\gamma_j$ and $A_3$ correspond to $\\gamma_{j+1}$.\n", + "and $A_3=A_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $A_2$ corresponds to $\\gamma_j$ and $A_3$ corresponds to $\\gamma_{j+1}$.\n", "\n", "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." ] @@ -641,7 +640,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 12 + "prompt_number": 11 }, { "cell_type": "code", @@ -665,7 +664,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 13 + "prompt_number": 12 }, { "cell_type": "code", @@ -684,7 +683,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 14 + "prompt_number": 13 }, { "cell_type": "code", @@ -699,13 +698,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 15 + "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We got our coefficintes, but how are these guys related with the matrix $A$ that we need to build in order to solve our system?" + "We got our coefficients, but how are these guys related with the matrix $A$ that we need to build in order to solve our system?" ] }, { @@ -714,7 +713,7 @@ "source": [ "##How to build the A matrix\n", "\n", - "This is the moment, where you should grab a piece of paper and write some terms of the $U_n$ for a panel $i$. After writing couple of $j$-terms, you should notice that. (tip: write the terms counting from zero, so then you match this with the code)\n", + "This is the moment when you should grab a piece of paper and write some terms of the $U_n$ for a panel $i$. After writing a couple of $j$-terms, you should notice that. (tip: write the terms counting from zero, so then you match this with the code)\n", "\n", "* For $j=0$ you only have contribution from the first and second integral ($A_1$ and $A_2$), which are the coefficients related with $\\gamma_j$. \n", "\n", @@ -722,12 +721,12 @@ "* For $j=N$ (last panel) you only have contribution from the third integral ($A_3$), which is the coefficient related with $\\gamma_{j+1}$. \n", "\n", "\n", - "* For $ 0
\n" ] @@ -739,7 +738,19 @@ "#In code, except for the kutta condition (in cell after)...\n", "\n", "def A_normal(panels,A1,A2,A3):\n", - " \"\"\"\n", + " \"\"\"Builds the normal matrix\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: panels of the geometry\n", + " A1: term related to the first integral in U_n\n", + " A2: term related to the second integral in U_n\n", + " A3: term related to the third integral in U_n\n", + " \n", + " Returns\n", + " -------\n", + " A_n: Nx(N+1) matrix, where N is number of panels. \n", + " \n", " \"\"\"\n", " N = len(panels)\n", " A_n = numpy.zeros((N, N+1), dtype=float) \n", @@ -758,7 +769,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 16 + "prompt_number": 15 }, { "cell_type": "markdown", @@ -796,7 +807,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 17 + "prompt_number": 16 }, { "cell_type": "markdown", @@ -834,7 +845,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 18 + "prompt_number": 17 }, { "cell_type": "code", @@ -864,7 +875,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 19 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -891,7 +902,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 20 + "prompt_number": 19 }, { "cell_type": "markdown", @@ -910,13 +921,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 21 + "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we have the solution of our system we can get the surface pressure coefficient by calculating the tangential velocity. So let's keep coding (and doing a little bit more of math)." + "Now we have the solution of our system, we can get the surface pressure coefficient by calculating the tangential velocity. So let's keep coding (and doing a little bit more of math)." ] }, { @@ -934,7 +945,7 @@ "\n", "$$C_{p_i} = 1 - \\left(\\frac{U_{t_i}}{U_\\infty}\\right)^2$$\n", "\n", - "So, we have to compute the tangential velocity. However, we can not escape from the math. To calculate $U_t$, we have to do some integral, do you remember?. Guess what, yes! we have the singularities issue again. In this case, the integrals we have to solve analytically are:\n", + "We have to compute the tangential velocity. However, we can not escape from the math. To calculate $U_t$, we have to do some integrals, do