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FDS Verification Guide: general edits #14306

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99 changes: 47 additions & 52 deletions Manuals/FDS_Verification_Guide/FDS_Verification_Guide.tex
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Expand Up @@ -3587,7 +3587,7 @@ \subsection{Finite Rate Reactions (\texorpdfstring{\ct{reactionrate\_arrhenius}}
\caption[Species evolution in a 0-order 1-step finite rate reaction]{Time evolution of species mass fraction for a one-step zero-order Arrhenius finite rate reaction. The left plot is using RK2-Richardson ODE solver and the right plot is using CVODE ODE solver.}
\label{fig:Arrhenius_0Order_1step}
\end{figure}
The second finite rate test case is a one-step, second-order propane reaction, Eq.~(\ref{eq:1step_propane}). The table below shows the reaction rate input parameters. In this case, $a_{\alpha}=[1,1,0,0]$ for propane, oxygen, carbon monoxide, and water vapor respectively. This makes the reaction second-order as $\mathcal{O}=\sum a_{\alpha}$. Species evolutions for the one-step second-order reaction are shown in Fig.~\ref{fig:Arrhenius_2Order_1step}.
The second finite rate test case is a one-step, second-order propane reaction, Eq.~(\ref{eq:1step_propane}). The table below shows the reaction rate input parameters. In this case, $a_{\alpha}=[1,1,0,0]$ for propane, oxygen, carbon monoxide, and water vapor respectively. This makes the reaction second-order as $\sum a_{\alpha}=2$. Species evolutions for the one-step second-order reaction are shown in Fig.~\ref{fig:Arrhenius_2Order_1step}.
\begin{table}[ht]
\begin{center}
\caption[Arrhenius values for a single step C$_3$H$_8$ reaction]{Arrhenius values for a single step C$_3$H$_8$ reaction; $\alpha$ = [$\mathrm{C_3H_8}$ $\mathrm{O_2}$ $\mathrm{CO_2}$ $\mathrm{H_2O}$].}
Expand All @@ -3600,12 +3600,11 @@ \subsection{Finite Rate Reactions (\texorpdfstring{\ct{reactionrate\_arrhenius}}
\end{table}
\begin{figure}[h!]
\centering
\setlength{\tabcolsep}{-10pt}
\begin{tabular*}{\textwidth}{lr}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_arrhenius_2order_1step}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_arrhenius_2order_1step_cvode}
\end{tabular*}
\caption[Species evolution in a 2-order 1-step finite rate reaction]{Time evolution of species mass fraction for a one-step second-order Arrhenius finite rate reaction. The left plot is using RK2-Richardson ODE solver and the right plot is using CVODE ODE solver.}
\begin{tabular}{c}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_arrhenius_2order_1step} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_arrhenius_2order_1step_cvode}
\end{tabular}
\caption[Species evolution in a 2-order 1-step finite rate reaction]{Time evolution of species mass fraction for a one-step second-order Arrhenius finite rate reaction. The top plot is using RK2-Richardson ODE solver and the bottom plot is using CVODE ODE solver.}
\label{fig:Arrhenius_2Order_1step}
\end{figure}
Multi-step Arrhenius finite rate reactions are also examined. First, we consider a two-step forward propane reaction:
Expand Down Expand Up @@ -3661,23 +3660,21 @@ \subsection{Finite Rate Reactions (\texorpdfstring{\ct{reactionrate\_arrhenius}}

\begin{figure}[h!]
\centering
\setlength{\tabcolsep}{-10pt}
\begin{tabular*}{\textwidth}{lr}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2step}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2step_cvode}
\end{tabular*}
\caption[Species evolution in a 1.75-order 2-step finite rate reaction]{Time evolution of species mass fraction for a two-step Arrhenius finite rate propane reactions. The left plot is using RK2-Richardson ODE solver and the right plot is using CVODE ODE solver.}
\begin{tabular}{c}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2step} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2step_cvode}
\end{tabular}
\caption[Species evolution in a 1.75-order 2-step finite rate reaction]{Time evolution of species mass fraction for a two-step Arrhenius finite rate propane reactions. The top plot is using RK2-Richardson ODE solver and the bottom plot is using CVODE ODE solver.}
\label{fig:Arrhenius_175Order_2step}
\end{figure}

\begin{figure}[h!]
\centering
\setlength{\tabcolsep}{-10pt}
\begin{tabular*}{\textwidth}{lr}
\includegraphics[height=1.8in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2stepr}
\includegraphics[height=1.8in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2stepr_cvode}
\end{tabular*}
\caption[Species evolution in a 1.75-order 2-step reversible finite rate reaction]{Time evolution of species mass fraction for a two-step reversible Arrhenius finite rate propane reactions. The left plot is using RK2-Richardson ODE solver and the right plot is using CVODE ODE solver.}
\begin{tabular}{c}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2stepr} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_arrhenius_1p75order_2stepr_cvode}
\end{tabular}
\caption[Species evolution in a 1.75-order 2-step reversible finite rate reaction]{Time evolution of species mass fraction for a two-step reversible Arrhenius finite rate propane reactions. The top plot is using RK2-Richardson ODE solver and the bottom plot is using CVODE ODE solver.}
\label{fig:Arrhenius_175Order_2stepR}
\end{figure}

