Achievement of Continuous Wall Curvature in Design of Two-Dimensional Symmetrical Supersonic Nozzles
Abstract
Auxiliary boundary conditions are derived to assure continuity of wall curvature in applying the method of characteristics to the design of two-dimensional symmetrical supersonic nozzles. An illustrative example is included. The method of characteristics was first applied by Prandtl and Busemann to the evaluation of supersonic flows in 1929 (reference 1). Since then, a number of expositions (for example, see references 2, 3, and 4) have described various applications of characteristics to the design of two-dimensional supersonic nozzles. The problem considered was to determine wall contours that would transform a uniform or source flow usually at Mach number of unity to a uniform shock-free flow at some higher Mach number. The wall contours so determined usually contain discontinuities in curvature which are tolerable for fixed geometry designs. In varia- ble Mach number flexible-walled nozzles, however, a discontinuity in curvature implies a multivalued stress at a point, which in turn can only occur if there is a restraining moment. The design of flexible- walled supersonic wind tunnels usually does not include provision for such a restraining moment and hence the wall fairs the curvature across the discontinuity. If the characteristic diagram for the tunnel requires a discontinuity, then imperfections in the actual flow must appear.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1952
- Accession Number
- ADA380564
Entities
People
- J. C. Evvard
- Lawrence R. Marcus
Organizations
- National Aeronautics and Space Administration