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.

Data-driven turbulence modelling is becoming common practice in the field of fluid mechanics. Complex machine learning methods are applied to large high fidelity data sets in an attempt to discover relationships between mean flow features and turbulence model parameters. However, a clear discrepancy is emerging between complex models that appear to fit the high fidelity data well a priori and simpler models which subsequently hold up in a posteriori testing through CFD simulations. With this in mind, a novel error quantification technique is proposed consisting of an upper and lower bound, against which data-driven turbulence models can be systematically assessed. At the lower bound is models that are linear in either the full set or a subset of the input features, where feature selection is used to determine the best model. Any machine learning technique must be able to improve on this performance for the extra complexity in training to be of practical use. The upper bound is found by the stable insertion of the high fidelity data for the Reynolds stresses into CFD simulation. Three machine learning methods, Gene Expression Programming, Deep Neural Networks and Gaussian Mixtures Models are presented and assessed on this error quantification technique. We further show that for the simple canonical cases often used to develop data-driven methods, lower bound linear models can provide very satisfactory accuracy and stability with limited scope for substantial improvement through more complex machine learning methods.

This paper shows the current research to move towards the full digital design of a gas turbine. In the last years new manufacturing technologies, such as additive manufacturing, become more common for gas turbine applications, allowing greater flexibility in the design space. There is a need to fully exploit this flexibility and to design and validate in a digital environment new solutions. This work shows how optimization methods, mainly based on topology optimization strategies, requires more accurate estimator for critical applications, such as high temperature components of high pressure stages. For this reason a comparison of recent Gene Expression Programming and Neural Networks in topology optimization are shown. In particular it is shown how a RANS estimator in fluid topology optimization is capable of obtaining predictions compatible to high fidelity DES.