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Manuals/FDS_Technical_Reference_Guide/Appendices.tex

Lines changed: 129 additions & 12 deletions
Original file line numberDiff line numberDiff line change
@@ -846,7 +846,8 @@ \chapter{Analytical Jacobian for Mixing and Detailed Chemistry}
846846

847847
The system of ODEs for concentration and temperature contains additional terms to account for turbulent mixing. Following the theory of Sec.~\ref{sec:subgrid_evironment}, we can derive these ODEs as follows.
848848

849-
\subsection*{Mass Balance}
849+
\section{Mass Balance}
850+
\label{mass_balance_mixing_chem}
850851

851852
Each cell in divided in two zones, unmixed and mixed. Chemical reaction is only allowed in the mixed zone. The total mass in the cell is $\rho V_c$ where $V_c$ is the cell volume. For the purposes of discussing the time integration for mixing and chemical kinetics, the variable $t$ here can be taken as zero at the start of an LES time step. Thus, we are concerned with integration of the state of mixing and reaction within the cell from $0 \le t \le \delta t_{\mathrm{LES}}$. The mass in the unmixed portion of the cell is $U(t)$ and the mass in the mixed zone is $M(t)$:
852853
\begin{align} \label{eq:mixedAndUnmixedZoneMass}
@@ -925,7 +926,10 @@ \subsection*{Mass Balance}
925926
\frac{\d {\hat{C}_{k}}}{\d t} &= \dot{\hat{C}}_k = \dot{\omega}_k + \frac{\hat{\rho} \widetilde{Y}_k^0}{W_k} \frac{\zeta}{(1-\zeta) \tau_{\rm mix}} - \hat{C}_{k} \left[ \frac{1}{\hat{T}} \frac{\d \hat{T}}{\d t} + \frac{\sum{\dot{\omega}_j}}{\sum{\hat{C}_j}}+\frac{\zeta}{(1-\zeta)\tau_{\rm mix}}\frac{\hat{W}}{\widetilde{W}^0} \right]
926927
\end{align}
927928

928-
\subsection*{Energy Balance}
929+
Deatails of chemistry source term $\dot{{\omega}_k}$ can be found in Section \ref{chem_source_term}.
930+
931+
\section{Energy Balance}
932+
\label{energy_balance_mixing_chem}
929933

930934
Now consider the total internal energy balance in the mixing zone:
931935

@@ -972,8 +976,11 @@ \subsection*{Energy Balance}
972976

973977
Eqs.~(\ref{eq:jspeciemolarconcentration2}) and (\ref{eq:tempeqn}) will be used in CVODE as the ODE RHS.
974978

979+
Deatails of chemistry source term $\dot{{\omega}_j}$ can be found in Section \ref{chem_source_term}.
980+
975981

976-
\subsection{Analytical Jacobian formulation}
982+
\section{Analytical Jacobian formulation}
983+
\label{jacobian_mixing_chem}
977984

978985
Providing an analytical Jacobian to the CVODE solver can significantly accelerate the chemistry calculations. The Jacobian for the given system can be written as:
979986

@@ -991,6 +998,7 @@ \subsection{Analytical Jacobian formulation}
991998
\frac{\partial \boldsymbol{\dot{\hat{C}}}}{\boldsymbol{\partial \hat{C}}}& \frac{\partial \dot{\hat{T}}}{\partial \boldsymbol{\hat{C}}}\\
992999
\frac{\partial \boldsymbol{\dot{\hat{C}}}}{\partial \hat{T}}& \frac{\partial \dot{\hat{T}}}{\partial \hat{T}}
9931000
\end{bmatrix}
1001+
\label{eq:jacobian_mix_chem}
9941002
\end{align}
9951003

9961004

@@ -1014,12 +1022,7 @@ \subsection{Analytical Jacobian formulation}
10141022
\end{align}
10151023

