Flamelet Connection to Turbulence Kinetic Energy Dissipation Rate

TL;DR

The paper addresses closing turbulent non-premixed flame simulations by linking subgrid flamelet chemistry to resolved turbulence through the turbulence kinetic energy dissipation rate $\epsilon$, focusing on subgrid strain-rate $S^*$ and vorticity $\omega$ in a Rotational Flamelet Model (RFM). It derives rotating-frame relations that connect $\epsilon$ to $S^*$ and $\omega$ via Kolmogorov-scale arguments, establishing explicit formulas such as $S^* = \tfrac{1}{2}\sqrt{ \frac{C_{vd}\,\epsilon}{\nu[ S_1^2 + 1 - S_1 ]} }$, $\omega = \sqrt{ \frac{2[ C_{ke} - C_{vd}/2 ] \epsilon}{\nu} }$, and $\frac{1}{\rho}\frac{\partial^2 p}{\partial x_i^2} = (C_{ke} - C_{vd})\frac{\epsilon}{\nu}$ with $\tfrac{C_{vd}}{2} < C_{ke} < C_{vd}$. By comparing CFM and RFM for $\mathrm{H_2/N_2-O_2}$ and $\mathrm{JP-5}$–air, the work shows that vorticity materially alters flamelet behavior and that, for the same $\epsilon$, multiple flamelet states can exist due to the dependence of scalar dissipation on $\omega$. The proposed $\epsilon$-based coupling enables two-way subgrid–resolved-scale interaction without introducing progress variables, providing a physically grounded pathway to improve LES/RANS closures for turbulent non-premixed flames and offering applicability to FPV frameworks with appropriate extensions.

Abstract

The turbulence kinetic energy dissipation rate $ε$, from a turbulent combustion computation using either Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES), is proposed for closure with a sub-grid non-premixed flamelet model. The intentions are to avoid the creation of artificial tracking or progress variables and to relate accurately the physics of turbulent non-premixed combustion at the resolved length scales to the small-scale physics where the mixing and chemical reactions occur. The analysis addresses the relations between $ε$ and the strain rate, vorticity, viscous dissipation rate, scalar gradients, scalar dissipation rate, and burning rate at the smallest turbulence length scales where diffusion-controlled burning is faster than at larger length scales and thereby dominant. The imposed strain rate and vorticity on these smallest eddies are determined from the kinetic energy dissipation rate. Thus, an $ε$ value at a specific time and location determines the two mechanical constraints (vorticity and strain rate) on the inflow to the counterflow flamelet. $ε$ affects the sign of the Laplacian of pressure, which must be negative to allow the existence of the counterflow. Using different flamelet models, with and without vorticity, different results for maximum flamelet temperature, integrated flamelet burning rate, and maximum flamelet scalar dissipation rate are obtained. Flamelet models that consider the centrifugal effect of vorticity produce substantial enhancements in the accuracy and completeness of information for a turbulent combustion computation. $ε$ may be used as a tracking variable that connects the sub-grid flamelet model to resolved-scale RANS or LES computations.

Figures (13)

• Figure 1: Transformation to $\xi, \chi, z'$ rotating coordinate system from $x', y', z'$ Newtonian system. $\theta$ increases in the counterclockwise direction.
• Figure 2: Comparison of three flamelet models for $\mathrm{H_2/N_2-O_2}$ diffusion flames with $T_{max}$ as a function of stoichiometric SDR value ($\chi_{st}$): red, classical result from FlameMaster; black, Rotational Flamelet with zero vorticity; blue, Rotational Flamelet with vorticity.
• Figure 3: Comparison of three flamelet models for $\mathrm{H_2/N_2-O_2}$ diffusion flames with $T_{max}$ as a function of applied compressive strain rate $S^*$: red, classical result from FlameMaster; black, Rotational Flamelet with zero vorticity; blue, Rotational Flamelet with vorticity.
• Figure 4: Comparison of three flamelet models for $\mathrm{H_2/N_2-O_2}$ diffusion flames with $T_{max}$ as a function of $\epsilon / \nu_{\infty}$: red, classical result from FlameMaster; black, Rotational Flamelet with zero vorticity; blue, Rotational Flamelet with vorticity.
• Figure 5: Comparison of three flamelet models for $\mathrm{H_2/N_2-O_2}$ diffusion flames with $\chi_{st}$ as a function of $S^*$: red, classical result from FlameMaster; blue, Rotational Flamelet with zero vorticity; black, Rotational Flamelet with vorticity.