## 54

so that

In our example

so that

Therefore, the diameter of the cylinder required is 22 cm and the piston

### Thermal efficiency

Similarly crude approximations lor thermal efficiency of Stirling engines may be used. The most efficient engines approach values a little in excess of 00 per cent of the therniodynamically ideal Carnot value. Most arc nearer 50 per cent of the Carnot value and very little has to be overlooked or eliminated before the efficiency is down to 40 or even 30 per cent of the Carnot value. Design modifications to developed engines so as to cfleet economies or simplification in production should, therefore, always be carefully assessed for lhe ellect on efficiency.

Depending on one's philosophy as an optimist or as a realist, a probable value of 40 to 50 per cent of the Carnot efficiency may be assumed. Hie thermal efficiency of an engine may then be estimated simply as the ratio:

Of course now lite problem arises as to what values to use for the temperatures. As a general rule, for engines equipped with non-special high-temperature steels for the hot parts, an average temperature of 600 "C may be the maximum tolerable. For the cooler, in temperate /ones with adequate water cooling available, a temperature in the range 20-80°C may be achieved. Let us assume a value of 20 X. Then the engine efficiency may be estimated:

or even more approximately:

I his must be recognized as a rather high efficiency to be achieved only by

I Note llic use of absolute temperatures in computing the thermal efficiencies. Temperatures measured (by thermocouple or mercury in glass thermometers) in degrees Centigrade may he converted to the thermodynamic'scale temperatures, in Kelvin, by the addition «if 273, thus:

Similarly, temperatures measured in degrees 1-nhreuheit must he converted for thermodynamic calculations to the absolute tcmpcraluic degree.«; Runkinc by the addition of 460. Thus

Single degrees have exactly the same magnitude of temperature change in the Centigrade and Kelvin scales ami arc eipial to 1.8 degrees in the Fahrenheit and Rankine scales, the most careful attention in design to minimize losses. Most engines will operate initially at one half or less of the above efficiency but can often be developed to approach the 30 per cent value if high efficiency is ¡he prime interest.

It must he emphasized that such calculation methods are suitable only for crude design approximations. Nevertheless, they provide a ready means for 'baek-of-envelopc' estimations which may be useful in technical meetings or at the concept stages of new, previously unexplored, projects.

### Compression ratio

Whatever type of engine configuration adopted, it is difficult to increase the volume compression ratio much above the value VmilV' Vmin - 2.5. Attempts to increase this compression ratio will almost certainly result in there being inadequate void volume in the internal heat exchangers. This will result in either inadequate surface area for heat transfer or high pressure drops because of excessive aerodynamic friction pressure.

As a consequence of the low volume compression ratio the pressure ratio (PmaJPmia) in Stirling engines is very low compared with internal combustion engines. It rarely exceeds a value greater than 2. Furthei-morc, the rates of pressure change aie very low for the pressure characteristic is virtually sinusoidal in form. This has important consequences to engine design particularly with regard to bearings and shafts,

Consider now the pressure level in the engine. If the minimum cycle pressure is 0.1 MN/nr (I atmosphere) and the pressure compression ratio is 2, then the maximum pressure will be 0.2 MN/nr (2 atmospheres) and the mean pressure will be 0.15 MN/nr <1.5 atmospheres). If now tlr minimum pressure is elevated to IOMN/m? (100 atmospheres) the maximum pressure will, to a first approximation, increase to 20 MN/nr' (200 atmospheres) with a mean pressure of 15 MN/nr (150 atmospheres. The range of the pressure excursion (pm„Jpm{a) has increased from 0.2-0.1 0.1MN/m2 (2-1-1 atmosphere) to 20 10 10MN/nr (200 - 100- 100 atmospheres). This elevation of the mean pressure lev* I from 0.15 to 15 MN/nr (1.5 to 150 atmospheres) resulted in an increas e in the range of the pressure excursion from 0.1 to 10 MN/nr (.1 to 10 ) atmospheres). The work produced is directly proportional to the range i f the pressure excursion and. therefore, to the general pressure level in 111? engine. Increase in tlie pressure level will increase the engine outpit directly.

The work of the engine may be estimated from the mean pressure of the engine. However the cylinders must be designed to withstand th: maximum cylinder pressure. Given the pressure ratio (pnn„/pn,iJ ~ /, then, approximately, p = (i)p...,

## 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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