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Merge pull request #125 from su2code/feature_nemo_fix
Fix spacing for NEMO thermodynamic model eqns
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_docs_v7/Thermochemical-Nonequilibrium.md

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@@ -46,13 +46,15 @@ $$
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0 & \text{for monatomic species and electrons,}
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\end{cases}
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$$
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\
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where $$\xi$$ is an integer specifying the number of axes of rotation,
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$$
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e^{vib}_s =\begin{cases}
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\frac{R}{M_s} \frac{\theta^{vib}_s}{exp\left( \theta^{vib}_s / T^{ve}\right) - 1} & \text{for polyatomic species,}\\
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0 & \text{for monatomic species and electrons,}
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\end{cases}
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$$
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\
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where $$\theta^{vib}_s$$ is the characteristic vibrational temperature of the species, and
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@@ -73,7 +75,7 @@ where $$\theta^{el}_s$$ is the characteristic electronic temperature of the spec
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| --- | --- |
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| `NEMO_EULER`, `NEMO_NAVIER_STOKES` | 7.0.0 |
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The source terms in the species conservation equations are the volumetric mass production rates which are governed by the forward and backward reaction rates, $$R^f$$ and $$R^b$$, for a given reaction $r$, and can be expressed as
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The source terms in the species conservation equations are the volumetric mass production rates which are governed by the forward and backward reaction rates, $$R^f$$ and $$R^b$$, for a given reaction $$r$$, and can be expressed as
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$$
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\dot{w}_s = M_s \sum_r (\beta_{s,r} - \alpha_{s,r})(R_{r}^{f} - R_{r}^{b}).
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$$
@@ -98,7 +100,7 @@ $$
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T_r = (T)^{a_r}(T^{ve})^{b_r}.
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$$
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The value of he equilibrium constant $K_{eq}$ is expressed as
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The value of he equilibrium constant $$K_{eq}$$ is expressed as
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$$
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K_{eq} = \exp( A_0 \left(\frac{T^c}{10,000}\right) + A_1 + A_2 \log \left( \frac{10,000}{T^c} \right) + A_3 \left( \frac{10,000}{T^c} \right) + A_4 \left( \frac{10,000}{T^c} \right)^2 ),
@@ -146,7 +148,7 @@ where $$\sigma_s$$ is the effective collision~cross-section.
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| `NEMO_NAVIER_STOKES` | 7.0.0 |
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Mass, momentum, and energy transport in fluids are all governed by molecular collisions, and expressions for these transport properties can be derived from the kinetic theory. The mass diffusion fluxes, $\mathbf{J}_s$, are computed using Fick's Law of Diffusion:
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Mass, momentum, and energy transport in fluids are all governed by molecular collisions, and expressions for these transport properties can be derived from the kinetic theory. The mass diffusion fluxes, $$\mathbf{J}_s$$, are computed using Fick's Law of Diffusion:
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$$
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\mathbf{J}_s = - \rho D_s \nabla(Y_s) + Y_s \sum_k \rho D_k \nabla(Y_k)
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$$

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