Near-wall behavior of RANS turbulence models and implications for wall functions Georgi Kalitzin * , Gorazd Medic, Gianluca Iaccarino, Paul Durbin Flow Physics and Computation Division, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3030, USA Received 4 June 2004; received in revised form 22 September 2004; accepted 6 October 2004 Available online 23 November 2004 Abstract The paper proposes a novel wall-function formulation applicable to any RANS turbulence model. It is based on the assumption of wall layer universality, applied to the entire model. The approach is implemented via tables for the tur- bulence quantities and the friction velocity u s . The influence of numerical errors on the wall-function solution is inves- tigated and improvements are proposed. Numerical results are presented for a flat plate boundary layer at zero pressure gradient and for a flow with pressure gradient driven separation. The behavior of RANS turbulence models in the near wall region is also analyzed. The models considered are: Spalart–Allmaras, k–x, k–g and v 2 –f. The analysis of the v 2 –f model resulted in new analytical solutions in the viscous sublayer and logarithmic layer. The analytical solutions for the Spalart–Allmaras model can be used directly as a simple wall function. Ó 2004 Elsevier Inc. All rights reserved. 1. Motivation and background The size of industrial CFD problems has grown considerably in recent years and, despite a rapid increase in computational resources, there are still many applications for which the grid resolution is insufficient for wall integration and accurate wall functions are a necessity. For example, computation of rotating stall in turbomachinery requires large scale, detailed flow-field predictions in the entire compressor [18]; assuming that a high quality grid is employed in each blade passage, the computational grid would easily exceed 50 million cells. Wall functions are also an essential ingredient for the development of Cartesian Immersed Boundary RANS methods [7]. Shortcomings of existing wall functions motivate further research in this field. 0021-9991/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2004.10.018 * Corresponding author. Tel.: +1 650 723 8476; fax: +1 650 725 3525. E-mail address: kalitzin@stanford.edu (G. Kalitzin). Journal of Computational Physics 204 (2005) 265–291 www.elsevier.com/locate/jcp