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Stirling Engines: Technical Information
Stirling Engines: How They Work (Non Technical Terms)

Graphic courtesy of Dr. Israel Urieli of Ohio University.

The engine estimate derived from the Beale equation is shown below.
The Beale Equation Parameters


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=147 psi) 1 MPa 147 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 147 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.

  Gas Circuit Scaling Spreadsheet
  From CH. 5 & 6 of 'The Regenerator and the Stirling Engine' by Dr. Allan J. Organ, ISBN1860580106       
  Instructions for use: Enter Data Values in the area under 'Enter Values'. The values to be entered are three of the four values of Power, rpm, pref and Vsw of the machine you want to create. This is called the Derivative Machine. You must also enter the values of the gas which you are using as the working fluid. The values for the three most popular are listed. You may use other gases by determining the values for the specific gas you want to use and entering it   2/1/03 22:14  
    Enter Results  
    Values Here  
P Power in Watts 350.00 350.00 Watts
rpm Revolutions per Minute 1000 1000 rpm
pref Reference Pressure (Mpa) 1 ATM=0.101325 Mpa 1.000 1.00 Mpa
Vsw Swept Volume in CC (cm3)   187.67 cm3
  Values of Gas Parameters Hydrogen=1, Helium=2, Nitrogen (Air)=3 3    
Gas Constant =(J/kg °K) 4120, 2080, 287 287 287 (J/kg-°K)
g Specific Heat Ratio (Cp/Cv) 1.41 1.66 1.41 1.41 1.41 (Cp/Cv)
mref  Gas Viscosity (Pa-s) 8.4E-06 1.69E-05 1.70E-05 1.69E-05 0.0000169 Pa-sec
    Inches mm  
Lref, Sth Reference Length or Thermodynamic Stroke =(Vsw)1/3 2.2540 57.253 mm
Lrd Length of Regenerator '=(lrd )* (Sthd 0.9278 24 mm
Dh Diameter of the Regenerator Housing 4.517 114.723 mm
Affrd Free Flow Area of Regenerator = (affrd)*(Sthd) 16.022 10337 mm2
dw Diameter of Regenerator Wire = 4*(rhrd)* (1- ¶v)/(¶v)  0.0026 0.0664 mm
mw Mesh Number of Regenerator Wire Mesh =4*(1- ¶v)/(3.14159*dw) 153 6.0379 wires/mm
nr Number of Gauzes in the Regenerator 'Stack' 177 177 gauzes
Ntcr Thermal Capacity Ratio of the Regenerator NTCR=(Tref)(rw)(cw)/Pref 1315 1315 ratio
Nf Fourier Modulous of Regenerator Nf=a/(ns)(dw)2 8.657 8.657 ratio
Tnxed Number of Tubes in the Expansion Exchanger =Affxed/((0.25*3.14159)*(dxed)2) 71 71 tubes
Lxed Length of Expansion Exchanger Tubes '=(lxed )* (Sthd) 5.3610 136 mm
dxe Diameter of Expansion Exchanger Tubes = 4 * rhxed  0.0972 2.469 mm
Tnxcd Number of Tubes in the Compression Exchanger =Affxcd/((0.25*3.14159)*(dxed)2) 1622 1622 tubes
Lxcd Length of Compression Exchanger Tubes '=(lxcd )* (Sthd) 1.8340 47 mm
dxc Diameter of Compression Exchanger Tubes = 4 * rhxcd  0.0320 0.813 mm

Last Updated on 2/1/2003
By T.Gentry

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