## 3 0 I

lio. 5. I I Work diagrams lor engines having Ihc optimum combiunlion of design parameters. The figure shows work diagrams foi engines having optimum combinations of the design parameters a, A r, and A, ;is determined hy rcicroncc to the three-dimensional representation shown in l-ig. 5.13. In all eases, she diagram at left is for the expansion space, (he centre diagram lot (he compression space, and the diagram at right is for the total working-spate, l-'ig. 5.14(a) shows work diagrams for the cycle, optimized using the power parameter /',.„„„, with «,,,„ ('-45 n radians, k„p, 2A>, t 0.3, and X = 1.0. as determined in Fig. 5.13(a). Fig. 5.14(b) shows work diagrams for the cycle, optimized using the power parameter JY(pailI*V'r), with ^, = 0.54 tt radians, = 0.74. r <1.3, and X=I.O as determined in Fig. 5.13(b).t Fig. 5.14(c) shows work diagrams fur a cycle having a combination similar to l-ig. 5.14(h), but with the dead space reduced to Ihc same overall value as in l-ig. 5.14(a) (same size of regenerator and heat exchangers). The net cycle Output of this case is superior to case <rt). hy an even greater margin than case (b>.

f For purposes of comparison, all the work diagrams arc drawn with pressures as fractions of the maximum pressure, and with the same maximum value of (he lot.il working-space, r-l.^.i. 11.» --------- .»:„.._ i... » -1.1... . . . «. • .

The two machines represented in Figs. 5.14(a) and 5.14(b) arc comparable therefore in terms of size and weight. The maximum pressure and the maximum total enclosed volume are the same, although the dead volume in one machine is nearly twice as great as in the other. Despite this, the net work output of the machine in Fig. 5.14(b) is 1.38 times that of the machine in Fig. 5.14(a). When the dead volume of Fig. 5.14(b) is reduced to an amount comparable with that of Fig. 5.14(a) (as in machine represented by Fig. 5.14(c)) the ratio of net work output increases to 2.24 in favour of the machine in Fig. 5 14(c). This example is a convincing justification for optimization on the basis of the power parameter

Walker (1962) has drawn a corresponding comparison for refrigerating machines. Use of the cooling parameter QJ(P^vt) for optimization studies is preferred, because it leads to a machine configuration having the maximum cooling capacity for a given size and weight.

CONSOLIDATED DliSIGN < HARTS

Despite the interest and attraction of diagrams such as Fig. 5.13, it can readily be understood that there exists a virtually infinite array of possible permutations of engine design parameters. It would be a tedious matter to search through the variations for an optimum combination. To overcome the difficulty, consolidated design charts have been prepared, and arc presented in Fig. 5.15 (for prime movers) and Fig. 5.16 (for refrigera! ing machines).

Fig. 5.15 was prepared using the power parameter Pl{pmaxVT) as the basis for optimization. Surfaces, similar to that shown in Fig. 5.13, were generated for the value ol P/(pmu„ VT) with different values of o and k and constant values of t and A'. The apex of the surface was established, and the apex values of P/{pmnt V,), aoplf and Kop, were plotted on appropriate charts, constituting Fig. 5.15. These were all drawn on the common basis of expansion-space temperature Tn, with the compression-space temperature n/ways maintained constant at 300 K. The apexes of Other surfaces, with different values of r and .V, were determined, and plotted to obtain the complete consolidated chart. A similar technique was used to obtain the consolidated chart for the refrigerating machines, with optimization based on the cooling parameter QR/(pII,ax^/i) (F'g- 5.16).

The work was carried out. using a self-optimizing digital computer program (with automatic use of recognized hill-climbing techniques), to locate the apex of the surface from any given fixed values of t and X and starting values of a and k, as described by Walker (1962).

Use of the consolidated chart for design

The design charts ol Figs. 5.15 and 5.16 arc recommended for use in

## 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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