Machine Learning for Turbulence Model Development Using a High-Fidelity HPT Cascade Simulation

Nonlinear turbulence closures were developed that improve the prediction accuracy of wake mixing in low-pressure turbine (LPT) flows. First, Reynolds-averaged Navier–Stokes (RANS) calculations using five linear turbulence closures were performed for the T106A LPT profile at isentropic exit Reynolds numbers 60,000 and 100,000. None of these RANS models were able to accurately reproduce wake loss profiles, a crucial parameter in LPT design, from direct numerical simulation (DNS) reference data. However, the recently proposed kv2¯ω transition model was found to produce the best agreement with DNS data in terms of blade loading and boundary layer behavior and thus was selected as baseline model for turbulence closure development. Analysis of the DNS data revealed that the linear stress–strain coupling constitutes one of the main model form errors. Hence, a gene-expression programming (GEP) based machine-learning technique was applied to the high-fidelity DNS data to train nonlinear explicit algebraic Reynolds stress models (EARSM), using different training regions. The trained models were first assessed in an a priori sense (without running any RANS calculations) and showed much improved alignment of the trained models in the region of training. Additional RANS calculations were then performed using the trained models. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e., previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, turbulent kinetic energy (TKE) production, wake-loss profiles, and wake maturity, across all cases.

Section: Introductionmentioning

confidence: 99%

Development and Use of Machine-Learnt Algebraic Reynolds Stress Models for Enhanced Prediction of Wake Mixing in Low-Pressure Turbines

Akolekar

Weatheritt

Hutchins

et al. 2019

“…The result is a dissipation rate consistent with the LES fields and the RANS transport equations. For more information on this process see earlier work on turbine blade flows [9].…”

Section: Methodology For Reynolds Stress Closurementioning

confidence: 99%

“…Recently, a comparison of neural networks and GEP to regress non-linear stress-strain relationships showed very similar predictive performance, yet the GEP optimization was at a fraction of the cost [8]. Further, GEP was applied to high-pressure turbines and showed improvement over the linear model [9]. These studies looked primarily at the stress-strain relationship, yet researchers are also exploring other model components.…”

Section: Introductionmentioning

confidence: 99%

Applying Machine Learnt Explicit Algebraic Stress and Scalar Flux Models to a Fundamental Trailing Edge Slot

Sandberg

Tan

Weatheritt

et al. 2018

Machine learning was applied to large-eddy simulation (LES) data to develop nonlinear turbulence stress and heat flux closures with increased prediction accuracy for trailing-edge cooling slot cases. The LES data were generated for a thick and a thin trailing-edge slot and shown to agree well with experimental data, thus providing suitable training data for model development. A gene expression programming (GEP) based algorithm was used to symbolically regress novel nonlinear explicit algebraic stress models and heat-flux closures based on either the gradient diffusion or the generalized gradient diffusion approaches. Steady Reynolds-averaged Navier–Stokes (RANS) calculations were then conducted with the new explicit algebraic stress models. The best overall agreement with LES data was found when selecting the near wall region, where high levels of anisotropy exist, as training region, and using the mean squared error of the anisotropy tensor as cost function. For the thin lip geometry, the adiabatic wall effectiveness was predicted in good agreement with the LES and experimental data when combining the GEP-trained model with the standard eddy-diffusivity model. Crucially, the same model combination also produced significant improvement in the predictive accuracy of adiabatic wall effectiveness for different blowing ratios (BRs), despite not having seen those in the training process. For the thick lip case, the match with reference values deteriorated due to the presence of large-scale, relative to slot height, vortex shedding. A GEP-trained scalar flux model, in conjunction with a trained RANS model, was found to significantly improve the prediction of the adiabatic wall effectiveness.

“…Using the eddy viscosity calculated via a least square optimized approach [29], shear stress profiles, calculated based on LES data, from the three wake regions and different phases have been shown in Fig. 12 for the 1B2U case.…”

Section: Comparison Of Modelsmentioning

confidence: 99%

“…The algorithm not only improved the Reynolds stress prediction, but also improved the mean flow features for a few canonical cases [28]. GEP was applied for the first time on a turbomachinery component when an a priori study was conducted for high pressure turbines [29]. The EARSMs developed brought about a 32% reduction in error over the baseline case in an a priori sense.…”

Section: Introductionmentioning

confidence: 99%

Machine-Learnt Turbulence Closures for Low-Pressure Turbines With Unsteady Inflow Conditions

Akolekar

Sandberg

Hutchins

et al. 2019

The design of low-pressure turbines (LPTs) must account for the losses generated by the unsteady interaction with the upstream blade row. The estimation of such unsteady wake-induced losses requires the accurate prediction of the incoming wake dynamics and decay. Existing linear turbulence closures (stress–strain relationships), however, do not offer an accurate prediction of the wake mixing. Therefore, machine-learnt, nonlinear turbulence closures (models) have been developed for LPT flows with unsteady inflow conditions using a zonal-based model development approach, with an aim to enhance the wake mixing prediction for unsteady Reynolds-averaged Navier–Stokes calculations. High-fidelity time-averaged and phase-lock averaged data at a realistic isentropic Reynolds number and two reduced frequencies, i.e., with discrete incoming wakes and with wake “fogging,” have been used as reference data for a machine learning algorithm based on gene expression programing to develop models. Models developed via phase-lock averaged data were able to capture the effect of certain prominent physical phenomena in LPTs such as wake–wake interactions, whereas models based on the time-averaged data could not. Correlations with the flow physics lead to a set of models that can effectively enhance the wake mixing prediction across the entire LPT domain for both cases. Based on a newly developed error metric, the developed models have reduced the a priori error over the Boussinesq approximation on average by 45%. This study thus aids blade designers in selecting the appropriate nonlinear closures capable of mimicking the physical mechanisms responsible for loss generation.