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Copy file name to clipboardExpand all lines: Manuals/FDS_User_Guide/FDS_User_Guide.tex
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@@ -7741,6 +7741,26 @@ \section{Level Set Model for Wildland Fire Spread}
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For all models, the total mineral content $S_{\rm t}=0.056$, the effective mineral content $S_{\rm e}=0.01$, the heat of combustion $\Delta H=18600$~kW/kg, density $\rho_{\rm p}=510$~kg/m$^3$, moisture content of fine, medium, and large dead vegetation, $M_{\rm d,1}=0.03$, $M_{\rm d,2}=0.04$, $M_{\rm d,3}=0.05$, moisture content of live woody and herbaceous vegetation $M_{\rm l,w}=M_{\rm l,h}= 0.70$.
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\end{sidewaystable}
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\subsection{Custom Wind Speed Function}
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The default Rothermel-Albini formulation~\cite{Rothermel:1972,Albini:1976} represents the influence of wind on the head fire spread rate as
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\be
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R = R_{\rm 0} \, (1+\phi_{\rm W})
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\ee
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where the no-wind, no-slope spread rate, $R_{\rm 0}$, is increased by a factor $\phi_W$, which is a function of the wind speed. In the default model the wind speed is taken as the value at mid-flame height, $U_{\rm mf}$.
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This introduces two complications. The first is determining the functional form of $\phi_W$. The default formulation is an empirical function which depends on fuel bed properties. However, this has not been rigorously validated for all possible fuel configurations - the original fit was determined with just three fuel bed types~\cite{Rothermel:1972}. In addition, the relationship assumes a reference wind which is unaffected by the fire, which can be contradictory to the approach of \ct{LEVEL_SET_MODE=4}. Therefore, it may be preferable to specify a custom function $\phi_W$ to better match observational data for a given fuel type. This can be done by specifying a \ct{RAMP} using \ct{VEG_LSET_WIND_RAMP}:
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\begin{lstlisting}
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&SURF ..., VEG_LSET_WIND_RAMP='WR' /
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&RAMP ID='WR', Z = 0, F=0 /
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&RAMP ID='WR', Z = 10, F=4 /
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\end{lstlisting}
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Here, the variable \ct{Z} represents the reference wind speed in m/s and \ct{F} is the value of $\phi_W$. In this example the spread rate increases linearly with wind speed between 0~m/s and 10~m/s, but any functional form can be represented in a piecwise manner using the \ct{RAMP}.
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The second complication is determining the appropriate mid-flame wind speed. In the default formulation the wind is taken from a reference height of 6.1~m (based on a standard weather station measurement height of 20~ft). This is then re-scaled to an assumed mid-flame height (one fuel-bed height above the fuel) using an assumed logarithmic profile of the wind. This is the so-called wind adjustment factor~\cite{Andrews:2012,Bova:IJWF2015}. However, these assumptions may begin to break down, for example, when the wind profile is not logarithmic. Therefore, it is possible to specify a reference wind height via \ct{VEG_LSET_WIND_HEIGHT} on the \ct{SURF} line. The wind sampled at this height will be directly used in the $\phi_{\rm W}$ function, without any adjustment, whether using the default model or a custom \ct{RAMP}. Note that it is possible to include an adjustment factor when using \ct{VEG_LSET_WIND_HEIGHT} by implicitly including this factor when specifying a \ct{VEG_LSET_WIND_RAMP}.
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\subsection{Level Set Vegetation Drag}
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When a surface is defined using level set fuel parameters, a drag force is applied in the gas phase grid cell adjacent to the boundary following the same approach described for the Boundary Fuel Model in Section~\ref{info:boundary_fuel_model}. In this case, the fuel surface-area to volume ratio (\ct{VEG_LSET_SIGMA}), packing ratio (\ct{VEG_LSET_BETA}), and depth (\ct{VEG_LSET_HT}) are either obtained from the default fuel models or specified by the user for a custom fuel. The shape factor (\ct{SHAPE_FACTOR}) and drag coefficient (\ct{DRAG_COEFFICIENT}) can also be modified from their default values of 0.25 and 2.8, respectively. A comparison of the consistency of the level set drag with the particle and boundary models is included in Figure~\ref{ground_vegetation_drag_fig}.
The Society of Fire Protection Engineers (SFPE) has developed a standard entitled {\em S.02 -- Calculation Methods to Predict the Thermal Performance of Structures \& Fire Resistive Assemblies}~\cite{SFPE_S.02} that contains an appendix with verification cases to benchmark basic heat transfer calculations. This section contains several of these cases.
