Animation of the Beta type Stirling engine with Rhombic drive.
hot gas in heater tube or expansion space.
heater
regenerator
cylinder wall
displacer
connecting duct
cold gas in cooler tube or compression space
cooling water
power piston
displacer drive rod
Degree of cycle (of cylinder 1).
0
30
60
90
120
150
180
210
240
270
300
330
360
Animation speed (cycles/minute.) Stops after 3 minutes.
0
5
10
15
20
25
30
35
40
45
50
55
60
CALCULATED OUTPUTS.
%
100-
90-
80-
70-
60-
50-
40-
30-
20-
10-
0-
Live Volumes, red= hot, green= total, blue= cold
( % of maximum total live volume)
0
30
60
90
120
150
180
210
240
270
300
330
360
Angle degree
'Rhombic drive
' ____________________
' | |
' | (hot) |
' | Expansion Space |
' | __________________ |
' || ||
' || DISPLACER ||
' ||__________________||
' | | |
'Compression Space| | | (cold)
' | | |
' Power Piston | ======== | ======= |
' | ||| |
' |||
' <-----> ||| <------>
' EX3 ----|||---- EX3
' _|_ =crankshaft / | \
' | CR3 / | \ CR3
' RC3 / | \ RC3
' _|___/ | \___|_
' |RC1\ | /RC1|
'R=crank \ | /
' CR1 \ | / CR1
'CR1=CR3=bar \ | /
' -----------
' <-----> <----->
' EX1 EX1
' CROSS BAR
'
HPA= hot piston area
HD= hot cylinder dead volume
CPA= cold piston area
CD= cold cylinder dead volume
OVERLAP= overlap volume in cold space
RA=2*pie/360
AL3= degree crank angle offset between crank 1 and crank 3.
In a normal Rhombic drive CR1=CR3, RC1=RC3, EX1=EX3, AL3=0
H= hot cylinder volume
X= (-DEGREE+150)*RA;
H=HPA*(SQR((RC1+CR1)^2-EX1^2)-RC1*SIN(X)-SQR(CR1^2-(EX1-RC1*COS(X))^2))+HD
C= cold cylinder volume
Y= (-DEGREE+150-AL3)*RA;
C=CPA*(-Math.sqrt((CR3-RC3)^2-EX3^2)-(RC3*SIN(Y)
-SQR(CR3^2-(EX3-RC3*Math.cos(Y))^2)))+CD+((HAV-H-HD)/HPA)*CPA-OVERLAP
Hot active volume =
HAV=HPA*(SQR((CR1+RC1)^2-EX1^2)-SQR((CR1-RC1)^2-(EX1^2)))
-------------------------------------------------------------------------
Info about the GM GPU-3
http://arrow.dit.ie/cgi/viewcontent.cgi?article=1033&context=engdoc
The Combined Otto and Stirling Cycle Prime-Mover-Based Power Plant
Barry Cullen BE
Page 161, 162
table 6.1 GM GPU-3 engine dimensions
[98]
Specifications
Value
Heater
24.53 Mean tube length (cm)
15.54 Heat transfer length (cm)
11.64 Cylinder tube (cm)
12.89 Regenerator tube (cm)
0.302 Tube inside diameter (cm)
0.483 Tube outside diameter (cm)
40 No. tubes per cylinder
5 No. tubes per regenerator
Cooler
4.61 Tube length (cm)
3.55 Heat transfer length (cm)
0.108 Tube inside diameter (cm)
0.159 Tube outside diameter (cm)
312 No. tubes per cylinder
39 No. tubes per regenerator
Regenerators
2.26 Length (inside) (cm)
2.26 Diameter (inside) (cm)
8 No. per cylinder
Material
Stainless steel wire cloth
79 x 79 No. wires, per cm
0.004 Wire diameter (cm)
308 No. layers
30.3 Filler factor, (%)
5 Angle of rotation between adjacent screens (deg)
0.8 Mesh porosity
Cold End Connecting Ducts
1.59 Length (cm)
0.597 Duct inside diameter (cm)
8 No. ducts per cylinder
0.279 Cooler end cap (cm3)
Drive
4.6 Connecting rod length (cm)
1.38 Crank radius (cm)
2.08 Eccentricity (cm)
Miscellaneous