10161024
\subsection*{Calculation of $\frac{\partial \boldsymbol{\dot{\hat{C}}_A}}{\mathbf{\partial \hat{C}}}$}
1017-
Here, $\dot{\hat{C}}_{k,A} = \dot{\omega}_{k}$.
1018-
By taking derivative of Eq.~(\ref{eq:chemistry_ode_system}) with respect to concentration, we can write:
1019-
\begin{align}\label{eq:JacCAC}
1020-
\frac{\partial \dot{\omega}_k}{\partial \hat{C}_{l}} &= \sum_{i=1}^{N_{reac}} \left[ \nu_{ki} \ r_i \ \frac{\partial b_i}{\partial \hat{C}_{l}} + b_i \nu_{ki} \ \left( k_{f,i} \nu_{li}^{'} \ \frac{\prod_{j=1}^{N_{\rm s}} (\hat{C}_j)^{{\nu}_{ji}^{'}} }{\hat{C}_{l}} - k_{r,i} \ \nu_{li}^{''} \ \frac{\prod_{j=1}^{N_{\rm s}} (\hat{C}_j)^{{\nu}_{ji}^{''}} }{\hat{C}_{l}} \right) \right],
1021-
\end{align}
1022-
Here, the $\frac{\partial b_i}{\partial \hat{C}_{l}}$ term can be calculated using Eqs.~(\ref{eq:reac_mod_coeff})-(\ref{eq:falloff_Fi}).
1025+
Here, $\dot{\hat{C}}_{k,A} = \dot{\omega}_{k}$. This term can be be calculated using Eq. \ref{eq:Jac1st} detailed in Section \ref{chem_source_term}.
10231026

10241027
\subsection*{Calculation of $\frac{\partial \boldsymbol{\dot{\hat{C}}_B}}{\mathbf{\partial \hat{C}}}$}
10251028

@@ -1064,7 +1067,9 @@ \subsection*{Calculation of $\frac{\partial \boldsymbol{\dot{\hat{C}}_A}}{\parti
10641067
\begin{align}\label{eq:JacCAT}
10651068
\frac{\partial {\dot{\hat{C}}_{k,A}}}{\partial \hat{T}} = \frac{\partial \dot{\omega}_k}{\partial \hat{T}}
10661069
\end{align}
1067-
This can be calculated similar to Eq. ?? as written before.
1070+
This term can be be calculated using Eq. \ref{eq:Jac2nd} detailed in Section \ref{chem_source_term}.
1071+
1072+
10681073

10691074

10701075
\subsection*{Calculation of $\frac{\partial \boldsymbol{\dot{\hat{C}}_B}}{\partial \hat{T}}$}
@@ -1091,7 +1096,7 @@ \subsection*{Calculation of $\frac{\partial \dot{\hat{T}}_A}{\mathbf{\partial \h
10911096
\begin{align}\label{eq:JacTAC}
10921097
\frac{\partial {\dot{\hat{T}}_{k,A}}}{\partial \hat{C}_{l}} = \frac{\partial}{\partial \hat{C}_{l}} \left( -\frac{1}{\hat{\rho} \hat{c}_p} \sum{\hat{h}_j W_j \dot{\omega}_j }\right)
10931098
\end{align}
1094-
This can be obtained by Eq. ??
1099+
This term can be be calculated using Eq. \ref{eq:Jac3rd} detailed in Section \ref{chem_source_term}.
10951100

10961101
\subsection*{Calculation of $\frac{\partial \dot{\hat{T}}_B}{\mathbf{\partial \hat{C}}}$}
10971102
\begin{align}\label{eq:JacTBC}
@@ -1104,7 +1109,7 @@ \subsection*{Calculation of $\frac{\partial \dot{\hat{T}}_A}{\partial \hat{T}}$}
11041109
\begin{align}\label{eq:JacTAT}
11051110
\frac{\partial {\dot{\hat{T}}_{k,A}}}{\partial \hat{T}} = \frac{\partial}{\partial \hat{T}} \left( -\frac{1}{\hat{\rho} \hat{c}_p} \sum{\hat{h}_j W_j \dot{\omega}_j }\right)
11061111
\end{align}
1107-
This can be obtained by Eq. ??
1112+
This term can be be calculated using Eq. \ref{eq:Jac4th} detailed in Section \ref{chem_source_term}.
11081113

