Calculation of unsteady flow past a cube on the wall of a narrow channel using URANS and the Spalart–Allmaras turbulence model

Abstract

UDC 532.517.4 The results of numerical simulation of fully developed turbulent flow in a channel with the cube on the lower wall (for the characteristic Reynolds number Re = 40,000) within the framework of the traditional approach to the solution of unsteady Reynolds-averaged Navier-Stokes equations (URANS) in combination with the semiempirical Spalart-Allmaras turbulence model (with a correction for rotation) have been presented. A de- tailed comparative analysis of the results of numerical simulation of local and integral flow characteristics and the Martinuzzi experimental data has shown that the self-oscillating regime of flow past the cube is a su- perposition of oscillations of the arms of a horseshoe vortex and the rear arched and detached vortex struc- tures. Using fast Fourier transformation, it has been found that the oscillations are of a bimodal character in the longitudinal and vertical directions, whereas in the transverse direction, they are of a unimodal character. Introduction. The problem on unsteady flow past a cube in a narrow channel with the fully developed turbu- lent flow being formed at the inlet is of particular interest for testing today's calculation algorithms of computational hydrodynamics. In this case channel flow is of a self-oscillating character and is distinguished by a complex vortex structure (Fig. 1). Flow separation begins ahead of the cube and further develops from its frontal face side and on the lateral walls. A horseshoe vortex that interacts with the near wake of the cube results. We recognize the following basic large-scale flow elements for their subsequent analysis and comparison to experimental data: 1) a horseshoe vor- tex; 2) a vortex ensemble consisting of a vortex attached to the face side of the cube and two columnar vortices near the lateral walls; 3) a rear detached vortex; 4) an attached vortex behind the end wall of the cube, which is not iden- tified in the Martinuzzi experiment, as should be noted, but is visualized in many calculations; 5) an arched vortex with two oppositely rotating bends, which is formed in the near wake. Experimental data to which we compare results of numerical investigations were obtained by Martinuzzi (1) and have been introduced into the ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) databank (2). About ten large-scale numerical investigations based on solution of steady and unsteady Reynolds-aver- aged Navier-Stokes equations (RANS ⁄ URANS) and on application of the large-eddy model (see, e.g., (3-5)) have been carried out over a period of 15 years. It is noteworthy that, except for the results obtained by Durbin with the V2F turbulence model (6), none of the works gives satisfactory agreement between the results of calculations within the framework of the RANS ⁄ URANS methodology and the experimental data. This work is primarily aimed at substantiating the applicability of the URANS approach to the prediction of turbulent separated flows. The commercial FLUENT v6.3 package (7) is used. Preliminary verification and approval of the package with a catalog of semiempirical models realized in it, which were carried out on two-dimensional test problems such as flow past a circular cylinder (8) and circulation flow in a square cavity with a moving upper bound- ary (9, 10), have shown satisfactory correlation with experimental data, when the two-parametric model of shear-stress transfer MSST and the Spalart-Allmaras (SA) vortex-viscosity model were selected. It has been shown in (8-10) that the SA model in its traditional formulation substantially overstates turbulent-viscosity values, which renders it unsuit- able for calculations of turbulent separated flows. For further testing, we have selected the SA model modified with allowance for rotation.