you remember? Guess what, yes! we have the singularities issue again. In this case, the integrals we have to solve analytically are:\n", "\n", "\\begin{equation}\n", " I_3=\\frac{1}{2\\pi} \\int^l_0 \\frac{y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", @@ -944,7 +955,7 @@ " I_4=\\frac{1}{2\\pi l} \\int^l_0 \\frac{s\\,y^*_{i}}{(x^*_{i}-s)^2 + (y^*_{i})^2} {\\rm d}s\n", "\\end{equation}\n", "\n", - "So, after we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", + "After we integrate, using that at the center point $r_{i,j}=r_{i,j+1}$ and $\\theta_{i,j+1}-\\theta_{i,j}=\\pi$ we get that:\n", "\n", "\n", "\\begin{equation}\n", @@ -961,21 +972,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So, following the same idea that we use to build the **A** matrix, we define:\n", + "Following the same idea that we use to build the **A** matrix, we define:\n", "\n", - "$B_1$ the term related to the first integral:\n", + "$B_1$, the term related to the first integral:\n", "\n", "\\begin{equation}\n", " \\int_j f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $B_2$ the term related to the second integral:\n", + "$B_2$ the term related to the second integral:\n", "\n", "\\begin{equation}\n", " \\int_j s\\,f_j(s) {\\rm d}s\\;(-\\sin(\\beta_i)) + \\int_j s\\,g_j(s) {\\rm d}s\\;\\cos(\\beta_i)\n", "\\end{equation}\n", "\n", - "and $B_3=B_2$ the term related to the third integral. We want to keep the three terms to avoid confusions. $B_2$ correspond to $\\gamma_j$ and $B_3$ correspond to $\\gamma_{j+1}$.\n", + "and $B_3=B_2$, the term related to the third integral. We want to keep the three terms to avoid confusions. $B_2$ correspond to $\\gamma_j$ and $B_3$ correspond to $\\gamma_{j+1}$.\n", "\n", "Then, using the information from the analytical solutions when $i=j$ and our integral functions, we can build three different functions that return these coefficients." ] @@ -1005,7 +1016,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 22 + "prompt_number": 21 }, { "cell_type": "code", @@ -1030,7 +1041,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 23 + "prompt_number": 22 }, { "cell_type": "code", @@ -1049,7 +1060,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 24 + "prompt_number": 23 }, { "cell_type": "code", @@ -1063,7 +1074,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 25 + "prompt_number": 24 }, { "cell_type": "markdown", @@ -1077,7 +1088,18 @@ "collapsed": false, "input": [ "def A_tangential(panels,B1,B2,B3):\n", - " \"\"\"\n", + " \"\"\"Builds the tangential matrix\n", + " \n", + " Arguments\n", + " ---------\n", + " panels: panels of the geometry\n", + " B1: term related to the first integral in U_t\n", + " B2: term related to the second integral in U_t\n", + " B3: term related to the third integral in U_t\n", + " \n", + " Returns\n", + " -------\n", + " A_t: Nx(N+1) matrix, where N is number of panels. \n", " \"\"\"\n", " N = len(panels)\n", " A_t = numpy.zeros((N, N+1), dtype=float) \n", @@ -1096,7 +1118,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 26 + "prompt_number": 25 }, { "cell_type": "code", @@ -1107,7 +1129,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 27 + "prompt_number": 26 }, { "cell_type": "code", @@ -1120,7 +1142,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 28 + "prompt_number": 27 }, { "cell_type": "markdown", @@ -1138,7 +1160,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 29 + "prompt_number": 28 }, { "cell_type": "code", @@ -1150,7 +1172,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 30 + "prompt_number": 29 }, { "cell_type": "markdown", @@ -1177,7 +1199,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 31 + "prompt_number": 30 }, { "cell_type": "code", @@ -1188,13 +1210,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 32 + "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "From [Lesson 10](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb) we kow the exact solution for zero angle of attack, so let copy that solution, to compare with our result." + "From [Lesson 10](http://nbviewer.ipython.org/github/barbagroup/AeroPython/blob/master/lessons/10_Lesson10_sourcePanelMethod.ipynb) we know the exact solution for zero angle of attack, so let's copy that solution, to compare with our result." ] }, { @@ -1216,7 +1238,7 @@ ] } ], - "prompt_number": 33 + "prompt_number": 32 }, { "cell_type": "code", @@ -1238,7 +1260,7 @@ ] } ], - "prompt_number": 34 + "prompt_number": 33 }, { "cell_type": "code", @@ -1268,7 +1290,7 @@ "pyplot.ylim(-0.65, 1.)