Turbulence-Resolving Integral Simulations for Wall-Bounded Flows

Abstract

The physical fidelity of turbulence models can benefit from a partial resolution of fluctuations, but doing so often comes with an increase in computational cost. To explore this trade-off in the context of wall-bounded flows, this paper introduces a framework for Turbulence-Resolving Integral Simulations (TRIS) with the goal of efficiently resolving the largest motions using a two-dimensional, three component representation of the flow defined by instantaneous wall-normal integrals of velocity and pressure. Self-sustaining turbulence with qualitatively realistic large-scale structures is demonstrated for TRIS on an open-channel (half-channel) flow configuration using moment-of-momentum integral equations derived from Navier-Stokes with relatively simple closure approximations. Evidence from Direct Numerical Simulations (DNS) suggests that TRIS can theoretically resolve 35-40% of the turbulent skin friction enhancement for friction Reynolds numbers between 180 and 5200, without a noticeable decrease or increase as a function of Reynolds number. The current implementation of TRIS can match this resolution while simulating one flow through time in ~1 minute on a single processor, even for very large Reynolds numbers. The framework facilitates a detailed apples-to-apples comparison of predicted statistics against data from DNS. Comparisons at friction Reynolds numbers of 395 and 590 show that TRIS generates a relatively accurate representation of the flow, while highlight discrepancies that demonstrate a need for improving the closure models. The present results for open-channel flow represent a proof of concept for TRIS as a new approach for wall-bounded turbulence modeling, motivating extension to more general flow configurations such as boundary layers on immersed objects.