In the ease of a prime mover, it is necessary first to establish the permissible temperature in the expansion space TR. This is dictated by the nature of the thermal source, and by the materials to be used for the expansion-space heat exchanger and expansion cylinder. At the chosen temperature, a vertical line is drawn through the three charts. Where this line intersects the sets of curves, and at an appropriate value of the dead-space ratio X. the corresponding optimum value of both phase angle at and swcpt-volumc ratio u may be determined from the scales. The value of the engine-power parameter (P/pn„xVr) niay be determined also. With 7't known, Tc may be estimated (it is about 300 K with a water-cooled engine), so that r can be calculated. With r, X, a and k thus established it is possible to proceed to the detailed design of the engine, utilizing the summary of design equations given earlier.

It cannot be over-emphasized that the predictions of Schmidt-cycle calculations are highly optimistic. Experience suggests that it is unwise to expect from a practical engine more than 30 to (SO per cent of the power and efficiency predicted by Schmidt-type analyses.


In the Schmidt theory no explicit account is taken of the physical characteristics of the working fluid, except its behaviour as a perfect gas (i.e. il obeys the characteristic gas equation PV—RT). However, the assumptions on which the theory is based imply the use of an idealized working fluid, having properties not found in nature. The assumption that there are no aerodynamic-friction losses could only be true if the working lluid were to have zero viscosity. Similarly, the assumptions of perfect regeneration and isothermal compression and expansion can only be attained if the working fluid were to have unreal values for specific heat and thermal conductivity.

In practice there appear to be only three working fluids of significant interest: air, helium, and hydrogen. Air is of interest because it is so freely available. Helium and hydrogen are of interest because their thermophysical characteristics are such as to permit high rales of heat transfer and flow to occur, with relatively low aerodynamic-flow losses. In terms of engine performance, hydrogen is better than helium, and is also

Flo. 5.15. Design ehnri Kit Stirlmp engines. The optimum combination of swcpt-volumc ratio k and phase ancle a (in rr radians) may he determined for Riven values of the dead-space ratio X and the tempcrnluic ratio r. Assuming Tr 300 K. and with the metallurgical limit Controlling ilie expansion space temperature I,-. draw n vertical line through T, Intersection ol this line with the selected value for X occurs at the optimum values for k and it. The appropriate value of the non-dimensional power parameter P/n V. is determined from the upper diagram. Practical engines may produce 0.3 to 0.4

Expansion space temperature <K)

very much cheaper, but is highly combustible in the presence of air or oxygen.

Engines of high specific output and high thermal efficiency, operating at high pressures and high speeds (i.e. greater than 2000 rev/min), must use hydrogen or helium as the working fluid, in order to achieve the rates of heat and mass transfer necessary, with tolerable flow losses. The sealing problems are very severe, however. Furthermore, the control systems needed to vary engine output are complicated, since they must incorporate reservoirs, valves, and, perhaps, a compressor to vary the pressure level, while conserving the working fluid. The cost of machines of this type is high, and applications are likely to be limited to relatively large engines, where the advantages of low noise (and pollution) levels justify increased cost, compared with internal-combustion engines. Cooling engines of high output (or those intended for refrigeration at cryogenic temperatures) must also use helium or hydrogen as the working fluid.

Engines using air as working fluid cannot achieve the high rates of heat and mass transfer found in hydrogen or helium engines. Such machines are. typically, large heavy engines of low specific output and low thermal efficiency. However, the working fluid can readily be replenished from atmospheric air. so that the sealing and materials problems are substantially eliminated, and the machines can be simple, cheap, and reliable. Air engines have such a poor performance that they offer 110 serious competition lo internal-combustion engines, in either automotive or general-purpose applications. There is, however, an urgent and increasing need for low-power (less than one horsepower) engines of high reliability and moderate efficiency, capable of operating unattended for long periods (in excess of one year) and utilizing fossil, or radioisotope, fuels. The engines are required lo drive electric-power generators for navigational, meteorological, and telecommunications purposes. Stirling-cycle air engines appear admirably suited for this purpose.

The comparative performance of Stirling engines with air. hydrogen, and helium is shown in Fig. 5.17. lhis is a reproduction of material presented by Meijer (1970a), based on advanced simulation calculations for a single-cylinder Stirling engine of 165.5 kW (225 hp). The figure shows how the engine's thermal efficiency is related to power density (in terms of kilowatt per litre of cylinder swept-volume) at different speeds and with three different working fluids (air. hydrogen, and helium). At high power densities and high speeds, hydrogen is appreciably better than helium.

Fio. 5.16. Design chart for Stirling-cycle cooling engines. Optimum values lor swcpl-voluine ratio ic and phase angle a may he determined tor given values of the dead-space ratio X and the expansion-space temperature I',. with T, - W0 K. by «hawing o vertical line on the chart thruugh TB The cooling capacity in terms of heal lifted in the expansion space,

Solar Stirling Engine Basics Explained

Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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