\n", "pyplot.gca().invert_yaxis()\n", "pyplot.title('Number of panels : %d' % N)\n", - "#pyplot.savefig('CP_0.pdf'); add this line to save fig" + "#pyplot.savefig('CP_0.pdf'); add this line to save fig;" ], "language": "python", "metadata": {}, @@ -1278,17 +1300,17 @@ "output_type": "display_data", "png": 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Vqk0bFew1SLkXH2NyfuVKE9SRI+ZnCv/8rbdS9dpVr15dzZ8/37Tdwmrf87xM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\nkiUsWrSIcePG2f/g7t3Qty8UFMSuuBjzw0icROjYLRERiTM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"text": [ - "" + "" ] } ], - "prompt_number": 35 + "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Nice!! our solution match with the theoretical one. However the purpouse of use vortices as our singularities is to get some lift and see how our model behaves. So let's calculate solve the problem for an angle of attack $\\alpha=10$ degrees. We pick $10\u00b0$ because we have some experimental data for the coefficient of pressure of the upper face, to compare. [Gregory & O'Reilly pressure data.](http://turbmodels.larc.nasa.gov/naca0012_val.html)" + "Nice!! Our solution matches with the theoretical one. However, the purpouse of using vortices as our singularities is to get some lift and see how our model behaves. Let's calculate solve the problem for an angle of attack $\\alpha=10$ degrees. We pick $10\u00b0$ because we have some experimental data for the coefficient of pressure of the upper face, to compare. See [Gregory & O'Reilly pressure data.](http://turbmodels.larc.nasa.gov/naca0012_val.html)" ] }, { @@ -1310,7 +1332,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 36 + "prompt_number": 35 }, { "cell_type": "code", @@ -1323,7 +1345,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 37 + "prompt_number": 36 }, { "cell_type": "code", @@ -1335,7 +1357,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 38 + "prompt_number": 37 }, { "cell_type": "code", @@ -1348,7 +1370,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 39 + "prompt_number": 38 }, { "cell_type": "code", @@ -1360,7 +1382,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 40 + "prompt_number": 39 }, { "cell_type": "code", @@ -1372,7 +1394,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 41 + "prompt_number": 40 }, { "cell_type": "code", @@ -1383,13 +1405,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 42 + "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "As we mention before we have some experimental data for the upper face, so let's import that data to compare with our results. " + "As we mentioned before, we have some experimental data for the upper face, so let's import that data to compare with our results. " ] }, { @@ -1401,7 +1423,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 43 + "prompt_number": 42 }, { "cell_type": "code", @@ -1434,7 +1456,7 @@ "pyplot.ylim(y_start, y_end)\n", "pyplot.gca().invert_yaxis()\n", "pyplot.title('Angle of attack 10 deg, Number of panels : %d' % N, fontsize=20)\n", - "#pyplot.savefig('CP_10.pdf'); add this line to save fig" + "#pyplot.savefig('CP_10.pdf'); add this line to save fig;" ], "language": "python", "metadata": {}, @@ -1444,11 +1466,11 @@ "output_type": "display_data", "png": 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q0LRpU6ZPn+53Casou/ylWfN/QC0n00ehy1gFaAPcBnwMNHK2kv79+xMbGwtA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"text": [ - "" + "" ] } ], - "prompt_number": 53 + "prompt_number": 43 }, { "cell_type": "markdown", @@ -1521,8 +1543,7 @@ ], "language": "python", "metadata": {}, - "outputs": [], - "prompt_number": 55 + "outputs": [] }, { "cell_type": "markdown", @@ -1530,11 +1551,11 @@ "source": [ "We can calculate the value of the lift coefficients for different number of panels and compare it with the value of the experimental data.