6.99 Cylinder bore at liner (cm)
7.01 Cylinder bore above liner (cm)
0.952 Displacer rod diameter (cm)
2.22 Piston rod diameter (cm)
6.96 Displacer diameter (cm)
0.159 Displacer wall thickness (cm)
3.12 Displacer stroke (cm)
0.163 Expansion space clearance (cm)
0.03 Compression space clearance (cm)
521 Buffer space maximum volume (cm3)
233.5 Total working space minimum volume (cm3)
Page 163
Table 6.2 GM GPU-3 engine dead volumes
Specifications—Engine Dead Volume
Value (cm^3)
Heater
9.68 Insulated portion of heater tubes next to expansion space
47.46 Heated portion of heater tubes
13.29 Insulated portion of heater tubes next to regenerator
2.74 Additional volume in four heater tubes used for instrumentation
7.67 Volume in header
+ -----
80.8 Total
Cooler
13.13 Volume in cooler tubes
Regenerators
7.36 Entrance volume into regenerator
53.4 Volume within matrix and retaining disks
2.59 Volume between regenerators and coolers
2.18 Volume in snap ring grooves at end of coolers
+ -----
65.5 Total
Expansion Space Clearance Volume
3.34 Displacer clearance (around displacer)
7.41 Clearance volume above displacer
1.74 Volume from end of heater tubes into cylinder
+ -----
12.5 Total
Compression Space Clearance Volume
3.92 Exit volume from cooler
2.77 Volume in cooler end caps
3.56 Volume in cold end connecting ducts
7.29 Power piston clearance (around power piston)
1.14 Clearance volume between displacer and power piston
2.33 Volume at connections to cooler end caps
0.06 Volume in piston “notches”
0.11 Volume around rod in bottom of displacer
21.18 Total
+ -----
193.15 Total dead volume
39.18 Minimum live volume
+ -----
232.3 Calculated minimum total working space volume
233.5 Measured value of minimum total working space volume (by volume
displacement)
2.5 Change in working space volume due to minor engine modification
+ -----
236.0 Total
Table 6.3 Working fluid properties GM GPU-3
Specifications Value
Gas
Working Gas Helium
System Temperatures
Source temperature (K) 1100
Hot side gas temperature (K) 922
Sink temperature (K) 286
Cold side gas temperature (K) 286
Ambient temperature (K) 293
Properties—Helium
Specific heat capacity, constant
volume Cv (J/kgK) 3120
Specific heat capacity, constant
pressure cp (J/kgK) 5197
Specific gas constant, R (J/kgK) 2077
Kinematic viscosity, ? (@600K) (m2/s) 394 x 10-6
Prandtl number, Prhelium 0.676
Conductivity, k (@600K) (W/mK) 252 x 10-3
Conductivity, k (@290K) (W/mK) 149 x 10-3
Dynamic viscosity, µ (@600K) (Ns/m2) 320 x 10-7
Dynamic viscosity, µ (@290K) (Ns/m2) 195 x 10-7
Properties—Air
Specific heat capacity, constant
pressure cp (J/kgK) 1120
Prandtl Number, Prair (1100K) 0.72
Properties – Water
Specific heat capacity, (J/kgK) 4198
Prandtl number, Prwater (286K) 8.8
http://www.erc.uct.ac.za/jesa/volume21/21-2jesa-strauss-dobson.pdf
Page 23 (7 in pdf)
Table 1: Core information of the documented
low power baseline and high power baseline
measurements conducted by Thieme (1979,1981)
Low power High power
baseline baseline
Working fluid Helium Hydrogen
