When looking at different cooling methods, the first thing you need to know is how much energy (heat!) you need to remove. You have to know your energy inputs and outputs. The inputs are primarily the sun or solar radiation, but they can also be air from the outside. We’ll focus on solar radiation input, as it’s the biggest factor. Our outputs are our cooling mechanisms. Probably the most common method is simple air exchange with the outside air. We’ll add to that list geothermal and water chillers, but we can even include evaporative coolers and traditional air conditioners. We’ll start out with a very rough way to estimate and go into more accurate forms in subsequent blogs.
Estimating Input using the Solar Constant
The average solar radiation received by the earth is about 1300W/m^2. After atmospheric absorption, it’s around 1000W/m^2. That makes things easy. All you have to do to get your radiation input is to multiply the surface area of your greenhouse by 1000. My greenhouse is 8.9m^2 so my energy input is 8900W or 8.9kW.
Energy Input = 1000W/m^2 * GH Surface Area(m^2)
Now that we have a rough estimate how much energy we need to remove, we can look at how we can cool that with different methods.
This type of cooling requires 4 basic parts: geothermal temperature, setpoint, tubing, and a means of transferring the energy into the water. For our setpoint, we are using 32C and assuming the geothermal temperature is 15C.
We assume for simplicity that we are able to transfer all the energy input from the sun into the water. This is really important but we could dedicate an entire article on just this topic. I’ll briefly mention a few methods of getting the energy into the water and move on. Methods include: copper/aluminum air-to-water heat exchangers, tubing distributed in the greenhouse flooring (using the surface area of the greenhouse flooring to transfer the heat), direct radiation to a water reservoir.
We also don’t assume any bonus energy transfers from condensation or evaporation.
We are going to use a script I wrote to try to figure out how much tubing we are going to need to bury underground. We run it like this:
python3 tube_length_calc.py –greenhouse redhouse.json
redhouse.json is my greenhouse and you will want to edit it for yours. We just need greenhouse_dimensions and optionally “pump_flow_rate” for this script. We can also change the flow rate with the “–flow_rate” option.
Tubing diameter : Watts per meter tube length
1/2in (0.0127m) : 0.72W
Using the –tube_diameter argument we can see how much doubling the tubing size helps:
python3 tube_length_calc.py –greenhouse redhouse.json –tube_diameter 0.0254
Tubing diameter : Watts per meter tube length
1in (0.0254m) : 1.44W
I use 1/2″ tubing, so to get enough cooling for 8900W, I’d need 8900/0.72 = 12420 meters of tubing length. That’s a lot of tubing! Is it correct? I am not sure. My script is open source, so feel free to look at it and check it. We need to be clear what the script is telling us. It is trying to transfer all the solar radiation to the soil. That is a factor of the thermal conductivity of soil, the temperatures of each, and the surface area in contact. We can play around with our setpoint, the flow rate and the tubing diameter and this will change out outcome. Most likely, geothermal will be a supplementary method used with other cooling methods. So we can play around with the energy input as well.
Air is going to be similar to water in how we figure out how effective it will be. We will use our tube_length_calc.py script to figure out cooling potential per meter length of tubing. We will use the same setpoint of 32C and 15C for the geothermal temperature. We will use 0.102m for the tubing diameter (4in pipe), and an air-flow rate of 94 liters per second (about 200 cubic feet per minute). Like our water calculations, we are not assuming any condensation/evaporation effects which are complicated and unreliable.
python3 tube_length_calc.py –greenhouse redhouse.json –tube_diameter 0.102 –flow_rate 94
This gives us a rate of 5.77W/m of tubing. If we use 0.152m tubing (6 inches), we get 8.59W.
We require 1038 meters of tubing for my greenhouse. That’s still a lot of tubing, but much less.
Is geothermal air better than water?
It certainly transfers more per meter of tubing because of the increase in surface area. Water of the same tubing size has identical using this script. The differences are going to be in the transfer of energy to air. Air doesn’t absorb much visible light. So all energy absorption comes from its atoms bumping into things that do absorb the direct solar radiation. This is a slow process because air has the worst thermal conductivity of almost anything. The good news is the surface area is huge: effectively the entire surface area of everything in your greenhouse.
Energy transfers to water much more easily (24 times better) and can store 4 times the energy per gram, but performance is going to greatly depend on surface area of radiation to water heat exchange and the water to soil heat exchange (the tubing diameter).
Condensing Air Conditioner
These are the easiest to estimate for because they usually come with a rating in BTU/hr. 1W = 3.412BTU/hr, so we can do a simple conversion to get the required size of air conditioner. 8900 x 3.412 = 30367 BTU/hr. These are expensive up front and expensive also to run.
Another expensive option is a water chiller. There are two varieties air cooled and water cooled. If you have need of both heating and cooling, the water cooled option is a good one. Either option is a good addition to a geothermal water system. It can also be used to cool LEDs if those are water cooled. These are usually rated in “tons”. Each ton is equivalent to 12,000 BTU/hr or about 3500W per ton. For my greenhouse without geothermal, I’d need a 3 ton.
Water cooled chillers require a second water loop to transfer the heat. It can be transferred to a pool heater system, a water cooling tower, or even used to heat water for your home.
I want to look more into both advanced estimation solar input and these different cooling methods including more in subsequent blogs, so stay tuned.