Merge pull request #16065 from rmcdermo/master

Manuals: add citation for discussion of min time scale

Author: rmcdermo

Manuals/Bibliography/FDS_general.bib

@@ -1342,6 +1342,16 @@ @report{Childs
 	year = {1998},
 }
 
+
+@article{Chin:2023,
+	title = {{Chapman–Jouguet deflagration criteria and compressibility dynamics of turbulent fast flames for turbulence-induced deflagration-to-detonation transition}},
+	author = {Hardeo Chin and Jessica Chambers and Alexei Poludnenko and Vadim N. Gamezo and Kareem A. Ahmed},
+	journal = {Physics of Fluids},
+        doi = {10.1063/5.0144662},
+	volume = {35},
+	year = {2023},
+}
+
 @article{Chow:1,
 	title = {{Discussion on Two Plume Formulae with Computational Fluid Dynamics}},
 	author = {Chow, W.K. and Yin, R.},

Manuals/FDS_Technical_Reference_Guide/Combustion_Chapter.tex

@@ -141,7 +141,7 @@ \subsection{Reaction Time Scale Model}
 
 It is important to consider the behavior of an SGS model as the LES filter width (cell size) varies. The mixing times for diffusion, SGS advection, and buoyant acceleration scale differently with filter width and if we look to the limits of the filter scales an interesting picture emerges.  Referring to Fig.~\ref{fig_reaction_time_scale}, let us move from left to right along the horizontal axis following the thick black line which represents our time scale model for a hypothetical flow condition.
 
-First, notice that the reaction time scale, $\tau_{\rm mix}$, has a lower bound, $\tau_{\rm min}$, which for filter widths corresponding to DNS can be thought of as a chemical time scale, $\tau_{\rm chem}$. This lower bound is of the order of the traversal time of the flame thickness, $\tau_{\rm chem} \sim \delta/s_{\rm L}$, where $\delta=D_{\rm F}/s_{\rm L}$, $D_{\rm F}$ is the diffusivity of the fuel, and $s_{\rm L}$ is the laminar flame speed. For filter widths corresponding to LES simulations, it is not appropriate to invoke flame thicknesses and laminar flame speeds. Rather, the lower bound of $\tau_{\rm mix}$ is the filter width divided by a turbulent flame speed, which can vary depending on the fuel and configuration from approximately 10~m/s to 100~m/s. We take the value to be 100~m/s so as to form a lower bound. This lower bound only serves to prevent fictitiously high reaction rates on coarse grids---the actual mixing time scale is chosen based on the solid black line in Fig.~\ref{fig_reaction_time_scale}.
+First, notice that we assign a lower bound to the time scale curve. For filter widths corresponding to DNS, this can be thought of as a chemical time scale, $\tau_{\rm chem}$. For larger cell sizes we assign a minimum time scale corresponding to the maximum deflagration rate across the cell, which is on the order of 100~m/s \cite{Chin:2023}. This lower bound only serves to prevent fictitiously high reaction rates on coarse grids---the actual mixing time scale is chosen based on the solid black line in Fig.~\ref{fig_reaction_time_scale}.
 
 Referring now to the solid line in Fig.~\ref{fig_reaction_time_scale}, for relatively small scales, we expect the mixing time to vary as the square of the filter width because the mixing is controlled by molecular diffusion.  In this regime, denoted $\tau_{\rm d}$, the numerical solution is a DNS. This scaling law is valid while $\Delta$ is less than the Kolmogorov scale, $\eta$, the length scale of the smallest turbulent eddies (for this discussion we assume the Schmidt number (Sc) is of order unity). For a sufficiently high Reynolds number flow (such that an inertial subrange exists), as the filter width increases beyond the Kolmogorov scale we encounter a regime, marked $\tau_{\rm u}$, where turbulent advection controls the rate of mixing. Here the mixing time varies as the two-thirds power of the filter width \cite{Pope:2000}.  This is the regime where most LES submodels are valid (It is important to appreciate that fire differs from turbulent combustion in that the assumption of locally high Re is frequently invalid).