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Details of these experiments can be found in Sec.~\ref{Sandia_Plume_Description}.
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The Fire Laboratory for Accreditation of Models by Experimentation (FLAME) facility\cite{OHern:2005,Blanchat:2001} at Sandia National Laboratories in Albuquerque, New Mexico, is designed specifically for validating models of buoyant fire plumes. The plume source is 1~m in diameter surrounded by a 0.5~m steel ``ground plane''. Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF) techniques were used to obtain instantaneous joint scalar and velocity fields.
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The Fire Laboratory for Accreditation of Models by Experimentation (FLAME) facility~\cite{OHern:2005,Blanchat:2001} at Sandia National Laboratories in Albuquerque, New Mexico, is designed specifically for validating models of buoyant fire plumes. The plume source is 1~m in diameter surrounded by a 0.5~m steel ``ground plane''. Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF) techniques were used to obtain instantaneous joint scalar and velocity fields.
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\subsection{Sandia 1 m Helium Plume}
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\label{Sandiaplume}
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Calculations of the Sandia 1 m helium plume are run at three grid resolutions: 6 cm, 3 cm, and 1.5cm. To give the reader with a qualitative feel for the results, Fig.~\ref{Sandia_He_1m_image} provides a snapshot of density contours from the simulation. The calculations are run in parallel on 16 processors; the outlined blocks indicate the domain decomposition. Data for vertical velocity, radial velocity, and helium mass fraction are recorded at three levels downstream from the base of the plume, $z = [0.2, 0.4, 0.6]$ m, corresponding to the experimental measurements of O'Hern et al.~\cite{OHern:2005}. Results for the mean and root mean square (RMS) profiles are given in Figs.~\ref{Sandia_He_1m_velocity} - \ref{Sandia_He_1m_massfraction}. The means are taken between $t=10$ and $t=20$ seconds in the simulation.
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Calculations of the Sandia 1 m helium plume are run at five grid resolutions: 20~cm, 10~cm, 6~cm, 3~cm, and 1.5~cm. Figure~\ref{Sandia_He_1m_image} provides a snapshot of density contours from the simulation. Data for vertical velocity, radial velocity, and helium mass fraction are recorded at three levels above the base of the plume, $z = [20, 40, 60]$~cm, corresponding to the experimental measurements of O'Hern~et~al.~\cite{OHern:2005}. Results for the mean and root mean square (RMS) profiles are given in Figs.~\ref{Sandia_He_1m_velocity} - \ref{Sandia_He_1m_massfraction}. The means are taken between $t=10$ and $t=20$ seconds in the simulation.
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The domain is 3~m by 3~m by 4~m. The boundary conditions are open on all sides with a smooth solid surface surrounding the 1~m diameter helium pool. The ambient and helium mixture temperature is set to 12~$^\circ$C and the background pressure is set to 80900~Pa to correspond to the experimental conditions. The helium/acetone/oxygen mixture molecular weight is set to 5.45~kg/kmol. The turbulent Schmidt and Prandtl numbers are left at the FDS default value of 0.5. The helium mixture mass flux is specified as 0.0605~kg/s/m$^2$. This case was studied previously by DesJardin et al.~\cite{DesJardin:2004}.
