Stirling engine LTD (Low Temperature Differential) plate size / energy

[jeff jones]

i need a simple calculation of a stirling ltd surface area calculation per watt produced and would a very rough surface and very large surface area hinder heat flow if the distance to re generator is extreme /would folding the surface area of a flat plat ltr help increase the power of engine

most small ltd engines use smooth aluminum to transfer but would crimping the metal and diffuser to match the crimp increase surface area and turbulence near the metal allowing for increased heat transferance

 

[anorlunda]

For the benefit of others providing answers, I found the following.

 

[jeff jones]

i need a simple plate size calculation.

the power piston size is dependent on the displacer size but if i add additional ripples to increase surface area will it increase the power piston displacement
a given temp for engine is 70 degrees for cool side and 140 for warm side
both will be using water to transport heat and cold

both hot and cold engine sides will be made of aluminum block w fast flow pumping for heat transfer
aluminum block will have as much of a ripple or crease or fold to maximize heat transfer

i just need a simple calc using a plate size ,so that i can see how much more energy can be utilized by simply increasing heat transfer area compared to increasing flat plate size

 

[Baluncore]

The hot plate and cold plate will be a similar size to the displacer. The displacer will need to have a large surface area and thermal mass to get high heat transfer. The limit to heat transfer will be to the air in the displacer cylinder, so the plates might best have a shape that fits well with the displacer on the inside rather than the water outside. Maybe concentric circle displacer with grooves in the end plates to fit.

You might do better with the hot plate above or on one side to reduce heat losses.

 

[essenmein]

Posting to see other replies and because i find it interesting.

I did find this link:
https://www.stirlingengine.com/low-temperature/

But not sure it addresses the OP's question.

 

[jeff jones]

Nope
I am seeing YouTubers post LTD Stirling's as large as 48 inches but no real math to back up design
I think that a rough thermal surface that has massive surface area should be easy to find a simple calce to throw at it
I would like a very large surface area under pressure to increase hp
But until I have a base line to work w I can't really estimate the output
I do know that a 300 c difference is nice for betas and gammas but I only have a small difference and if this works as good as I think it can then the temp difference will be even less
As long as I can do a rough calc for plate size/temp difference=watt
Also
Plate size meaning heated surface area not displacer size

 

[Baluncore]

Plate size meaning heated surface area not displacer size

The hot plate heats the displacer through the air gap.
The displacer moves to the cold plate, heating the air it passes, increasing the pressure.
That pressure moves the piston, increases the volume, so lowers the temperature slightly.

The cold plate cools the displacer through the air gap.
The displacer moves to the hot plate, cooling the air it passes, lowering the pressure.
That depression allows the piston to return, reduces the volume, so raises the temperature slightly.

The hot plate stays hot because of contact with the 140°C hot water heat source.
The cold plate stays cold because of contact with the 70°C cooler water heat sink.

The limit to power is the rate of heat flow. It is highly probable that the limiting factor will be the transfer of heat through air from the inside of the end plates to the displacer. The external plate area will be sufficient even if it is flat. The ripples therefore need to increase the area of the displacer to end plate contact, or you need a greater area of displacer.

 

[Baluncore]

There is no simple relationship between external exchange area and engine power.

There are four thermal surfaces in series. Heat flow across each surfaces is proportional to temperature difference and area.

Start with the heat source, water at 140°C, and the sink water at 70°C. Assume the internal hot air contact is at 130°C and the internal cold air contact at 80°C. The temperature difference available is then 50°C.

If you double the area of both external water contact surfaces the temperature lost across each interface will fall from 10°C to 5°C. The temperature difference available is then 60°C. Increasing the external water area to 200% does increase available power, but only by 20%.

So the area of the water contact is not a strict limitation to power. With Stirling engines all things are relative, and ratiometric. Adjusting the compression ratio, internal pressure or regenerator capacity can make a bigger difference.

See; Stirling Engine Design Manual, By William R Martini - NASA (1978). Or;
Mechanical Efficiency of Heat Engines, By James R. Senft - Cambridge University Press (2007).

 

[jeff jones]

Thank u