Robust data-driven turbulence closures for improved heat transfer prediction in complex geometries

Data-driven turbulence closures have been used to successfully improve the prediction of first order effects in flows where the test case is similar to the training conditions. In this work, we examine the ability of such closures to improve second order effects, such as heat transfer for complex geometries. First, an upper bound for the available performance of the data-driven model is shown by inserting the Reynolds stresses from the high fidelity training data in a stable manner to a modified Reynolds-Averaged Navier–Stokes (RANS) model. Data-driven closures are then developed from this data set with a focus on robustness and the improvement in the heat transfer effects analysed. The geometries considered are four topology optimised square ducts. Each duct is optimised with varying weights of a multi-objective function to maximise heat transfer and minimise pressure losses. One duct is used in training and the remaining three are set aside for testing the developed closure. For the training case, it is found that simple data-driven closures for the Reynolds stresses alone, are capable of improving prediction of the velocity and temperature fields by 38.2% and 34.8% respectively even in complex geometries. These improvements are largely retained in the testing cases demonstrating the robust generalisation of the developed model for this class of flow.