Expand All @@ -3698,12 +3695,11 @@ \subsection{Finite Rate Reactions (\texorpdfstring{\ct{reactionrate\_arrhenius}}

\begin{figure}[h!]
\centering
\setlength{\tabcolsep}{-10pt}
\begin{tabular*}{\textwidth}{lr}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_equilibrium_species}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_equilibrium_species_cvode}
\end{tabular*}
\caption[Species evolution in an equilibrium case]{Time evolution of species mass fraction for a two-step Arrhenius finite rate reaction compared to Cantera values. The left plot is using RK2-Richardson ODE solver and the right plot is using CVODE ODE solver.}
\begin{tabular}{c}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_equilibrium_species} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_equilibrium_species_cvode}
\end{tabular}
\caption[Species evolution in an equilibrium case]{Time evolution of species mass fraction for a two-step Arrhenius finite rate reaction compared to Cantera values. The top plot is using RK2-Richardson ODE solver and the bottom plot is using CVODE ODE solver.}
\label{fig:Arrhenius_2Order_1stepb}
\end{figure}

Expand All @@ -3712,7 +3708,7 @@ \subsection{Finite Rate Reactions (\texorpdfstring{\ct{reactionrate\_arrhenius}}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_equilibrium_temperature} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_equilibrium_pressure} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_equilibrium_temperature_cvode} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_equilibrium_pressure_cvode} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_equilibrium_pressure_cvode}
\end{tabular*}
\caption[Temperature and pressure evolution for equilibrium case]{Time evolution of temperature (left) and pressure (right) for two-step Arrhenius finite rate propane reactions compared to Cantera values. The top row is using RK2-Richardson ODE solver and the bottom row is using CVODE ODE solver.}
\label{fig:Arrhenius_175Order_23stepb}
Expand Down Expand Up @@ -3752,12 +3748,11 @@ \subsection{Finite Rate Reactions (\texorpdfstring{\ct{reactionrate\_arrhenius}}

\begin{figure}[h!]
\centering
\setlength{\tabcolsep}{-10pt}
\begin{tabular*}{\textwidth}{lr}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_jones_lindstedt_species}
\includegraphics[trim={20pt 0pt 20pt 0pt}, clip, height=1.8in]{SCRIPT_FIGURES/reactionrate_jones_lindstedt_species_cvode}
\end{tabular*}
\caption[Species evolution in Jones-Lindstedt case]{Time evolution of species mass fraction for Jones-Lindstedt four-step Arrhenius finite rate reaction compared to Cantera values. The left plot is using RK2-Richardson ODE solver and the right plot is using CVODE ODE solver.}
\begin{tabular}{c}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_jones_lindstedt_species} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/reactionrate_jones_lindstedt_species_cvode}
\end{tabular}
\caption[Species evolution in Jones-Lindstedt case]{Time evolution of species mass fraction for Jones-Lindstedt four-step Arrhenius finite rate reaction compared to Cantera values. The top plot is using RK2-Richardson ODE solver and the bottom plot is using CVODE ODE solver.}
\label{fig:jones_lindstedt_species}
\end{figure}

Expand Down Expand Up @@ -4302,38 +4297,38 @@ \section{Smoke Detector Model (\texorpdfstring{\ct{smoke\_detector}}{smoke\_dete


\section{Aerosol Behavior}
\subsection{Gravitational Settling and Deposition of Aerosols\\(\texorpdfstring{\ct{aerosol\_gravitational\_deposition}}{aerosol\_gravitational\_deposition})}
\subsection{Gravitational Settling and Deposition of Aerosols\\(\texorpdfstring{\ct{aerosol_gravitational_deposition}}{aerosol\_gravitational\_deposition})}
\label{aerosol_gravitational_deposition}

