Merge pull request #14265 from rmcdermo/master

Manuals: make UL logo larger

Author: rmcdermo

Manuals/Bibliography/FDS_Logo_Lock.png

@@ -153,7 +153,7 @@
 
 \newcommand{\logosigs}{
 \begin{minipage}[b]{6.25in}
-\parbox[b]{.5\textwidth}{\flushleft{\includegraphics[height=1.05in]{../Bibliography/FDS_Logo_lock}}}
+\parbox[b]{.5\textwidth}{\flushleft{\includegraphics[height=1.5in]{../Bibliography/FDS_Logo_lock}}}
 \hfill
 \parbox[b]{.5\textwidth}{\flushright{\includegraphics[height=1in]{../Bibliography/nistident_flright_vec}}}
 \end{minipage}

Manuals/Bibliography/commoncommands.tex

@@ -373,34 +373,34 @@ \subsection{Finite-Rate Chemistry (Detailed Chemical Mechanism)}
 \be
 \eta_{\mathrm{fall-off},i} =  \frac{P_{i}}{1+P_{i}} F_i
 \ee
-Here, $\mathrm{P_{i}}$ is the reduced pressure, calculated as follows:
+Here, $P_i$ is the reduced pressure, calculated as follows:
 \be
-P_{i} =  \frac{k_{low,i}}{k_{f,i}} \eta_{\mathrm{tb},i}
+P_{i} =  \frac{k_{\mathrm{low},i}}{k_{f,i}} \eta_{\mathrm{tb},i}
 \ee
-Here, $k_{low,i}$ is the low pressure limit reaction rate, calculated using an equation similar to Eq.~(\ref{eq:rate_cons}). The $A_{low,i}$, $n_{low,i}$, and $E_{a,low,i}$ should be available in the mechanism file for the given fall-off reaction.
+Here, $k_{\mathrm{low},i}$ is the low pressure limit reaction rate, calculated using an equation similar to Eq.~(\ref{eq:rate_cons}). The $A_{\mathrm{low},i}$, $n_{\mathrm{low},i}$, and $E_{a,\mathrm{low},i}$ should be available in the mechanism file for the given fall-off reaction.
 \begin{equation}\label{eq:low_rate_cons}
-k_{low,i} = A_{low,i}\;T^{n_{low,i}}\;\mathrm{e}^{-E_{a,low,i}/RT}
+k_{\mathrm{low},i} = A_{\mathrm{low},i}\;T^{n_{\mathrm{low},i}}\;\mathrm{e}^{-E_{a,\mathrm{low},i}/RT}
 \end{equation}
-And, $\mathrm{F_{i}}$ is the fall-off blending factor:
+And, $F_i$ is the fall-off blending factor:
 \begin{equation}\label{eq:falloff_Fi}
 \begin{aligned}
 F_i &= 1, \ \text{for Lindermann fall-off reaction} \\
-    &= exp\left( {\left[1+ {\left[\frac{log P_{r,i} + c}{n-d(log P_{r,i} + c)} \right]}^2 \right]^{-1} {log \ F_{cent} }} \right) , \ \text{for Troe fall-off reaction} \\
+    &= \exp\left( {\left\{1+ {\left[\frac{\log[P_{r,i}] + c}{n-d(\log[P_{r,i}] + c)} \right]}^2 \right\}^{-1} {\log[F_{\mathrm{cent}}] }} \right) , \ \text{for Troe fall-off reaction} \\
 \end{aligned}
 \end{equation}
 Where, 
 \be
-F_{\text{cent}} = (1 - A_{troe}) \exp\left(-\frac{T}{T_3}\right) + A_{troe} \exp\left(-\frac{T}{T_1}\right) + \exp\left(-\frac{T_2}{T}\right) \
+F_{\mathrm{cent}} = (1 - A_{\mathrm{Troe}}) \exp\left(-\frac{T}{T_3}\right) + A_{\mathrm{Troe}} \exp\left(-\frac{T}{T_1}\right) + \exp\left(-\frac{T_2}{T}\right) \
 \ee
-Here, $A_{troe}$, $T_1$, $T_2$, and $T_3$ are the specified parameters in the mechanism file. Additionally, $d=0.14$, $c=-0.4 - 0.67 \log F_{cent}$, and $n=0.75 - 1.27\log F_{cent}$.
+Here, $A_{\mathrm{Troe}}$, $T_1$, $T_2$, and $T_3$ are the specified parameters in the mechanism file. Additionally, $d=0.14$, $c=-0.4 - 0.67 \log(F_{\mathrm{cent}})$, and $n=0.75 - 1.27\log(F_{\mathrm{cent}})$.
 
 Please note, the SRI fall-off reaction is not yet implemented and will be incorporated in the future. Also, other pressure-dependent reactions, except fall-off reactions, are not yet implemented and will be incorporated if the need arises.
 
 To solve the reactive system, we assume a constant pressure reactor. For that, the concentration ODEs in the form of Eq.~(\ref{eq:chemistry_ode_system}) need to be solved along with a ODE of temperature given by:
 \begin{equation}\label{eq:TemperatureDerivative}
-\frac{\d T}{\d t} = \dot{T} = -\frac{1}{\rho c_p} \sum_{j=1}^{N_{\text{s}}}h_j W_j \dot{\omega_j} 
+\frac{\d T}{\d t} = \dot{T} = -\frac{1}{\rho c_p} \sum_{j=1}^{N_{\mathrm{s}}}h_j W_j \dot{\omega_j}
 \end{equation} 
-Here,  $\rho$  is the density $\mathrm{(kg/m^3)}$, $c_p$ is the specific heat of the mixture (J/kg/K), $h_k$ is the absolute enthalpy that includes enthalpy of formation (J/kg), $W_j$ is the molecular weight (kg/kmol) of species $j$, and $\dot{\omega}$ is the species production rate given by Eq.~(\ref{eq:chemistry_ode_system}).
+Here,  $\rho$  is the density (\si{kg/m^3}), $c_{\mathrm{p}}$ is the specific heat of the mixture (\si{J/(kg.K)}), $h_k$ is the absolute enthalpy that includes enthalpy of formation (J/kg), $W_j$ is the molecular weight (kg/kmol) of species $j$, and $\dot{\omega}$ is the species production rate given by Eq.~(\ref{eq:chemistry_ode_system}).
 To solve the system of ODEs, we first convert the mass fraction of species to molar concentrations using $C_j=Y_j\rho/W_j$. Then, CVODE from Sundials \cite{cvodeDoc:2024} is used to solve the system of ODEs by supplying an analytical Jacobian. The details of analytical Jacobian formulation is provided in the Appendix \ref{chemistry_analytical_jacobian}.