New insights to the potential flows around axisymmetric bodies

by Mr. Idan Wallershtein

Bgu

at Astrophysics and Cosmology Seminar

Wed, 21 Oct 2020, 11:10
Remote Zoom Seminar

Abstract

We derive new analytical and semi-analytical results for potential flows around axisymmetric bodies. Starting with the well-known problem of an incompressible potential flow around a 2D disk or a 3D sphere, we study generalizations involving an arbitrary number of dimensions, non-spherical bodies, compressible effects, and the transition to the supersonic regime.

Inviscid, incompressible flows are analytically known only around a handful of simple bodies, in particular hyperspheres. We expand the list of flows for which the potential and the body shape can be simultaneously expressed as finite combinations of elementary functions. Compressibility effects are examined for polytropic fluids around d-dimensional hyperspheres by generalizing the Janzen-Rayleigh expansion of the potential in the incident Mach number squared, \mathcal{M}_\infty^2, which was until now limited to \mathcal{M}^4_\infty order in 3D. For instance, we show that the flow in front of an arbitrary prolate spheroid approximately scales onto a universal function. Finally, we present a new attack on the transonic controversy: can shock-free potential flows exceed the critical Mach number \mathcal{M}_{cr}, i.e. reach supersonic velocities anywhere on the body.

Created on 17-10-2020 by Zitrin, Adi (zitrin)
Updaded on 17-10-2020 by Zitrin, Adi (zitrin)