Computational Fluid Dynamics is one of the most relied upon tools in the design and analysis of components in turbomachines. From the propulsion fan at the inlet, through the compressor and combustion sections, to the turbines at the outlet, CFD is used to perform fluid flow and heat transfer analyses to help designers extract the highest performance out of each component. In some cases, such as the design point performance of the axial compressor, current methods are capable of delivering good predictive accuracy. However, many areas require improved methods to give reliable predictions in order for the relevant design spaces to be further explored with confidence. This paper illustrates recent developments in CFD for turbomachinery which make use of machine learning techniques to augment prediction accuracy, speed up prediction times, analyse and manage uncertainty and reconcile simulations with available data. Such techniques facilitate faster and more robust searches of the design space, with or without the help of optimization methods, and enable innovative designs which keep pace with the demand for improved efficiency and sustainability as well as parts and asset operation cost reduction.

This work shows the application of Gene Expression Programming to augment RANS turbulence closures for flows though complex geometries. Specifically, an optimized internal cooling channel of a turbine blade, designed for additive manufacturing. One of the challenges in internal cooling design is the heat transfer accuracy of the RANS formulation in comparison to higher fidelity methods, which are still not used in design on account of their computational cost. However, high fidelity data can be extremely valuable for improving current lower fidelity models and this work shows the application of data-driven approaches to develop turbulence closures for an internally ribbed duct. Different approaches are compared and the results of the improved model are illustrated; first on the same geometry, and then for an unseen predictive case. The work shows the potential of using data-driven models for accurate heat transfer predictions even in non-conventional configurations and indicates the ability of closures learnt from complex flow cases to adapt successfully to unseen test cases.

Fluid topology optimisation has become a popular approach for optimisation of geometries in aero-thermal applications. However, one of the main limitations of current approaches considering turbulent flow is the fidelity of the Reynolds Averaged Navier–Stokes models employed. In response, this paper shows the development of the first data-driven fluid topology optimisation technique based on the continuous adjoint method. The technique first extracts data from a high fidelity simulation of a standard topology-optimised geometry. These data are fed through a symbolic regression-based machine learning algorithm called gene expression programming, to learn an explicit model for the anisotropy tensor. The novel aspect of the work is the derivation of the adjoint form of the generalised explicit algebraic stress model such that the developed turbulence model can be inserted directly into the primal and adjoint system of equations. This allows a second, data-driven optimisation to be performed. Finally, a high fidelity simulation of the resulting geometry is also conducted to allow comparison against the standard geometry. The method is first applied to the back-facing step to verify the approach and then to a 2D u-bend configuration. The data-driven optimisation was able to find geometries exhibiting significant reductions in pressure loss when compared with results from the standard optimisation.

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 wella prioriand simpler models which subsequently hold up ina posterioritesting 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.