The Epiphany onE PUCK on Kickstarter is sure to interest anyone with even a passing interest in power generation or Stirling engines. The device uses the Stirling cycle and is supposed to generate 5W (one amp at 5V) to charge USB devices. It’s supposed to run off either a hot drink as shown or turn it over and run it off a cold drink.
The company involved makes claims of achieving very high efficiency, but doesn’t actually put a number on it other than claiming the 5W electrical output from a hot drink. I claim that even if they were to achieve the theoretical maximum Carnot efficiency this design cannot work. So I don’t even need to challenge the company’s Stirling engine efficiency claims. The reason I can make this claim is that they have a completely unworkable design as far as is shown in their video for basic heat transfer. You don’t have to take my word for it, I’ll give you the information so you can verify this experimentally yourself. You don’t need a lot of expensive equipment. All you need is a mug, a source of boiling hot water, an accurate thermometer (a digital instant read would be great), and to really finish the job you should have an IR thermometer to simplify reading the temperature on a piece of metal.
Figure 1 The One Puck engine, the hope and the reality.
Figure 1 shows the hope that someone might have for the One Puck system. Let me be clear, the company has not claimed anything on the left side of the diagram except the 5W output, the hot water input, and an assumed cooling into the room air although that isn’t specified. I’m merely showing the minimum heat flow that would be required for a completely ideal system. As the system departs from ideal the heat flow required increases.
On the right side of figure 1 I’m showing experimentally verified heat flow and temperatures (using very generous allowances) for the design shown in their video. I’m also showing the ideal Stirling engine power output for the revised Th and Tc values.
Here are my claims:
- The heating scheme won’t work: Transferring the heat from the mug to the One Puck device underneath is so inefficient as to be unworkable. The temperature on the disk reaches a peak of 60 degC after 10 minutes and then starts cooling. Heat flow with the hot plate of the engine at 50 degC is 3w.
- The cooling scheme won’t work: The cooling scheme shown with a small disk on the bottom will never be able to cool the engine adequately. For this experiment I’m actually testing cooling with an upward facing cooling surface which theoretically makes it about twice as efficient. Even with this advantage, it is hopelessly inadequate. Using an aluminum plate with approximately the same surface area as the One Puck, a 72 degC plate temperature is only able to reject 13.5 watts of heat into 20 degC air. Estimated cooling at 31 degC is 2.9W (to match the heating value above).
Figure 2. The basic equipment setup used for the tests.
The basic setup for these test is shown in figure 2. I’m pretty sure everyone has the necessary tools except perhaps the IR thermometer.
Engine heating tests
A list of the specific details of the engine heating test:
- I used a ceramic mug filled with 13 oz of water for all tests. (.368 kg of water) which fills the mug to about .25 inches (6mm) below the top.
- The mug was preheated with boiling water before each test. If the mug is not preheated the water temperature immediately drops to about 82 degC as the water transfers some of its heat to warming up the ceramic mug. By preheating the mug a peak water temperature of 92 degC is normally achieved. You can try this yourself quite easily. The mug was covered with plastic to minimize heat loss from the top of the mug.
- An aluminum disk (from one of my engines) 4 inches in diameter and .090 thick (102 x 2.3 mm) was used to simulate the heating surface on the One Puck (see figure 3). The aluminum disk was placed on a Styrofoam block to minimize any cooling of the disk. On an actual engine it would need to be transferring more that 20 watts into the engine.
- Instant reading thermometers were used to measure water temperature. The aluminum plate temperature was measured using an IR thermometer. The tape is necessary on shiny metal surfaces for accurate temperature measurement.
- Temperatures were recorded over a period of 12.5 minutes
Figure 3. The basic test setup for heating an aluminum disk below the mug
Figure 4 shows a plot of the results. The hot mug transfers heat very slowly to the aluminum disk, eventually reaching maximum temperature of 60 degC after about 600 seconds.
