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This paper presents the development of accurate turbulence closures for low-pressure turbine (LPT) wake mixing prediction by integrating a machine-learning approach based on gene expression programming (GEP), with Reynolds-averaged Navier-Stokes (RANS)-based computational fluid dynamics (CFD). In order to further improve the performance and robustness of GEP-based data-driven closures, the fitness of models is evaluated by running RANS calculations in an integrated way, instead of an algebraic function. Using a canonical turbine wake with inlet conditions prescribed based on high-fidelity data of the T106A cascade, we demonstrate that the "CFD-driven"machine-learning approach produces physically correct non-linear turbulence closures, i.e., predict the right down-stream wake development and maintain an accurate peak wake loss throughout the domain. We then extend our analysis to full turbine blade cases and show that the model development is sensitive to the training region due to the presence of deterministic unsteadiness in the near-wake. Models developed including the near-wake have artificially large diffusion coefficients to over-compensate for the vortex shedding steady RANS cannot capture. In contrast, excluding the near-wake in the model development produces the correct physical model behavior, but predictive accuracy in the near-wake remains unsatisfactory. This can be remedied by using the physically consistent models in unsteady RANS. Overall, the "CFD-driven"models were found to be robust and capture the correct physical wake mixing behavior across different LPT operating conditions and airfoils such as T106C and PakB. © 2021 by ASME.

Department of Mechanical Engineering

World University root node

Journal of Turbomachinery

Integration of Machine Learning and Computational Fluid Dynamics to Develop Turbulence Models for Improved Low-Pressure Turbine Wake Mixing Prediction

Existing Reynolds Averaged Navier–Stokes-based transition models do not accurately predict separation induced transition for low pressure turbines. Therefore, in this paper, a novel framework based on computational fluids dynamics (CFD) driven machine learning coupled with multi-expression and multi-objective optimization is explored to develop models which can improve the transition prediction for the T106A low pressure turbine at an isentropic exit Reynolds number of Re2is = 100, 000. Model formulations are proposed for the transfer and laminar eddy viscosity terms of the laminar kinetic energy transition model using seven non-dimensional pi groups. The multi-objective optimization approach makes use of cost functions based on the suction-side wall-shear stress and the pressure coefficient. A family of solutions is thus developed, whose performance is assessed using Pareto analysis and in terms of physical characteristics of separated-flow transition. Two models are found which bring the wall-shear stress profile in the separated region at least two times closer to the reference high-fidelity data than the baseline transition model. As these models are able to accurately predict the flow coming off the blade trailing edge, they are also able to significantly enhance the wake-mixing prediction over the baseline model. This is the first known study which makes use of ‘CFD-driven’ machine learning to enhance the transition prediction for a non-canonical flow. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Energies

Transition Modeling for Low Pressure Turbines Using Computational Fluid Dynamics Driven Machine Learning

This paper presents an assessment of machine-learned turbulence closures, trained for improving wake-mixing prediction, in the context of LPT flows. To this end, a three-dimensional cascade of industrial relevance, representative of modern LPT bladings, was analyzed, using a state-of-the-art RANS approach, over a wide range of Reynolds numbers. To ensure that the wake originates from correctly reproduced blade boundary-layers, preliminary analyses were carried out to check for the impact of transition closures, and the best-performing numerical setup was identified. Two different machine-learned closures were considered. They were applied in a prescribed region downstream of the blade trailing edge, excluding the endwall boundary layers. A sensitivity analysis to the distance from the trailing edge at which they are activated is presented in order to assess their applicability to the whole wake affected portion of the computational domain and outside the training region. It is shown how the best-performing closure can provide results in very good agreement with the experimental data in terms of wake loss profiles, with substantial improvements relative to traditional turbulence models. The discussed analysis also provides guidelines for defining an automated zonal application of turbulence closures trained for wake-mixing predictions. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Assessment of Machine-Learned Turbulence Models Trained for Improved Wake-Mixing in Low-Pressure Turbine Flows

Australasian Fluid Mechanics Conference

CFD-Based Boundary Layer Prediction of Axisymmetric Bodies of Revolution

This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method Weatheritt and Sandberg (2016) [8], but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model. © 2020 Elsevier Inc.

Journal of Computational Physics

RANS turbulence model development using CFD-driven machine learning

APS Division of Fluid Dynamics Meeting Abstracts, G17.

CFD-ready Turbulence Models from Gene Expression Programming: Concepts

University of Melbourne

Turbulence Model Development and Implementation for Low Pressure Turbines Using a Machine Learning Approach

International Society of Air Breathing Engines

Turbulence Model Development for Low \&amp; High Pressure Turbines Using a Machine Learning Approach

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. Copyright © 2019 by ASME

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

Non-linear 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 exit Mach number 0.4 and 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 kv2w 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 geneexpression programming (GEP) based machine-learning technique was applied to the high-fidelity DNS data to train non-linear explicit algebraic Reynolds stress models (EARSM). In particular, the GEP algorithm was tasked to minimize the weighted difference between the DNS and RANS anisotropy tensors, using different training regions. The trained models were first assessed in an a priori sense (without running any CFD) 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, TKE production, wake-loss profiles and wake maturity, across all cases, in particular those trained on just the wake region. © 2018 ASME.