Chapter 3c - Function set 'define' to define a specific Stirling engine configuration

One of the main purposes of this web resource is to develop a computer simulation of a Stirling engine. Before any simulation can take place we need to define a specific configuration. Thus we need to specify the type and geometry of the engine, the three heat exchangers, the working gas and the operating conditions. Once these have been specified then we can go to three levels of simulation: an Isothermal Schmidt analysis, an Ideal Adiabatic analysis, and a Simple analysis to evaluate the effect of non ideal heat exchangers.

In this section we consider the function set define , which includes the system definition and the Schmidt analysis. The program system is written in the MATLAB language and includes eight m-files as shown in the functional block diagram:

This function set has the following purposes:

• Specify values for the global variables in the define function needed to define a specific engine configuration. The engine function includes three alpha engines as case studies - the classic Ford-Philips 4-215 , the D-90 Ross Yoke-drive , and the Ross Rocker-V (new - not in the block diagram). The Ford engine includes tubular heat exchangers and a matrix mesh regenerator, and the D-90 Yoke-drive and the RockerV engines have annular and slotted heat exchangers and wrapped foil regenerators, so the three machines cover all the heat exchanger and regenerator options of current Stirling engine designs.

• Specify values for the working gas and operating conditions and Schmidt analysis of the engine to evaluate nominal enclosed mass of working gas as well as the Isothermal Schmidt performance of the machine. There is the optional capability of doing a pV or p-theta plot.

• Do a particle trajectory plot using the plotmass function , showing particles of equal mass flowing through the engine over a cycle using Natural Coordinates, as defined by Allan Organ: 'Natural' coordinates for analysis of the practical Stirling cycle (ImechE, 1992). Refer also to Chapter 9 of his book: The Regenerator and the Stirling Engine (John Wiley, 1997). This plot enables a better understanding of the process.

The nineteen functions comprising the set are included in the eight m-files: define.m , engine.m , heatex.m , regen.m , gas.m , and operat.m , and the two plotting routines plotpv.m and plotmass.m . All the global variables required for the simulation are declared in the header m-file define.m , and the main purpose of invoking the function set ' define ' is to assign values to these global variables. These will subsequently be used in the 'adiabatic' and 'simple' simulations following. Notice that the function m-file engine.m includes three engine configuration functions: sindrive for a basic sinusoidal drive (eg the swashplate drive in the Ford-Philips engine), yokedrive for a Ross yoke-drive machine, and rockerVdrive for a Ross RockerV engine. This is a tutorial system and user is expected to augment it as required for any specific requirements. To this end the program system has been written in a universal and uniform style with strict rules regarding structure, variable names, and commenting, thus making it a self documenting system. All of the eight m-files shown above can be downloaded and copied onto any system which has MATLAB installed, or the complete program set can be downloaded in compressed format sea.zip ( sea = s tirling e ngine a nalysis)

A typical execution output of the program is shown in the output file define.out for the D-90 Ross yoke drive engine, as well as the pV , p-theta , and particle mass flow diagrams. Note that this set of routines was not designed to be executed independently, but as a precursor to the Ideal Adiabatic simulation or the Simple simulation routines, which will be discussed in detail later.

Note that the engine modules are for Alpha machines, including a Sinusoidal drive, a Ross Yoke-drive and a Rocker-V drive machine. The heat exchanger types include tubular, annular gap, and slot heat exchangers, and the regenerator matrix types include screen mesh and rolled foil matrices. Working gas types include air, helium, and hydrogen.
Update 2016: I have decided to include a free piston Beta drive engine configuration assuming that both the piston and displacer motions are sinusoidal. The betadrive function has been added to the function m-file engine.m .

Stirling Cycle Machine Analysis by Israel Urieli is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License