Nonexistence of irrotational flow around solids with protruding corners

TL;DR

This paper investigates the non-existence of irrotational inviscid flows around solids with protruding corners, revealing fundamental limitations for various geometries and flow conditions.

Contribution

It extends classical non-existence results to multiple protruding corners and different flow regimes, including compressible and incompressible flows, highlighting new geometric constraints.

Findings

No compressible flow around certain two-corner bodies.

Bounded polygons cannot support small Mach number flows with finite velocity.

Irrotational flow around smooth protruding corners with non-zero velocity at infinity does not exist.

Abstract

We motivate and discuss several recent results on non-existence of irrotational inviscid flow around bounded solids that have two or more protruding corners, complementing classical results for the case of a single protruding corner. For a class of two-corner bodies including non-horizontal flat plates, compressible subsonic flows do not exist. Regarding three or more corners, bounded simple polygons do not admit compressible flows with arbitrarily small Mach number, and any incompressible flow has unbounded velocity at at least one corner. Finally, irrotational flow around smooth protruding corners with non-vanishing velocity at infinity does not exist. This can be considered vorticity generating by a slip-condition solid in absence of viscosity.