11091114
\subsection*{Calculation of $\frac{\partial \dot{\hat{T}}_B}{\partial \hat{T}}$}
11101115

@@ -1114,6 +1119,118 @@ \subsection*{Calculation of $\frac{\partial \dot{\hat{T}}_B}{\partial \hat{T}}$}
11141119
&= - \frac{\zeta}{(1-\zeta) \tau_{\rm mix}} \frac{1}{\hat{c}_p} \left[ \sum{\hat{C}_{p,j}\widetilde{Y}_j^0} + \frac{1}{\hat{c}_p}\left( \sum{\hat{h}_j \widetilde{Y}_j^0} - \widetilde{h}^0 \right) \frac{\partial \hat{c}_p}{\partial \hat{T}} \right]
11151120
\end{align}
11161121

1122+
\section{Chemistry Source Term Calculation}
1123+
\label{chem_source_term}
1124+
1125+
The system of ODEs to solve a detailed chemical mechanism is given by Eqs.~(\ref{eq:chemistry_ode_system}) and (\ref{eq:TemperatureDerivative})
1126+
\begin{equation}\label{eq:chemistry_ode_system_appendix}
1127+
\frac{\d C_k}{\d t} = \dot{\omega}_k = \sum_{i=1}^{N_{\rm r}} b_i \ \nu_{ki} \ r_i, j=1,2,3,...,N_{\rm s}
1128+
\end{equation}
1129+
\begin{equation}\label{eq:TemperatureDerivativeAppendix}
1130+
\frac{\d T}{\d t} = \dot{T} = -\frac{1}{\rho c_p} \sum_{j=1}^{N_{\rm s}}h_j W_j \dot{\omega}_j
1131+
\end{equation}
1132+
For Eq.~(\ref{eq:chemistry_ode_system_appendix}), $C_j$ is the molar concentration \si{(kmol/m^3)} of the $j$th species; $b_i$ is the reaction rate modification coefficient of the $i$th reaction due to third-body effects and pressure; $\nu_{ki} = {\nu}_{ki}^{''} - {\nu}_{ki}^{'}$; and $r_i$ is the reaction progress rate of the $i$th reaction.
1133+
\begin{equation}\label{eq:reaction_progress_rate_appendix}
1134+
r_i = k_{f,i} \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{'}} - k_{r,i} \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{''}}
1135+
\end{equation}
1136+
For Eq.~(\ref{eq:TemperatureDerivativeAppendix}), $\rho$ is the density \si{(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_appendix}).
1137+
1138+
The system of ODEs can be represented by:
1139+
\be
1140+
\begin{aligned}
1141+
f &= \left[ \frac{\d C_1}{\d t} \ \frac{\d C_2}{\d t} \ldots \ \frac{\d C_{N_{\rm s}}}{\d t} \ \frac{\d T}{\d t} \right]^T \
1142+
&= \left[ \dot{\omega}_1 \ \dot{\omega}_2 \ldots \ \dot{\omega}_{N_{\rm s}} \ \dot{T} \right]^T \
1143+
\end{aligned}
1144+
\ee
1145+
1146+
Providing an analytical Jacobian to the CVODE solver can significantly accelerate the chemistry calculations. The Jacobian for the given system can be written as:
1147+
\be
1148+
\begin{aligned}
1149+
J &=
1150+
\begin{bmatrix}
1151+
\frac{\partial\dot{\omega}_1}{\partial C_1}& \frac{\partial \dot{\omega}_2}{\partial C_1} & \ldots & \frac{\partial \dot{\omega}_{N_{\rm s}}}{\partial C_1} & | & \frac{\partial \dot{T}}{\partial C_1}\\
1152+
\frac{\partial\dot{\omega}_1}{\partial C_2}& \frac{\partial \dot{\omega}_2}{\partial C_2} & \ldots & \frac{\partial \dot{\omega}_{N_{\rm s}}}{\partial C_2} & | &\frac{\partial \dot{T}}{\partial C_2}\\
1153+
\ldots & \ldots & \ldots & \ldots & | & \ldots\\
1154+
\frac{\partial \dot{\omega}_1}{\partial C_{N_{\rm s}}}& \frac{\partial \dot{\omega}_2}{\partial C_{N_{\rm s}}} & \ldots & \frac{\partial \dot{\omega}_{N_{\rm s}}}{\partial C_{N_{\rm s}}} & | & \frac{\partial \dot{T}}{\partial C_{N_{\rm s}}}\\
1155+
---& --- & --- & --- & | & ---\\
1156+
\frac{\partial \dot{\omega}_1}{\partial T}& \frac{\partial \dot{\omega}_2}{\partial T} & \ldots & \frac{\partial \dot{\omega}_{N_{\rm s}}}{\partial T} & | & \frac{\partial \dot{T}}{\partial T}\\
