diff --git a/Modelling Compressibility Effects In Potential Flow.ipynb b/Modelling Compressibility Effects In Potential Flow.ipynb new file mode 100644 index 0000000..5cb60ae --- /dev/null +++ b/Modelling Compressibility Effects In Potential Flow.ipynb @@ -0,0 +1,1167 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:0d56755d3bc9a466dda3a9ed19fd878546679f8fa0f19906b39a7f17e250a3fa" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\LARGE \\textbf{Modelling Compressability Effects Using Potential Flow}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\large \\text{Matthew Glasstone}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\textit{The George Washington University}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\textit{School Of Engineering and Applied Science}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\textit{Department of Mechanical and Aerospace Engineering}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\textit{Final Project for: MAE 6226}$$" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Motivation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All information comes from John D. Andersons book Fundamentals of Aerodynamics.\n", + "\n", + "Potential flow theory has a range of useful applications, many of which have been covered already in MAE6226. The backbone of potential flow theory is the principle of superposition. This allows for complex geometries to be analyzed by adding together the solutions of simpler geometries. This allows us to apply potential flow for everything from the visualization of flow over a cylinder to finding the lift of an airfoil.\n", + "\n", + "A series of assumptions are necessary in order to apply potential flow theory. These are:\n", + "* Steady flow\n", + "* Incompressible fluid\n", + "* Inviscid\n", + "* Irrotaitonal\n", + "\n", + "As was said best by John von Neumann, the result of these assumptions is that the flow is \"so unphysical that the only fluid to obey the assumptions is 'Dry Water'\". Using clever math, the incompressible fluid assumption can be relaxed at low to moderate Mach numbers. By reducing the number of assumptions, the \"realism\" of the modelled flows can be increased. " + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "The Math - The Velocity Potential Equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Starting from first principles, the velocity potential equation can be derived for a compressible fluid. \n", + "\n", + "$$\\left[1-\\frac{1}{a^2} \\left(\\frac{\\partial\\phi}{\\partial x}\\right)^2\\right] \\frac{\\partial^2\\phi}{\\partial x^2} + \\left[1-\\frac{1}{a^2} \\left(\\frac{\\partial\\phi}{\\partial y}\\right)^2\\right] \\frac{\\partial^2\\phi}{\\partial y^2} - \\frac{2}{a^2}\\left(\\frac{\\partial\\phi}{\\partial x}\\right)\\left(\\frac{\\partial\\phi}{\\partial y}\\right)\\frac{\\partial^2\\phi}{\\partial x \\partial y} = 0$$\n", + "\n", + "This equation has two unknowns: a, the local speed of sound, and $\\phi$, the velocity potential. In order to reduce the velocity potential equation to a partial differential equation of a single unkown, the local speed of sound can be written in terms of the velocity potential $\\phi$ and the speed of sound of the free stream $a_0$. This equation is shown below:\n", + "\n", + "$$a^2 = a_0^2 - \\frac{\\gamma -1}{2}\\left[\\left(\\frac{\\partial\\phi}{\\partial x}\\right)^2 + \\left(\\frac{\\partial\\phi}{\\partial y}\\right)^2 \\right]$$\n", + "\n", + "In its current form, the velocity potential equation is exact and holds for all Mach numbers and geometries.\n", + "\n", + "Unforunately, the velocity potential equation is also non-linear. This prevents the principle of superposition from being applied during analysis, a major problem if we want to analyze any complex geometries. By limiting the range of Mach numbers and possible geometries, the velocity potential equation can be linearized. \n", + "\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "The Math - The Linearized Velocity Potential Equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The velocity vectors of a flow can be rewritten in terms of a mean flow component and a perturbation component. For an arbitrary flow with the free stream flowing soley in the x direction, the velocity vectors can be written in terms of their mean flow and perturbation components. $\\hat{u}$ and $\\hat{v}$ are called the perturbation velocities.\n", + "\n", + "$$u = U_\\infty + \\hat{u} \\quad v = \\hat{v}$$\n", + "\n", + "Similarly, a perturbation velocity potential, $\\hat{\\phi}$ can be defined such that:\n", + "\n", + "$$\\phi = U_\\infty x + \\hat{\\phi} \\quad \\hat{u} = \\frac{\\partial\\hat{\\phi}}{\\partial x} \\quad \\hat{v} = \\frac{\\partial\\hat{\\phi}}{\\partial y}$$\n", + "\n", + "The perturbation velocity potential can be substituted into the velocity potential equation to obtain the perturbation velocity potential equation, shown below.