Ideal Adiabatic AnalysisLessons 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.dat DoublePressure Hydrogen Helium Argon Net work [J] 3.706 7.412 3.706 3.706 3.706 Efficiency [-] 0.6251 0.6251 0.6246 0.5992 0.5992 Work, expansion space [J] 5.929 11.86 5.934 6.184 6.184 Work, compression space [J] -2.222 -4.445 -2.228 -2.479 -2.479 Heater, heat transfer [J] 5.928 11.86 5.934 6.184 6.184 Kooler, heat transfer [J] -2.222 -4.445 -2.228 -2.479 -2.479 Total mass of gas [g] 0.2496 0.4991 0.01737 0.03460 0.3455 Mean Pressure [Pa] 2.000e+5 4.000e+5 2.000e+5 2.000e+5 2.000e+5 Max Pressure [Pa] 2.733e+5 [Pa] 5.466e+5 2.733e+5 2.761e+5 2.761e+5 Min Pressure [Pa] 1.434e+5 [Pa] 2.867e+5 1.433e+5 1.402e+5 1.402e+5 Regenerator, heat into gas [J] 32.46 64.93 32.17 22.91 22.91 Regenerator, heat out of gas [J] -32.46 -64.93 -32.17 22.91 -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 lag 75 85° 95.569° 105° 115° Net work [J] 3.541 3.678 3.706 3.628 3.439 Efficiency [-] 0.6188 0.6218 0.6251 0.6283 0.6317 Work, expansion space [J] 5.722 5.915 5.929 5.774 5.443 Work, compression space [J] -2.182 -2.237 -2.222 -2.146 -2.004 Heater, heat transfer [J] 5.722 5.915 5.928 5.774 5.443 Kooler, heat transfer [J] -2.182 -2.237 -2.222 -2.146 -2.005 Total mass of gas [g] 0.2478 0.2487 0.2496 0.2504 0.2512 Mean Pressure [Pa] 200000 2.000e+5 2.000e+5 2.000e+5 2.000e+5 Max Pressure [Pa] 283000 2.784e+5 2.733e+5 2.687e+5 2.639e+5 Min Pressure [Pa] 137600 1.403e+5 1.434e+5 1.462e+5 1.492e+5 Regenerator, heat into gas [J] 26.75 29.65 32.46 34.72 36.85 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/Vswc 0.75 1 1.25 1.5 1.75 Net work [J] 3.538 3.706 3.731 3.68 3.589 Efficiency [-] 0.6172 0.6251 0.6298 0.6329 0.6353 Work, expansion space [J] 5.733 5.929 5.924 5.814 5.65 Work, compression space [J] -2.195 -2.222 -2.193 -2.134 -2.061 Heater, heat transfer [J] 5.733 5.929 5.924 5.814 5.65 Kooler, heat transfer [J] -2.195 -2.222 -2.193 -2.134 -2.061 Total mass of gas [g] 0.2544 0.2496 0.2455 0.2421 0.2392 Mean Pressure [Pa] 200000 200000 200000 200000 200000 Max Pressure [Pa] 283000 273300 266800 262100 258500 Min Pressure [Pa] 137900 143400 147200 150100 152300 Regenerator, heat into gas [J] 31.07 32.46 33.18 33.76 34.18 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/Vswc 0.75 1 1.25 1.5 Net work [J] 0.6189 0.6467 0.6434 0.6255 Efficiency [-] 0.1493 0.1534 0.155 0.1554 Work, expansion space [J] 4.143 4.215 4.151 4.024 Work, compression space [J] -3.524 -3.569 -3.507 -3.398 Heater, heat transfer [J] 4.134 4.215 4.151 4.024 Kooler, heat transfer [J] -3.524 -3.569 -3.507 -3.398 Total mass of gas [g] 0.3459 0.344 0.3423 0.3407 Mean Pressure [Pa] 200000 200000 200000 200000 Max Pressure [Pa] 264400 261300 260300 260200 Min Pressure [Pa] 148600 150400 151100 151200 Regenerator, heat into gas [J] 8.644 9.572 10.25 10.77 Regenerator, heat out of gas [J] -8.643 -9.572 -10.25 -10.77

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Last revised: 01/01/15