1157+
\end{bmatrix}
1158+
&=\begin{bmatrix}
1159+
\frac{\partial \mathbf{\dot{\omega}}}{\mathbf{\partial C}}& \frac{\partial \dot{T}}{\partial \mathbf{C}}\\
1160+
\frac{\partial \mathbf{\dot{\omega}}}{\partial T}& \frac{\partial \dot{T}}{\partial T}
1161+
\end{bmatrix}
1162+
\label{eq:jacobian_chem}
1163+
\end{aligned}
1164+
\ee
1165+
1166+
This Jacobian is the first part of equations \ref{eq:jspeciemolarconcentration3} and \ref{eq:tempeqn2} for the mixing and chemistry Jacobian matrix (\ref{eq:jacobian_mix_chem}).
1167+
1168+
\subsection*{Calculation of $\frac{\partial \mathbf{\dot{\omega}}}{\mathbf{\partial C}}$}
1169+
By taking derivative of Eq.~(\ref{eq:chemistry_ode_system_appendix}) with respect to concentration, we can write:
1170+
\begin{equation}\label{eq:Jac1st}
1171+
\begin{aligned}
1172+
\frac{\partial \dot{\omega}_k}{\partial C_l} &= \sum_{i=1}^{N_{reac}} \left[ \nu_{ki} \ r_i \ \frac{\partial b_i}{\partial C_l} + b_i \nu_{ki} \ \left( k_{f,i} \nu_{li}^{'} \ \frac{\prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{'}} }{C_l} - k_{r,i} \ \nu_{li}^{''} \ \frac{\prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{''}} }{C_l} \right) \right],
1173+
\end{aligned}
1174+
\end{equation}
1175+
Here, the $\frac{\partial b_i}{\partial C_l}$ term can be calculated using Eqs.~(\ref{eq:reac_mod_coeff})-(\ref{eq:falloff_Fi}).
1176+
1177+
\subsection*{Calculation of $\frac{\partial \mathbf{\dot{\omega}}}{\partial T}$}
1178+
By taking derivative of Eq.~(\ref{eq:chemistry_ode_system_appendix}) with respect to temperature, we can write:
1179+
\begin{multline}\label{eq:Jac2nd}
1180+
\frac{\partial \dot{\omega}_k}{\partial T} = \sum_{i=1}^{N_{reac}} \left[ \nu_{ki} \ r_i \ \frac{\partial b_i}{\partial T} + b_i \nu_{ki} \ \left\{ \frac{\partial k_{f,i}}{\partial T} \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{'}} + k_{f,i} \frac{\partial}{\partial T} \left( \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{'}} \right) \right. \right. \\
1181+
- \left. \left. \frac{\partial k_{r,i}}{\partial T} \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{''}} - k_{r,i} \frac{\partial}{\partial T} \left( \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{''}} \right) \right\} \right]
1182+
\end{multline}
1183+
Similar to $\frac{\partial b_i}{\partial C_l}$, $\frac{\partial b_i}{\partial T}$ can be calculated using Eqs.~(\ref{eq:reac_mod_coeff})-(\ref{eq:falloff_Fi}).
1184+
\begin{equation} \label{eq:kfTmpDerivative}
1185+
\frac{\partial k_{f,i}}{\partial T} = \frac{k_{f,i}}{T} \left( n_{f,i} + \frac{E_{a,i}}{RT} \right) \ \text{using Eq. \ref{eq:rate_cons}}
1186+
\end{equation}
1187+
\begin{equation}\label{eq:krTmpDerivative}
1188+
\begin{aligned}
1189+
\frac{\partial k_{r,i}}{\partial T} &= \frac{\partial}{\partial T} \left( \frac{k_{f,i}}{K_i} \right) \
1190+
&= k_{r,i} \left( \frac{1}{k_{f,i}} \frac{\partial k_{f,i}}{\partial T} - \frac{1}{K_i} \frac{\partial K_i}{\partial T} \right)
1191+
\end{aligned}
1192+
\end{equation}
1193+
Here, $K_i$ is the concentration equilibrium constant obtained using Eq.~(\ref{eq:equilibrium_const}). Through mathematical derivation, it can be shown that:
1194+
\begin{equation}\label{eq:EqConstTmpDerivative}
1195+
\begin{aligned}
1196+
\frac{1}{K_i} \frac{\partial K_i}{\partial T} = -\frac{1}{T} \left( \sum_{i=1}^{N_{\rm s}} {\nu}_{ji}^{''} - \sum_{i=1}^{N_{\rm s}} {\nu}_{ji}^{'} \right) + \frac{1}{R T} \left( \frac{\Delta G_{\mathrm{rxn}}}{T} + \Delta S_{\mathrm{rxn}} \right)