\n", + "\n", + "$$\\left[a^2 - \\left(U_\\infty + \\frac{\\partial \\hat{\\phi}}{\\partial x}\\right)^2 \\right]\\frac{\\partial^2 \\hat{\\phi}}{\\partial x^2} + \\left[a^2 - \\left(\\frac{\\partial \\hat{\\phi}}{\\partial y}\\right)^2 \\right]\\frac{\\partial^2 \\hat{\\phi}}{\\partial y^2} - 2\\left(U_\\infty + \\frac{\\partial \\hat{\\phi}}{\\partial x}\\right)\\left(\\frac{\\partial \\hat{\\phi}}{\\partial y}\\right)\\frac{\\partial^2 \\hat{\\phi}}{\\partial x \\partial y} = 0$$\n", + "\n", + "Using the energy equation for compressible fluids, written in terms of Mach number and $\\gamma$, we can rewrite the perturbation velocity equation as follows:\n", + "\n", + "$$\\left(1-M_\\infty ^2\\right)\\frac{\\partial\\hat{u}}{\\partial x} + \\frac{\\partial\\hat{v}}{\\partial y} = M_\\infty ^2 \\left[\\left(\\gamma +1 \\right)\\frac{\\hat{u}}{U_\\infty} + \\frac{\\gamma + 1}{2}\\frac{\\hat{u}^2}{U_\\infty ^2} + \\frac{\\gamma -1}{2}\\frac{\\hat{v}^2}{U_\\infty ^2}\\right]\\frac{\\partial\\hat{u}}{\\partial x} + M_\\infty ^2 \\left[\\left(\\gamma -1\\right)\\frac{\\hat{u}}{U_\\infty} + \\frac{\\gamma+1}{2}\\frac{\\hat{v}^2}{U_\\infty ^2} + \\frac{\\gamma -1}{2}\\frac{\\hat{u}^2}{U_\\infty ^2} \\right]\\frac{\\partial\\hat{v}}{\\partial y} + M_\\infty ^2 \\left[\\frac{\\hat{v}}{U_\\infty} \\left(1+\\frac{\\hat{u}}{U_\\infty}\\right)\\left(\\frac{\\partial \\hat{u}}{\\partial y} + \\frac{\\partial \\hat{v}}{\\partial x} \\right) \\right]$$\n", + "\n", + "This equation is still exact for irrotational, isentropic flow. The left-hand side of the equation is now linear while the right-hand side remains nonlinear.\n", + "\n", + "In order to linearize the right-hand side of the equation, we will limit the size of the perturbations by considering only slender bodies at small angles of attack. Once we have constrained the geometry, order of mangnitude arguments are applied in order to cancel out negligible terms.\n", + "\n", + "Since we have limited the size of the perturbations, compared to the magnitude of the mean flow any perturbations are negligible in magnitude. Thus:\n", + "\n", + "$$\\frac{\\hat{u}}{U_\\infty},\\frac{\\hat{v}}{U_\\infty} \\ll 1 \\quad and \\quad \\frac{\\hat{u}^2}{U_\\infty ^2}, \\frac{\\hat{v} ^2}{U_\\infty ^2} \\ll 1$$\n", + "\n", + "Assuming small perturbations is not enough to linearize the right-hand side of the equations. In order to fully linearize the perturbation velocity equation, we must also limit the mach number range.\n", + "\n", + "For $0 \\leq M_\\infty 0.8$ or $M_\\infty \\geq 1.2$, the magnitude of \n", + "\n", + "$$M_\\infty ^2 \\left[\\left(\\gamma +1 \\right)\\frac{\\hat{u}}{U_\\infty} + \\text{ ... } \\right]\\frac{\\partial \\hat{u}}{\\partial x} \\ll \\left(1-M_\\infty ^2 \\right)\\frac{\\partial \\hat{u}}{\\partial x} $$\n", + "\n", + "so ignore that term on the right-hand side of the perturbation velocity equation.\n", + "\n", + "For $M_\\infty \\leq 5$ \n", + "\n", + "$$M_\\infty ^2 \\left[\\left(\\gamma -1 \\right)\\frac{\\hat{u}}{U_\\infty} + \\text{ ... } \\right]\\frac{\\partial \\hat{v}}{\\partial y} \\ll \\frac{\\partial \\hat{v}}{\\partial y}$$\n", + "\n", + "so that term is also ignored.\n", + "\n", + "In a similar vien, \n", + "\n", + "$$M_\\infty ^2 \\left[\\frac{\\hat{v}}{U_\\infty} \\left(1 + \\frac{\\hat{v}}{U_\\infty} \\right)\\left(\\frac{\\partial \\hat{u}}{\\partial y} + \\frac{\\partial \\hat{v}}{\\partial x} \\right) \\right] \\approx 0$$\n", + "\n", + "Using these order-of-magnitude arguments, the perturbation velocity equation reduces to:\n", + "\n", + "$$\\left(1 - M_\\infty ^2 \\right)\\frac{\\partial \\hat{u}}{\\partial x} + \\frac{\\partial \\hat{v}}{\\partial y} = 0$$\n", + "\n", + "Rewriting this in terms of the pertubation velocity potential,\n", + "\n", + "$$\\left(1 - M_\\infty ^2 \\right)\\frac{\\partial ^2 \\hat{\\phi}}{\\partial x^2} + \\frac{\\partial ^2 \\hat{\\phi}}{\\partial y^2} = 0$$\n", + "\n", + "This equation is linear and closely resembles Laplace's equation, the fundamental equation that all of potential flow is based on. In the form given above, the equation is valid for:\n", + "* Flows in the range of mach 0 to 0.8 and mach 1.2 to 5\n", + "* Geometries that are thin with small angles of attack" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "The Math - The Prandtl-Glauert Compressability Correction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The perturbation velocity potential can be rewritten using a coordinate transform so that it exactly resembles Laplace's equation. This coordinate transform is called the Prandtl-Glauert Compressability Correction.