A Data-Driven Method for the Derivation of Explicit Algebraic Reynolds Stress Models Applied to the Wake Losses of Low-Pressure Turbine Cascades

Abstract

This paper introduces and validates a data-driven approach to improve the prediction of linear eddy viscosity models (LEVMs). The general approach is adopted in order to improve the wake mixing of low-pressure turbine (LPT) cascades. The approach is based on the modification of the Boussinesq assumption. It follows the rationale applied in the derivation of explicit algebraic Reynolds stress models (EARSMs) by including additional second-order tensors, as suggested by Pope (1975, “A More General Effective-Viscosity Hypothesis,” J. Fluid Mech., 72(2), pp. 331–340. 10.1017/S0022112075003382 ) . The unknown scalar functions that determine the contributions of each second-order tensor to the Reynolds stresses are approximated as polynomials. A metamodel-assisted multi-objective optimization determines the value of each of the polynomial coefficients. The optimization minimizes the difference between the result of the EARSM simulation and reference data provided by a high-fidelity large eddy simulation (LES). In this study, tailor made EARSMs are calibrated in order to improve the prediction of the kinetic energy loss distribution in the wake of the T106C LPT cascade with an isentropic Reynolds number of 80,000. We showed that the wake losses predicted by state-of-the-art Reynolds-averaged Navier–Stokes (RANS) turbulence models cannot reproduce the reference (LES) data. In the following, we investigated the influence of each polynomial coefficient of the (EARSM) on the flow solutions within a sensitivity study. The models generated by the approach reduced the deviations in total kinetic energy loss between the (LES) reference solution and the baseline model by approximately 70%. The turbulent quantities are analyzed to identify the physical correlations between the model inputs and the improvement. The transferability of the models to unseen test cases was assessed using the MTU-T161 (LPT) cascade with an isentropic Reynolds number of 90,000. A decrease of up to 80% is achieved regarding the deviations between the (LES) reference and the baseline RANS model. In summary, the suggested approach was able to generate tailor made EARSM models that reduce the deviations between RANS and LES for the mixing of turbulent wake flows.