Numerical Solutions for Laminar Boundary Layer Behind Blast Waves.

Abstract

Abstract : Numerical solutions are obtained for plane (sigma = 0) and axisymmetric (sigma = 1) laminar boundary layers induced by blast waves of the form x sub s about t to the 2/(sigma bar + 3) power, where x sub s is the distance of the blast wave from the blast origin; t is time; sigma bar is 0, 1, or 2 for plane, cylindrical, and spherical waves, respectively. Explicit dependence on time is eliminated by a similarity transformation. The entire region between the shock (x = x sub s) and the blast origin (x = 0) is considered, except for a small region near x = 0 where the equations are singular. Numerical results are presented for ideal air with sigma bar = 0, sigma = 0; sigma bar = 1, sigma = 0; sigma bar = 1, sigma = 1 and sigma bar = 2, sigma = 1. Wall shear and heat transfer are found to increase with xi = 1-x/x sub s at a rate faster than that indicated by previous solutions for the flow directly behind the shock ( xi - square 1). The results are applicable in the laminar-boundary-layer region, P at infinity X sub s or = 0 (10-3-.001-.01 atm/ft, where P at infinity is ambient pressure. (Author)