\n", + "\n", + "Define $\\beta^2 = 1-M_\\infty^2$ so that the perturbation velocity equation becomes:\n", + "\n", + "$$\\beta^2\\frac{\\partial ^2 \\hat{\\phi}}{\\partial x^2} + \\frac{\\partial ^2 \\hat{\\phi}}{\\partial y^2} = 0$$\n", + "\n", + "Let us transform the independent variables x and y into a new space, $\\xi$ and $\\eta$. This transformation is defined by:\n", + "\n", + "$$\\xi = x \\quad \\eta = \\beta y \\quad \\bar{\\phi}(\\xi,\\eta) = \\beta \\hat{\\phi}(x,y) $$\n", + "\n", + "Applying the chain rule, it can be shown that in the transformed coordinate system that the perturbation velocity potential equation becomes:\n", + "\n", + "$$\\frac{\\partial ^2 \\bar{\\phi}}{\\partial \\xi^2} + \\frac{\\partial ^2 \\bar{\\phi}}{\\partial \\eta^2} = 0$$\n", + "\n", + "For a given airfoil given by $y = f(x)$, $\\eta = q(\\xi)$ in transformed coordinates, it can be shown using a flow tangency condition that:\n", + "\n", + "$$\\frac{df}{dx} = \\frac{dq}{d\\xi}$$\n", + "\n", + "This implies that the $\\beta^2 = 1-M_\\infty^2$ transformation relates the compressible flow in (x,y) space to the incompressible flow in $(\\eta,\\xi)$ space over the same airfoil. " + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Demonstration of Prandtl-Glauert Compressability Correction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to demonstrate the Prandtl-Glauert compressability correction, a previous code from the AeroPython lessons will be modified to take into account compressability effects. The code applies the vortex-source panel method to model flow over an airfoil at a specified angles of attack. The code was orginally written for the MAE6226 Aero/Hydrodynamics course at GWU, lesson 11. Unless otherwise noted, the code is left as it was in the lesson. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy\n", + "from scipy import integrate\n", + "from matplotlib import pyplot" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# reads of the geometry from a data file\n", + "with open ('naca0012.dat') as file_name:\n", + " x, y = numpy.loadtxt(file_name, dtype=float, delimiter='\\t', unpack=True)\n", + "\n", + "# plots the geometry\n", + "%matplotlib inline\n", + "\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = x.min(), x.max()\n", + "y_min, y_max = y.min(), y.max()\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 = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "pyplot.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('y', fontsize=16)\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.plot(x, y, color='k', linestyle='-', linewidth=2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Panel:\n", + " \"\"\"Contains information related to one 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 = math.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 = math.acos((yb-ya)/self.length)\n", + " elif xb-xa > 0.:\n", + " self.beta = math.pi + math.acos(-(yb-ya)/self.length)\n", + " \n", + " # location of the panel\n", + " if self.beta <= math.pi:\n", + " self.loc = 'extrados'\n", + " else:\n", + " self.loc = 'intrados'\n", + " \n", + " self.sigma = 0. # source strength\n", + " self.vt = 0. # tangential velocity\n", + " self.cp = 0. # pressure coefficient\n", + " self.cpPrandtl = 0. # Prandtl-Glauert correct pressure coefficient\n", + " self.cpKarman = 0. # Karman-Tsien compressability correction" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def define_panels(x, y, N=40):\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 (default 40).\n", + " \n", + " Returns\n", + " -------\n", + " panels -- Numpy array of panels.\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\n", + " x_circle = x_center + R*numpy.cos(numpy.linspace(0, 2*math.pi, N+1)) # x-coord of the circle points\n", + " \n", + " x_ends = numpy.copy(x_circle) # projection of the x-coord on the surface\n", + " y_ends = numpy.empty_like(x_ends) # initialization of the y-coord Numpy array\n", + "\n", + " x, y = numpy.append(x, x[0]), numpy.append(y, y[0]) # extend arrays using numpy.append\n", + " \n", + " # computes the y-coordinate of end-points\n", + " I = 0\n", + " for i in xrange(N):\n", + " while I < len(x)-1:\n", + " if (x[I] <= x_ends[i] <= x[I+1]) or (x[I+1] <= x_ends[i] <= x[I]):\n", + " break\n", + " else:\n", + " I += 1\n", + " a = (y[I+1]-y[I])/(x[I+1]-x[I])\n", + " b = y[I+1] - a*x[I+1]\n", + " y_ends[i] = a*x_ends[i] + b\n", + " y_ends[N] = y_ends[0]\n", + " \n", + " panels = numpy.empty(N, dtype=object)\n", + " for i in xrange(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": [ + "N = 40 # number of panels\n", + "panels = define_panels(x, y, N) # discretizes of the geometry into panels\n", + "\n", + "# plots the geometry and the panels\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", + "y_min, y_max = min( panel.ya for panel in panels ), max( panel.ya 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 = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "pyplot.