SHOCK-BOUNDED, SELF-SIMILAR FLOWS WITH VOLUMETRIC MASS, MOMENTUM, AND ENERGY ADDITION
Abstract
Self-similar flows with volumetric mass, momentum, and energy addition are investigated. Unsteady flows bounded by shock waves and equivalent steady hypersonic flows over slender bodies are considered, and the form of the shock shape and of the volumetric sources for self-similar motion are noted. For unsteady flows, it is found that the shock shape mu t have the form R sub O=ct to the m power (where R sub O = shock ordinate, t = time) and that the mass, momentum, and energ sources must be expressible in the fom of a funtion of r/R sub O times t to the -1 power, t to the m-2 power, and t to the 2m-3 power, respectively (where r is the lateral ordinate). If the sources introduce only sll perturbations in an otherwise self-similar flow, solutions can be obtained for sources expressible as a function of r/R sub O times t to arbitrary constant exponents. Thus, the small perturbation case is less restrictive with regard to the functional form of the sources. For equivalent steady hypersonic flows, the streamwise distance, x, replaces t in the above expressions. Numerical perturbation solutions are obtained for the effect of a uniform transverse magnetic field on piston-driven flows and blast waves. The firstorder effect of body-thickness raio on the hypersonic flow (in the limit of infinite Mach number) over slender power law bodies is aso reated. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 28, 1962
- Accession Number
- AD0288290
Entities
People
- Harold Mirels
- James F. Mullen