MATHEMATICAL THEORY OF STEADY COMPRESSIBLE SWIRL FLOWS WITH CLOSED STREAMLINES AT HIGH REYNOLDS NUMBERS,
Abstract
The paper presents a theory of axi-symmetric steady compressible swirl flows in which the stream lines are closed, under the assumption that the Reynolds number is large. In principle the flow field is determined by the equations for an inviscid flow; but, if the stream lines are closed, additional conditions arise which are primarily determined by the dissipative terms. They arise by purely mathematical arguments as the solvability conditions for the approximation of the next order in a development with respect to the reciprocal of the Reynolds number. These conditions can be interpreted in physical terms. Various transformations are carried out, to prepare the equations for numerical work. The mathematical structure of the operators occurring in the solvability conditions and its relation to the parameters which are suggested by physical considerations is studied in detail. The solution for the potential vortex is compatible with this approach only if the viscosity coefficient is constant with the Prandtl number is 1/2. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1967
- Accession Number
- AD0659743
Entities
People
- David E. Greene
- Karl G. Guderley
Organizations
- Air Force Research Laboratory