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.
The following assumptions are basis of the ideal adibatic analysis :