\caption[Sandia 1~m helium plume image]{A snapshot of FDS results at 1.5 cm resolution for the Sandia 1m helium plume showing density contours. The rows of measurement devices are visible near the base. The calculations are run in parallel on 16 processors; the outlined blocks indicate the domain decomposition.}
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\caption[Sandia 1~m helium plume image]{A snapshot of FDS results at 1.5 cm resolution for the Sandia 1~m helium plume showing density contours. The rows of measurement devices are visible near the base. The calculations are run in parallel on 16 processors; the outlined blocks indicate the domain decomposition.}
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\label{Sandia_He_1m_image}
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\end{center}
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\end{figure}
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\newpage
@@ -1055,7 +1054,7 @@ \subsection{Sandia 1 m Helium Plume}
{FDS predictions of mean and root mean square (RMS) vertical velocity profiles for the Sandia 1~m helium plume experiment. Results are shown for 6 cm, 3 cm, and 1.5 cm grid resolutions. With $z$ being the stream-wise coordinate, the bottom row is at $z=0.2$ m, the middle row is at $z=0.4$ m, and the top row is at $z=0.6$ m.}
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{FDS predictions of mean and root mean square (RMS) vertical velocity profiles for the Sandia 1~m helium plume experiment. Results are shown for five grid resolutions and three elevations, $z$, above the base of the plume.}
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\label{Sandia_He_1m_velocity}
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\end{figure}
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@@ -1069,7 +1068,7 @@ \subsection{Sandia 1 m Helium Plume}
{FDS predictions of mean and root mean square (RMS) radial velocity profiles for the Sandia 1~m helium plume experiment. Results are shown for 6 cm, 3 cm, and 1.5 cm grid resolutions. With $z$ being the stream-wise coordinate, the bottom row is at $z=0.2$ m, the middle row is at $z=0.4$ m, and the top row is at $z=0.6$ m.}
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{FDS predictions of mean and root mean square (RMS) radial velocity profiles for the Sandia 1~m helium plume experiment. Results are shown for five grid resolutions and three elevations, $z$, above the base of the plume.}
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\label{Sandia_He_1m_velocity_rms}
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\end{figure}
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@@ -1083,7 +1082,7 @@ \subsection{Sandia 1 m Helium Plume}
\caption[Sandia 1~m helium plume mean and RMS mass fraction profiles]
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{FDS predictions of mean and root mean square (RMS) helium mass fraction profiles for the Sandia 1~m helium plume experiment. Results are shown for 6 cm, 3 cm, and 1.5 cm grid resolutions. With $z$ being the stream-wise coordinate, the bottom row shows data at $z=0.2$ m, the middle row shows data at $z=0.4$ m, and the top row shows data at $z=0.6$ m.}
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{FDS predictions of mean and root mean square (RMS) helium mass fraction profiles for the Sandia 1~m helium plume experiment. Results are shown for five grid resolutions and three elevations, $z$, above the base of the plume.}
When multiple infinitely fast reactions are present it is not trivial to correctly partition the limiting reactant and maintain species bounds. FDS uses a special subcycling algorithm by Kahaner \cite{Kahaner:1989} to maintain boundedness for species when time integrating the ODEs for the chemical reaction step (the method is further discussed in the FDS Tech Guide \cite{FDS_Math_Guide}). In this section, we examine two test cases designed to verify the time integration method.
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The first case, \ct{bound_test_1}, consists of two independent reactions, one with air as the limiting reactant, one with fuel as the limiting reactant. The stoichiometry of each reaction is the same: $\mathrm{F} + \mathrm{A} \rightarrow 2\,\mathrm{P}$. The initial volume fractions of determine which species are limiting. The results are shown in Fig.~\ref{fig:bound_test_1}. For the first reaction, $X_{\rm F1}$ is initially 0.3 and $X_{\rm A1}$ is initially 0.2. Therefore, all the A1 is converted to P1, which has a final volume fraction of $X_{\rm P1}=0.4$. In the second reaction, the initial fuel volume fraction is $X_{\rm F2}=0.1$ (limiting) and the initial air volume fraction is $X_{\rm A2}=0.4$. As can be see in Fig.~\ref{fig:bound_test_1}, the resulting final values give a product volume fraction of twice the limiting reactant, $X_{\rm P2}=0.2$.
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The first case, \ct{bound_test_1}, consists of two independent reactions, one with air as the limiting reactant, one with fuel as the limiting reactant. The stoichiometry of each reaction is the same: $\mathrm{F} + \mathrm{A} \rightarrow 2\,\mathrm{P}$. The initial volume fractions determine which species are limiting. The results are shown in Fig.~\ref{fig:bound_test_1}. For the first reaction, $X_{\rm F1}$ is initially 0.3 and $X_{\rm A1}$ is initially 0.2. Therefore, all the A1 is converted to P1, which has a final volume fraction of $X_{\rm P1}=0.4$. In the second reaction, the initial fuel volume fraction is $X_{\rm F2}=0.1$ (limiting) and the initial air volume fraction is $X_{\rm A2}=0.4$. As can be seen in Fig.~\ref{fig:bound_test_1}, the resulting final values give a product volume fraction of twice the limiting reactant, $X_{\rm P2}=0.2$.
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