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('y', fontsize=16)\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.plot(x, y, color='k', linestyle='-', linewidth=2)\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='#CD2305');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "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*math.pi/180 # degrees --> radians" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this code we will assme the freesteam speed given in terms of Mach number." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "u_inf = 0.6 # freestream speed\n", + "alpha = 4 # angle of attack (in degrees)\n", + "freestream = Freestream(u_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral(x, y, panel, dxdz, dydz):\n", + " \"\"\"Evaluates the contribution of a panel at one point.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y -- Cartesian coordinates of the point.\n", + " panel -- panel which contribution is evaluated.\n", + " dxdz -- derivative of x in the z-direction.\n", + " dydz -- 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 - math.sin(panel.beta)*s))*dxdz \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))*dydz)\n", + " / ((x - (panel.xa - math.sin(panel.beta)*s))**2 \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 8 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def source_matrix(panels):\n", + " \"\"\"Builds the source matrix.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- NxN matrix (N is the number of panels).\n", + " \"\"\"\n", + " A = numpy.empty((panels.size, panels.size), dtype=float)\n", + " numpy.fill_diagonal(A, 0.5)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def vortex_array(panels):\n", + " \"\"\"Builds the vortex array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels - array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " a = numpy.zeros(panels.size, dtype=float)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " a[i] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.sin(p_i.beta), -math.cos(p_i.beta))\n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def kutta_array(panels):\n", + " \"\"\"Builds the Kutta-condition array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " N = panels.size\n", + " a = numpy.zeros(N+1, dtype=float)\n", + " # contribution from the source sheet of the first panel on the last one\n", + " a[0] = 0.5/math.pi*integral(panels[N-1].xc, panels[N-1].yc, panels[0], \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta))\n", + " # contribution from the source sheet of the last panel on the first one\n", + " a[N-1] = 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[N-1], \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on the last one\n", + " a[N] -= 0.5/math.pi*integral(panels[-1].xc, panels[-1].yc, panels[0], \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta))\n", + " # contribution from the vortex sheet of the last panel on the first one\n", + " a[N] -= 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[-1], \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on itself\n", + " a[N] -= 0.5\n", + " # contribution from the vortex sheet of the last panel on itself\n", + " a[N] -= 0.5\n", + " \n", + " # contribution from the other panels on the first and last ones\n", + " for i, panel in enumerate(panels[1:-1]):\n", + " # contribution from the source sheet\n", + " a[i+1] = 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " + integral(panels[N-1].xc, panels[N-1].yc, panel, \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta)) )\n", + "\n", + " # contribution from the vortex sheet\n", + " a[N] -= 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " + integral(panels[-1].xc, panels[-1].yc, panel, \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta)) )\n", + " \n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_matrix(panels):\n", + " \"\"\"Builds the matrix of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- (N+1)x(N+1) matrix (N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = numpy.empty((N+1, N+1), dtype=float)\n", + " \n", + " AS = source_matrix(panels)\n", + " av = vortex_array(panels)\n", + " ak = kutta_array(panels)\n", + " \n", + " A[0:N,0:N], A[0:N,N], A[N,:] = AS[:,:], av[:], ak[:]\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 