On the Feasibility of Helicity-Based Corrections of Turbulence Models for Improving RANS Predictions of Centrifugal Compressor Stages

In order to face the challenges of energy transition, turbomachinery designers claim for appropriate numerical tools able to keep up with robust, and fast design iterations. In order to face the challenges of energy transition, turbomachinery designers claim for appropriate numerical tools able to keep up with robust, and fast design iterations. High fidelity analyses are becoming feasible for assessing the performance of selected geometries, however RANS-based CFD codes are still the workhorse exploited for daily design and optimization iterations when a large number of geometrical configurations are needed to scrutinize a wide and complex design space. The proper selection of the numerical framework, and in particular of the turbulence model, is always critical in order to guarantee a sufficient confidence level in the predicted results, and, at the same time, robustness and numerical stability with quick simulations. Major sources of inaccuracy are often associated with 3D flow features, secondary flows, flow separations, and shock wave boundary layer interaction. The present work proposes helicity-based corrections for the production terms of two-equation turbulence models as a mean of improving predictions of the aforementioned flow features. A discussion on the treatment of helicity-based terms when changing frame of reference represents one novelty aspect of the paper. The numerical framework is first validated on a transonic axial fan test case (NASA Rotor 67) and then applied to the analysis of two centrifugal compressor stages for in the high peripheral Mach number regime. The feasibility of the helicity-based approach is proven via a comparison with the available experimental data in terms of spanwise distributions of flow quantities and performance characteristics of work input and polytropic efficiency. The impact of turbulence modeling on the prediction of the flow field details is investigated, to assess the capability of a steady state numerical approach to identify the physical mechanisms that limit the operating range at low mass flows.