Collision of a Vortex Pair with a Contaminated Free Surface
Abstract
Collision of a viscous vortex pair with a free, contaminated surface is studied numerically. The Froude number is assumed to be small so the surface remains flat. The full Navier-Stokes equations and a conservation equation for the surface contaminant are solved numerically by a finite difference method. The shear stress at the free surface is proportional to the contamination gradient, and simulations for several values of the proportionality constant (W) , as well as Reynolds numbers, have been performed. The evolution is also compared with full-slip and no-shp boundaries. As the vortices approach the surface, the upwelling between them pushes the contaminant outward, reducing the amount directly above the vortices, and leading to a clean region for low W, as well as for a full-slip boundaries. As W is increased the clean region becomes smaller, and eventually no clean region is formed. Except for very low W, the contaminant layer leads to the creation of secondary vortices, causing the original vortices to rebound in a similar way as vortices colliding with a no- slip boundary. For one case, the numerical results are compared with experimental measurements with satisfactory results. Computations of a vortex pair colliding obliquely with a contaminated surface and head-on collision of axisymmetric vortex rings are also presented.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1990
- Accession Number
- ADA251101
Entities
People
- Amir Hirsa
- Gretar Tryggvason
- Javad Abdollahi-alibeik
- William W. Willmarth
Organizations
- University of Michigan