Discovering new scaling laws in turbulent boundary layers via multi-expression programming

Abstract

Flow turbulence modeling is an expensive computational operation that is often run with simulations using physical simplifications to reduce the cost. Large-eddy simulations (LES) of turbulent flow often make use of wall models in order to lower the computational cost of the simulation in the regions near solid walls, where typically the flow activity contains the smallest structures. Instead of resolving the boundary layer spatiotemporal scales, an algebraic expression for the fluid velocity field yields the wall shear stress, which is then used as a boundary condition to the outer flow, also known as wall modeling. Recently, novel wall model formulations are being developed using data-driven methods which exploit datasets generated with accurate wall-resolved large eddy simulation. However, it is still unclear what dimensional groups should be used to normalise such datasets when the wall shear stress is the target output, rather than a known quantity. The first goal of this dissertation is to explore such relevant groups across the dataset using machine learning applications as multi-expression genetic programming, a tool that allows to derive optimal expressions based on a population of initial candidates and a fitness function. The second goal is to be able to use it to find a correcting expression that yields the wall shear stress given other data and the defined groups.