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4 changes: 2 additions & 2 deletions Manuals/FDS_User_Guide/FDS_User_Guide.tex
Original file line number Diff line number Diff line change
Expand Up @@ -7759,7 +7759,7 @@ \section{Level Set Model for Wildland Fire Spread}
\end{lstlisting}
\ct{VEG_LSET_ROS_00} is the no-wind, no-slope rate of spread for the given fuel model. \ct{VEG_LSET_SIGMA} (\unit{\per\meter}) and \ct{VEG_LSET_BETA} are the average surface-to-volume ratio ($\sigma$) and packing ratio ($\beta$) of the underlying vegetation. \ct{VEG_LSET_HT} (m) is the height of the vegetation. When the fire front arrives at a given surface cell, fuel vapors are generated at a rate given by
\be
\dot{m}_{\rm f}'' = (1-\nu_{\rm char}) \frac{m_{\rm f}''}{\delta t} \; {\rm kg}/({\rm m}^2 \cdot {\rm s}) \quad ; \quad \delta t = \frac{75600}{\sigma} \; \unit{s}
\dot{m}_{\rm f}'' = (1-\nu_{\rm char}) \frac{m_{\rm f}''}{\delta t} \; {\rm kg}/({\rm m}^2 \cdot {\rm s}) \quad ; \quad \delta t = \frac{75600}{\sigma} \; \unit{s} \label{eq:ls_mlr}
\ee
Here, $m_{\rm f}''$ is the dry fuel loading in units of \unit{kg/m^2} (\ct{VEG_LSET_SURF_LOAD}, default 1.0~\unit{kg/m^2}); $\nu_{\rm char}$ is the char fraction (\ct{VEG_LSET_CHAR_FRACTION}, default 0.2); and $\delta t$ is the duration of the fire at a given location. The expression for the burn duration is given by Albini~\cite{Albini:1976}, but you can enter your own burn duration using \ct{VEG_LSET_FIREBASE_TIME} (s).

Expand Down Expand Up @@ -7848,7 +7848,7 @@ \subsubsection{Examples of Uncoupled Level Set Calculations}
\subsubsection{Examples of Coupled Level Set Calculations}
\label{level_set_fuel_model_1}

In this example, \ct{WUI/level_set_fuel_model_1.fds}, a fire is ignited directly in the center of a square patch of flat terrain, $L=1000$~m on a side, with no wind. \ct{VEG_LSET_FUEL_INDEX=1} (Short Grass) is selected as the vegetation type. The simulation is performed on a uniform mesh with $\dx=25$~m grid cells. For this type of vegetation, the mass loss rate is calculated to be $\dot{m}''=0.00955$~\unit{kg/m^2.s}, the heat of combustion is assumed to be $\Delta H=18607$~kJ/kg, and the local duration of burning is calculated to be $\Delta t=6.584$~s. These values are all reported in the file \ct{level_set_fuel_model_1.out}. After 10~h of simulation, the fire sweeps over the entire domain, consuming $\dot{m}'' L^2 \Delta t \approx 62877$~kg of vegetation. The left hand side of Fig.~\ref{level_set_fuel_model_1_fig} displays the fire intensity (burning rate) after 5~h, and the right hand side displays the integrated mass loss. Note that in this case the rate of spread is ${\rm ROS} \approx 0.03$~m/s, which means that the fire front crosses a single grid cell in approximately $\dx/{\rm ROS} \approx 830$~s, a much greater time period than the vegetation burning time, $\Delta t$. To ensure a relatively smooth fire front and burning rate, the mass loss rate and burning duration are adjusted by dividing and multiplying these values, respectively, by $\dx/{\rm ROS}$.
In this example, \ct{WUI/level_set_fuel_model_1.fds}, a fire is ignited directly in the center of a square patch of flat terrain, $L=1000$~m on a side, with no wind and a uniform mesh with $\dx=25$~m grid cells. \ct{VEG_LSET_FUEL_INDEX=1} (Short Grass) is selected as the vegetation type. For this type of vegetation, the fuel load is $m''=0.1659$~\unit{kg/m^2} and the burning rate is determined from Eq.~\ref{eq:ls_mlr} (with a burning duration of $\Delta t=6.584$~s). These values are all reported in the file \ct{level_set_fuel_model_1.out}. Given the default char yield of 0.2, the total mass consumed after the fire has spread over the full domain should be $(1-\nu_{\rm char}) m'' L^2 \approx 132720$~kg. The left hand side of Fig.~\ref{level_set_fuel_model_1_fig} displays the fire intensity (burning rate) after 5~h, and the right hand side displays the integrated mass loss. Note that in this case the rate of spread is ${\rm ROS} \approx 0.03$~m/s, which means that the fire front crosses a single grid cell in approximately $\dx/{\rm ROS} \approx 830$~s, a much greater time period than the vegetation burning time, $\Delta t$. To ensure a relatively smooth fire front and burning rate, the mass loss rate and burning duration are adjusted following a mass conserving scheme described in the FDS Technical Reference Guide~\cite{FDS_Math_Guide}.

\begin{figure}[ht]
\includegraphics[trim=.5in 0 .5in 0, clip, height=2.4in]{SCRIPT_FIGURES/level_set_fuel_model_1.png}
Expand Down
4 changes: 2 additions & 2 deletions Utilities/Python/FDS_verification_dataplot_inputs.csv
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Expand Up @@ -471,7 +471,7 @@ d,leak_test_2,HVAC/leak_test_2_git.txt,HVAC/leak_test_2.csv,1,2,Time,pres_1|pres
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Expand Down Expand Up @@ -852,4 +852,4 @@ d,rms_cov_corr,Controls/rms_cov_corr_git.txt,Controls/rms_cov_corr.csv,1,2,Time,
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s,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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