The unsteady wake transition behind a wall-mounted large-depth-ratio prism

Abstract

The wake of a long rectangular wall-mounted prism is investigated at Reynolds numbers of $Re=250\unicode{x2013}1200$ by directly solving the Navier–Stokes equations. The aim of this study was to examine the unsteady transition mechanism in the wake of a large-depth-ratio (streamwise length to width) prism as well as to characterize the unsteady wake evolution at low Reynolds numbers. The results highlighted that increasing Reynolds number significantly altered the dominance of upwash and downwash flows in the time-averaged flow and changed the characteristics of coherent structures, including their size, dominant frequency and interaction with other structures in the flow. The wake is, therefore, categorized into three regimes within the transition process: steady regime at $Re \leq 625$ , regular unsteady regime at $625 < Re < 750$ and irregular unsteady regime at $Re \geq 750$ . Particularly, the wake started to exhibit unsteady features at $Re=625\unicode{x2013}650$ , which transitioned to an early irregular unsteady wake topology at $Re=750$ . At $Re \geq 675$ , horseshoe vortices transformed to vortex loops. There were hairpin-like structures formed on the upper and side faces of the long prism. The results further indicated that the transition to unsteadiness is attributed to separated leading-edge shear-layer instabilities and interactions of the shear layer with the horseshoe structures. The wake was more complex due to the interactions of multiple coherent structures in the flow, which resulted in a multiple-periodicity wake system. A skeleton model is proposed for a large-depth-ratio prism, to incorporate details of the unsteady flow features and specify various flow coherent structures at low Reynolds numbers.