A-priori testing of an eddy viscosity model for the density-weighted subgrid scale stress tensor in turbulent premixed flames

In this study, we report on the direct measurement of the density-weighted subgrid scale (SGS) stress tensor in turbulent premixed flames. In large-eddy simulations (LES), this unresolved tensor is typically modelled using eddy viscosity approaches. Additionally to the direct measurement, we provide a pure experimentally based a-priori test of the commonly used eddy viscosity model suggested by Smagorinsky. For two turbulent premixed V-shaped methane–air flames, a statistical analysis is presented where the correlation between the directly measured SGS stress tensor and the eddy viscosity model following Smagorinsky is tested. The measurement strategy is based on the application of a dual-plane stereo-PIV technique which enables the measurement of the 3D flow field in two parallel planes. This allows the determination of velocities as well as velocity gradients in all three directions. Here, a vector resolution of 118 μm was achieved. For a priori testing, the data are subjected to a spatial filtering procedure that reproduces the application of the filter function in LES. The calculation of velocity gradients is performed after the application of this spatial averaging. Additionally to the velocity field, the flame front position is deduced from the clearly observable step in the tracer particle number density between burnt and unburnt regions of the flame. This facilitates the direct single-shot-based evaluation of all components of the density-weighted SGS stress tensor. Additionally, the model expressions related to these terms can be determined, which is done in this first study for the static Smagorinsky model. With that, the instantaneous local comparison between directly measured stress terms and modelled terms is possible, based on the instantaneous local evaluation procedure. The measurement procedure is described, and first results are presented and discussed. They show a rather poor performance of the static form of the Smagorinsky model (with fixed Smagorinsky constant). Our future aims are to use the directly measured SGS data for the a-priori comparison with more advanced models.