## Heat Exchangers In Stirling Engines

The diagrams given in Fig. 7.5 are somewhat complicated but worthy of close attention to appreciate a fundamental aspect of Stirling engine operation. Each diagram contains two curves, superimposed. One curve represents the mass-flow rates into and out of the expansion space; the other represents mass-flow rates into and out of the compression space. Curves above the zero datum line represent flow into the expansion space and oia of the compression space. Curves below the zero datum line represent tlow on; of the expansion space and into the compression space. When these are superimposed as in Fig. 7.5 the areas where the curves overlap represent the period of net flow through the dead space, that is through the heat exchangers. Referring to Fig. 7.5, the period A -B represents the flow of fluid through the heal exchangers towards the expansion space with fluid flowing from the compression space into the dead space and from the dead space into the expansion space-

In period B—C fluid flows from the dead space into both the compression space and the expansion space This can be thought of as the phase of emptying the dead space. In period C—D the fluid flows through the dead space towards the compression space with fluid leaving the expansion space and entering the compression space. Finally the period D—A is the phase of filling the dead space when fluid is flowing into the dead space from both the compression and expansion spaces.

The important point to appreciate is that net flow through the dead space, in effect, the regenerator, heater, and cooler, does not occur for much more than half the total cycle lime, and further, the mean rate of the net flow is substantially below the mean rates of flow into and out of the two compression and expansion spaces.

Most of the relations found in the literature for heat transfer and fluid friction depend on equations based on groupings of dimensioniess groups with appropriate coefficients and power indices i.e., the Dittus-Boelter equation for the heat transfer in turbulent flow in smooth circular pipes is:

and /i - heat-transfer coefficient k ~ thermal conductivity p= gas density i? - gas velocity

The heat transferred:

where Q = rate of heat transfer

A =area for heat transfer = ttc/Lm AT- temperature difference between ihe gas and wall temperature L - length of tube n - number of tubes. Given the continuously variable flow rates suggested in Fig. 7.5 plus the cyclic pressure variation over a ratio of p,naJpmir = 2 approximately, it is clear that the velocity v and the density p will vary continuously, with consequent profound effects on the heat-transfer coefficient and the actual heal transfer. Variation in the rate of heal transfer will reflect on the temperature difference AT with consequent variations in temperature which in turn will cause variations, albeit minor, in the thermophysical properties of the gas, thermal conductivity, specific heat, and viscosity.

It is evident from the above thai the thcrmofluid processes in a Stirling engine are entirely and continuously transitory in nature. Thus far. no simple design procedures for handling this type of flow have become generally available. It is necessary therefore in preliminary design work to assume a reasonable value lor mean flow rates and to calculate the heat transfer and friction effects for thai assumed flow. This will allow an initial determination of the tube diameters and lengths or of fin widths and depths for the heaicr and cooler and also for estimation of the matrix diameter and length for the regenerator.

It must be recognized that the use of a mean rate of flow is a crude approximation to the real situation. Modifications of the design are to be anticipated for the optimum engine performance either in the light of more sophisticated analysis once the design is established or as the result of actual testbed operating experience.

Nevertheless a stari has to be made somewhere and curves such as those given in Fig. 7.5 will be found useful in arriving at representative mean flow rates for use in conjunction with the steady-flow heat-transfer and friction data found in Ihe literature.

## 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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