On a separation criterion for symmetric elliptic bluff body flows

TL;DR

This paper introduces an analytical criterion to determine the flow separation point for elliptic bluff bodies, enabling precise calculation of the separation Reynolds number for flow past a circular cylinder.

Contribution

It presents a novel analytical criterion based on wall normal velocity variation, providing an exact method to compute the separation Reynolds number in flow past elliptic cylinders.

Findings

Derived a new separation criterion for elliptic bluff body flows.

Successfully calculated the separation Reynolds number for a circular cylinder.

Validated the criterion with computational Navier-Stokes solutions.

Abstract

A new analytical criterion that captures the onset of separation of flow past elliptic cylinders is derived by considering the variation of the wall normal velocity in Reynolds number parameter space. It is shown that this criterion can be used to calculate the separation Reynolds number Re_s for the classical problem of flow past a circular cylinder, a contentious and unresolved issue till date. The two dimensional Navier-Stokes equations are solved computationally and an exact value of Re_s is obtained by applying the aforementioned criterion.