Skip to content
Merged
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
32 changes: 20 additions & 12 deletions Manuals/FDS_Verification_Guide/FDS_Verification_Guide.tex
Original file line number Diff line number Diff line change
Expand Up @@ -3999,29 +3999,37 @@ \section{Mixing with detailed chemistry (\ct{edc\_mixing\_cvode})}

This implementation has been validated against results obtained using Cantera~\cite{cantera:2023}. Note that Cantera does not provide a direct method to solve the coupled mixing-chemistry ODE system as done here in FDS; therefore, in Cantera an operator splitting approach was employed, where mixing and chemistry are handled sequentially. Specifically, within each CFD timestep (0.1 s), substeps for chemistry calculations in Cantera are kept sufficiently small (0.0001 s) to resolve the fast dynamics. All comparisons are carried out using the GRI-Mech 3.0 chemical mechanism~\cite{gri3:1999}.

Figure~\ref{fig:edc_mixing_cvode_onecfdstep_vary_zeta0} presents comparisons of temperature and OH mass fraction between FDS and Cantera within a single CFD timestep for five constant-volume ignition delay cases, with varying initial unmixed fractions \(\zeta_0 = 1.0, 0.75, 0.5, 0.25, 0.0\).
Figures~\ref{fig:edc_mixing_cvode_onecfdstep_vary_zeta0_1} and~\ref{fig:edc_mixing_cvode_onecfdstep_vary_zeta0_2} presents comparisons of temperature and OH mass fraction between FDS and Cantera within a single CFD timestep for five constant-volume ignition delay cases, with varying initial unmixed fractions \(\zeta_0 = 1.0, 0.75, 0.5, 0.25, 0.0\).

Figure~\ref{fig:edc_mixing_cvode_multicfdstep_vary_zeta0} shows similar comparisons over multiple CFD timesteps for the same ignition delay cases and initial unmixed fractions. These results also verify that elemental mass is conserved throughout the entire process.

Finally, Figure~\ref{fig:edc_mixing_cvode_onecfdstep_vary_taumix} compares temperature and OH mass fraction for a single CFD timestep across five cases with varying mixing times \(\tau_{\text{mix}} = 0.1, 0.01, 0.001, 0.0001, 0.00001\) s. As the mixing time decreases, the solution becomes independent of \(\tau_{\text{mix}}\), approaching the well-stirred reactor limit corresponding to (\(\zeta_0 = 0.0\)).

\begin{figure}[p]
\begin{tabular*}{\textwidth}{lr}
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta1p0_TMP} &
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta1p0_OH} \\
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p75_TMP} &
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p75_OH} \\
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p5_TMP} &
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p5_OH} \\
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p25_TMP} &
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p25_OH} \\
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p0_TMP} &
\includegraphics[height=1.6in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p0_OH}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta1p0_TMP} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta1p0_OH} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p75_TMP} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p75_OH} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p5_TMP} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p5_OH} \\
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p25_TMP} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p25_OH}
\end{tabular*}
\caption[Results of the \ct{edc\_mixing\_cvode} test cases]{Comparison of CVODE substeps for a single CFD step of 0.1 s, showing the effect of varying the initial unmixed fraction between FDS and Cantera. The simulation uses the Methane GRI mechanism with an equivalence ratio of 0.6, a mixing time of 0.01 s, and an initial temperature of 1200 K.}
\label{fig:edc_mixing_cvode_onecfdstep_vary_zeta0}
\label{fig:edc_mixing_cvode_onecfdstep_vary_zeta0_1}
\end{figure}

\begin{figure}[p]
\begin{tabular*}{\textwidth}{lr}
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p0_TMP} &
\includegraphics[height=2.2in]{SCRIPT_FIGURES/EDC_OneCFDStep_Methane_grimech30_Zeta0p0_OH}
\end{tabular*}
\caption[Results of the \ct{edc\_mixing\_cvode} test cases]{Continued from Figure~\ref{fig:edc_mixing_cvode_onecfdstep_vary_zeta0_1}.}
\label{fig:edc_mixing_cvode_onecfdstep_vary_zeta0_2}
\end{figure}


\begin{figure}[p]
\begin{tabular*}{\textwidth}{lcr}
\includegraphics[height=1.6in,width=0.32\textwidth]{SCRIPT_FIGURES/EDC_MultiCFDStep_Methane_grimech30_Zeta1p0_TMP} &
Expand Down