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\subsection{Case 1: Lumped Mass Subjected to Standard Fire}
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\label{SFPE_Case_1}
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A plate ($\rho=7850$~kg/m$^3$, $c=0.52$~kJ/(kg~K), $\epsilon=0.7$) that has a thickness of 4~cm and an initial temperature of 20~°C is heated on the top and bottom surfaces according to the standard ISO~834 fire curve
where the time, $t$, is in seconds. If the thermal conductivity of the material is relatively large, the temperature in the section can be taken as uniform. For the convection heat transfer coefficient, $h=25$~W/(m$^2$~K), calculate the temperature of the plate as a function of time (Fig.~\ref{fig:SFPE_Case_1}).
\caption[The SFPE heat transfer verification Case 1]{Temperature of a 4~cm thick plate that is heated top and bottom by the standard fire curve.}
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\label{fig:SFPE_Case_1}
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\end{figure}
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\FloatBarrier
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\subsection{Case 2: Lumped Mass Subjected to Incident Flux}
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\label{SFPE_Case_2}
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A 1~cm thick horizontal flat plate ($\rho=7850$~kg/m$^3$, $c=0.56$~kJ/(kg~K), $\epsilon=0.9$) with an initial temperature of 20~°C is exposed from above with a radiant heater set to an incident flux of 50~kW/m$^2$. The gas temperature is 20~°C and $h=12$~W/(m$^2$~K). Assuming that the bottom and sides of the plate are perfectly insulated, and that the thermal conductivity of the material is sufficiently large to assume a uniform temperature with depth, calculate the temperature of the plate as a function of time (Fig.~\ref{fig:SFPE_Case_2}).
\caption[The SFPE heat transfer verification Case 2]{Temperature of a 1~cm thick plate that is heated on top via an incident flux and insulated below.}
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\label{fig:SFPE_Case_2}
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\end{figure}
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\FloatBarrier
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\subsection{Case 6: 2-D Heat Transfer with Cooling by Convection}
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\label{SFPE_Case_6}
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@@ -5039,11 +5072,7 @@ \subsection{Case 6: 2-D Heat Transfer with Cooling by Convection}
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\subsection{Case 7: 2-D Heat Transfer by Convection and Radiation}
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\label{SFPE_Case_7}
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A 0.2 m by 0.2 m square column ($k=1$~W/(m~K), $\rho=2400$~kg/m$^3$, $c=1$~kJ/(kg~K), $\epsilon=0.8$) is heated according to the ISO~834 time-temperature curve
where the time, $t$, is in seconds. Assuming that $h=10$~W/(m$^2$~K) and that the initial temperature is $T_\infty=273$~K, calculate the temperature at the column center, corner and middle side surface as a function of time (Fig.~\ref{fig:SFPE_Case_7}).
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A 0.2 m by 0.2 m square column ($k=1$~W/(m~K), $\rho=2400$~kg/m$^3$, $c=1$~kJ/(kg~K), $\epsilon=0.8$) is heated according to the ISO~834 time-temperature curve, Eq.~(\ref{ISO_834}). Assuming that $h=10$~W/(m$^2$~K) and that the initial temperature is $T_\infty=273$~K, calculate the temperature at the column center, corner and middle side surface as a function of time (Fig.~\ref{fig:SFPE_Case_7}).
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\begin{figure}[ht]
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\centering
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The level set model determines a wind-aided head fire spread rate based on the function
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\be
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R = R_{\rm 0} \, (1+\phi_{\rm W})
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\ee
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where the no-wind, no-slope spread rate, $R_{\rm 0}$, is increased by a factor $\phi_W$, which is a function of the wind speed. Note that there may be an additional term accounting for slope, $\phi_{\rm S}$, but this is excluded for simplicity in this example. The ability to customize the form of $\phi_W$ as a function of the reference wind speed, using \ct{VEG_LSET_WIND_RAMP}, is tested here. A line fire is ignited on a level set surface with a no-wind, no-slope spread rate, \ct{VEG_LSET_ROS_00}, of 0.03~m/s. The wind speed, using a flat wind profile, is progressively increased from 0~m/s to 5~m/s. In the first case,\ct{LS_wind_ramp_lin.fds}, the wind ramp is set to reproduce a linear function
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\be
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R = R_{\rm 0} \, (1+0.4 \, U)
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\ee
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and in the second case, \ct{LS_wind_ramp_quad.fds}, it is set to match a quadratic function
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\be
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R = R_{\rm 0} \, (1+ 0.1 \, U^2)
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\ee
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The maximum spread rate as a function of wind speed is plotted in Figure~\ref{fig:LS_wind_ramp} to confirm that the functions are properly applied.
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