12 + }, + { + "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 * math.cos(freestream.alpha - panel.beta)\n", + " b[N] = -freestream.u_inf*( math.sin(freestream.alpha-panels[0].beta)\n", + " +math.sin(freestream.alpha-panels[N-1].beta) )\n", + " \n", + " return b" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "A = build_matrix(panels) # calculates the singularity matrix\n", + "b = build_rhs(panels, freestream) # calculates the freestream RHS" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "variables = numpy.linalg.solve(A, b)\n", + "\n", + "for i, panel in enumerate(panels):\n", + " panel.sigma = variables[i]\n", + "gamma = variables[-1]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_tangential_velocity(panels, freestream, gamma):\n", + " \"\"\"Computes the tangential velocity on the surface.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " gamma -- circulation density.\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = numpy.empty((N, N+1), dtype=float)\n", + " numpy.fill_diagonal(A, 0.0)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " # contribution from vortex on itself\n", + " A[i, N] = -0.5\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " # contribution from the sources\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " -math.sin(p_i.beta), math.cos(p_i.beta))\n", + " # contribution the vortices\n", + " A[i,N] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + "\n", + " b = freestream.u_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n", + " \n", + " var = numpy.append([panel.sigma for panel in panels], gamma)\n", + " \n", + " vt = numpy.dot(A, var) + b\n", + " for i, panel in enumerate(panels):\n", + " panel.vt = vt[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes the tangential velocity at each panel center.\n", + "get_tangential_velocity(panels, freestream, gamma)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The AeroPython code has been left alone up until now. So far we have calculated the flow field in the incompressible space, the Prandtl-Glauert compressability correction can now be applied to transform the flow field into the compressible space. \n", + "\n", + "When the correction is applied, it is assumed that the free stream velocity is given in terms of Mach number." + ] + }, + { + "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\n", + " #modify the code to apply the Prandtl-Glauert compressability correctio\n", + " panel.cpPrandtl = panel.cp/((1-freestream.u_inf**2)**0.5)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes surface pressure coefficient\n", + "get_pressure_coefficient(panels, freestream)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 19 + }, + { + "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.cpPrandtl for panel in panels ), max( panel.cpPrandtl 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 == 'extrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'extrados'], \n", + " [panel.cpPrandtl for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=2, marker='*', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cpPrandtl for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + "pyplot.legend(['inner', 'outer','compressible outer','compressible inner'], 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", + "pyplot.title('Effect of Prandtl-Glauert Compressibilty Correction at M=0.6');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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axeLFi5kyZQpjx46lQ4cOZGdns2zZMkaOHMmzzz7LunXrvO43YsQI7r77btav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+ "text": [ + "" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The effect of the Prandtl-Glauert compressibility correction is to stretch the graph vertically. This stretching effect is more pronounced for $C_p$ with a larger amplitude. A trait of compressible flow is that the coefficient of pressure can be larger than 1 at stagnation points. This trait is demonstrated for the corrected inner flow stagnation point at the leading edge, plotted above.\n", + "\n", + "The effect of the compressibility for a range of mach numbers is shown below. Only the top data (extrados) is plotted for clarity.\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "u_inf = numpy.linspace(0.05,0.7,15); # freestream speed\n", + "alpha = 2 # angle of attack (in degrees)\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", + "\n", + "for i, U in enumerate(u_inf):\n", + " freestream = Freestream(U, alpha) # instantiation of the object freestream\n", + "\n", + " A = build_matrix(panels) # calculates the singularity matrix\n", + " b = build_rhs(panels, freestream) # calculates the freestream RHS\n", + "\n", + " # solves the linear system\n", + " variables = numpy.linalg.solve(A, b)\n", + "\n", + " for i, panel in enumerate(panels):\n", + " panel.sigma = variables[i]\n", + " gamma = variables[-1]\n", + " # computes the tangential velocity at each panel center.