Ideal Adiabatic Analysis

Purpose of the ideal adiabatic analysis is to develop a tool, in this case a program, which provides information about the performance of a proposed Stirling Engine. The term adiabatic basically means in general "no heat transfer", for Stirling engines that refers to no transfer of heat in the compression and expansion space. The derivation of the needed differential equations ( yes calculus ) is an order of magnitude more difficult than for the equations related to the ideal isothermal analyis and so are the program and associated computer memory and computation time. But it is hoped that the produced results are significant closer to reality. Running the developed program can be done without having any mathematical background nor having detailed knowledge of the underlying physics. But is worthwhile to keep the following in mind.

The Stirling engines to be analyzed consist of five subspaces connected in linear fashion as shown in the Figure below. The cooler, regenerator, and heater space have constant volumes Vk, Vr, and Vh, respectively. Both, the compression and the expansion space , are each divided into a fixed clearance volume, Vclc and Vcle respectively, and a time-dependent volume which varies between 0 and their respective maxima, Vswc and Vswe. The precise variation of Vswc and Vswe during a complete cycle depends on the mechanical drives employed. Typical arrangements of the five subspace are shown below. For the alpha-type everything can be stacked into a single cyclinder. In the beta-type both the power piston and displacer are housed in a single cyclinder while in the gamma-type they occupy separate cyclinders. Delta-type engines cannot be analyzed under the assumption of adiabatic expansion and compression space because by the very function of these engines heat transfer is supposed to take place in these spaces.

Most commonly used arrangements

The following assumptions are basis of the ideal adibatic analysis :

  1. The engine turns at constant speed. Therefore, time and crank angle Θ are proportional to each other. The result of the analysis will among many other things produce a value for the net work of the proposed engine and a prescribed speed. If that value is positive you can use that power to motor whatever you have in mind. If it comes out negative your engine is useless at the given speed.

  2. Any pressure drops due to flow resistances and pressure differentials needed to accelerate the working gas are neglected. Hence, the pressure, p , has at a given instant the same value everywhere inside the engine and varies only with time. Correspondingly, kinetic energies of the working gas are neglected in the law of conservation of energy.

  3. Leakage of gas to the outside of the engine, including crank case, is assumed to be zero.

  4. Both, the compression and expansion space, volumes Vc and Ve, are adiabatic. This means that no heat gets exchanged in these two spaces between the gas and the surrounding walls nor with the piston/displacer surfaces. The temperature in these spaces is uniform but varies during a cycle due to changes in pressure, volume and gas coming from/leaving to the adjacent kooler and heater space, respectively.

  5. The temperature in the kooler space is uniform and constant in time. This demands extremely good heat transfer performance.

  6. The temperature in the heater space is uniform and constant in time. This demands extremely good heat transfer performance.

  7. The temperature in the regenerator varies linearly between the temperature in the heater section to that in the kooler section. It does not vary in time. Again, this demands extremely good heat transfer performance.

  8. An ideal gas with constant specific heats is used as working fluid.

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Zig Herzog © 2014
Last revised: 12/27/05