Figure 4 Heating test for simulated One Puck engine with disk below mug.
The reason for the poor heat transfer is easy to understand if you look at the bottom of a mug. I have a lot of different mugs and they all have a relatively thin ring of contact on the bottom (see figure 5). A machined flat bottom that mated perfectly with the aluminum plate would help increase heat transfer, but even that would not completely solve the problem. Most ceramics have a thermal conductivity of around 1.5 W/m-K which compares poorly with a good conductor like aluminum with around 200. The result is that the more heat you conduct through the ceramic, the greater temperature drop through the ceramic.
Figure 5. The bottom of mugs usually have a thin ring making surface contact.
Using the data for the aluminum plate temperatures at 90 seconds and 270 seconds, we can compute the heat flow into the aluminum disk using the rate of temperature increase. Because the disk is mostly insulated from cooling, almost all the heat going into the aluminum disk will raise its temperature. The computation in table 1 shows about 2.8 watts when the water temperature is about 89 degC and the aluminum plate is at 49 degC. I use a power of 3w at 50 degC for the diagram in figure 1.
|Aluminum disk temperature @ 90 seconds, degC||54.400|
|Aluminum disk temperature @ 270 seconds, degC||43.900|
|Time between measurements, seconds||180.000|
|mass of aluminum disk, kg||0.052|
|Cp, Specific heat of aluminum, J/kg-K||910.000|
|Rate of heat going into aluminum to raise its temperature= mass x Cp x degC/sec = watts||2.760|
Table 1 Rate of heat transfer to the aluminum disk
When doing your Carnot cycle calculations (we’ll do those later), you don’t get credit for the temperature of the water as your heat source, you have to use the temperature of the heated operating gas in the engine. For my purposes here I’ll just leave it at the aluminum plate temperature. The operating gas in the engine (it might be air or something else) will never have a temperature as high as the aluminum plate. There always has to be a temperature difference for heat flow.
Engine cooling tests
Before I can do a cooling experiment I need to get some heat into the aluminum plate. At the same time I can show you how the heat transfer could be improved but still not adequate for what this ideal engine needs. Here’s the setup.
Figure 6. The cooling test with the mug sitting on Styrofoam and an aluminum plate on top.
All the same setup notes apply for the cooling test as for the heating test except for a few changes:
- A larger aluminum plate (figure 6) is used to simulate approximately what I estimate the dimensions for the One Puck for cooling. I estimate the One Puck at about 5 inches in diameter (it might be smaller but I wanted to err in the company’s favor). I have a plate of aluminum that is 4.75 x 5.0 x .125 inches. The surface area of one side is 23.75 in^2 which is about 20% larger than a 5 inch diameter disk. As an extra bonus the bottom of the plate where it is outside the rim of the mug can also contribute to cooling. We’ll also be using this plate facing upward which helps the heat transfer by letting the heated air rise directly instead of flowing around to the edge as is the case for a downward facing disk. Heat transfer analysis shows that an upward facing disk will transfer about twice as much heat as the downward facing disk. So everything would seem to be in the One Puck’s favor.
- I also perform a reference test. The reference test removes the aluminum plate and replaces it with a Styrofoam block. This allows me to compare measurements of the mug and hot water both with and without the cooling effect of the aluminum plate. Figure 2 shows the reference test setup.
Figure 7. Results for mug with aluminum plate on top.
If you compare figure 7 with figure 4 you will see that even though the aluminum plate used in figure 7 is larger and thicker (it weighs 2.6 times as much) it heats up quicker (around 300 vs 600 seconds) and gets hotter (about 72 vs 60 degC). Heating the plate above the mug works a lot better than below, but you might not like the condensed liquid on the bottom of the One Puck dripping back into your coffee.
