Synthetic wall boundary conditions for the direct numerical simulation of wall-bounded turbulence

Abstract

We report on the simulation of a turbulent channel flow in a reduced computational domain where the wall no-slip boundary condition is replaced with a synthetic boundary condition on a horizontal plane in the wall layer. The simulation is carried out at a moderate Reynolds number (R τ=180). The boundary condition consists of a planar velocity field reconstructed at each instant from a combination of proper orthogonal decomposition (POD) spatial eigenfunctions, which are supposed to be known a priori. Two different techniques are used to reconstruct the temporal coefficients of the combination. The coefficients are first integrated from a dynamical model [29 Podvin, B., Fraigneau, Y., Lusseyran, F. and Gougat, P. 2006. A reconstruction for the flow past an open cavity. J. Fluids Eng., 128(3): 531[Crossref], [Web of Science ®] , [Google Scholar]] (B. Podvin, A pod-based model for the wall layer of a turbulent channel flow, Phys. Fluids 21(1) (2009), p. 015111) derived for one wall-normal POD mode. The coefficients are then estimated from flow information on the reduced domain as described in [30 Podvin, B., Fraigneau, Y., Laval, J. P. and Jouanguy, J. 2010. On self-similarity in the wall layer of a turbulent channel flow. J. Fluids Eng., 134: 042102 [Google Scholar]] (Podvin et al., On self-similarity in the wall layer of a turbulent channe flow, J. Fluids Eng. 134 (2010), p. 042102). Synthetic wall conditions are tested at y+=17 and y+=50. When only one wall-normal POD mode is used, the low-dimensional model appears to provide some agreement, while the estimation technique fails to reproduce the statistics of a full channel flow. The statistics improved significantly when the higher order wall-normal POD modes were included in the estimation procedure. Contributions to the Reynolds stress were examined: Vortex stretching was more easily reproduced than vorticity transfer, and adjusted more rapidly to the feedback-estimated boundary condition.