__Stirling Engines: How They Work
(Non Technical Terms)__
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*Cm**^{3}*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 |