Remove align* environments (#47)

Author: d-montgomery

docs/fuelprops.rst

@@ -68,23 +68,21 @@ follows\ :footcite:p:`constantinou_new_1994` \ :footcite:p:`constantinou_estimat
 
 .. math::
 
-   \begin{align*}
-    M_{w,i} &= \bigg[\sum_{k = 1}^{N_{g_1}}\mathbf{N}_{ik}m_{w1k} \bigg] \times 10^{-3}, \\
-    T_{c,i} &= 181.28 \ln  \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} t_{c1k} + \sum_{j=1}^{N_{g_2}}         \mathbf{M}_{ij} t_{c2j} \bigg],\\
-    p_{c,i} &= \Bigg( \bigg[  \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} p_{c1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij}     p_{c2j} + 0.10022\bigg]^{-2}  + 1.3705\Bigg)\times 10^{5}, \label{eq:gcm-pc}\\
-    V_{c,i} &= \Bigg( \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} v_{c1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij}      v_{c2j} \bigg] -0.00435 \Bigg)\times 10^{-3}, \\
-    T_{b,i} &= 204.359 \ln  \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} t_{b1k} + \sum_{j=1}^{N_{g_2}}  \mathbf{M}_{ij} t_{b2j}\bigg],\\
-    T_{m,i} &= 102.425 \ln  \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} t_{m1k} + \sum_{j=1}^{N_{g_2}}  \mathbf{M}_{ij} t_{m2j}\bigg],\\
-    \Delta H_{f,i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} h_{f1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} h_{f2j} \bigg] + 10.835\Bigg) \times 10^3,\\
-    \Delta G_{f,i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} g_{f1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} g_{f2j} \bigg] -14.828 \Bigg) \times 10^3,\\
-    \Delta H_{v,\textit{stp},i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} h_{v1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} h_{v2j} \bigg] + 6.829\Bigg) \times 10^3, \\
-    \omega_i &= 0.4085 \ln  \bigg( \Big[  \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} \omega_{1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} \omega_{2j} + 1.1507\Big]^{1/0.5050} \bigg), \label{eq:gcm-omega}\\
-    V_{m,\textit{stp},i} &= \Bigg( \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} v_{m1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} v_{m2j} \bigg] + 0.01211 \Bigg)\times 10^{-3}, \\
-    C_{p,i} & =\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pA1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pA2_j} -19.7779\bigg]  \nonumber \\
-        & +\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pB1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pB2_j} + 22.5981\bigg] \theta \nonumber\\
-        & +\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pC1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pC2_j} - 10.7983\bigg] \theta^2 \\
-    \theta &= \frac{T - 298.15}{700}
-    \end{align*}
+   M_{w,i} &= \bigg[\sum_{k = 1}^{N_{g_1}}\mathbf{N}_{ik}m_{w1k} \bigg] \times 10^{-3}, \\
+   T_{c,i} &= 181.28 \ln  \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} t_{c1k} + \sum_{j=1}^{N_{g_2}}         \mathbf{M}_{ij} t_{c2j} \bigg],\\
+   p_{c,i} &= \Bigg( \bigg[  \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} p_{c1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij}     p_{c2j} + 0.10022\bigg]^{-2}  + 1.3705\Bigg)\times 10^{5}, \label{eq:gcm-pc}\\
+   V_{c,i} &= \Bigg( \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} v_{c1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij}      v_{c2j} \bigg] -0.00435 \Bigg)\times 10^{-3}, \\
+   T_{b,i} &= 204.359 \ln  \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} t_{b1k} + \sum_{j=1}^{N_{g_2}}  \mathbf{M}_{ij} t_{b2j}\bigg],\\
+   T_{m,i} &= 102.425 \ln  \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} t_{m1k} + \sum_{j=1}^{N_{g_2}}  \mathbf{M}_{ij} t_{m2j}\bigg],\\
+   \Delta H_{f,i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} h_{f1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} h_{f2j} \bigg] + 10.835\Bigg) \times 10^3,\\
+   \Delta G_{f,i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} g_{f1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} g_{f2j} \bigg] -14.828 \Bigg) \times 10^3,\\
+   \Delta H_{v,\textit{stp},i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} h_{v1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} h_{v2j} \bigg] + 6.829\Bigg) \times 10^3, \\
+   \omega_i &= 0.4085 \ln  \bigg( \Big[  \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} \omega_{1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} \omega_{2j} + 1.1507\Big]^{1/0.5050} \bigg), \label{eq:gcm-omega}\\
+   V_{m,\textit{stp},i} &= \Bigg( \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} v_{m1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} v_{m2j} \bigg] + 0.01211 \Bigg)\times 10^{-3}, \\
+   C_{p,i} & =\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pA1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pA2_j} -19.7779\bigg]  \nonumber \\
+       & +\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pB1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pB2_j} + 22.5981\bigg] \theta \nonumber\\
+       & +\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pC1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pC2_j} - 10.7983\bigg] \theta^2 \\
+   \theta &= \frac{T - 298.15}{700}
 
