Deterministic Stress Modeling for Multistage Compressor Flowfields

Unsteadiness is one of the main characteristics in turbomachinery flows. Local unsteady changes in static pressure must exist within a turbo-machine in order for that machine to exchange energy with the fluid. The primary reason for unsteady effects lies in the interaction between moving and stationary blade rows. The industrial design process of aero-engines and gas turbines is still based on Reynolds-averaged Navier-Stokes (RANS) techniques where the coupling of blade rows is carried out by mixing-planes. However, this methodology does not cover deterministic unsteadiness in an adequate way. For standard aero-optimization, detailed unsteadiness is not essential to the designer of turbomachines but rather its effect on the time averaged solution. The time averaged deterministic unsteadiness can be expressed in terms of deterministic stresses. The present paper presents two different modeling strategies for deterministic stresses that constitute an improvement of the conventional steady mixing-plane approach. Whilst one of the presented models operates with deterministic flux terms based on preliminary unsteady simulations, the other one, a novel transport model for deterministic stress, is a stand-alone approach based on empirical correlations and a wide range of numerical experiments. A 4.5 stage transonic compressor is analyzed regarding blade row interaction effects and their impact on the time averaged solution. The two models are applied to the compressor and their solutions are compared to conventional mixing-plane, time accurate and experimental data. The results for the speedline, the wake shapes, the radial distributions and the rotor blade loadings show that the deterministic stress models strongly improve the RANS solution towards the time accurate and the experimental methods.