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RANS SOLUTIONS IN COUETTE FLOW WITH STREAMWISE VORTICES

Philippe R. Spalart
Boeing Commercial Airplanes P.O. Box 3707, Seattle, WA 98124, USA

A. Garbaruk
New Technologies & Services St-Petersburg 197198, Russia

Michael Kh. Strelets
New Technologies & Services St-Petersburg 197198, Russia

Résumé

Plane Couette flow is solved for with conventional Reynolds-Averaged Navier-Stokes (RANS) turbulence models, without temporal (t) or streamwise (x) dependence, but with periodic conditions in the lateral z direction and non-zero velocity components in all three directions. Thus, (U,V,W) are functions of (y,z). This is motivated by experimental and DNS observations of large and powerful streamwise vortices with minimal t and x dependence, which raised the possibility that RANS models may allow such vortices to form, with a defendable scale separation away from the modeled turbulence. We find that some RANS models indeed support vortices, which then make a large (near 50%) contribution to the momentum transport in the core region and tangibly increase the skin-friction coefficient Cf at a given Reynolds number, in broad agreement with DNS results and some experiments. The velocity profile with vortices follows the logarithmic law much longer than it does without vortices or in Poiseuille flow, a fact we actually view as largely fortuitous. To date, only models equipped with a Quadratic Constitutive Relation (QCR) have succeeded in creating the vortices. The Linear Eddy-Viscosity Models (LEVM) tested damp the vortices, and return unidirectional solutions with only U varying with y; so did an Explicit Algebraic Reynolds Stress Model. The existence of such "2.5D" solutions is favorable in terms of agreement with experiment and may partly explain the wide experimental scatter, and also a warning of the possible appearance of striations in routine 3D CFD solutions. It is also a warning that the results of Direct Numerical Simulation will depend noticeably on the lateral period, unless it is made very large.