Crypto-steady supersonic pressure-exchange: A simple analytical model

This paper is motivated by a long-range goal of developing a new class of turbo-machines, where fluid impellers, created through supersonic wave structures, replace mechanical impellers. This paper is an exploratory study to show how effectively supersonic wave structures can fulfil this goal, and to provide some fundamental insight as to the behavior. A comparison, at a fundamental level, of the spectrum of flow-induction devices from mechanical turbo-machinery to direct flow induction including steady-flow ejectors, wave rotors, and pressure-change devices is explored. While the authors have been studying various flow-induction devices intended to lead to practical solutions, the details of the flow interactions are obscured by the geometries and the complex interactions. This paper attempts to take a step backward and look at the simplest conceivable model that demonstrates the phenomena thought to be the key to a new technology. This model is a crypto-steady supersonic pressure-exchange process occurring behind a supersonic frictionless semi-infinite flat-plate having a pressure differential between both sides of the plate. It is found that very high compressor efficiencies and energy-transfer rates are possible, even with the presence of a supersonic-flow structure. Because of the high efficiencies, the analysis shows that there is potential for the development of a new generation of direct-flow induction devices far simpler and more compact than conventional turbomachinery, yet far more efficient than conventional ejectors and wave rotors. Fundamental information is provided which will facilitate exploiting supersonic pressure-exchanges, in practical crypto-steady flow-induction devices.