Numerical solutions for unsteady laminar boundary layers behind blast waves

Abstract

Numerical solutions are obtained for plane (σ=0) and axisymmetric (σ=1) laminar boundary layers induced by blast waves of the form xs∼t2/(σ+3), where xs is the distance of the blast wave from the blast origin; t is time; and σ̄ 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=xs) 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 σ̄=0, σ=0; σ̄=1, σ=0; σ̄=1, σ=1; and ⩽=2, σ=1. Wall shear and heat transfer are found to increase with ξ=1 −x/xs at a rate faster than that indicated by previous solutions for the flow directly behind the shock (ξ2<<1). The results are applicable in the laminar boundary layer region, p∞xs?O (10−1) atm‐cm, where p∞ is ambient pressure.