##### From Mechanical Efficiency of Heat Engines

## OPTIMUM SWEPT VOLUME RATIO AND PHASE ANGLE

When making comparisons of engine output, it is only fair to consider engines of the same size. A natural nominal measure of size for gamma Stirling engines is the total combined swept volumes of the piston and displacer. This is the size measure advocated in the earlier optimizations of indicated work (Kirkley, 1962; Walker, 1962). The optimization problem then becomes one of partitioning a given total swept volume between the piston and displacer sections of the engine, i.e., choosing * ?*, to maximize the work per cycle. The other parameter subject to optimization is the phase angle, * ?*, by which the motion of the displacer leads that of the piston.

A fair comparison also requires that the engines have the same characteristic pressure. The mean cycle pressure is the most natural and intuitive pressure against which to compare gamma engine performance. It is also the easiest characteristic pressure to maintain and measure in practice, because it automatically tends, or can easily be made, to equalize to the buffer or surrounding atmospheric pressure, as has been already noted in earlier chapters.

Presented in Table 10.1 are the results of numerical calculations using Equations (10.1), (10.2), and (3.2) for a range of values of temperature ratio * ?*, mechanism effectiveness E, and dead space ratio * ?*. The table shows the values * ?** and * ?** of swept volume ratio and phase angle that yield the maximum specific shaft work...

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SWEPT VOLUME RATIO SELECTION In applying the optimization Table 10.1, it is important to keep in mind the interchange between mechanical efficiency and maximum shaft output. As can be seen from the...

THE SCHMIDT MODEL FOR GAMMA ENGINES The gamma-type Stirling engine can be mathematically described by the following parameters and variables: V 1 = displacer swept volume V 2 = piston swept volume V...

PHASE ANGLE Examination of the optimization table reveals that the optimum phase angle ?* tends to be lower for poorer mechanisms and for higher temperature ratios. Although 90 is usually considered...

INDICATED WORK A closed-form expression for the indicated work per cycle of a Schmidt gamma Stirling can be written in the following way: where X and Y are the functions defined above in the set of...

This chapter applies the Fundamental Efficiency Theorem to a central problem in basic Stirling engine design, that of identifying optimal engine geometry. This problem was treated in Chapter 7 for...