Vorticity estimation utilizing the rotation of finite line segments

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.In a fluid flow field where velocities are measured or numerically calculated, the vorticity value at a point in the field is usually estimated by approximating partial derivatives of velocity with ratios of velocity differences and spatial differences. Based on the fundamental definition of rotation, this paper presents an alternate approach to estimate vorticity, by using the instantaneous relative angular velocity of finite line segments radiating from the point to adjacent points in the fluid. The number, length and placement of line segments are varied to find their effects on predicted vorticity values in four laminar flow fields with known vorticity. Equations are also derived for a configuration consisting of four independent finite line segments which has application to a square numerical velocity mesh and to instrumentation such as hot wire vorticity probes and vane vorticity meters. The results presented are relevant to both experimental and computational fluid mechanics.