Two-dimensional and axisymmetric viscous flow in apertures

Abstract

The flow in a plane liquid jet from an aperture is obtained by direct simulation of the Navier–Stokes equations. The gas–liquid interface is tracked using the level set method. Flows are calculated for different Reynolds and Weber numbers. When We = ∞, the maximum value of the discharge coefficient appears around Re = O(100). The regions that are vulnerable to cavitation owing to the total stress are identified from calculations based on Navier–Stokes equations and viscous potential flow; the two calculations yield similar results for high Reynolds numbers. We prove that the classical potential flow solution does not give rise to a normal component of the rate of strain at the free streamline. Therefore, the normal component of the irrotational viscous stresses also vanishes and cannot change the shape of the free surface. The results of calculations of flows governed by the Navier–Stokes equations are close to those for viscous potential flow outside the vorticity layers at solid boundaries. The Navier–Stokes solutions for the axisymmetric aperture are also given for two values of Reynolds numbers. The results for axisymmetric and planar apertures are qualitatively similar, but the axisymmetric apertures have a lower discharge coefficient and less contraction.