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Actual real world design question - nocarename - 07-16-2021
I'm aware that this isn't a mechanical engineering forum, but where else am I going to go? I've been doing some back of the envelope math and I can't see how this fails so far and I'd like to know what I'm missing.
The idea is to have an air conditioning unit that runs off solar power, which, I know, is easily enough done with some photovoltaic cells, a couple batteries, an inverter and a normal air conditioner.
Instead, the thought is to skip the electrical step in pursuit of higher efficiencies. Have a concentrating solar mirror setup running a stirling engine and the stirling engine pressurizing a hydraulic system that then powers the compressor for the air conditioner.
The design
Incoming solar power is concentrated by a fresnel mirror. The mirror is built out of (at most) four identical segments, each 1mx1m, that provide a 90 degree sector for the array of mirrors.
The stirling engine would be about 5HP powered by the reflected sunlight concentrated on the hot end.
The air conditioner would be designed for 1 ton of cooling and the hydraulic power system would be sized to power that requirement.
My math
The sun - Flat on, at Earth we get at least 1321W/m^2 in orbit. I'll allow 1kW/m^2. That gives me 3kW of power with just 3 mirrors.
The mirror - The lowest reflectivity listed for aluminum on the table I found is 86.8% All the others are higher, so I'll use 87%. So I have 2610W.
Stirling engine - I'm using 70% for the efficiency here, because I have no idea what the air temperature is going to be, or what the mirrors will be able to bring the high temperature portion up to and I found one list where the efficiency for an engine that used pyrex as 72% because parts started to melt then, and worse than that seems reasonable. Which gives us 1827W to play with.
Hydraulics - We're building for a efficiency here, 90% should be achievable, let's set that to 85%. Available power there is 1552.95W.
Air conditioner - 1 ton of cooling is equivalent to taking 3516.8525W out of the space being cooled. Average COP for an air sourced heat pump is usually about 3, and you can get higher efficiencies if you want it only move heat in one direction. We should be able to get enough efficiency with a COP of less than 2.5.
For comparison: Photoelectric and conventional cooling
I found a 1 ton unit that takes 900W electric from Mitsubishi, which seems reasonable (and has a COP of about 4). The best efficiency for a solar panel that I could find is 23%, so you'd need 3.9m^2 to power the unit, which is just under the area I allowed for my design -
If you used all four mirrors instead of just three, that is.
So, can anyone tell me where I've dropped a digit? The fact that this looks so doable and no one seems to be flogging it is bothering me.
RE: Actual real world design question - Dartz - 07-16-2021
Your stirling engine will not be that efficient. You need to get the temperature up, up, up to make it work. You need a decent cold-sink also.
You need space for mirror array in the garden, while solar panels can be bolted to a roof.
You will need to adjust the mirrors to track the sun to get the best benefit.
Also, you see how big the molten salt plants can get with massive fields of mirrors?
I know I can get 1kWp of PV, and an inverter, for probably less than a stirling engine and complex, curved mirror assembly will cost. It'll be more reliable as it has no moving parts --- and I can add battery banks to the system to use any excess power at night.
RE: Actual real world design question - Black Aeronaut - 07-19-2021
Something similar has been done with absorption chiller systems. The heat source used was evacuated tube thermal solar collectors - they're so effective at gather solar heat that they even work on cloudy days (Dewar bottles for the effin' win, yo). While the absorption chiller system isn't the most efficient in the world, the evacuated tubes should provide ample enough heat that such a system can build up an ice bank during the daylight hours for night time cooling.
You'll still need a power source to run the pumps and fans, but with the solar-fired absorption chiller system doing the hard work of actually cooling, a couple of solar cells and batteries with an automatic charger should be able to do that quite handily. Though if you don't use DC motors, you'll need an inverter, too.
This isn't a new idea, either. It's been around for a while if the publication date on this report to the US Dept of Energy is to be believed.
https://www.osti.gov/biblio/6742944-solar-evacuated-tube-collector-absorption-chiller-systems-simulation