Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions

Abstract

Large eddy simulations are presented for the flow in a periodic channel segment, which is laterally constricted by hill-shaped obstructions on one wall, having a height of 33% of the unconstricted channel. The Reynolds number, based on channel height, is 21,560. Massive separation thus arises on the hills’ leeward sides, the length of which is about 50% of that of the periodic segment. After reattachment, the flow is allowed to recover over about 30% of the segment length before being strongly accelerated over the windward side of the next hill. The principal challenge of this flow arises from the separation on the curved hill surface and the fact that the reattachment point, and hence the whole flow, are highly sensitive to the separation process. Simulations were performed with three grids, six subgrid-scale models and eight practices of approximating the near-wall region in simulations on the two coarser grids. These were supported by wall-resolved and wall-function simulations for fully-developed channel flow. The principal objective is to identify the sensitivity of the predictive accuracy to resolution and modelling issues. Coarse-grid simulations are judged by reference to data derived from two independent highly-resolved simulations obtained over identical meshes of close to 5 million nodes. Similarly, coarser-grid simulations were also performed with the two codes to enhance confidence in the results. The principal message emerging from the simulations is that grid resolution, especially in the streamwise direction around the mean separation position, has a very strong influence on the reattachment behaviour and hence the whole flow. This has serious implications for even more challenging high-Reynolds-number cases in which separation occurs from gently curved surfaces. The near-wall treatment, including the details of the numerical implementation of the wall laws, is also shown to be influential, most prominently on the coarsest grid. The application of the no-slip conditions at the wall at which separation occurs is found to cause substantial errors, especially in conjunction with poor streamwise resolution, even if the wall-nearest grid nodes are within the semi-viscous sublayer, in the range 5≲ y +≲15. The sensitivity to subgrid-scale modelling is shown to be more modest, with those models returning relatively low subgrid-scale viscosity giving the closest accord with the highly-resolved simulation.