Large Eddy Simulation of Heat Transfer in Boundary Layer and Backstep Flow Using PANS

Developing boundary layer flow and the flow over a backward-facing step are studied here. The LRN PANS k − ε [1] and the WALE turbulence model [2] are used as SGS models. The PANS (Partially AveragedNavier-Stokes) modelling approach [3, 4] is a modified k − ε model that can operate in both RANS and LES mode. An extension of PANS based on a four-equation k− ε− ζ − f model was recently proposed [5]. Synthetic, anisotropic, turbulent fluctuations are prescribed at the inlet to trigger the momentum equations into turbulenceresolving mode. The effect of the amplitude of the synthetic fluctuations is investigated. Different values of fk are used. Two different discretization approaches are compared: 100% central differencing (CDS) or 95% CDS and 5% van Leer second-order bounded upwinding scheme. One 2D RANS simulation using the k − ω SST model is made for the backstep flow. A detailed comparison is made between 2D RANS and PANS including an analysis of the balancing terms in the momentum and temperature equations. 1. The LRN PANS k − ε turbulence model The Low-Reynolds-Number partially averaged Navier-Stokes (LRN PANS) turbulence model reads [1] ∂k ∂t + ∂ūjk ∂xj = ∂ ∂xj [( ν + νt σku ) ∂k ∂xj ] + Pk − ε ∂ε ∂t + ∂ūjε ∂xj = ∂ ∂xj [( ν + νt σεu ) ∂ε ∂xj ] + Cε1Pk ε k − C∗ ε2 ε k νt = Cμfμ k ε , C∗ ε2 = Cε1 + fk fε (Cε2f2 − Cε1), σk ≡ σk f 2 k fε , σεu ≡ σε f 2 k fε σk = 1.4, σε = 1.4, Cε1 = 1.5, Cε2 = 1.9, Cμ = 0.09, fε = 1 In the baseline model, fk = 0.4. The damping functions are defined as f2 = [ 1− exp ( − y 3.1 ) ]2{ 1− 0.3exp [