Engine 3F Efficiency Analysis part 3

Let me summarize what has been covered and what remains in this efficiency analysis:

Component Power percentage of total power Efficiency analysis
Heat lost directly to the environment 40.3w 58.4% Part 1
Thermal shorting: heat conduction directly from the hot end to the cold end 5.9w 8.6% Part 2
Gross engine power: includes net shaft power, plus internal losses Part 3
Thermodynamic cycle losses
Regenerator losses
Total 69w 100%

The gross engine power includes not only the measured net shaft power, but also the internal engine losses. These losses are primarily the friction of the dynamic seals (piston seal and displacer shaft seal), bearing friction, and the power required to move the operating gas back and forth by the displacer.

Although I have measured the net output power at 1.16w, I have no measure of the gross engine power or of the internal engine losses. I can, however, compute an upper limit for the gross engine power from my Stirling engine simulator. As an absolute upper power limit we can use the measured temperatures of 450F for Th and 90F for Tc. Using these values yields the first computed row in the table below. This simulator makes some idealized assumptions that make it virtually impossible for the real engine to output more power than the simulator. I consider this value of 2.34w to be an overly generous estimate of the gross power generated by the engine.

For this engine operating at 3.5 Hz, my heat transfer computations indicate the closest the operating gas can get to the measured external temperatures is a delta T of about 20 degC. The second data row in the table uses these temperature limits to compute the maximum estimated gross power. The third data row lists what I estimate to be the minimum gross power that could support a measured output power of 1.16w. It leaves only .25w for all the engine losses.

Condition Th Tc Power Computed Power Measured Power Difference
Measured temperatures 450F (232C) 90F (32.2C) 2.34w 1.16w 1.18w
Maximum estimated gross power 413.6F (212C) 125.6F (52C) 1.79w 1.16w .63w
Minimum estimated gross power 389.3F (198.5C) 150F (65.5C) 1.41w 1.16w .25w

Based both on these calculations and on my experiences measuring power and friction in this engine, I feel reasonably confident that the gross engine power falls in the range of 1.41w to 1.79w. Using the average I will call the gross engine power 1.6w +/- 0.2w. Now we can fill in another block in the table:

Component Power percentage of total power Efficiency analysis
Heat lost directly to the environment 40.3w 58.4% Part 1
Thermal shorting: heat conduction directly from the hot end to the cold end 5.9w 8.6% Part 2
Gross engine power: includes net shaft power, plus internal losses 1.6 +/- .2w 2.3% Part 3
Thermodynamic cycle losses
Regenerator losses
Total 69w 100%

So far we’ve accounted for 47.8w and we have 21.2w remaining for the last two items.

Engine power computations

The following values were used in the engine simulator to compute power:
Power cylinder 31.75mm dia x 63.5mm stroke
Displacer 44.5mm dia x 63.5mm stroke
Dead volumes: hot, cold, regenerator = 10, 60, 31 cm^3
Engine cycles/sec = 3.5
Average pressure = .968 atm (to account for 900ft elevation)

The computed power output of the simulator is reduced by the isentropic compression heating value (also from the simulator) so that the first data row in the table is 2.73w (1-14.33%) = 2.34w.