A computational study is presented which investigates the predictive performance of two non-linear turbulence closures in simulating the physics pertinent to decelerating turbomachinery flows. The compared approaches are a cubic non-linear k-ε model and an algebraic Reynolds stress model. They have been considered as promising closures for improving the industry CFD state-of-the-art accounting for non-equilibrium effects. The authors adopt a parallel multi-grid algorithm, which is developed with a finite element formulation based on a highly accurate stabilized Petrov-Galerkin method. The finite element formulation is here applied on equal-order Q1-Q1 as well as mixed Q2-Q1 element pairs, and the accuracy of the latter approximation is assessed on near-wall flows simulation. The parallel solution algorithm for Reynolds Averaged Navier-Stokes modeling exploits an overlapping domain decomposition technique based on an “inexact explicit non linear Schwarz method”. The compressor flow considered for model benchmarking is highly challenging because of the transitional nature of the flow and the existence of significant leading- and trailing-edge separations. The potential of non-isotropic closures has been investigated. The algebraic stress model is shown to provide a better base-line for non-equilibrium effects simulation with respect to the cubic k-ε model. As it is shown for the studied compressor cascade, the cubic eddy-viscosity model exhibits some predictive weaknesses, among them an excessive turbulence attenuation that results in un-realistically delayed transition to turbulence.
Non-linear and hysteretical finite element formulation applied to magnetostrictive materials