The Three-Dimensional Steady Radial Expansion of a Viscous Gas from a Sonic Source into a Vacuum

• Published in: SIAM journal on applied mathematics Vol. 21; no. 3; pp. 393 - 406
• Main Authors: Bush, William B., Rosen, Robert
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01-11-1971
• Subjects: Boundary conditions; Continuum modeling; Flow distribution; Fluids; Infinity; Mathematical constants; Navier-Stokes equations; Reynolds number; Shear stress; Specific heat; Vacuum; Variables; Viscosity
• ISSN: 0036-1399; 1095-712X
• DOI: 10.1137/0121042

The three-dimensional steady radial expansion of a viscous, heat-conducting, compressible fluid from a spherical sonic source into a vacuum is analyzed using the Navier-Stokes equations as a basis. It is assumed that the model fluid is a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Limiting forms for the flow variable solutions are studied for the Reynolds number based on the sonic source conditions, 1/δ, going to infinity and the Newtonian parameter, ε, both fixed and going to zero. For the case of the viscosity-temperature exponent, ω,$1/2 \leqq \omega < 1$, it is shown that the velocity as well as the pressure approach zero as the radial distance goes to infinity. The formulations of the distinct regions that span the domain extending from the sonic source to the vacuum are presented. For δ → 0, ε fixed, there are three such regions; for δ → 0, ε → 0, there are six.