1197+
\end{aligned}
1198+
\end{equation}
1199+
Here, $\Delta S_{\mathrm{rxn}}$ is the change in entropy, and can be calculated similar to the process described in Section \ref{sec:equilChem}.
1200+
\begin{equation}\label{eq:ConcTmpDerivative}
1201+
\begin{aligned}
1202+
\frac{\partial}{\partial T} \left( \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{'}} \right) &= - \frac{1}{T} \left( \sum_{j=1}^{N_{\rm s}} {\nu}_{ji}^{'} \right) \left( \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{'}} \right) \\
1203+
\frac{\partial}{\partial T} \left( \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{''}} \right) &= - \frac{1}{T} \left( \sum_{j=1}^{N_{\rm s}} {\nu}_{ji}^{''} \right) \left( \prod_{j=1}^{N_{\rm s}} (C_j)^{{\nu}_{ji}^{''}} \right){}
1204+
\end{aligned}
1205+
\end{equation}
1206+
In the above derivation, the relation $\frac{\partial C_j}{\partial T} = - \frac{C_j}{T}$ is used.
1207+
Using Eqs.~(\ref{eq:kfTmpDerivative})-(\ref{eq:ConcTmpDerivative}), all the terms of Eq.~(\ref{eq:Jac2nd}) can be calculated.
1208+
1209+
1210+
\subsection*{Calculation of $\frac{\partial \dot{T}}{\partial \mathbf{C}}$}
1211+
By taking derivative of Eq.~(\ref{eq:TemperatureDerivativeAppendix}) with respect to concentration, we can write:
1212+
\begin{equation} \label{eq:Jac3rd}
1213+
\begin{aligned}
1214+
\frac{\partial \dot{T}}{\partial C_l} &= \frac{\partial}{\partial C_l} \left( -\frac{1}{\rho c_p} \sum_{j=1}^{N_{\rm s}}h_j W_j \dot{\omega}_j \right) \\
1215+
&= -\left( \frac{1}{\rho} \frac{\partial \rho}{\partial C_l} + \frac{1}{c_p} \frac{\partial c_p}{\partial C_l} \right) \dot{T} - \frac{1}{{\rho} c_p} \sum_{j=1}^{N_{\rm s}}h_j W_j \frac{\partial \dot{\omega}_j}{\partial C_l}
1216+
\end{aligned}
1217+
\end{equation}
1218+
Using the relations $\frac{\partial \rho}{\partial C_l} = W_l$ and $\frac{\partial c_p}{\partial C_l} = - \frac{W_l}{\rho}\left( c_p -c_{p,l} \right)$, we can rewrite Eq. ~(\ref{eq:Jac3rd}) as:
1219+
\begin{equation} \label{eq:Jac3rd_final}
1220+
\frac{\partial \dot{T}}{\partial C_l} = \frac{W_l c_{p,l}}{\rho c_p} \dot{T} - \frac{1}{{\rho} c_p} \sum_{j=1}^{N_{\rm s}}h_j W_j \frac{\partial \dot{\omega}_j}{\partial C_l}
1221+
\end{equation}
1222+
Here, $c_{p,l}$ is the specific heat of species $l$. The last term Eq.~(\ref{eq:Jac3rd_final}) can be obtained using Eq. \ref{eq:Jac1st}.
1223+
1224+
\subsection*{Calculation of $\frac{\partial \dot{T}}{\partial T}$}
1225+
By taking derivative of Eq.~(\ref{eq:TemperatureDerivativeAppendix}) with respect to temperature, we can write:
1226+
\begin{equation} \label{eq:Jac4th}
1227+
\begin{aligned}
1228+
\frac{\partial \dot{T}}{\partial T} &= \frac{\partial}{\partial T} \left( -\frac{1}{\rho c_p} \sum_{j=1}^{N_{\rm s}}h_j W_j \dot{\omega}_j \right) \\
1229+
&=\frac{\dot{T}}{T} - \frac{1}{c_p} \frac{\partial c_p}{\partial T} \dot{T} - \frac{1}{\rho c_p} \sum_{j=1}^{N_{\rm s}} \left[ h_j \frac{\partial \dot{\omega}_j}{\partial T} + \dot{\omega}_j c_{p,j} \right] W_j
1230+
\end{aligned}
1231+
\end{equation}
1232+
To derive the above equation, the relations $\frac{\partial \rho}{\partial T} = -\frac{\rho}{T}$ and $\frac{\partial h_j}{\partial T} = c_{p,j}$ are used. The term $\frac{\partial \dot{\omega}_j}{\partial T}$ can be obtained using Eq.~(\ref{eq:Jac2nd}).
1233+
11171234

