Improved Non-Equilibrium Turbulence Closure Modeling for Axial Flow Compressors Simulation

The present paper investigates the predictive attitude of three non conventional turbulence closures in simulating the physics pertinent to decelerating turbomachinery flows. The performance of a cubic k-ε model and an algebraic Reynolds stress model adopting a non-linear link between turbulence and velocity gradients have been exploited with reference to their capabilities in predicting anisotropy effects and the sensibility to streamlines curvature. In addition, a modification of the kinetic energy production term in standard isotropic model has been also tested, in accord with Kato and Launder formulation. To put in evidence the predictive capabilities of such models a comparison with the standard Launder and Sharma turbulence closure will be carried out. The authors adopt a multi-level parallel solver developed in the framework of a finite element (FE) method based on a stabilized Petrov-Galerkin formulation. The FE method is here applied on mixed Q2-Q1 element shape functions. The solution scheme is based on a Multigrid (MG) solver properly developed to operate in a parallel environment. To increase the performance of MG schemes in solving self-adjoint elliptic problems a remedial strategy consisting of a LFMG-type scheme named Hybrid Linear Full Multi-Grid technique (HLFMG) has been proposed. The parallel algorithm follows a Single Program Multiple Domains (SPMD) scheme. The subdomains fields for Reynolds Averaged Navier-Stokes problem are generated by the adoption of an original overlapping domain decomposition technique. In the present paper we analyze a two-dimensional leading edge and both a DCA (2D) and NACA65 (3D) compressor cascades. The flows considered for model benchmarking are highly challenging because of the possibly transitional nature of the flow and the existence of three-dimensional phenomena and of significant separation regions. The potential of non-standard closures has been investigated in terms of both velocity and turbulent variables. In the leading edge test-case, the cubic k-ε model is shown to provide a better base-line for nonequilibrium effects simulation with respect to the algebraic stress model. The Kato and Launder modification has shown poor predictive attitude in representing the flow downstream the impingement and it has not adopted for the other test-cases. In the DCA simulation the presence of large transition regions leads to a degradation of the predictions of the cubic model. Algebraic stress model has shown performances comparable to the cubic model ones. The 3D linear cascade flow simulations put in evidence that the standard and algebraic Reynolds stress approaches have similar performance, clearly worse respect to the cubic model.