Direct evaluation of the subgrid scale scalar flux in turbulent premixed flames with conditioned dual-plane stereo PIV

With the dual-plane stereo PIV technique the instantaneous three-dimensional resolved rate-of-strain tensor is directly measured in turbulent premixed flames. Simultaneously, also the instantaneous subgrid scale (SGS) scalar flux is measured with fine resolution, where for the latter term the conditioned particle image velocimetry (CPIV) technique is applied. The subgrid resolution reaches 118 μm, allowing a 9 × 9 resolution of a subgrid filter with width Δ = 1 mm. This combined measurement approach allows the a-priori comparison of models for the SGS scalar flux term with direct measurements which is important for large eddy simulation methods in turbulent premixed flames. Two different flame conditions of a premixed V-shaped turbulent flame are investigated where the turbulence intensity is varied by a factor of nearly three. The instantaneous radial and axial SGS fluxes are compared with the following three models: gradient model with Smagorinsky approach for the turbulent viscosity, Clark model, and extended gradient model with an anisotropy term. None of these models shows a good correlation with the directly measured flux. The anisotropy term alone (being nearly similar to the Clark model) shows, however, a right trend behaviour. An analysis of the data indicates a significant dependency of the experimentally determined SGS flux on the Favre averaged reaction progress (spatially averaged over the SGS area). A relatively simple closure for the SGS flux, which describes the dilatation due to the gasdynamic expansion, and which is a function proportional to (c̄ - c̃), shows a rather good correlation with direct measurement for some of the components. A successful SGS scalar flux model for premixed turbulent flames most likely needs to include at least two different effects.