Introduction H YDROCARBON-FUELED scramjet propulsion appears to offer promising performance at hypersonic speeds. For example, Fig. 1 shows performance, measured by thrust coefficient and specific impulse, as functions of nozzle efficiency based on one-dimensional calculations provided in Ref. 1. However, up to the present time, the potential performance indicated by these predictions has not been demonstrated experimentally. Perhaps the sensitivity to nozzle efficiency provides a clue to the difficulty in actually achieving high propulsive efficiency. Possible sources of loss in nozzle efficiency include errors in nozzle design or manufacture, nonuniform entrance flow, shear in nonuniform streams, wall friction, separation, nonequilibrium flow, incomplete expansion, and shock waves. Some of these potential losses, such as errors in design or manufacture, can be avoided or minimized. The question addressed in this note is, to what extent might nonuniform flow entering a scramjet nozzle result in unavoidable loss of exit momentum? To answer this question, the following procedure has been adopted: 1) Specify a form of inlet nonuniformity. In this investigation, a so-called fictitious or average uniform axial entrance flow is subdivided into two adjacent streams having the same pressure, the same total momentum, and the same total energy as the average uniform stream, but different initial Mach numbers. 2) Approximate the nozzle flow by a model that will exhibit the effects of the entrance nonuniformity isolated from other flow parameters. To this end, the two streams, depicted in Fig. 2, are assumed to be nonmixing and inviscid. Then the unrecoverable loss will be measured by the difference between the exit momentum achieved when the average stream is expanded isentropically to exit pressure and the total combined exit momenta of the two adjacent streams when they are isentropically expanded to the same exit pressure. 3) Calculate the exit momenta by one-dimensional isentropic ideal gas formulas. This approximation would be inappropriate for the design of a scramjet nozzle, or the accurate analysis of the nozzle flow, but by treating each of the streams on the same approximate basis, the unrecoverable loss resulting from the specified entrance nonuniformity can be estimated as a function of chosen inlet parameters. Effects of nonuniform flow in convergent-divergent nozzles have been examined, using a one-dimensional model. The one-dimensional predictions show surprisingly good agreement with a three-dimensional analysis and with wind-tunnel tests. Decher also estimated the effects of flow nonuniformities on nozzle exit momentum for convergent-divergent nozzles. Initial conditions are prescribed in the subsonic part of the flow, and the analysis is linearized by assuming relatively small variations in initial profiles. In Ref. 4, the theory is applied to nozzle performance calculations and includes mixing effects.
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Nov 1, 2021
Xianwu Lin + 1
Open Access