\n", + " get_tangential_velocity(panels, freestream, gamma)\n", + " # computes surface pressure coefficient\n", + " get_pressure_coefficient(panels, freestream)\n", + " \n", + " pyplot.plot([panel.xc for panel in panels if panel.loc == 'extrados'], \n", + " [panel.cpPrandtl for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + " pyplot.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cpPrandtl for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + "\n", + "cp_min, cp_max = min( panel.cpPrandtl for panel in panels ), max( panel.cpPrandtl 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", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(-1.2, 1.5)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Effect of Prandtl-Glauert Compressibility Correction at M=0.05-0.7');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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kyIrQUBmWJ4+2ISlaVFbOn5++DcmOHSIhISIlSoi88YZITEzGCz93TsI6dZKW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\noyNipzXO+SiwQ0ppR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+ "text": [ + "" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The effect of the stretching due to the Prandtl-Glauert compressibility correction is shown in the figure above. The figure clearly highlights how at low Mach numbers the effect of the correction is quite small. This accurately models how at low Mach numbers the effect of compressbility is quite low. This is the reason that that fluids are considered incompressible at low Mach numbers. As the mach number increases, the effect of compressability becomes more pronounced." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Improved Compressibility Corrections" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After the Prandtl-Glauert, several attempts were made to improve the accuracy of the correction. The Prandtl-Glauert compressability correction tends to underpredict the data. The major cause of this underprediction is due to the linearity of the correction. Another compressability correction, called the Karman-Tsien correction, tries to take into acount the non-linearity of the compressability effect. The equation for the Karman-Tsien correction is:\n", + "\n", + "$$C_p = \\frac{C_\\text{p,0}}{\\sqrt{1-M_\\infty ^2} + \\left[M_\\infty ^2 / \\left(1+ \\sqrt{1-M_\\infty ^2} \\right)\\right]C_\\text{p,0}/2 }$$\n", + "\n", + "The the Karman-Tsien correction is implemented and the effect is shown below." + ] + }, + { + "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\n", + " #modify the code to apply the Prandtl-Glauert compressability correction\n", + " panel.cpPrandtl = panel.cp/(1-freestream.u_inf**2)**0.5\n", + " #modify the code to apply the Karman-Tsien compressability correction\n", + " panel.cpKarman = panel.cp/((1-freestream.u_inf**2)**0.5 + freestream.u_inf**2/(1+(1-freestream.u_inf**2)**0.5)*panel.cp/2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 22 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "u_inf = numpy.linspace(0.05,0.7,15); # freestream speed\n", + "alpha = 2 # angle of attack (in degrees)\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", + "\n", + "for i, U in enumerate(u_inf):\n", + " freestream = Freestream(U, alpha) # instantiation of the object freestream\n", + "\n", + " A = build_matrix(panels) # calculates the singularity matrix\n", + " b = build_rhs(panels, freestream) # calculates the freestream RHS\n", + "\n", + " # solves the linear system\n", + " variables = numpy.linalg.solve(A, b)\n", + "\n", + " for i, panel in enumerate(panels):\n", + " panel.sigma = variables[i]\n", + " gamma = variables[-1]\n", + " # computes the tangential velocity at each panel center.\n", + " get_tangential_velocity(panels, freestream, gamma)\n", + " # computes surface pressure coefficient\n", + " get_pressure_coefficient(panels, freestream)\n", + " \n", + " pyplot.plot([panel.xc for panel in panels if panel.loc == 'extrados'], \n", + " [panel.cpKarman for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + " pyplot.