Direct numerical simulation of vortex-induced instability for a zero-pressure-gradient boundary layer.

Abstract

Vortex-induced instability caused by a free-stream vortical excitation is explored here quantitatively with the help of controlled computational results. First, the computed results are compared with experimental results in Lim etal. [Exp. Fluids 37, 47 (2004)10.1007/s00348-004-0783-5] for the purpose of validation of the three-dimensional (3D) computations. Thereafter, the computed results are explained using methods developed to study nonlinear and spatiotemporal aspects of receptivity and instability for incompressible flows. Here a zero-pressure-gradient (ZPG) boundary layer is perturbed by a constant strength vortex traveling at a fixed height, moving with constant speed, as in the cited experiment. The vortex is created by a translating and rotating circular cylinder in the experiment, with absolute control of the physical parameters. The sign of the translating vortex is fixed by the direction of rotation of the translating cylinder. A high accuracy computing method is employed to solve the 3D Navier-Stokes equation (NSE) for different translation speeds and signs of the free-stream vortex. A nonlinear disturbance enstrophy transport equation (DETE) for incompressible flows is used to explain the vortex-induced instability. This equation is exact and explains the instabilities, as governed by the NSE. The DETE approach has been successfully developed to explain two-dimensional (2D) vortex-induced instability in Sengupta etal. [Phys. Fluids 30, 054106 (2018)10.1063/1.5029560], to trace the linear and nonlinear stages of disturbance growth. Apart from quantification of vortex-induced instability, another major goal is to show how the disturbance evolves from an initial 2D to a 3D stage. While the sign of the translating vortex is important in creating the response field, we additionally highlight the distinct differences caused by increased translation speed and strength of the free-stream vortex on the overall instability. These explain creation of small-scale vortices via the instability of an equilibrium flow, even though the excitation is 2D only. For some cases, this causes 3D bypass transition. We also show a case which demonstrates strong unsteady separation with inflectional velocity profiles, yet the disturbance flow remains essentially 2D, which can be termed a bypass transition.