Heater-tube gas temp. 697 °C 677 °C
Mean compression
space pressure 4.13 MPa 6.92 MPa
Engine speed 2503 rpm 1504 rpm
Page 24 (8 in pdf)
Table 2: Comparison of the measured and simulated low power baseline measurement
by Thieme (1979)
Measured results Simulated results with % error
Urieli method Alternative method
Exp. space average temperature 851 K 878 K (3.2%)
Comp. space average temperature 371 K 350 K (-5.7%)
Exp. space pressure swing 2.89 MPa 3.16 MPa (9.3%)
Comp. space pressure swing 2.94 MPa 3.01 MPa (2.4%)
Heat input to working fluid per cycle 272 J 313 J 273 J
(15.1%) (0.4%)
Heat out of working fluid per cycle 177 J 115 J 165 J
(-53.9%) (-6.78%)
Indicated output power and efficiency 3.7 kW @ 0.303 5.61 kW @ 0.43 4.39 kW @ 0.386
(51.6%) (18.6%)
Brake output power and efficiency 2.65 kW @ 0.217 4.56 kW @ 0.35 3.34 kW @ 0.294
(72.1%) (26.0%)
Page 24 (8 in pdf)
Table 3: Comparison of the measured and simulated high power baseline measurement
by Thieme (1981)
Measured results Simulated results with % error
Urieli method Alternative method
Exp. space average temperature 847 K 887 K (4.7%)
Comp. space average temperature 345 K 335 K (-2.9%)
Exp. space pressure swing 4.23 MPa 4.81 MPa (13.7%)
Comp. space pressure swing 4.43 MPa 4.77 MPa (7.7%)
Heat input to gas per cycle 444 J 507 J 432 J
(14.2%) (-2.7%)
Heat out of working fluid per cycle 245 J 170 J 248 J
(-30.6%) (1.2%)
Indicated output power and efficiency 4.91 kW @ 0.406 6.29 kW @ 0.494 4.47 kW @ 0.413
(28.1%) (-9.0%)
Brake output power and efficiency 4.16 kW @ 0.344 5.54 kW @ 0.435 3.72 kW @ 0.344
(33.2%) (-10.6%)
Page 29 (13 in pdf)
General Motors GPU-3 Stirling engine
General
Configuration Single-cylinder, uniform diameter
bore. Rhombic drive
crank mechanism
Working fluid(s) He, H2 Rated maximum output 8.95 kW with
Hydrogen at 69 bar and 3600 rpm
Bore 69.9 mm
Stroke (piston and displacer) 31.2 mm
Working fluid circuit dimensions
Heater
Mean tube length 245.3 mm
Length exposed to heat source 77.7 mm
Tube length(cylinder side) 116.4 mm
Tube length (regenerator side) 128.9 mm
Tube inside diameter 3.02 mm
Tube outside diameter 4.83 mm
No. complete tubes per cylinder 40
No. of tube per regenerator 5
Cooler
Tube length 46.1 mm
Length exposed to coolant 35.5 mm
Tube inside diameter 1.08 mm
Tube outside diameter 1.59 mm
No. of tubes per cylinder 312
No. of tubes per regenerator 39
Compression-end connecting ducts
Length 15.9 mm
Duct inside diameter 5.97 mm
No. of ducts per cylinder 8
Cooler end cap 279 mm3
Regenerators
Housing inside length 22.6 mm
Housing internal diameter 22.6 mm
No. regenerators per cylinder 8
Mesh material Stainless steel
Mesh no. 7.9 wires/mm
Wire diameter 0.04 mm
No. of layers 308
Porosity 70%
Screen-to-screen rotation 5°
Drive mechanism
Crank eccentricity, r 13.8 mm
Connecting rod length, l 46.0 mm
Désaxé offset, e 20.8 mm
Linear expansion space clearance 1.63 mm
Linear compression space clearance 0.3 mm
Minimum working space volume 232 350 mm3
http://mac6.ma.psu.edu/stirling/drives/beta_rhombic/index.html
rhombic drive
