Data-driven scalar-flux model development with application to jet in cross flow

Abstract

The classical gradient-diffusion hypothesis has known deficiencies when applied to cooling applications. In this paper, the gene-expression programming (GEP) method, a machine learning approach, has been applied to develop scalar-flux models via symbolic regression. The scalar-flux, the unclosed term of the mean passive-scalar transport equation, is treated by considering the polynomial basis and scalar invariants available from computable Reynolds-averaged quantities. This method has been applied to develop and then assess a model for the test case of jet in crossflow. A high-fidelity database was first probed for insight into which of the candidate bases are the most suitable as modelling terms. The high dimensionality of the function space, spanned by the basis, was then reduced by basic statistical techniques. The resulting data-driven model is presented and tested for a range of different jet in crossflow cases. Compared with eddy-diffusivity models, the new model is shown to produce reliably more accurate results. This demonstrates that the current framework can be used for scalar-flux modelling in complex three-dimensional flows and has potential to provide generalized form closures with improved predictive accuracy for the same classes of flows they were trained on.