Vortex dynamics of accelerated flow past a mounted wedge

Abstract

This study is concerned with the simulation of a complex fluid flow problem involving flow past a wedge mounted on a wall for channel Reynolds numbers Rec = 1560, 6621, and 6873 in uniform and accelerated flow medium. The transient Navier–Stokes (N–S) equations governing the flow have been discretized using a recently developed second order spatially and temporally accurate compact finite difference method on a nonuniform Cartesian grid by the authors. Almost all the flow characteristics of a well-known laboratory experiment of Pullin and Perry [“Some flow visualization experiments on the starting vortex,” J. Fluid Mech. 97(2), 239–255 (1980)] have been captured by our numerical simulation, and we provide a qualitative and quantitative assessment of the same. Furthermore, the influence of the parameter m, controlling the intensity of acceleration, has been discussed in detail along with the intriguing consequence of non-dimensionalization of the N–S equations pertaining to such flows. The simulation of the flow across a time span significantly greater than the aforesaid lab experiment is the current study's major achievement. Meanwhile, a grid independence study performed in the process confirmed that our simulation is devoid of any under-resolution or numerical artifact. For the accelerated flow, the onset of shear layer instability leading to a more complicated flow toward transition to turbulence has also been aptly resolved. The quality of our simulation is validated by the close similarity of our simulation to the high Reynolds number experimental results of Lian and Huang [“Starting flow and structures of the starting vortex behind bluff bodies with sharp edges,” Exp. Fluids 8(1–2), 95–103 (1989)] for the accelerated flow across a typical flat plate. All three steps of vortex shedding, including the exceedingly intricate threefold structure, have been captured quite efficiently.