Stretch-rate relationships for turbulent premixed combustion LES subgrid models measured using temporally resolved diagnostics

Temporally resolved measurements of turbulence–flame interaction were used to experimentally determine relationships for the strain-rate and curvature stretch-rate exerted on a premixed flame surface. These relationships include a series of transfer functions that are analogous to, but not equal to, stretch-efficiency functions. The measurements were obtained by applying high-repetition-rate particle image velocimetry in a turbulent slot Bunsen flame and were able to resolve the range of turbulent scales that cause flame surface straining and wrinkling. Fluid control masses were tracked in a Lagrangian manner as they interacted with the flame surface. From each interaction, the spatially and temporally filtered subgrid strain-rate and curvature stretch-rate were measured. By analyzing the statistics of thousands of turbulence–flame interactions, relationships for the strain-rate and curvature stretch-rate were determined that are appropriate for Large Eddy Simulation. It was found that the strain-rate exerted on the flame during these interactions was better correlated with the strength of the subgrid fluid-dynamic strain-rate field than with previously used characteristic strain-rates. Furthermore, stretch-efficiency functions developed from simplified vortex–flame interactions significantly over-predict the measurements. Hence, the proposed relationship relates the strain-rate on the flame to the filtered subgrid fluid-dynamic strain-rate field during real turbulence–flame interactions using an empirically determined Strain-Rate Transfer function. It was found that the curvature stretch-rate did not locally balance the strain-rate as has been proposed in previous models. A geometric relationship was found to exist between the subgrid flame surface wrinkling factor and subgrid curvature stretch-rate, which could be expressed using an empirically determined wrinkling factor transfer function. Curve fits to the measured relationships are provided that could be implemented in numerical simulations of turbulent premixed combustion.