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cpKarman for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + "\n", + "cp_min, cp_max = min( panel.cpKarman for panel in panels ), max( panel.cpKarman 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", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(-1.5, 1.6)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Effect of Karman-Tsien Compressibility Correction at M=0.05-0.7');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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PPy5SrJjIRx9dXdarxWKxWCyZEDJzDJwx5htjzKYUtgfTOUQWqsybMSQmhs27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BAAAg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\n2H+497WBE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+ "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At lower Mach numbers the effect of the Karman-Tsien compressibility correction is negligible. This is similar to the Prandtl-Glauert. At higher Mach numbers, the effect of the Karman-Tsien correction is larger than the Prandtl-Glauert correction. This is a manifestation of the Prandtl-Glauert correction underestimating the data." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Limitations of Compressability Corrections" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Shown below are the effect of the Prandtl-Glauert and Karman-Tsien compressability corrections at M=0.999. Both corrections are only valid in the Mach 0 to 0.7 range so this is well outside of the range that the compressabilty corrections can be applied. M=0.999 was chosen in order to make the $\\frac{1}{\\sqrt{1-M^2}}$ terms that appear in both compressability corrections blow up." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "u_inf = 0.999; # freestream speed\n", + "alpha = 2 # angle of attack (in degrees)\n", + "\n", + "\n", + "freestream = Freestream(u_inf, alpha) # instantiation of the object freestream\n", + "\n", + "A = build_matrix(panels) # calculates the singularity matrix\n", + "b = build_rhs(panels, freestream) # calculates the freestream RHS\n", + "\n", + "# solves the linear system\n", + "variables = numpy.linalg.solve(A, b)\n", + "\n", + "for i, panel in enumerate(panels):\n", + " panel.sigma = variables[i]\n", + "\n", + " gamma = variables[-1]\n", + "# computes the tangential velocity at each panel center.\n", + "get_tangential_velocity(panels, freestream, gamma)\n", + "# computes surface pressure coefficient\n", + "get_pressure_coefficient(panels, freestream)\n", + " \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 == 'extrados'], \n", + " [panel.cpPrandtl for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cpPrandtl for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + "cp_min, cp_max = min( panel.cpPrandtl for panel in panels ), max( panel.cpPrandtl 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", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Prandtl-Glauert Compressability Correction at M=0.999');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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UVEr0tLkkOMjr3mx33XVXwtuQaptirpinwqaYK+apsIU15uVJiaQtrObPn5/oJqQcxTx4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\n2lTTFgLOQZ06/lBWdeokujUiIiJSVVTTFnLr10P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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The effect of the Prandtl-Glauert Compressability correction at M=0.999 is to modify the coefficients of pressure to unreasonably high values." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "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 == 'extrados'], \n", + " [panel.cpKarman for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cpKarman for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='*', markersize=6)\n", + "cp_min, cp_max = min( panel.cpKarman for panel in panels ), max( panel.cpKarman 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", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Karman-Tsien Compressibility Correction at M=0.999');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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7/sRbtTrfzzv9nDq9vqyszMdc9DNvwzAH99ac4T/54XW+aFGZL1jgPneu++zZ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\nFJDGnhGq03aIREvJWgKlcbw96RTz6Cn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+ "text": [ + "" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Karman-Tsien compressability correction at M=0.999 no longer resembles the incompressible coefficients of pressure at all. Instead, the coefficients of pressure around the airfoil are distorted wildily in unrealistic places." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Citation:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Anderson, John D. \"Subsonic Compressible Flow Over Airfoils: Linear Theory.\" *Fundamentals of Aerodynamics.* 5th ed. Boston: McGraw-Hill, 2001. 587-604. Print." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 25 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file