Now look at the metal plate temperature around 300 seconds. I didn’t take enough points to actually find the exact peak, but this is close enough. What happens at the peak temperature is that the aluminum plate is dissipating heat (rejecting its heat into the air) at the same rate it is picking up heat from the water and ceramic mug. At the peak temperature the aluminum plate is also neither heating nor cooling, so we don’t need to calculate the heat being used to change the temperature of the aluminum. All we have to do now is figure out how much heat the hot water and ceramic mug are providing when the aluminum plate was at 72 degC. Figure 7 shows the water temperature was about 85 degC when the aluminum plate was at 72 degC.
Here’s where the reference test comes in. I perform an identical test to the one I just did but I replaced the metal plate with a block of Styrofoam. Any difference in heat loss between the two should be due to the heat being thrown off by the aluminum plate.
Figure 8. Plot for reference mug configuration with Styrofoam covers on top and bottom of mug.
The reference test plot in figure 8 shows the mug hot water reaches 85 degC at about 400 seconds. It takes about 100 seconds longer because without the aluminum plate the water is cooling more slowly.
I’ve added a linear curve fit to the data with the equation that gives the temperature vs time for the water in the time period of interest. All we need from the equation is the slope, −0.0130 degC/second. Table 2 shows the steps required to compute the heat loss. You’ll have to supply the actual mass of the water you use, the mass of your mug, and your temperature change rate. First a discussion of the need to include the ceramic mug.
When you pour hot water into the mug, some of the heat is transferred within tens of seconds to the ceramic mug. The result is the water cools as the mug heat up. Now the thermal mass that you need to be concerned with is both the water and the ceramic mug. They are both storing and releasing heat.
|Cp, heat capacity, J/kg-K||4200||850|
|temperature rate, degC/sec, reference test||0.013||0.013|
|Cp x mass x temperature rate = Watts||20.147||4.995|
|total watts (reference test)||25.142|
|Aluminum plate test||water||ceramic mug|
|temperature rate, degC/sec, aluminum plate test||0.020||0.020|
|Cp x mass x temperature rate||30.996||7.684|
|total watts (aluminum plate test)||38.680|
|heat dissipated by aluminum plate into the air = test with aluminum plate watts – reference test watts.||13.538|
Table 2 Computing the heat rejected by the aluminum plate
The experimental results show that the aluminum disk tested is able to transfer 13.5 w of heat when the plate is at 72 degC. The table also shows that your basic mug with really hot water but covered is still throwing off 25 watts through the sides.
Because 72 degC is too hot for a cold plate we need to scale down the heat rejection to a cold plate temperature of something lower to match the heating capability of the aluminum disk heating test. I’ll pick 31 degC.
If we take the difference in temperature between the plate and the air, and divide by the number of watts of heat rejected we get:
(72 degC- 20 degC)/13.5W13.5W = 3.85 degC/watt
Using this number we can estimate the heat rejection at 31 degC:
(31 degC −20 degC)/3.85 degC/ watt = 2.9 watts.
Now let me make it clear that this is not the correct value because the degC/watt changes as the temperature difference changes. It would be best to run an experiment with the plate temperature at 31 degC and the air at 20 degC. The value shown by the estimation I’m using will be higher than the real value so the error is in favor of the One Puck.
Now for Carnot efficiency (still assuming the ideal Stirling engine but with our real measurements for some of the other parts of the engine):
Here’s the equation:
Maximum possible efficiency = 1 – Tc/Th
Where Th = absolute temperature of the hot operating gas (Kelvin or Rankine scale).
Tc = Absolute temperature of the cold gas.
For a Th= 50 degC and Tc= 31 degC:
Efficiency = 1 – (31+273))/(50+273) = .059 or 5.9%
I’ve filled in the diagram (figure 1) with the values determined from these experiments. the design is only able to support a heat flow through the engine of about 3 watts so the best possible power output would be .059 x 3 = 0.18 watts.
I hope I’ve convinced you that the One Puck is not possible in any form resembling what has been pitched. It’s not even close.