Effect of RANS Method on Stall Inception Eigenvalue Approach

Abstract

The effect of mesh, turbulence model and discretization scheme in Reynolds-averaged Navier-Stokes method (RANS) on a stall inception eigenvalue approach is investigated in a transonic compressor rotor. The most influencing flow structures on the result of eigenvalue approach are also identified. The compressor stall point is calculated by a recently developed eigenvalue model. Based on the 3D Navier-Stokes equations, the body-force term and small disturbance were used to transform the original equations into the eigenvalue approach. Because the eigenvalue mainly relies on the results from RANS, the sensitivity of the eigenvalue to the mesh density, turbulence model, and numerical scheme needs to be clearly identified before it is applied to engineering. The effect of mesh density is firstly specified. Several grids with different densities and distributions are employed in RANS. The eigenvalue results indicate that the solution converges at the same grid density as RANS does. Besides, the eigenvalue approach has the ability to predict a more accurate stall point compare to RANS with a coarse computational grid. The investigation of the detailed flow field indicates that the flow structures in the vicinity of blade tip region change significantly with three different grid densities, the eigenvalue is also influenced. Two important flow mechanisms are found to be the decisive factors for the eigenvalue, namely the blockage generated by the shock-vortex interaction, the separated flow and the wake near the trailing edge. These flow patterns are consistent with the flow mechanisms of the compressor stall inception. Further investigations are conducted with four different turbulence models combined with three different spatial discretization schemes. Calculated eigenvalue proves that the turbulence model changes the eigenvalue with an over-prediction of stall point at about 1%. The spatial discretization scheme has small effect on stall point prediction using k-ε and SA models, whereas it has large effect when using SST model. The scheme shows great influence in the simulations with specific turbulence model by changing the predicted stall point at least 1.7%. The existence of blockage, the separation and the wake flow are identified as the major and secondary factor which contributes to an unstable prediction of eigenvalue approach, respectively.