Graphic courtesy of Dr. Israel Urieli of Ohio University.

The Desired Stirling Engine

The first consideration in order to construct an engine that matches your application is of course 'What is the application?'    How many Watts of power are needed ? At what RPM ? What heat of what quality is available ?  What is the fuel ?  Are there any size or weight constraints to be considered ?  What cooling methods are available ? Air or Liquid ?

The answers to these questions allow the use of  some well known, relatively simple, math equations to give a crude estimate of the main parameters of the engine.  Equations such as the West Equation and the Beale Equation are examples of such equations.  Using the data gathered from the answers to the questions above and the Beale Equation (for instance) the volume and physical size of the engine can be suggested.  There are of course more assumptions made to use the Beale equation.  Things like the temperature ratio of 3:1 hot to cold demand that the fuel and/or heat source be of high quality (i.e. high temperature heat, high heat value fuel).

To decribe an engine to produce 350 Watts of power at about 1000 RPM (multiply Hz times 60 to get RPM) pressurized with about 10 atmospheres of gas (.101 MPa is about 14.7 psi) and having a swept volume of about 128 cubic centimeters.  128 cc swept volume gives a thermodynamic reference length of ~5 cm. (~2 in.), (cube root of volume).  This assumes a square stroke (stroke equal to the piston diameter) which probably means a kinematic engine.  If this were a free-piston the stroke would probably be shorter, the diameter larger and the frequency higher for the same power output.  There are other complexities of a free-piston engine that will not be addressed here. 
 

The Beale Equation Spread Sheet (Excel97)
 
 

The Beale Equation Parameters

Watts=Nb*Mpa*Cm³*Hz

Beale Number	Nb=0.1112	Nb=0.1112
Volume (swept) in Cubic Centimeters	185 cc	11.2 cu. in
Frequency Hz (Hz = RPM/60)	17 Hz	1000 RPM
Pressure MPa (1 MPa=145 psi)	1 MPa	145 psi
Power  W (Watts)	350 W	350 W
Diameter of Piston cm.	5.7 cm.	~2.25 in.
Length of Stroke cm.	5.7 cm.	~2.25 in.

The results obtained suggest an initial configuration of a two cylinder alpha engine of 185 cubic centimeters swept volume operating at 1000 RPM with an average internal pressure of 145 psi.  The cylinder diameter is approximately 5.7 cm and the stroke is 5.7 cm.  At this point the mechanical transmission and the gas used as the working fluid has not been selected.  Note that the gas selected will have no real impact on the parameters described above but will greatly impact the number of channels and tubes of the heat exchangers as well as the parameters of the regenerator.  At this point we will invoke the principles of scaling and similarity to go forward with this engine.

On to Scaling and Gas Circuit Development