FDS Verification Guide: add section for pine_wood_TGA test cases

Author: ericvmueller

Manuals/FDS_Verification_Guide/FDS_Verification_Guide.tex

@@ -5553,6 +5553,76 @@ \subsection{TGA of various Mediterranean vegetation (\texorpdfstring{\ct{Morvan\
 \label{fig:Morvan_TGA}
 \end{figure}
 
+\subsection{Complex multi-component pyrolysis with oxidative reactions (\texorpdfstring{\ct{pine\_wood\_TGA}}{pine\_wood\_TGA})}
+\label{pine_wood_TGA}
+
+These cases test the formulation of the solid-phase reaction model for multiple oxidative reactions which are not assumed to be first order. The generalized reaction rate for material $i$ undergoing its $j$th reaction ($r_{ij}$) is as follows:
+\be
+  r_{ij} = A_{ij} \; \rho_{{\rm s},i}^{n_{{\rm s},ij}} \;  T_{\rm s}^{n_{{\rm t},ij}} \; \exp \left(-\frac{E_{ij}}{R \, T_{\rm s}} \right) X_{\rm O_2}^{n_{{\rm O_2},ij}}
+  \label{eq:rr}
+\ee
+
+We make use of data for pine wood from Anca-Couce et al.~\cite{Anca-Couce:2012}, who ran TGA tests at different heating rates (\qty{2.5}{\kelvin\per\minute}, \qty{5}{\kelvin\per\minute}, and \qty{10}{\kelvin\per\minute}) and different oxygen concentrations (\qty{0}{\percent}, \qty{4.3}{\percent}, \qty{8.2}{\percent}, and \qty{20.5}{\percent}). Following the approach of Anca-Couce et al.~\cite{Anca-Couce:2012}, we assume three reactions: non-oxidative pyrolysis, oxidative pyrolysis, and char oxidation. The first two reactions proceed in parallel and form char from the original material, which is then able to react. We further consider that the original material may be a single component, leading to three reactions:
+\begin{align}
+\mathrm{R1} &: \mbox{pine} \rightarrow \nu_{\rm char,1} \,\mbox{char} + \nu_{\rm fv,1} \,\mbox{fuel vapor} \\
+\mathrm{R2} &: \mbox{pine} + \nu_{\rm O_2,2} \, {\rm O_2} \rightarrow \nu_{\rm char,2} \,\mbox{char} + \nu_{\rm fv,2} \,\mbox{fuel vapor} \\
+\mathrm{R3} &: \mbox{char} + \nu_{\rm O_2,3}\, {\rm O_2} \rightarrow \nu_{\rm ash,3} \,\mbox{ash} + \nu_{\rm CO_2,3} \, {\rm CO_2}
+\end{align}
+or a mixture of three distinct components each with unique reaction parameters:
+\begin{align}
+\mathrm{R1} &: \mbox{pine-1}\rightarrow \nu_{\rm char,1} \,\mbox{char} + \nu_{\rm fv,1} \,\mbox{fuel vapor} \\
+\mathrm{R2} &: \mbox{pine-1} + \nu_{\rm O_2,2} \, {\rm O_2} \rightarrow \nu_{\rm char,2} \,\mbox{char} + \nu_{\rm fv,2} \,\mbox{fuel vapor} \\
+\mathrm{R3} &: \mbox{pine-2} \rightarrow \nu_{\rm char,3} \,\mbox{char} + \nu_{\rm fv,3} \,\mbox{fuel vapor} \\
+\mathrm{R4} &: \mbox{pine-2} + \nu_{\rm O_2,4} \, {\rm O_2} \rightarrow \nu_{\rm char,4} \,\mbox{char} + \nu_{\rm fv,4} \,\mbox{fuel vapor} \\
+\mathrm{R5} &: \mbox{pine-3} \rightarrow \nu_{\rm char,5} \,\mbox{char} + \nu_{\rm fv,5} \,\mbox{fuel vapor} \\
+\mathrm{R6} &: \mbox{pine-3} + \nu_{\rm O_2,6} \, {\rm O_2} \rightarrow \nu_{\rm char,6} \,\mbox{char} + \nu_{\rm fv,6} \,\mbox{fuel vapor} \\
