Session: 34-10 Turbulence modeling methods 1

Paper Number: 121023

121023 - A Data Driven Method for the Derivation of Explicit Algebraic Reynolds Stress Models Applied to the Wake Losses of Low-Pressure Turbine Cascades 

This paper introduces and validates a data driven approach to improve modelling deficits of linear eddy viscosity models (LEVMs). The suggested approach is applied to the wake mixing of low pressure turbine (LPT) cascade flows operating below a Reynolds number of 100,000.

The approach extends a LEVM to an explicit algebraic Reynolds stress model (EARSM) by considering additional contributions to the Reynolds stress tensor besides the strain rate tensor. It modifies the Boussinesq assumptions following the rationale applied in the derivation of EARSMs by including additional second order tensors. The unknown scalar functions that determine the contributions of each second order tensor to the Reynolds stresses are approximated by polynomials. In consequence, the remaining modelling task is the determination of the polynomial coefficients. To do so, we use a meta-model assisted multi-objective optimization. Its physics-based objective functions determine the differences in the distribution of user selected flow quantities (such as. Reynolds stresses, the total pressure loss or any other available variable) between the Reynolds-averaged Navier-Stokes (RANS) solution computed by the EARSM and a high fidelity reference. To ensure the stability of the models, the solution space is restricted by additional numerical objective functions. We utilize the well-known Kriging approach as a cost-efficient meta-model to approximate the physics-based objective functions. To minimize the objective functions, we apply the non-dominated sorting genetic algorithm (NSGA) III.

We use the k-ω of Wilcox as baseline model for the introduced framework and employ it on the wake mixing of two LPT cascades. As reference data to train the new models, we use a LES simulation of the T106C LPT cascade with a Reynolds number of 80,000 and an isentropic exit Mach number of 0.65. For this case, the physics-based objective functions compute the difference in the total kinetic energy loss in the wake. As the modelling approach focuses on the wake mixing, we restrict the numerical domain to the region downstream of the blade trailing edge prescribing the LES data as inlet boundary condition. A sensitivity study by varying each polynomial coefficient of the EARSM identifies the main drivers to reduce the modelling errors in the wake. The subsequent optimization generates new models that improve the prediction of the wake losses by up to 73.6% with respect to the baseline k-ω model for the training case. We further evaluate additional turbulent quantities in order to investigate the mechanism that leads to the change of the stagnation pressure in the wake. To assess the prediction quality of several models of the pareto front, they are applied to the mid-section of the MTU-T161 LPT cascade with a Reynolds number of 90,000 and an isentropic exit Mach number of 0.6. The best of the new models achieves an improvement of 69.5%. However, the results highlight the need for validation with several test cases as one of the selected models only reports an improvement of 7%.

In summary, the presented approach is capable to enhance the prediction of wake losses of LPT cascades under cruise conditions of modern turbofan engines. Furthermore, it highlights its potential for the application to other RANS modelling deficits.

Presenting Author: Johannes Deutsch Institute of Jet propulsion and Turbomachinery, RWTH Aachen University

Presenting Author Biography: Johannes Deutsch is a PhD candidate at the Institute of Jet Propulsion and Turbomachinery of the RWTH Aachen University in Germany. His research focuses on the use of Scale Resolving Simulations to improve RANS predictions for turbomachinery applications.

Authors:

Johannes Deutsch Institute of Jet propulsion and Turbomachinery, RWTH Aachen University
Nima Fard Afshar Institute of Jet propulsion and Turbomachinery, RWTH Aachen University
Stefan Henninger Institute of Jet Propulsion and Turbomachinery, RWTH Aachen University
Peter Jeschke Institute of Jet Propulsion and Turbomachinery, RWTH Aachen University