## 4 Theoretical Analysis Of Stirling Engi

introduction

Tiieouhticai. analyses of Stirling engines have been developed with varying degrees of sophistication.

The most simple analysis is that for the ideal Stirling cycle, where the thermodynamic cycle comprises two isothermal and two constant-volume regenerative processes. However this involves such gross idealization of the process occurring in an actual Stirling engine as to be suitable only for the most elementary, preliminary design calculations.

A more realistic analysis was devised by Gustav Schmidt (1871). This has become the classical analysis of the cycle and is believed to give a more reasonable approximation of engine performance. Nevertheless, the analysis remains very highly idealized, so that in practice the indicated performance of an engine will likely be no better than 60 per cent of the predicted Schmidt cycle performance and. often, a good ileal less.

The reason for this is, primarily, that the Schmidt cycle presumes the processes of compression and expansion to be isothermal. In practical engines running at 1000 or more revolutions per minute, this is not the case. The processes of compression and expansion in the engine cylinders are more nearly adiabatic than isothermal. This innocent sounding difference wreaks a profound redistribution of the cyclic mass variation of the working fluid and, consequently, on the performance of the engine.

Following the introduction of the Schmidt analysis in 1871, nearly a century was to elapse before Finkelstein (1960a) devised a generalized analysis permitting the theoretical investigation of engines with processes of compression and expansion other than isothermal. The Schmidt cycle with isothermal compression and expansion processes then became a special case of the generalized Finkelstein analysis. Another special ease is the cycle with adiabatic processes in the engine cylinder, called here the Finkelstein adiabatic cycle. With the generalized theory other cases of limited heat transfer in the engine cylinders may also be considered.

Further developments of the adiabatic model to account for secondary effects, primarily aerodynamic-flow losses, and thermal effects are possible. These make the adiabatic model the preferred level of analysis for routine performance predictions. The analysis is sufficiently complex to require the use of digital computing machines, but only to a moderate extent, involving little computer time and reasonable expenditures.

k i- . i I .i « ii r • i program now installed on a commercial computer network and available for general use on payment of a royalty fee. Later in the closing years of the 1970s substantial efforts were devoted to Stirling engine simulation by other workers and a variety of advanced engine simulation programs have become available.

A comprehensive discussion of the generalized I inkelstein analysis and the subsequent nodal analysis programs is beyond die scope of this present work. Therefore in this chapter we shall attempt;

(a) to summarize equations fot the ideal Stirling cycle,

(b) to present in reasonably comprehensive detail the Schmidt isothermal analysis,

(c) to outline the I inkelstein adiabatic analysis,

(d) to compare and comment briefly on the advanced level analyses for Stirling engines making reference to the source documents for those who wish to investigate further.

idp.ai stirling cyc lp

Equations for analysis of the ideal Stirling cycle are summarized below. Again the reader is advised that the gross idealization of the Stirling cycle precludes the use of these equations for anything other than the most elementary investigations.

The principal deficiency of the ideal cycle is that il assumes all the working fluid is. instantaneously, at the same condition in either the compression or expansion spaces. This implies that the internal void volume of the regenerator is zero and requires the pistons, or other reciprocating elements, to move with a discontinuous motion. The processes of expansion and compression are assumed to be isothermal and the cITcctsof imperfect regeneration, and aerodynamic pressure drops are not considered.

A more complete treatment of the ideal cycle, contributed by Rallis, is reproduced in Chapter 2. With reference to l ig. 2.3 and the discussion of the ideal cycle given in Chapter 2 the equations for the ideal cycle may be summarized as follows:

Required daia

(i) Some reference temperature and pressure, or volume, say, conditions, at state I.

(ii) Temperature ratio t= Tmin/Tmox.

(iii) Volume ratio r= VmnJVm{n.

For unit mass of working fluid, assumed to be a perfect gas. then

= IJ'I' In from it,.« i'l,om<»l.>rioli/> .iniiilin.i

Process parameters

(a) Isothermal compression process (1—2).

In this process, heat is abstracted from the working fluid and rejected from the cycle at the minimum cycle temperature. Work is clone on the working lluid equal in magnitude to the heat rejected from the cycle. There is no change in internal energy, and there is a decrease in entropy.

## 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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