+\mathrm{R7} &: \mbox{char} + \nu_{\rm O_2,3}\,{\rm O_2} \rightarrow \nu_{\rm ash,3} \,\mbox{ash} + \nu_{\rm CO_2,3} \,{\rm CO_2}
+\end{align}
+
+Rather than use the parameters proposed by Anca-Couce et al.~\cite{Anca-Couce:2012}, a fitting excersise was carried out using FDS and the reaction parameters in the following table are used. Note that we assume $n_T$ from Eq.~\ref{eq:rr} is zero.
+\begin{center}
+\begin{tabular}{|l|l|l|l|l|l|l|l|}
+\hline 
+Model & Reaction & A & E & $n_{s}$ & $n_{\rm O_2}$ & $\nu_{\rm char}$ & $\nu_{\rm ash}$\\ 
+ & & \si{(kg/m^3)^{1-n_s}/s} & J/mol & (-) & (-) & kg/kg & kg/kg & 
+ \hline \hline
+1-component & R1 & \num{1e7} & \num{1e5} & 0.5 & 0.0 & 0.31 & - \\
+1-component & R2 & \num{1e13} & \num{1.58e5} & 0.63 & 0.72 & 0.31 & - \\
+1-component & R3 & \num{7e6} & \num{1.9e5} & 0.56 & 0.68 & - & 0.02 \\
+\hline
+3-component & R1 & \num{1e11} & \num{1.5e5} & 0.56 & 0.0 & 0.25 & - \\
+3-component & R2 & \num{1e16} & \num{1.89e5} & 0.50 & 0.61 & 0.25 & - \\
+3-component & R3 & \num{1e15} & \num{1.93e5} & 1 & 0 & 0.25 & - \\
+3-component & R4 & \num{1e5} & \num{8.5e4} & 1 & 0.49 & 0.25 & - \\
+3-component & R5 & \num{1} & \num{4e4} & 1.25 & 0 & 0.25 & - \\
+3-component & R6 & \num{0} & \num{1.67e5} & 5.67 & 0.66 & 0.25 & - \\
+3-component & R7 & \num{8.31e7} & \num{1.24e5} & 0.56 & 0.68 & - & 0.02 \\
+\hline
+\end{tabular}
+\end{center}
+
+The figures below summarize the influence of heating rate and oxygen concentration for the 1- and 3-component models, respectively.
+
+\begin{figure}[h]
+\begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}r}
+\includegraphics[height=2.2in]{SCRIPT_FIGURES/pine_wood_TGA_1C_rate} &
+\includegraphics[height=2.2in]{SCRIPT_FIGURES/pine_wood_TGA_1C_oxygen}
+\end{tabular*}
+\caption[Results of 1-component pine\_wood\_TGA]{Results of performing the FDS TGA analysis on the Anca-Couce~\cite{Anca-Couce:2012} pine wood data, assuming one original component to the wood. (Left) Effect of heating rate at \qty{20.5}{\percent} oxygen. (Right) Effect of oxygen concentration at a \qty{5}{\kelvin\per\minute} heating rate.}
+\label{fig:pine_wood_TGA_3C}
+\end{figure}
+
+
+\begin{figure}[h]
+\begin{tabular*}{\textwidth}{l@{\extracolsep{\fill}}r}
+\includegraphics[height=2.2in]{SCRIPT_FIGURES/pine_wood_TGA_3C_rate} &
+\includegraphics[height=2.2in]{SCRIPT_FIGURES/pine_wood_TGA_3C_oxygen}
+\end{tabular*}
+\caption[Results of 3-component pine\_wood\_TGA]{Results of performing the FDS TGA analysis on the Anca-Couce~\cite{Anca-Couce:2012} pine wood data, assuming one original component to the wood. (Left) Effect of heating rate at \qty{20.5}{\percent} oxygen. (Right) Effect of oxygen concentration at a \qty{5}{\kelvin\per\minute} heating rate.}
+\label{fig:pine_wood_TGA_1C}
+\end{figure}
+
+
 \newpage