A Machine Learning Approach to Improve Turbulence Modelling from DNS Data Using Neural Networks

Abstract

In this paper, we investigate the feasibility of using DNS data and machine learning algorithms to assist RANS turbulence model development. High-fidelity DNS data are generated with the incompressible Navier–Stokes solver implemented in the spectral/hp element software framework Nektar++. Two test cases are considered: a turbulent channel flow and a stationary serpentine passage, representative of internal turbo-machinery cooling flow. The Python framework TensorFlow is chosen to train neural networks in order to address the known limitations of the Boussinesq approximation and a clustering based on flow features is run upfront to enable training on selected areas. The resulting models are implemented in the Rolls-Royce solver HYDRA and a posteriori predictions of velocity field and wall shear stress are compared to baseline RANS. The paper presents the fundamental elements of procedure applied, including a brief description of the tools and methods and improvements achieved.

Machine Learning Methods in CFD for Turbomachinery: A Review

“…ANNs provide the option of greater flexibility and are potentially able to perform wider searches of the parameter space. Frey et al [26] built on the work of Ling et al [27] and used relatively shallow neural networks trained on DNS data to improve the eddy viscosity term in the Boussinesq approximation. They applied this approach to a serpentine channel representative of internal cooling channels in turbine blades.…”

Error Quantification for the Assessment of Data-Driven Turbulence Models

“…It is apparent that if the opt n coefficients, extracted directly from the high fidelity data set can lead to oscillatory CFD simulations without some prior manipulation, then data-driven models learned from this data are at risk of exhibiting the same behaviour. Many works condition the data on some metric and train models only on selected regions in the flow (Frey Marioni et al 2021;Weatheritt et al 2017) with the effect of removing regions in which large magnitude opt n coefficients are present. Even in the case of non oscillatory solutions, the error metric used to find optimal models can be heavily skewed by large magnitude values and favour models which fit them better over the rest of the domain.…”

Development and Validation of a Machine Learned Turbulence Model

“…The studies that focused on RANS model augmentation can be further subdivided into three categories: (i) direct estimation of the turbulent eddy viscosity ( 𝑇 ) for linear models [47][48][49][50][51][52][53][54][55], (ii) correction terms for the linear models [56][57][58][59][60][61][62][63], and (iii) enhancement of the accuracy of the turbulence transport equations used in linear models [64][65][66][67][68]. Studies in category (i) have been applied for both incompressible [47][48][49][50] and compressible flows [51][52][53][54]. They have either used neural networks with two to six hidden layers with 20 to 40 neurons per layer or random forest models with three to four hidden layers with 64 to 128 trees.…”

“…Some studies performed optimization of the network size or the training parameters. For example, Marioni et al [47] used a random search to optimize hyperparameters, whereas studies [48] and [50] performed a parametric study. These studies mostly used five to twelve input features based on magnitude of rate-of-strain, vorticity magnitude, wall distance based Re, pressure gradients, velocity direction, and entropy for compressible flow.…”

“…For this purpose, Zhu et al [51,52] developed separate models for the inner layer, wake layer and the far-field. Marioni et al [47] used clustering of data to put equal importance to different flow regimes. Studies [51][52][53] introduced averaging of 𝜈 𝑡 over neighboring cells to enhance numerical stability.…”