The design and testing of supersonic nozzles

Abstract

The theory of the flow through a throat near sonic velocity is developed, and is followed by a discussion of the conventional method of designing supersonic nozzles using the method of characteristics. A method of improving the Mach number distribution of the nozzle using the experimental results is developed. The nozzles designed were tested in a 3-in. square wind tunnel in which the Mach number distribution was obtained by shaping the top wall of the working-section. The Mach number distribution along the bottom wall was determined from the pressures measured by a series of static pressure holes along the wall. Considerable difficulty was found in improving the distribution; this was considered to be due to the discontinuity in curvature at the point of inflexion and the influence on the boundary layer of the sudden relaxation of the pressure gradient along the wall. An alternative method of design was developed which avoided this discontinuity in curvature, and considerably better results were obtained when attempts were made to improve the experimental Mach number distribution. The flow through the throat of the liners was determined experimentally and compared with the theory. The agreement was good on the whole, although there were differences in the subsonic entry region because the bottom wall only became flat a short distance before the throat. In addition, tests were made which showed that the assumption of two-dimensional flow through the throat was justified. The method developed to improve the distribution in the nozzle was extended to derive liner shapes for Mach numbers differing by 0.10 from the design Mach number. It was found that changes of this order could be made fairly successfully but further modification was necessary to reach the standard required for tunnel use. The necessity for a smooth and accurately constructed liner surface is stressed. The limitations of the methods used for designing supersonic nozzles are discussed and several problems are mentioned which it is thought will need further consideration.