A priori tests of eddy viscosity models in square duct flow
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O R I G I NA L A RT I C L E
Davide Modesti
A priori tests of eddy viscosity models in square duct flow
Received: 9 March 2020 / Accepted: 11 July 2020 © The Author(s) 2020
Abstract We carry out a priori tests of linear and nonlinear eddy viscosity models using direct numerical simulation (DNS) data of square duct flow up to friction Reynolds number Reτ = 1055. We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components ai j responsible for turbulent secondary flows, namely the normal stress a22 and the secondary shear stress a23 . A priori tests on constitutive relations for ai j are performed using the tensor polynomial expansion of Pope (J Fluid Mech 72:331–340, 1975), whereby one tensor base corresponds to the linear eddy viscosity hypothesis and five bases return exact representation of ai j . We show that the bases subset has an important effect on the accuracy of the stresses and the best results are obtained when using tensor bases which contain both the strain rate and the rotation rate. Models performance is quantified using the mean correlation coefficient with respect to i j , which shows that the linear eddy viscosity hypothesis always returns very accurate values of DNS data C 12 > 0.99), whereas two bases are sufficient to achieve good accuracy of the the primary shear stress a12 (C 22 = 0.911, C 23 = 0.743). Unfortunately, RANS models rely on normal stress and secondary shear stress (C additional assumptions and a priori analysis carried out on popular models, including k–ε and v 2 – f , reveals that none of them achieves ideal accuracy. The only model based on Pope’s expansion which approaches ideal performance is the quadratic correction of Spalart (Int J Heat Fluid Flow 21:252–263, 2000), which has similar accuracy to models using four or more tensor bases. Nevertheless, the best results are obtained when using the linear correction to the v 2 – f model developed by Pecnik and Iaccarino (AIAA Paper 2008-3852, 2008), although this is not built on the canonical tensor polynomial as the other models. Keywords Eddy viscosity models · RANS · Square duct flow 1 Introduction The numerical solution of Reynolds-averaged Navier–Stokes (RANS) equations is a standard approach to evaluate flows of industrial interest. Two methodologies for RANS closure are available in the literature, namely eddy viscosity transport models and Reynolds stress transport models. The former stem from the analogy between Reynolds stresses and viscous stresses and are often referred to as first-order closures, whereas the latter require the solution of transport equations for each component of the Reynolds stress tensor and are therefore second-order closures. Eddy viscosity models are undoubtedly more popular in industry than Reynolds stress transport models, as they are easier to implement in existing flow solvers and they require less computational effort [37]. In their Communicated by Philippe Spalart. D. Modesti (B) Aerodynamics Group, Faculty of Aerospace Engineering
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