Machine learning approaches to model turbulent mixing in film cooling flows
Keywords: Mechanical Engineering.

Film cooling is a critical technology that allows gas turbine blades to operate in extremely high temperature environments. It consists of diverting cooler air from upstream engine components and ejecting that air through holes on the outer blade surface. More efficient film cooling systems would increase lifespan of the blades and lead to more powerful and efficient engines. The design process around such complex industrial flows involves numerical simulations in which flow turbulence is an important factor to consider. Since directly resolving turbulent motions is prohibitively expensive, virtually all design work uses low fidelity simulations, the so-called Reynolds-averaged Navier-Stokes (RANS) solvers, which depend heavily on turbulence models. In the RANS context, the mean temperature calculations rely on a model for the turbulent scalar flux, which captures the role of turbulence in mixing the cooler and hotter gas streams. Widely used models fail in many film cooling flows, and in the present work we leverage machine learning techniques to generate improved models. We mainly consider the jet in crossflow, a canonical fluid mechanics geometry that captures the basic physics of film cooling. The first step is to produce high fidelity simulations that resolve all of the turbulence and thus can be used as data. Next, the simulations were analyzed in order to better understand failures of the simple, widely used models. We discuss the phenomenon of counter gradient transport, whereby the turbulent scalar flux acts in the opposite direction that one would expect intuitively. The present work goes beyond previous research to explain physical reasons for this counter gradient transport in jets in crossflow. Armed with the high fidelity data and some understanding of the failures of traditional models, we proceeded to develop machine learning models for the turbulent scalar flux. Machine learning more generally, and deep learning in particular, were recently responsible for unprecedented advances in long standing problems in computer science when troves of data became available. Our hope was to reproduce this success in the field of turbulence modeling. First, we develop a simple model, based on the isotropic gradient diffusion hypothesis; the model coefficient, the turbulent diffusivity field, is prescribed by a random forest algorithm. We see encouraging results, particularly near the wall, because the model is able to recognize regions of reduced turbulent transport. Second, we propose a more complex model, that uses a generalized gradient diffusion hypothesis; the turbulent diffusivity matrix field is prescribed by a deep neural network based on a tensor basis expansion. This model form is generally more accurate and robust than our earlier random forest model and can produce reasonably accurate mean scalar concentrations. All our modeling efforts are shaped by numerical stability considerations and strictly enforce rotational invariance, so the resulting models are much more than just blind application of machine learning tools. Finally, the thesis discusses the issues of interpretation and generalization of machine-learned models; the frameworks discussed there can be expanded to other physical applications of machine learning