\n", "\n", - "The value of the experimental lift for $\\alpha = 10\u00b0$ was obtain from reference [4](https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises),\n", + "The value of the experimental lift for $\\alpha = 10\u00b0$ was obtained from reference [4](https://confluence.cornell.edu/display/SIMULATION/Flow+over+an+Airfoil+-+Exercises),\n", "\n", "$$ L_{exp} = 1.2219 $$\n", "\n", - "with this value as a reference we can plot de relative error as a function of the number of panels $N_p$ and see how our model behaves." + "With this value as a reference, we can plot de relative error as a function of the number of panels $N_p$ and see how our model behaves." ] }, { @@ -1548,8 +1569,7 @@ ], "language": "python", "metadata": {}, - "outputs": [], - "prompt_number": 56 + "outputs": [] }, { "cell_type": "code", @@ -1571,8 +1591,7 @@ ], "language": "python", "metadata": {}, - "outputs": [], - "prompt_number": 57 + "outputs": [] }, { "cell_type": "code", @@ -1591,49 +1610,30 @@ "pyplot.title('Percentage error vs number of panels', fontsize=20)\n", "\n", "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);\n", - "#pyplot.savefig('error.pdf'); add this line to save fig" + "#pyplot.savefig('error.pdf'); add this line to save fig;" ], "language": "python", "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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3Ag8Dv6XvyRhPEEXfDOKsW0/GkCRJLalVT8YAmAZ8jxiDtwtwKnBE+gF4L3An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\nIkmStJoiC711iIJtGXEo9u4hbKMd2I0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- "text": [ - "" - ] - } - ], - "prompt_number": 58 + "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "#For Np=400 the precentage error is:\n", - "L_400 = per_err[-1]\n", + "L_400_err = per_err[-1]\n", "\n", - "print ('L_400 = %.4f' %L_400)" + "print ('L_400_err = %.4f' %L_400_err)" ], "language": "python", "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "L_400 = 3.3855\n" - ] - } - ], - "prompt_number": 59 + "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "As we expected, when the number of panels increases, the percentage error decreases. For $Np >60$ the percentage error is less than $5\\%$ what is an acceptable value. As $Np$ keeps increasing, the error continues decreasing but slowly. For $Np=400$ the error is around $3.4\\%$, which is close to the value for $Np=200$ ($\\approx 3.5\\%$). Then, it is not worthy to solve for all this panels if we can get a similar performance for a smaller $Np$." + "As we expected, when the number of panels increases, the percentage error decreases. For $Np >60$ the percentage error is less than $5\\%$ which may be an acceptable value. As $Np$ keeps increasing, the error continues decreasing but slowly. For $Np=400$ the error is around $3.4\\%$, which is close to the value for $Np=200$ ($\\approx 3.5\\%$). Then, it is not worthwhile to solve for all these panels if we can get a similar result with smaller $Np$." ] }, { @@ -1688,162 +1688,7 @@ ], "language": "python", "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n", - "\n", - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 54, - "text": [ - "" - ] - } - ], - "prompt_number": 54 + "outputs": [] } ], "metadata": {} From c4898f7a4935ee40e7c96b0d6a25e0675a7b8cd8 Mon Sep 17 00:00:00 2001 From: Natalia Clementi Date: Wed, 27 May 2015 18:15:07 -0400 Subject: [PATCH 7/7] Fixing a little typo --- ...inear_vortex_Panel_Method-checkpoint.ipynb | 120 +++++------ clementi/Linear_vortex_Panel_Method.ipynb | 191 +++++++++++++++++- 2 files changed, 244 insertions(+), 67 deletions(-) diff --git a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb index 7971bb3..1f10b63 100644 --- a/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb +++ b/clementi/.ipynb_checkpoints/Linear_vortex_Panel_Method-checkpoint.ipynb @@ -2,7 +2,7 @@ "metadata": { "hide_input": false, "name": "", - "signature": "sha256:5d8e6960e66497e40f7e396fcb6e5f0c1fcfc5cd53c6b4489da6a310491cfc58" + "signature": "sha256:e4c84416c816dd77864dc50cef246ba32ce52d7cb5903fc802363c9858db5c33" }, "nbformat": 3, "nbformat_minor": 0, @@ -257,7 +257,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 2 + "prompt_number": 1 }, { "cell_type": "markdown", @@ -279,7 +279,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -326,7 +326,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 4 + "prompt_number": 3 }, { "cell_type": "code", @@ -379,7 +379,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 5 + "prompt_number": 4 }, { "cell_type": "code", @@ -392,7 +392,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 6 + "prompt_number": 5 }, { "cell_type": "code", @@ -433,11 +433,11 @@ "output_type": "display_data", "png": 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"text": [ - "" + "" ] } ], - "prompt_number": 7 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -468,7 +468,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 8 + "prompt_number": 7 }, { "cell_type": "code", @@ -482,7 +482,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 9 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -563,7 +563,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 10 + "prompt_number": 9 }, { "cell_type": "code", @@ -592,7 +592,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 11 + "prompt_number": 10 }, { "cell_type": "markdown", @@ -640,7 +640,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 12 + "prompt_number": 11 }, { "cell_type": "code", @@ -664,7 +664,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 13 + "prompt_number": 12 }, { "cell_type": "code", @@ -683,7 +683,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 14 + "prompt_number": 13 }, { "cell_type": "code", @@ -698,7 +698,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 15 + "prompt_number": 14 }, { "cell_type": "markdown", @@ -769,7 +769,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 16 + "prompt_number": 15 }, { "cell_type": "markdown", @@ -807,7 +807,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 17 + "prompt_number": 16 }, { "cell_type": "markdown", @@ -845,7 +845,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 18 + "prompt_number": 17 }, { "cell_type": "code", @@ -875,7 +875,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 19 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -902,7 +902,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 20 + "prompt_number": 19 }, { "cell_type": "markdown", @@ -921,7 +921,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 21 + "prompt_number": 20 }, { "cell_type": "markdown", @@ -1016,7 +1016,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 22 + "prompt_number": 21 }, { "cell_type": "code", @@ -1041,7 +1041,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 23 + "prompt_number": 22 }, { "cell_type": "code", @@ -1060,7 +1060,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 24 + "prompt_number": 23 }, { "cell_type": "code", @@ -1074,7 +1074,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 25 + "prompt_number": 24 }, { "cell_type": "markdown", @@ -1118,7 +1118,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 26 + "prompt_number": 25 }, { "cell_type": "code", @@ -1129,7 +1129,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 27 + "prompt_number": 26 }, { "cell_type": "code", @@ -1142,7 +1142,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 28 + "prompt_number": 27 }, { "cell_type": "markdown", @@ -1160,7 +1160,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 29 + "prompt_number": 28 }, { "cell_type": "code", @@ -1172,7 +1172,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 30 + "prompt_number": 29 }, { "cell_type": "markdown", @@ -1199,7 +1199,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 31 + "prompt_number": 30 }, { "cell_type": "code", @@ -1210,7 +1210,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 32 + "prompt_number": 31 }, { "cell_type": "markdown", @@ -1238,7 +1238,7 @@ ] } ], - "prompt_number": 33 + "prompt_number": 32 }, { "cell_type": "code", @@ -1260,7 +1260,7 @@ ] } ], - "prompt_number": 34 + "prompt_number": 33 }, { "cell_type": "code", @@ -1290,7 +1290,7 @@ "pyplot.ylim(-0.65, 1.)