On the chart below I’ve plotted all the data I collected versus time. It’s a little busy so I’ll explain it in detail before I go on to a plot that provides the data in a more useful format for Stirling engine evaluation.
The black line in the above chart is the engine speed in Hz (cycles/sec). (This engine is not self-starting). I spun the flywheel about 510 seconds into the test and the engine immediately accelerated to about 3.5 Hz (read from the scale on the right side of the plot). The engine speed increases as the hot plate temperature, Th, increases, follows the dip which I’ll explain in a moment, and eventually drops to zero after I shut off the heat.
The uppermost line representing Th uses colors to indicate the power setting on the resistance heater used to heat the hot plate of the engine. When the test started (time = 0), the heater was set to 12W. Because I don’t want to damage the ABS plastic used in the engine, I need to avoid exceeding 170 degF. When Th reached about 160 degF I reduced the heat to 7W to avoid overshooting 170 degF. As it became clear that 7w was not going to keep Th increasing, I increased the heating power first to 8W and eventually to 10w. A few degrees short of 170 degF I shut off the heater at 1710 seconds and the engine continued to run on residual heat until 2460 seconds.
The plot of the ambient air temperature, Tambient, is fairly constant as you would expect. The engine cold plate temperature, Tc, increases slightly as it rejects heat from the engine. Tc only reached about 7 degF hotter than Tambient because a small fan was used to help cool the cold plate. Without the fan the cold plate would have been about 20 degF hotter that the ambient temperature.
All of the temperature and speed data was taken continuously and the results averaged over 30 seconds before being recorded. The individual data points are visible on the Tc plot.
Temperature ratio plots
When evaluating the performance of Stirling engines, the absolute temperature ratio of the hot and cold reservoirs are more useful that the actual temperatures because the engine responds to the temperature ratio. Absolute temperature ratios provide the information in non-dimensional format so it is easier to compare different data. Converting the measured temperatures to absolute temperatures and then computing the ratios, the following plot provides the relevant information.
The above plot shows an almost linear relationship of engine speed to temperature ratio for speeds above about 3 Hz. I’ve split the data up into two sets represented by the red and blue colors. While the engine was being heated the data points are plotted in red, and while the heater was turned off the data points are in blue. The slight difference in the two plots above 3Hz is probably due to the engine not being in complete equilibrium. You can see the temperature ratio was changing significantly during each 30 second recording interval.
The following plot has some of the same data as the previous plot. I’m using only the data taken above an engine speed of 3.5 Hz so that I can find the best-fit linear equation to represent the engine’s unloaded speed vs temperature ratio. Now we have an equation for the unloaded engine’s speed versus temperature ratio that provides a good representation for this engine configuration from about 3.5 Hz to 6 Hz.
Another plot of the same data shows engine speed as a function of temperatures rather than temperature ratios. This plot might be more meaningful to those that are not accustomed to working with absolute temperature ratios.
This engine is running unloaded, so in these tests it is producing zero useful power. It is, however, generating power to overcome all the frictional resistance sources in the engine. Thermodynamically, I am interested in the power it is producing to overcome friction for two reasons.
First, I’d like to see the major sources of friction to know what I would work on to improve the engine performance.
Second, this is a research engine for me. It will never put out much power, but I’m interested in designing a much larger engine (probably in the 2W to 10W range) that operates over roughly the same temperature ratios. Anything I can learn about this engine’s performance and how it relates to my simulation will help me design my next engine successfully. When I design an engine with roughly 1000 times the displacement, 1mW of power or friction on this engine will be 1W on the larger engine. Even though I’m measuring minuscule amounts of power on this engine, I’m very much interested in the results.