Simulation of stopping vortices in the flow past a mounted wedge

TL;DR

This paper numerically investigates the formation and dynamics of stopping vortices in flow past a wedge, analyzing how deceleration rate affects vortex strength and structure using high-order finite difference methods.

Contribution

It introduces a detailed numerical simulation of stopping vortex formation with validation against experiments, highlighting the impact of deceleration rate on vortex strength and structure.

Findings

Stopping vortex strength depends on deceleration rate.

Vorticity distribution follows a Gaussian profile.

Validated numerical results with experimental data.

Abstract

This work is concerned with the numerical investigation of the dynamics of stopping vortex formation in the uniform flow past a wedge mounted on a wall for channel Reynolds number $Re_c=1560$. The streamfunction-vorticity ($\psi$-$\omega$) formulation of the transient Navier-Stokes (N-S) equations have been utilized for simulating the flow and has been discretized using a fourth order spatially and second order temporally accurate compact finite difference method on a nonuniform Cartesian grid developed by the author. The results are validated by comparing the simulated results of the early evolution of the flow with the experimental visualization of a well-known laboratory experiment of \cite{pullin1980} and a grid-independence study. The development of the stopping vortex and its effect on the starting vortex are discussed in details. The stopping flow is analysed in the light of the time interval through which the inlet velocity of the flow is decelerated. The criterion for the development of a clean vortex is provided in terms of the impulse associated with the deceleration. Our study revealed that the strength of the stopping vortex depends upon the rapidity of deceleration. The vorticity distribution along the diameter of the core of the stopping vortex is seen to follow a Gaussian profile.