Potential Flow Solution for Crossflow Impingement of a Slot Jet on a Circular Cylinder

Abstract

A closed-form solution has been obtained for the potential flow about a circular cylinder situated in an impinging slot jet. Among other results, the potential flow solution yields the free stream velocity for the boundary layer adjacent to the cylinder surface. A basic feature of the solution is the division of the flow field into subdomains, thereby making it possible to employ harmonic functions that are appropriate to each such subdomain. The boundary conditions on the free streamline and the conditions of continuity between the subdomains are satisfied by a combination of least squares and point matching constraints. Numerical evaluation of the solution was carried out for cylinder diameters greater or equal to the nozzle width and for a range of dimensionless separation distances between the nozzle and the impingement surface. Results are presented for the velocity and pressure distributions on the cylinder surface, for the position of the free streamline, and for the velocity gradients at the stagnation point. The latter serve as input information to the Nusselt number and skin friction expressions that are given by boundary layer theory. Comparisons were made with available experimental results for the pressure distribution, velocity gradient, and Nusselt number, and good agreement was found to prevail in the stagnation region.