Unsteady Subsonic/Supersonic Flow Simulations in 3D Unstructured Grids over an Acoustic Cavity

Abstract

In this study, the unsteady Reynolds-averaged Navier–Stokes (URANS) equations are employed in conjunction with the Menter Shear Stress Transport (SST)-Scale-Adaptive Simulation (SAS) turbulence model in compressible flow, with an unstructured mesh and complex geometry. While other scale-resolving approaches in space and time, such as direct numerical simulation (DNS) and large-eddy simulation (LES), supply more comprehensive information about the turbulent energy spectrum of the fluctuating component of the flow, they imply computationally intensive situations, usually performed over structured meshes and relatively simple geometries. In contrast, the SAS approach is designed according to “physically” prescribed length scales of the flow. More precisely, it operates by locally comparing the length scale of the modeled turbulence to the von Karman length scale (which depends on the local first- and second fluid velocity derivatives). This length-scale ratio allows the flow to dynamically adjust the local eddy viscosity in order to better capture the large-scale motions (LSMs) in unsteady regions of URANS simulations. While SAS may be constrained to model only low flow frequencies or wavenumbers (i.e., LSM), its versatility and low computational cost make it attractive for obtaining a quick first insight of the flow physics, particularly in those situations dominated by strong flow unsteadiness. The selected numerical application is the well-known M219 three-dimensional rectangular acoustic cavity from the literature at two different free-stream Mach numbers, M∞ (0.85 and 1.35) and a length-to-depth ratio of 5:1. Thus, we consider the “deep configuration” in experiments by Henshaw. The SST-SAS model demonstrates a satisfactory compromise between simplicity, accuracy, and flow physics description.