\n", "pyplot.gca().invert_yaxis()\n", "pyplot.title('Number of panels : %d' % N)\n", - "#pyplot.savefig('CP_0.pdf'); add this line to save fig" + "#pyplot.savefig('CP_0.pdf'); add this line to save fig;" ], "language": "python", "metadata": {}, @@ -1300,11 +1300,11 @@ "output_type": "display_data", "png": 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Vqk0bFew1SLkXH2NyfuVKE9SRI+ZnCv/8rbdS9dpVr15dzZ8/37Tdwmrf87xM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\nkiUsWrSIcePG2f/g7t3Qty8UFMSuuBjzw0icROjYLRERiTM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"text": [ - "" + "" ] } ], - "prompt_number": 35 + "prompt_number": 34 }, { "cell_type": "markdown", @@ -1332,7 +1332,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 36 + "prompt_number": 35 }, { "cell_type": "code", @@ -1345,7 +1345,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 37 + "prompt_number": 36 }, { "cell_type": "code", @@ -1357,7 +1357,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 38 + "prompt_number": 37 }, { "cell_type": "code", @@ -1370,7 +1370,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 39 + "prompt_number": 38 }, { "cell_type": "code", @@ -1382,7 +1382,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 40 + "prompt_number": 39 }, { "cell_type": "code", @@ -1394,7 +1394,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 41 + "prompt_number": 40 }, { "cell_type": "code", @@ -1405,7 +1405,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 42 + "prompt_number": 41 }, { "cell_type": "markdown", @@ -1423,7 +1423,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 43 + "prompt_number": 42 }, { "cell_type": "code", @@ -1456,7 +1456,7 @@ "pyplot.ylim(y_start, y_end)\n", "pyplot.gca().invert_yaxis()\n", "pyplot.title('Angle of attack 10 deg, Number of panels : %d' % N, fontsize=20)\n", - "#pyplot.savefig('CP_10.pdf'); add this line to save fig" + "#pyplot.savefig('CP_10.pdf'); add this line to save fig;" ], "language": "python", "metadata": {}, @@ -1466,11 +1466,11 @@ "output_type": "display_data", "png": 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q0LRpU6ZPn+53Casou/ylWfN/QC0n00ehy1gFaAPcBnwMNHK2kv79+xMbGwtA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"text": [ - "" + "" ] } ], - "prompt_number": 53 + "prompt_number": 43 }, { "cell_type": "markdown", @@ -1544,7 +1544,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 55 + "prompt_number": 44 }, { "cell_type": "markdown", @@ -1571,7 +1571,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 56 + "prompt_number": 45 }, { "cell_type": "code", @@ -1594,7 +1594,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 57 + "prompt_number": 46 }, { "cell_type": "code", @@ -1613,7 +1613,7 @@ "pyplot.title('Percentage error vs number of panels', fontsize=20)\n", "\n", "pyplot.plot(Np_list, per_err,color='r', linewidth=0, marker='o', markersize=6);\n", - "#pyplot.savefig('error.pdf'); add this line to save fig" + "#pyplot.savefig('error.pdf'); add this line to save fig;" ], "language": "python", "metadata": {}, @@ -1623,11 +1623,11 @@ "output_type": "display_data", "png": 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3Ag8Dv6XvyRhPEEXfDOKsW0/GkCRJLalVT8YAmAZ8jxiDtwtwKnBE+gF4L3An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\nIkmStJoiC711iIJtGXEo9u4hbKMd2I0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"text": [ - "" + "" ] } ], - "prompt_number": 58 + "prompt_number": 47 }, { "cell_type": "code", @@ -1645,11 +1645,11 @@ "output_type": "stream", "stream": "stdout", "text": [ - "L_400 = 3.3855\n" + "L_400_err = 3.3855\n" ] } ], - "prompt_number": 59 + "prompt_number": 48 }, { "cell_type": "markdown", @@ -1859,13 +1859,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 54, + "prompt_number": 49, "text": [ - "" + "" ] } ], - "prompt_number": 54 + "prompt_number": 49 } ], "metadata": {} diff --git a/clementi/Linear_vortex_Panel_Method.ipynb b/clementi/Linear_vortex_Panel_Method.ipynb index 4511165..1f10b63 100644 --- a/clementi/Linear_vortex_Panel_Method.ipynb +++ b/clementi/Linear_vortex_Panel_Method.ipynb @@ -2,7 +2,7 @@ "metadata": { "hide_input": false, "name": "", - "signature": "sha256:d9103dc4ef75113b3ccd3154e57dd4cd2735cb2549e0ea8b71d47d777d18a321" + "signature": "sha256:e4c84416c816dd77864dc50cef246ba32ce52d7cb5903fc802363c9858db5c33" }, "nbformat": 3, 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3Ag8Dv6XvyRhPEEXfDOKsW0/GkCRJLalVT8YAmAZ8jxiDtwtwKnBE+gF4L3An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\nIkmStJoiC711iIJtGXEo9u4hbKMd2I0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