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The Rao Method Optimum Nozzle Contour Program

Designs optimal supersonic nozzle contours


Calculates a supersonic exhaust nozzle contour that gives maximum thrust for its length.  Either the nozzle length or the nozzle area ratio may be specified.  As a special case, the method calculates an optimum nozzle contour for a fixed end point. The optimization method uses the calculus of variations for an ideal gas, constant gamma expansion. The optimization method has been expanded to treat irrotational flow with variable gamma. Conditions near the throat are found via a perturbation method to obtain the transonic flow solution.


Year - $500
Month - $30
Week - $20
Day - $15
Initiation Fee - $200
Export controlled
oncJustTrim.GIF (7441 bytes)
The program can also be used to calculate an optimum contour that is added at the end of an existing axisymetric contour. In this case the approach flow is determined by the existing contour and must be shock-free. A circular arc is attached tangent to the end of the existing contour, and the calculus of variations are used to design the wall downstream of the circular arc. Given a supersonic parallel inlet flow, the program can be used to calculate an optimum nozzle shape, with fixed length and area ratio. This capability is useful in the design of supersonic combustion ram (SCRAM) jet devices.
Constant or variable gamma perfect nozzles can be designed to yield a given design Mach number. Either transonic or parallel flow supersonic start conditions can be used. If a constant value of gamma is assumed, then perfect nozzles with prescribed area ratio can be designed.
All of the design options are provided for both planar and axisymetric nozzle geometry.