diff --git a/_docs_v7/Thermochemical-Nonequilibrium.md b/_docs_v7/Thermochemical-Nonequilibrium.md index ee748058..aff2df7c 100644 --- a/_docs_v7/Thermochemical-Nonequilibrium.md +++ b/_docs_v7/Thermochemical-Nonequilibrium.md @@ -46,6 +46,7 @@ $$ 0 & \text{for monatomic species and electrons,} \end{cases} $$ +\ where $$\xi$$ is an integer specifying the number of axes of rotation, $$ e^{vib}_s =\begin{cases} @@ -53,6 +54,7 @@ $$ 0 & \text{for monatomic species and electrons,} \end{cases} $$ +\ where $$\theta^{vib}_s$$ is the characteristic vibrational temperature of the species, and @@ -73,7 +75,7 @@ where $$\theta^{el}_s$$ is the characteristic electronic temperature of the spec | --- | --- | | `NEMO_EULER`, `NEMO_NAVIER_STOKES` | 7.0.0 | -The source terms in the species conservation equations are the volumetric mass production rates which are governed by the forward and backward reaction rates, $$R^f$$ and $$R^b$$, for a given reaction $r$, and can be expressed as +The source terms in the species conservation equations are the volumetric mass production rates which are governed by the forward and backward reaction rates, $$R^f$$ and $$R^b$$, for a given reaction $$r$$, and can be expressed as $$ \dot{w}_s = M_s \sum_r (\beta_{s,r} - \alpha_{s,r})(R_{r}^{f} - R_{r}^{b}). $$ @@ -98,7 +100,7 @@ $$ T_r = (T)^{a_r}(T^{ve})^{b_r}. $$ -The value of he equilibrium constant $K_{eq}$ is expressed as +The value of he equilibrium constant $$K_{eq}$$ is expressed as $$ 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. | `NEMO_NAVIER_STOKES` | 7.0.0 | -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: +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: $$ \mathbf{J}_s = - \rho D_s \nabla(Y_s) + Y_s \sum_k \rho D_k \nabla(Y_k) $$