This verification test consists of two test cases. The second case, \ct{aerosol\_gravitational\_deposition\_2}, reverses the z-component of gravity. The case consists of a box 10~cm on side with adiabatic, free-slip side walls. The box is filled with two gas species each having a molecular weight of 28.8~g/mol, a viscosity of 0.00002~\si{kg/(m.s}, a thermal conductivity of 0.025~\si{W/(m.K}, and specific heat of 1~\si{kJ/(kg.K}, and zero diffusivity. One of the gas species is defined as an aerosol with a diameter of 10~$\mu$m, a solid phase density of 2000~kg/m$^3$, and a solid phase conductivity of 1~\si{W/(m.K}. The initial mass fraction of the aerosol is 0.00001. \ct{STRATIFICATION}, \ct{NOISE}, and all aerosol behaviors except for \ct{GRAVITATIONAL\_SETTLING} and \ct{GRAVITATIONAL\_DEPOSITION} are turned off. Since the box has a constant density over its height, a uniform settling rate over time is expected.

\begin{figure}[ht]
\centering
\begin{tabular}{c}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_gas}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_wall} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_2_gas}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_2_wall}
\end{tabular}
\caption[Gas phase soot mass fractions and wall surface densities for gravitational deposition]{Time evolution of soot mass fraction in the gas (left) and soot surface density on the wall (right) for the \ct{aerosol\_gravitational\_deposition} (Top) and \ct{aerosol\_gravitational\_deposition\_2} (Bottom) cases.}
\label{fig:gravitational_deposition}
\noindent
\begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}r}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_gas} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_wall} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_2_gas} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_gravitational_deposition_2_wall}
\end{tabular*}
\caption[Gas phase soot mass fractions and wall surface densities for gravitational deposition]{Time evolution of soot mass fraction in the gas (left) and soot surface density on the wall (right) for the \ct{aerosol\_gravitational\_deposition} (Top) and \ct{aerosol\_gravitational\_deposition\_2} (Bottom) cases.}
\label{fig:gravitational_deposition}
\end{figure}

\subsection{Thermophoretic Settling and Deposition of Aerosols\\(\texorpdfstring{\ct{aerosol\_thermophoretic\_deposition}}{aerosol\_thermophoretic\_deposition})}
\subsection{Thermophoretic Settling and Deposition of Aerosols\\(\texorpdfstring{\ct{aerosol_thermophoretic_deposition}}{aerosol\_thermophoretic\_deposition})}
\label{aerosol_thermophoretic_deposition}

This verification test consists of two test cases. The second case, \ct{aerosol\_thermophoretic\_deposition\_2}, reverses the temperature gradient. The case consists of a box 1~cm on side with adiabatic, free-slip side walls and a 100 K temperature gradient over the height of the box. The box is filled with two gas species each having a molecular weight of 28.8~g/mol, a viscosity of 0.00002~\si{kg/(m.s}, a thermal conductivity of 0.025~\si{W/(m.K}, and specific heat of 1~\si{kJ/(kg.K}, and zero diffusivity. One of the gas species is defined as an aerosol with a diameter of 1~$\mu$m, a solid phase density of 2000~kg/m$^3$, and a solid phase conductivity of 1~\si{W/(m.K}. The initial mass fraction of the aerosol is 0.00001. The gas temperature is initialized to its steady-state temperature gradient. \ct{STRATIFICATION}, \ct{NOISE}, and all aerosol behaviors except for \ct{THERMOPHORETIC\_SETTLING} and \ct{THERMOPHORETIC\_DEPOSITION} are turned off. Thermophoretic settling rates are weakly dependent on the gas density. Since there is a temperature gradient, the settlings rates are not uniform over the height of the box. Unlike the gravitational settling case, this means over long enough time periods the overall settling rate is not linear in time; however, for a short time period a near linear settling rate is expected and can be determined analytically

\begin{figure}[ht]
\centering
\begin{tabular}{c}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_gas}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_wall} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_2_gas}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_2_wall}
\end{tabular}
\caption[Gas phase soot densities and wall surface densities for thermophoretic deposition]{Time evolution of soot density in the gas (left) and soot surface density on the wall (right) for the \ct{aerosol\_thermophoretic\_deposition} (Top) and \ct{aerosol\_thermophoretic\_deposition\_2} (Bottom) cases.}
\label{fig:thermophoretic_deposition}
\noindent
\begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}r}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_gas} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_wall} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_2_gas} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/aerosol_thermophoretic_deposition_2_wall}
\end{tabular*}
\caption[Gas phase soot densities and wall surface densities for thermophoretic deposition]{Time evolution of soot density in the gas (left) and soot surface density on the wall (right) for the \ct{aerosol\_thermophoretic\_deposition} (Top) and \ct{aerosol\_thermophoretic\_deposition\_2} (Bottom) cases.}
\label{fig:thermophoretic_deposition}
\end{figure}

\subsection{Turbulent Deposition of Aerosols (\texorpdfstring{\ct{aerosol\_turbulent\_deposition}}{aerosol\_turbulent\_deposition})}
Expand Down
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