Assessment of subgrid-scale models with a large-eddy simulation-dedicated experimental database: The pulsatile impinging jet in turbulent cross-flow

Abstract

Large-Eddy Simulation (LES) in complex geometries and industrial applications like piston engines, gas turbines, or aircraft engines requires the use of advanced subgrid-scale (SGS) models able to take into account the main flow features and the turbulence anisotropy. Keeping this goal in mind, this paper reports a LES-dedicated experiment of a pulsatile hot-jet impinging a flat-plate in the presence of a cold turbulent cross-flow. Unlike commonly used academic test cases, this configuration involves different flow features encountered in complex configurations: shear/rotating regions, stagnation point, wall-turbulence, and the propagation of a vortex ring along the wall. This experiment was also designed with the aim to use quantitative and nonintrusive optical diagnostics such as Particle Image Velocimetry, and to easily perform a LES involving a relatively simple geometry and well-controlled boundary conditions. Hence, two eddy-viscosity-based SGS models are investigated: the dynamic Smagorinsky model [M. Germano, U. Piomelli, P. Moin, and W. Cabot, “A dynamic subgrid-scale eddy viscosity model,” Phys. Fluids A 3(7), 1760–1765 (1991)] and the σ-model [F. Nicoud, H. B. Toda, O. Cabrit, S. Bose, and J. Lee, “Using singular values to build a subgrid-scale model for large eddy simulations,” Phys. Fluids 23(8), 085106 (2011)]. Both models give similar results during the first phase of the experiment. However, it was found that the dynamic Smagorinsky model could not accurately predict the vortex-ring propagation, while the σ-model provides a better agreement with the experimental measurements. Setting aside the implementation of the dynamic procedure (implemented here in its simplest form, i.e., without averaging over homogeneous directions and with clipping of negative values to ensure numerical stability), it is suggested that the mitigated predictions of the dynamic Smagorinsky model are due to the dynamic constant, which strongly depends on the mesh resolution. Indeed, the shear-stress near the wall increases during the vortex-ring impingement leading to a less refined mesh in terms of wall units, y+. This loss of resolution induces a poor damping of the dynamic constant, which is no longer able to adjust itself to ensure the expected y3-behavior near the wall. It is shown that the dynamic constant is never small enough to properly balance the large values of the squared magnitude of the strain-rate tensor, 2SijSij. The experimental database is made available to the community upon request to the authors.