 
 .. _eq-GCM-correlations:
@@ -154,9 +152,7 @@ Liquids\ :footcite:p:`viswanath_viscosity_2007`) provided :math:`T` in :math:`^{
 
 .. math::
 
-   \begin{align*}
    \nu_i = 10^{-6} \times \exp \bigg\{-3.0171 + \frac{442.78 + 1.6452 \,T_{b,i}}{T + 239 - 0.19 \,T_{b,i}} \bigg\}.
-   \end{align*}
 
 
 
@@ -196,14 +192,13 @@ with an updated :math:`\phi_i` parameter\ :footcite:p:`govindaraju_group_2016`:
 where
 
 .. math::
-   \begin{align*}
+
    Z_{c,i} &= 0.29056 - 0.08775 \omega_i,  \\
    \phi_i &= 
    \begin{cases}
        (1 - T_{r,i})^{2/7} - (1 - T_{r,\textit{stp},i})^{2/7}, & \text{ if } T \leq T_{c,i} \\
        - (1 - T_{r,\textit{stp},i})^{2/7}, & \text{ if } T > T_{c,i}
    \end{cases}. \label{eq:phi}
-   \end{align*}
 
 Density
 ^^^^^^^
@@ -251,20 +246,17 @@ The Lee-Kesler\ :footcite:p:`lee_generalized_1975` method defines
 
 .. math::
 
-   \begin{align*}
    f_i^{(0)} &= 5.92714 - \frac{6.09648}{T_{r,i}} - 1.28862 \ln T_{r,i} + 0.169347 \, T_{r,i}^6, \\
    f_i^{(1)} &= 15.2518 - \frac{15.6875}{T_{r,i}} - 13.4721 \ln T_{r,i} + 0.43577 \, T_{r,i}^6, \\
    f_i^{(2)} &= 0,
-   \end{align*}
 
 The Ambrose-Walton\ :footcite:p:`ambrose_vapour_1989` correlation sets:
 
 .. math::
-   \begin{align*}
+
    f_i^{(0)} &= \frac{- 5.97616\tau_i + 1.29874\tau_i^{1.5} - 0.60394\tau_i^{2.5} - 1.06841\tau_i^{5}}{T_{r,i}}, \\
    f_i^{(1)} &= \frac{- 5.03365\tau_i + 1.11505\tau_i^{1.5} - 5.41217\tau_i^{2.5} - 7.46628\tau_i^{5},}{T_{r,i}}, \\
    f_i^{(2)} &= \frac{- 0.64771\tau_i + 2.41539\tau_i^{1.5} - 4.26979\tau_i^{2.5} - 3.25259\tau_i^{5}}{T_{r,i}},
-   \end{align*}
 
 with :math:`\tau_i = 1 - T_{r,i}`.
 
@@ -275,9 +267,8 @@ Users also have the option to return the coefficients from an Antoine fit based
 the mixture vapor pressure calculated from Raoult's law above.  Antoine's equation is:
 
 .. math:: 
-   \begin{align*}
+
    \log_{10}\Big(\frac{p_{v,i}}{D_i}\Big) = A_i - \frac{B_i}{C_i + T},
-   \end{align*}
 
 where :math:`D_i` is a conversion factor for converting :math:`p_{v,i}` to units of bar (:math:`D_i = 10^5`) or dyne/cm :sup:`2` (:math:`D_i = 10^{-1}`) from Pa.
 This feature was added to provide `Pele <https://amrex-combustion.github.io>`_ users an option for estimating these coefficients for use in CFD
@@ -468,9 +459,8 @@ Mixture vapor pressure
 The vapor pressure of the mixture is calculated according to Raoult's law:
 
 .. math::
-   \begin{align*}
+
    p_{v} = \sum_{i = 1}^{N_c} X_i \, p_{\textit{sat},i}.
-   \end{align*}
 
 .. automethod:: FuelLib.fuel.mixture_vapor_pressure_antoine_coeffs
    :noindex:
@@ -479,9 +469,8 @@ Users also have the option to return the coefficients from an Antoine fit based
 the mixture vapor pressure calculated from Raoult's law above.  Antoine's equation is:
 
 .. math:: 
-   \begin{align*}
+
    \log_{10}\Big(\frac{p_{v}}{D}\Big) = A - \frac{B}{C + T},
-   \end{align*}
 
 where :math:`D` is a conversion factor for converting :math:`p_v` to units of bar (:math:`D = 10^5`) or dyne/cm :sup:`2` (:math:`D = 10^{-1}`) from Pa.
 This feature was added to provide `Pele <https://amrex-combustion.github.io>`_ users an option for estimating these coefficients for use in CFD