A Second Look at  Regenerator Analysis                                              

I purchased 100 square feet of aluminum screen ($28!) and also some cheep nylon netting to make the regenerator. The displacer/regenerator vessel has already been made with 16” x 16” x 8.5” dimensions. I have 60  layers of 15” x 15” screen alternated with nylon net insulation and was alarmed that it only filled the first two inches of the planed four inch thick regenerator. Will this be a good enough regenerator or should I buy more aluminum screen?

 I made an excel sheet that models the temperature profile across the regenerator. I first calculated out the solid and gas heat capacities of a regenerator unit cell. A unit cell has the volume that is between two holes in adjacent aluminum screens. Then I calculated how much heat it would take to warm a unit cell of cold air to the solid phase temperature for the first screen layer that it met. I included an efficiency factor; incoming air does not necessarily have the time to reach the solid phase temperature.

Knowing how much heat the solid phase gave up to the gas, I can calculate the new solid phase temperature. I repeated the calculation for each new cycle of unit volume gas crossing the first screen.  Similar calculations are done on the rest of the regenerator screens where the incoming gas temperature is from the previous screen cell from the previous cycle. After the whole column of unit cells from the cold space pass into the regenerator (195 cells in this example), I graph the instantaneous temperatures of the solid and the gas phases in the regenerator. When the air stops moving the gas phase temperature rapidly assumes the local solid phase temperature because the solid phase has 96 times the heat capacity of the gas phase by regenerator volume.

So how does this 60 aluminum screen regenerator perform? If incoming air warmed completely to the solid phase temperature (100% efficiency) then the whole 6.5 inch column of cold air would be warmed to the ambient regenerator temperature (60C) by the first ten aluminum screens! At 50% efficiency (the gas is warmed half way to the solid temperature by each screen) the gas is totally warmed by the 14^thscreen. At only 10% efficiency, gas is warmed by the 50^thscreen.  Indeed, if I put my lips on the regenerator material and blow, after 30 screens I cannot feel warm air come out the other side. I am estimating the regenerator efficiency is 50% + 25%. Certainly no additional layers of screen are needed in the regenerator.

 The biggest surprise for me was that the first big slug of cold air, never really cools down the first screen to the incoming gas temperature. The solid phase has a large heat capacity which takes a lot of gas phase to cool it down. This problem is compounded by a Zeno’s Paradox effect where the gas becomes increasingly inefficient at cooling the solid phase as gas temperatures approach solid phase temperatures. It takes an efficiency of 70% for the first screen to drop to 30C with incoming air of 20C. This is a bit disturbing because it means that the air coming back out of the regenerator’s cold side will be  warmer than it was on the way in. So in effect, some of the cool was left in there.

It hurts my head to think about it, but it looks like some of the cool from the air, stays trapped in the regenerator solid phase during the warming part of the cycle. If this occurs, the first screen’s starting temperature would be a little lower each cycle until it is at the cold space temperature. The same would be true at the hot end of the regenerator; heat would build up until the last screen reached the hot space temperature. Because the  air in the regenerator moves back and forth, an even temperature gradient would form across the regenerator. This makes intuitive sense to me but it is hard to prove. Technical articles I have looked at, do say there is an even temperature gradient across a regenerator.

I reworked the excel sheet to make the solid phase beginning temperature be a gradient from the cold space temperature to the hot space temperature. The 60 screen regenerator works even better with this model than with the non-gradient model. Even at 25 % efficiency, very little cool leaks out the hot side of the regenerator. In any case, I see no reason to add more screens to the regenerator.

If you want to play with the excel regenerator temperature profile sheet you can download it at https://docs.google.com/open?id=0B9fsJB6CcZqrSU5YTEZYUFB1U2s

The Terrapin: Vessel, Cold Heat Exchanger and Cold Air Pump.                                                                                                  

When building robotic projects, I have a tradition of naming them after the scientific name of the animals they resemble. This engine may well be feeble and slow and it has a boxy look about it. The scientific name of the box turtle is terrapene carolina. I was thinking of naming this engine, the terrapin. Hey, I have to call it something.

I chose the largest regenerator vessel volume (1.25 cu feet) that would still be in the proper compression range for a high temperature of up to 100C. It is about twice the size of the model I had originally envisioned, so I am going to be over-budget.

The regenerator vessel was made from a big plywood lined wood box whose floor is sealed with resin and whose walls are covered in glass.

The water cooled heat exchanger is a 13 foot coil of ¼ inch OD copper tubing alternating with one inch strips of ¼” wire mesh.

The cold coil fits snugly under a 3 ½ gallon HDPE paint bucket lid that was modified into a cold air pump with the help of some sheet metal work and some PVC backed polyester material from a cheap rain jacket. The pump draws air across the cool coil only during the cooling part of the engine cycle as the regenerator is moving up. During the warming part of the engine cycle, as the regenerator moves down, the already cooled air contained in the pump, moves into the regenerator to be warmed.