11181235
\chapter{The Unmixed Fraction}
11191236
\label{app:unmixed_fraction}

Manuals/FDS_Verification_Guide/FDS_Verification_Guide.tex

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -1484,7 +1484,7 @@ \subsection{Fire Plume using Constant Specific Heat Ratio (\texorpdfstring{\ct{f
14841484
\includegraphics[height=2.2in]{SCRIPT_FIGURES/fire_const_gamma_dH} &
14851485
\includegraphics[height=2.2in]{SCRIPT_FIGURES/fire_const_gamma_dP}
14861486
\end{tabular*}
1487-
\caption[Results of the \ct{fire\_const\_gamma} case]{Results of the \ct{fire\_const\_gamma} case.}
1487+
\caption[Results of the \ct{fire_const_gamma} case]{Results of the \ct{fire_const_gamma} case.}
14881488
\label{fig_fire_const_gamma}
14891489
\end{figure}
14901490

@@ -4743,7 +4743,7 @@ \section{Simple Thermocouple Model (\texorpdfstring{\ct{thermocouples}}{thermoco
47434743

47444744

47454745

4746-
\section{Heat Conduction through Insulated Steel (\texorpdfstring{\ct{insulated\_steel\_x}}{insulated\_steel\_x})}
4746+
\section{Heat Conduction through Insulated Steel (\texorpdfstring{\ct{insulated_steel_x}}{insulated\_steel\_x})}
47474747
\label{insulated_steel_pipe}
47484748
\label{insulated_steel_plate}
47494749

