Mean free path effects in the shock-implosion problem

• Published in: Physics of fluids (1994) 2009-02, Vol.21 (2), p.026101-026101-8
• Main Authors: Goldsworthy, M. J., Pullin, D. I.
• Format: Article
• Language: English
• Subjects: Compressible flows; shock and detonation phenomena; Exact sciences and technology; Fluid dynamics; Free molecular flows; Fundamental areas of phenomenology (including applications); Physics; Rarefied gas dynamics; Shock-wave interactions and shock effects
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3075952

The effects of finite Knudsen number in the problem of a cylindrically imploding shock wave in a monatomic gas are investigated. Numerical solutions of the flow field are obtained with initial conditions in the ranges 1.25 ≤ M 0 ≤ 5 and 0.005 ≤ Kn 0 ≤ 0.1 using the direct simulation Monte Carlo method. Results show that as Kn 0 decreases and M 0 increases, the maximum implosion temperature scales increasingly well with the similarity exponent predicted in the Guderley solution for an imploding strong shock in the Euler limit. When the radius of curvature is large, the cylindrical shock thickness is found to be almost identical to the thickness of a planar shock for a given shock Mach number. For small radii of curvature, the cylindrical shock was found to be thicker than the corresponding planar shock.