Ideal Adiabatic Analysis
Lessons learned

One of the first things I used the on-line program first was to try out variations of the Ross90.dat engine. Here are the input data to the program :

Engine Type ( alpha, beta, gamma )
Gas
Average pressure [kPa]
Temp in heater [K]
Temp in kooler [K]
Volume Phase Lag [°]
Clearance volume, compression space [cm³]
Swept volume, compression space [cm³]
Clearance volume, expansion space [cm³]
Swept volume, expansion space [cm³]
Kooler volume [cm³]
Regenerator volume [cm³]
Heater volume [cm³]
alpha
air
200
923
300
95.5690
8.0
61.0450
10.00
61.045
31.21
34.8900
28.5100

All of the statements made below must be taken with the thought in mind that the ideal adiabatic model used does not investigate whether the heater, regenerator, and kooler can indeed facilitate the calculated heats. It is implicitely assumed that they can. Heat transfer calculations are an entirely new ball game.

Changing mean pressure and working gas

Changing the mean pressures doubles the value of all relevant parameters except that of the efficiency which stays constant. This result could have been already obtained by inspection of the governing differential equations.

Changing the type of gas is a little bit more complex. The data are identical for air (the original version) and hydrogen, except for the mass of gas inside the engine. The reason for having essentially no difference in engine performance is related to the fact that both gases have two atoms per molecule and with that the ratio of specific heat capacities is (nearly) identical (1.4).

Helium and Argon give again identical performance values because they are both mono-atomic gases with a ratio of specific heat capacities of 1.667. They have though slightly lower efficiency than the air-H2 pair (0.5992 vs. 0.625) but at identical net work of 3.706 J. The penalty is a higher demand for heat supplied by the heater ( 6.184 vs. 5.93 J ) and higher heat rejection in the kooler ( 2.48 vs 2.22 J ). The most dramatic effect is on the demands on the regenerator. The heat in and out of the regenerator has dropped from 32.46 J for air/H2 to 22.91 J for the Helium/Argon pair.

 Ross90.datDouble
Pressure
HydrogenHeliumArgon
Net work [J] 3.7067.412 3.7063.7063.706
Efficiency [-] 0.62510.6251 0.62460.59920.5992
Work, expansion space [J]5.92911.86 5.9346.1846.184
Work, compression space [J]-2.222-4.445 -2.228-2.479-2.479
Heater, heat transfer [J]5.92811.86 5.9346.1846.184
Kooler, heat transfer [J]-2.222-4.445 -2.228-2.479-2.479
Total mass of gas [g]0.24960.4991 0.017370.034600.3455
Mean Pressure [Pa]2.000e+54.000e+5 2.000e+52.000e+52.000e+5
Max Pressure [Pa]2.733e+5 [Pa]5.466e+5 2.733e+52.761e+52.761e+5
Min Pressure [Pa]1.434e+5 [Pa]2.867e+5 1.433e+51.402e+51.402e+5
Regenerator, heat into gas [J]32.4664.93 32.1722.9122.91
Regenerator, heat out of gas [J]-32.46-64.93 -32.1722.91-22.91

Changing the volume phase lag

We keep all the original ross90.dat except for the volume phase lag which in the original version was at 95.569°. The remarkable feature of the table below is that there is a wide range of possible angles without having to pay a severe penalty as fas as net work is concerned. The volume phase lag with the highest network of 3.711 J (not shown in the table) is at some 93°. A little bit of surprise is that the efficiency is rising almost linearly even over the entire range investigated, even beyond the point of highest net work. Maximum and minimum mean engine pressure show similar behavior and the heat demand on the regenerator increases steadily with increasing volume phase lag.
Phase lag7585° 95.569°105°115°
Net work [J]3.541 3.678 3.7063.6283.439
Efficiency [-]0.6188 0.6218 0.62510.62830.6317
Work, expansion space [J]5.7225.915 5.9295.7745.443
Work, compression space [J]-2.182-2.237 -2.222-2.146-2.004
Heater, heat transfer [J]5.7225.915 5.9285.7745.443
Kooler, heat transfer [J]-2.182-2.237 -2.222-2.146-2.005
Total mass of gas [g]0.24780.2487 0.24960.25040.2512
Mean Pressure [Pa]2.000e+52.000e+5 2.000e+52.000e+52.000e+5
Max Pressure [Pa]2.830e+52.784e+5 2.733e+52.687e+52.639e+5
Min Pressure [Pa]1.376e+51.403e+5 1.434e+51.462e+51.492e+5
Regenerator, heat into gas [J]26.7529.65 32.4634.7236.85
Regenerator, heat out of gas [J]-26.75-29.65 -32.46-34.72-36.85

Changing the ratio of swept volumes of compression and expansion space

The original ross90.dat version has a ratio of the swept volume of the expansion space, Vswe, to that of the compression space, Vswc, of 1. Here we change the ratio but keep the sum of the two at a constant value of 2*61.0450 = 122.09 cm³.

Again, changes in all listed parameters are faiirly small over a wide range of change in the ratio between compression and expansion space. The net work produced peakes at a ratio of about 1.20. The efficiency seems to be increasing monotonically with ever increasing burden on the regenerator.

Vswe/Vswc0.751.00 1.251.501.75
Net work [J]3.5383.706 3.7313.6803.589
Efficiency [-]0.61720.6251 0.62980.63290.6353
Work, expansion space [J]5.7335.929 5.9245.8145.650
Work, compression space [J]-2.195-2.222 -2.193-2.134-2.061
Heater, heat transfer [J]5.7335.929 5.9245.8145.650
Kooler, heat transfer [J]-2.195-2.222 -2.193-2.134-2.061
Total mass of gas [g]0.25440.2496 0.24550.24210.2392
Mean Pressure [Pa]2.000e+52.000e+5 2.000e+52.000e+52.000e+5
Max Pressure [Pa]2.830e+52.733e+5 2.668e+52.621e+52.585e+5
Min Pressure [Pa]1.379e+51.434e+5 1.472e+51.501e+51.523e+5
Regenerator, heat into gas [J]31.0732.46 33.1833.7634.18
Regenerator, heat out of gas [J]-31.07-32.46 -33.18-33.76-34.18

Repeating previous investigation but at a heater temperature of 400 K. Not much of a change here.

Vswe/Vswc0.751.00 1.251.50
Net work [J]0.61890.6467 0.64340.6255
Efficiency [-]0.14930.1534 0.15500.1554
Work, expansion space [J]4.1434.215 4.1514.024
Work, compression space [J]-3.524-3.569 -3.507-3.398
Heater, heat transfer [J]4.1344.215 4.1514.024
Kooler, heat transfer [J]-3.524-3.569 -3.507-3.398
Total mass of gas [g]0.34590.3440 0.34230.3407
Mean Pressure [Pa]2.000e+52.000e+5 2.000e+52.000e+5
Max Pressure [Pa]2.644e+52.613e+5 2.603e+52.602e+5
Min Pressure [Pa]1.486e+51.504e+5 1.511e+51.512e+5
Regenerator, heat into gas [J]8.6449.572 10.2510.77
Regenerator, heat out of gas [J]-8.643-9.572 -10.25-10.77


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Zig Herzog © 2014
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Last revised: 01/01/15