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Two-Dimensional and Axisymmetric Viscous Flow in Apertures

By S. Dabiri1, W. A. Sirignano1 and D. D. Joseph2

1Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
2Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, MN 55455, USA

(Received 27 June 2007, Updated 27 March 2008)


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 level set method. Flows are calculated for different Reynolds and Weber numbers. When We = &infin the maximum value of the discharge coefficient appears around Re =O(100). The regions that are vulnerable to cavitation due to the total stress are identified from calculations based on Navier-Stokes equations and viscous potential flow; the two calculations yield similar results. 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, that 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.