MAE 298 SEMINAR: Moment-of-Momentum Integral Equations for Wall-Bounded Turbulent Flows

Abstract: The use of integral equations to analyze and predict boundary layers dates back over a century to the pioneering work of von Karman, establishing the momentum thickness as a physically meaningful length scale related to the skin friction. For internal flows, the momentum integral equation undergirds the definition of the hydraulic diameter as the length scale relating wall shear stress to pressure drop. More generally, integral equations are fruitful grounds for the development of reduced order models in many branches of fluid mechanics. Integral methods for turbulent boundary layers based on Reynolds averaging underwent extensive development in the 1960s and remain useful for low-cost rapid predictions to this day. Among the approaches explored then, moment-of-momentum equations were introduced based on weighting the integrals based on powers of the wall-normal distance. The Fukagata-Iwamoto-Kasagi (FIK) relation introduced for internal flows in 2002 led to a resurgence of interest in moment-of-momentum integral equations as analysis tools (e.g., for flow control) for wall-bounded turbulent flows.

First, this presentation will introduce first-order moment of momentum integral relations for turbulent boundary layers based on Reynolds-averaged equations. Comparison and contrast to the second-order moment method of FIK will clarify the interpretability of the resulting equations. Applications to the analysis of boundary layers including transition to turbulence, high-speed effects, and favorable/adverse pressure gradients will be shown. Second, instantaneous moment-of-momentum equations form the basis of a novel framework for Turbulence-Resolving Integral Simulations (TRIS). The use of a dynamical equation for the instantaneous first-moment of momentum integral allows for a compact representation of the self-sustaining process in wall-bounded turbulence, so that relatively realistic large-scale turbulence structure can be simulated with computational efficiency on coarse two-dimensional grids.

Bio: Perry Johnson earned his doctorate in 2017 from Johns Hopkins University, where his work on velocity gradient dynamics in turbulence won the Corrsin-Kovasznay award. He was then a postdoctoral fellow at the Center for Turbulence Research at Stanford University for three years, working on various topics related to small-scale turbulence, multiphase and particle-laden flows, and boundary layers. He joined the Department of Mechanical and Aerospace Engineering at UC Irvine in 2020 as an assistant professor. He is a recipient of the NSF CAREER, AFOSR YIP and ONR YIP awards. His recent research on the energy cascade was featured in Physics Today, and he co-authored a review of multiscale velocity gradient dynamics in this year’s issue of Annual Review of Fluid Mechanics.