@@ -4768,7 +4768,7 @@ \section{Heat Conduction through Insulated Steel (\texorpdfstring{\ct{insulated\
47684768
\includegraphics[height=2.2in]{SCRIPT_FIGURES/insulated_steel_pipe} \\
47694769
\multicolumn{2}{c}{\includegraphics[height=2.2in]{SCRIPT_FIGURES/insulated_steel_pipe_2d}}
47704770
\end{tabular*}
4771-
\caption[The \ct{insulated\_steel} test cases]{Steady-state temperature profile within an insulated steel plate and pipe. Note that the pipe conduction case has been performed as part of a 3-D calculation (upper right) and a 2-D, axi-symmetric calculation (bottom).}
4771+
\caption[The \ct{insulated_steel} test cases]{Steady-state temperature profile within an insulated steel plate and pipe. Note that the pipe conduction case has been performed as part of a 3-D calculation (upper right) and a 2-D, axi-symmetric calculation (bottom).}
47724772
\label{insulated_steel_fig}
47734773
\end{figure}
47744774

Source/dump.f90

Lines changed: 8 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -2456,9 +2456,9 @@ SUBROUTINE WRITE_SMOKEVIEW_FILE
24562456
IF (.NOT.SETUP_ONLY) THEN
24572457

24582458
! Mesh grid dimensions and neighbor information.
2459-
! Determine if the six mesh faces abut a single mesh (MESH_NEIGHBOR>0), nothing (MESH_NEIGHBOR=0),
2459+
! Determine if the six mesh faces abut a single mesh (MESH_NEIGHBOR>0), nothing (MESH_NEIGHBOR=0),
24602460
! or a combination of nothing and/or multiple meshes (MESH_NEIGHBOR=-1). Write six values to GRID line.
2461-
2461+
24622462
DO I=1,6
24632463
SELECT CASE(I)
24642464
CASE(1) ; IW1=1 ; IW2=IW1+M%JBAR*M%KBAR-1
@@ -2478,7 +2478,7 @@ SUBROUTINE WRITE_SMOKEVIEW_FILE
24782478
ENDDO
24792479

24802480
ENDIF
2481-
2481+
24822482
CALL EOL
24832483
WRITE(MYSTR,'(A,3X,A)') 'GRID',TRIM(MESH_NAME(NM)); CALL ADDSTR
24842484
WRITE(MYSTR,'(9I6)') M%IBAR,M%JBAR,M%KBAR,MESH_NEIGHBOR(1:6) ; CALL ADDSTR
@@ -9047,9 +9047,9 @@ REAL(EB) RECURSIVE FUNCTION GAS_PHASE_OUTPUT(T,DT,NM,II,JJ,KK,IND,IND2,Y_INDEX,Z
90479047
ELSE
90489048
PROBE_TMP = TMP(II,JJ,KK)
90499049
ENDIF
9050-
UU = U(II,JJ,KK)
9051-
VV = V(II,JJ,KK)
9052-
WW = W(II,JJ,KK)
9050+
UU = 0.5_EB*(U(MAX(0,II-1),JJ,KK)+U(MIN(IBAR,II),JJ,KK))
9051+
VV = 0.5_EB*(V(II,MAX(0,JJ-1),KK)+V(II,MIN(JBAR,JJ),KK))
9052+
WW = 0.5_EB*(W(II,JJ,MAX(0,KK-1))+W(II,JJ,MIN(KBAR,KK)))
90539053
VEL2 = UU**2+VV**2+WW**2
90549054
VEL = SQRT(VEL2)
90559055
DP = 0.5_EB*VEL2*RHO(II,JJ,KK)
@@ -9458,7 +9458,7 @@ REAL(EB) RECURSIVE FUNCTION GAS_PHASE_OUTPUT(T,DT,NM,II,JJ,KK,IND,IND2,Y_INDEX,Z
94589458
IF(FCVAR(II,JJ,KK,CC_IDRC,JAXIS)>0) GAS_PHASE_OUTPUT_RES = REAL(RC_FACE(FCVAR(II,JJ,KK,CC_IDRC,JAXIS))%UNKF,EB)
94599459
ENDIF
94609460

