Flamelet Connection to Turbulence Kinetic Energy Dissipation Rate

An analysis takes the variable value for turbulence kinetic energy dissipation rate $\epsilon$ as it might appear from a turbulent combustion computation using either Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES) and relates it to both viscous dissipation rate and turbulence kinetic energy at the Kolmogorov scale. The imposed strain rate and vorticity on these smallest eddies are readily and uniquely determined from knowledge of that kinetic energy and viscous dissipation rate. Thus, a given value of $\epsilon$ at a specific time and location determines the two mechanical constraints (vorticity and strain rate) on the inflow to the flamelet. It is also shown how $\epsilon$ affects the sign of the Laplacian of pressure, which must be negative to allow the existence of the flamelet. Using several different flamelet models, with and without vorticity and with and without differential mass transport, different results for maximum flamelet temperature, integrated flamelet burning rate, and stoichiometric flamelet scalar dissipation rate are obtained. For a given $\epsilon$ value, flamelet models that do not consider vorticity and differential diffusion produce substantial errors in the information to be provided to the resolved or filtered scales in a turbulent combustion computation.