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Lattimer et al. studied the thermal environment created by a fire impinging on a ceiling at the end of a corridor in~\cite{Lattimer:FTJ:2013}. The apparatus, shown in Figure~\ref{fig:lattimer}, consisted of a 2.4~m long 1.2~m wide corridor with a ceiling height of 2.1~m from the floor. The back wall and back 1.2~m of the side walls extended 1.2~m below the ceiling. The remaining 1.2~m of the side walls were extended 0.6~m below the ceiling. The overall apparatus was elevated 0.9~m off of the floor to allow air to flow into the bottom of the corridor from all sides. A 0.46~m deep by 1.15~m wide propane sand burner was centered on the back wall with the top surface located either 0.6~m or 1.1~m from the ceiling. Each separation distance was tested at four heat release rates ranging from 100-400~kW.
\caption{Lattimer fire impinging on a corridor ceiling experiments~\cite{Lattimer:FTJ:2013}.}
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\label{fig:lattimer}
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\end{figure}
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\section{Wasson Impinging Plumes}
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\label{Wasson_Impinging_Plumes_Description}
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Wasson studied the split between convection and radiation heat transfer from a diffusion flame impinging on a ceiling~\cite{Wasson2014:Thesis} using the apparatus shown in Fig.~\ref{Wasson_Impinging_Plumes_fig}. The ceiling was 1.2~m square with an adjustable ceiling height. The author used a 0.3~m square 0.15~m tall propane burner with 50~kW and 90~kW HRRs. The ceiling placement was varied to investigate the impact of different flame length to height ratios on the measured heat transfer rates. The experiments conducted by Wasson are shown in Table~\ref{Wasson_Exp}. Ceiling height, H, is the height between the top of the burner and the bottom of the ceiling.
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Wasson studied the split between convection and radiation heat transfer from a diffusion flame impinging on a ceiling~\cite{Wasson2014:Thesis} using the apparatus shown in Fig.~\ref{Wasson_Impinging_Plumes_fig}. The ceiling was 1.2~m square with an adjustable height. The fire was generated by a 30~cm square, 15~cm tall propane burner with heat release rates of 50~kW and 90~kW. The ceiling height was varied to investigate the impact of different flame length to height ratios on the measured heat transfer rates. The experimental matrix is shown in Table~\ref{Wasson_Exp}. Ceiling height, $H$, is the height between the top of the burner and the bottom of the ceiling.
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Heat fluxes at the stagnation point were measured using a high temperature hybrid heat flux gauge which operates as both a thermopile and a slug calorimeter~\cite{Diller:2015}. The author measured gas temperatures near the heat flux gauge using an aspirated thermocouple. The heat transfer coefficient was calculated by the author using four different approaches utilizing multiple heat flux gauges and gas temperature measurements. The heat fluxes measured by the author were not watercooled, and thus measured the net heat flux into the gauge which is a function of the gauge temperature. These values were converted to a water cooled heat flux for comparison in this analysis using the equation
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Heat fluxes at the stagnation point were measured using a high temperature hybrid heat flux gauge which operates as both a thermopile and a slug calorimeter~\cite{Diller:2015}. Wasson measured gas temperatures near the heat flux gauge using an aspirated thermocouple. The heat transfer coefficient was calculated using four different approaches utilizing multiple heat flux gauges and gas temperature measurements. The measured heat fluxes were not water-cooled; thus, the net heat flux is a function of the gauge temperature. These values were converted to ambient temperature for comparison in this analysis using the equation
where $\dot{q}''\subscript{tot,g}$ is the gauge heat flux, $\dot{q}''\subscript{net}$ is the measured net heat flux, $\sigma$ is the Stefan-Boltzmann constant, $T\subscript{gauge}$ is the gauge temperature, and T$_\infty$ is the reference temperature of the water cooled gauge (20~\degC~in this work). The heat transfer coefficients for each configuration were taken to be the median of the four methods across testing. Table~\ref{Wasson_Exp} summarizes the heat fluxes, gas temperatures, and heat transfer coefficients from this test series. Scenario 5 was omitted from benchmarking in due to high transience observed in the test data.
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where $\dot{q}''_{\rm gauge}$ is the gauge heat flux, $\dot{q}''_{\rmnet}$ is the measured net heat flux, $\sigma$ is the Stefan-Boltzmann constant, $T_{\rmgauge}$ is the gauge temperature, and $T_\infty$ is the reference temperature of the water cooled gauge (20~\degC). The heat transfer coefficients for each configuration were taken to be the median of the four methods across testing. Table~\ref{Wasson_Exp} summarizes the heat fluxes, gas temperatures, and heat transfer coefficients from this test series. Scenario 5 was omitted from benchmarking in due to high transience observed in the test data.
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\begin{table}[htbp!]
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\caption[Wasson Fire Impinging Ceiling Experiments]{Wasson fire impinging on an unconfined ceiling experiments.}
The number of radiation angles was increased to 400 in this work to reduce mesh artifacts in the discretization ~\cite{KimYJ_Trouve:FSJ2023}. The number of time steps between updates to the radiation equation was increased from the default 3 to 12 to maintain the same computational time for the radiation solver at the higher spatial resolution.
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The models used the two-step mixing-controlled combustion scheme with a gas phase reaction of propane, C$_3$H$_8$, with a soot yield of 0.024, carbon monoxide yield of 0.005~\cite{SFPE2016:appendix3}. A pilot fuel source of 1~\% of the fuel at the burner had an auto ignition temperature of 0~\degC~and the remaining fuel had a specified auto ignition temperature of 450~\degC~for propane~\cite{SFPE:Beyler}. Local flame extinction was disabled (\ct{SUPPRESSION=F}).
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The top of the fuel surface was defined as a prescribed heat release rate per unit area with a 10~\% random perturbation in the mass flux of fuel across the surface. The front surface temperature of the burner was set to 400~\degC.
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A small tilt in the flame can result in a large local temperature difference due to the high gradient in the stagnation region. A small ambient bias was introduced along one axis to simulate this effect. An ambient bias of 0.16~m/s agreed well with the experiments and was used in these models.
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It is assumed that the fuel propane, C$_3$H$_8$, has a soot yield of 0.024 and a carbon monoxide yield of 0.005~\cite{SFPE2016:appendix3}. The front surface temperature of the burner was set to 400~\degC.
Figure~\ref{Wasson_Heat_Flux} displays the predicted lateral profile of heat flux to the ceiling above a propane fire, compared to the measured peak value.
\caption[Wasson Impinging Plumes, heat flux to the ceiling]{Wasson Impinging Plumes, predicted lateral heat flux profile (dashed lines) compared to the measured peak value (solid line).}
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