Theory and calculations for an intrinsically irreversible acoustic prime mover using liquid sodium as primary working fluid

A theory describing a thermoacoustic heat engine using a liquid as primary working substance is developed and applied to the design of a high-power prime mover using liquid sodium. After an introduction that explains the physical principles of this type of engine in a heuristic way, expressions are derived for the acoustic variables and consequent energy flows in the engine. These expressions are easily understandable only in special limiting cases; to discuss practical applications, numerical computations are resorted to. It is found that a reasonably designed thermoacoustic prime mover using liquid sodium and operating between thermal reservoirs at 1000 and 400 K can generate about 60 W/sq cm of acoustic power at about one-third of Carnot's efficiency. The relative importance of various sources of inefficiency, such as viscosity, that are not essential to the production of power in this type of engine but are unavoidable in practice because of the thermophysical properties of real substances are also discussed.