9461-
CASE(194) ! F_Z UNKNOWN NUMBER
9461+
CASE(194) ! F_Z UNKNOWN NUMBER
94629462
GAS_PHASE_OUTPUT_RES = 0._EB
94639463
IF (CC_IBM) THEN
94649464
GAS_PHASE_OUTPUT_RES = REAL(FCVAR(II,JJ,KK,CC_UNKF,KAXIS),EB)
@@ -13097,7 +13097,7 @@ SUBROUTINE DUMP_CVODE_SUBSTEPS()
1309713097
DO ROWI = 1, TOTAL_SUBSTEPS_TAKEN
1309813098
WRITE(LU_CVODE_SUBSTEPS,TCFORM) (CVODE_SUBSTEP_DATA(ROWI,COLI),COLI=1,NCOLS)
1309913099
ENDDO
13100-
ENDIF
13100+
ENDIF
1310113101

1310213102
END SUBROUTINE DUMP_CVODE_SUBSTEPS
1310313103

Source/geom.f90

Lines changed: 3 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -22197,6 +22197,7 @@ SUBROUTINE READ_GEOM
2219722197
DEVC_ID,CTRL_ID,SURF_IDS(3),SURF_ID6(6),MOVE_ID
2219822198
CHARACTER(FN_LENGTH) :: BUFFER,FN_BINGEOM,BINARY_FILE
2219922199
CHARACTER(LABEL_LENGTH), ALLOCATABLE, DIMENSION(:) :: SURF_ID
22200+
CHARACTER(MESSAGE_LENGTH) :: FYI
2220022201
REAL(EB), ALLOCATABLE, DIMENSION(:) :: ZVALS,TFACES
2220122202
REAL(EB), ALLOCATABLE, TARGET, DIMENSION(:) :: VERTS,VERTS_AUX
2220222203
INTEGER, ALLOCATABLE, DIMENSION(:) :: SURF_ID_IND,POLY
@@ -22255,7 +22256,7 @@ SUBROUTINE READ_GEOM
2225522256

2225622257
NAMELIST /GEOM/ BNDF_GEOM,BINARY_FILE,CELL_BLOCK_IOR,CELL_BLOCK_ORIENTATION,COLOR,CYLINDER_ORIGIN,CYLINDER_AXIS,&
2225722258
CYLINDER_RADIUS,CYLINDER_LENGTH,CYLINDER_NSEG_THETA,CYLINDER_NSEG_AXIS,&
22258-
EXTRUDE,EXTEND_TERRAIN,FACES,ID,IJK,IS_TERRAIN,MOVE_ID,N_LAT,N_LEVELS,N_LONG,POLY,&
22259+
EXTRUDE,EXTEND_TERRAIN,FACES,FYI,ID,IJK,IS_TERRAIN,MOVE_ID,N_LAT,N_LEVELS,N_LONG,POLY,&
2225922260
RGB,SPHERE_ORIGIN,SPHERE_RADIUS,SPHERE_TYPE,SURF_ID,SURF_IDS,SURF_ID6,&
2226022261
TEXTURE_MAPPING,TEXTURE_ORIGIN,TEXTURE_SCALE,TRANSPARENCY,&
2226122262
VERTS,XB,ZMIN,ZVALS,ZVAL_HORIZON
@@ -24331,6 +24332,7 @@ SUBROUTINE SET_GEOM_DEFAULTS
2433124332
MOVE_ID = 'null'
2433224333
DEVC_ID = 'null'
2433324334
CTRL_ID = 'null'
24335+
FYI = 'null'
2433424336
HAVE_SURF = .TRUE.
2433524337
HAVE_MATL = .TRUE.
2433624338
TEXTURE_ORIGIN = 0.0_EB

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