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 Re _{τ}= 1055. We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components a_{ij} responsible for turbulent secondary flows, namely the normal stress a_{22} and the secondary shear stress a_{23}. A priori tests on constitutive relations for a_{ij} 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 a_{ij}. 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 DNS data C~ _{ij}, which shows that the linear eddy viscosity hypothesis always returns very accurate values of the primary shear stress a_{12} (C~ _{12}> 0.99), whereas two bases are sufficient to achieve good accuracy of the normal stress and secondary shear stress (C~ _{22}= 0.911 , C~ _{23}= 0.743). Unfortunately, RANS models rely on 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 20083852, 2008), although this is not built on the canonical tensor polynomial as the other models.
Original language  English 

Pages (fromto)  713734 
Number of pages  22 
Journal  Theoretical and Computational Fluid Dynamics 
Volume  34 
Issue number  56 
DOIs  
Publication status  Published  1 Dec 2020 
Keywords
 Eddy viscosity models
 RANS
 Square duct flow
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Datasets

Direct numerical simulation dataset of turbulent square duct flow
Modesti, D. (Creator), TU Delft  4TU.ResearchData, 10 Jul 2020
DOI: 10.4121/UUID:3226D808F35447B1B6F83A8048215193
Dataset