Do you have ideas or sources for refrigeration w/out electricity?

I don't have the space to construct anything underground. But my housemate and I both love fermented pickles--only they take up so much fridge space! I want to build something that will keep things at least cool even in our bone dry 108 degree summers. I have access to endless pallets. I know that refrigeration technology has been around for a good long time, using evaporation or airflow. I'm wondering if anyone has a practical design for this sort of thing.

Hot and dry?
You're in luck!
Evaporative Refrigerator No Moving Parts No Electricity

Not exactly wood working, but definitely doable.
Of course it presumes a ready supply of water.
Propane freezers/ refrigerators, air to soil geothermal heat exchange,RV air conditioner running off of solar PV, and pickles done in the traditional fashion of a culture that originated near  the equator, are other solutions.

Whereabouts are you, Corey? Where you are and what it's like, along with what you have access to, will determine what your best bet is.

I like a springhouse or wellhouse, but you need either a cold spring or a cold well for that to work properly, but you could pump well water out of a well, through copper tubing arranged around a metal cooler with the insulation on the outside, and bam, you've got a box that will stay as cold inside as that water can make it.

The Tudor-era monastic farmers would cool brewing areas and others that needed to stay cool by flooring with unfired clay, arranging windows so that there would be a cross-draught, and then wetting down the floor. The forced evaporation of the water by the wind off of the clay would cool the clay, and the whole room by extension.

And of course there's the bit about the giant unfired crockery filled with water with the wicking cloth draped under the lid to fall both into the water and down the sides of the vessel. The dry air forces the evaporation of the water, cooling the vessel and the water inside.

What is your situation?

-CK

In a hot and dry area I would do what the natives do in similar enviroments.
Ferment then dehydrate, I think alot of the good microbes are still alive just dormant.
Or you could figure out how to ferment at ambient temperature and only make weekly batches vs enough for "an entire year".

I like using kefir cultures to ferment my vegetables. It has 30-40 different species of good microbes.

I'm not sure what you thinking is with using pallets, but if you have the space to use pallets outside, and you have an area that is not getting any sun (poleward side of your dwelling), then you could take the pallets and assemble them to form a shed.  And then you fill the spaces within the individual pallets with earth material.  Use only the heaviest hardwood pallets for the internal layer with the more solid side of the pallets facing in.  You can put several pallets thickness on the outside, making the thing have a fair amount of thermal barrier from the external air.  keep adding a couple more layers of pallets without dirt after you are satisfied with the thickness.   Drape a sheet or two over the outer pallets, and have the sheet sitting in a trough of water on each side.  As the water evaporates into the drier air, it cools the air that surrounds outer layers of the pallet pile.  The biggest issue is building an operable insulated door that seals well to keep the air inside cold, but you should be able to figure it out if you have the doorway sit flush in the first place.  The doorway would be the only place that requires framing (for the purpose of sealing it all up) as the heavy hardwood pallets, if placed so that they are vertical and in a smaller gap than the top pallet, would hold up the ones above from causing structural issues.  When in doubt, though, brace it with some scrap wood.    

Some people bury an old fridge or freezer at ground level in a shady spot and use it like a root cellar (door opens at ground level). Maybe that would work.

You're not going to get "refrigeration" from evapoartive cooling, especially not in 108 degree weather.

If the humidity is single digits then you can use evap cooling to bring the temps down maybe 25-30 degrees.  That will drop 108 degrees down to low 80s, maybe high 70s if you have a REALLY effective evap cooler.  
You could get it own another 5-10 degrees with a two stage, indirect/direct cooler, but it would be cheaper to buy and operate a refrigerator.  

Sorry, but in real life you're not going to be able to get temperatures below 60 degrees without a heat-pump (i.e. a refrigerator)

In my experience, Peter is correct. An evaporative cooler brings the temperature down to a cooler level, around 20° F  to 30° F lower, but only under the right conditions. When I was a young person in worked a couple years in a commercial greenhouse operation that used a swamp cooler in one of the houses. The cooler mats ran the entire length of one end of the greenhouse. Electric pumps kept water flowing down the mats. Each mat had a giant fan (electric) blowing air through the mat. The set up kept that greenhouse cooler by about 20° F to 30° F depending upon the weather conditions. A simple home set up may not be as effective. And surely it would not bring the temperature down to refrigeration temperature. Things just feel cool in comparison to room temperature.

Without a spring, creek/river, or cave it would be difficult to cool foodstuff a low enough temperature  in such a hot environment without investing money. You could consider....
...a propane refrigerator (or an old kerosene one if you could find it).
...invest in a solar, wind, or hydro electricity generating array to power a standard DC or AC refrigerator.
...build a series of underground piping to tap into the cooler earth temperatures, then move the air via fans through a cooler box
...build the equivalent of an old fashioned icehouse with night time vents that channel cool night air into the "icehouse" ---- or purchase ice to cool the icehouse,
...use an old fashioned icebox. You'd need to buy block ice on a regular basis.
...use one of those super insulated modern coolers and buy ice as needed. These are popular here in my area. Some of those coolers are quite large.

Your goal is to achieve refrigeration temperature. That may be a challenge.

Just a few more comments....

When my grandmother didn't have refrigeration, but used a spring house, she would bring the butter or milk up to the house and store it in a larger porous clay crock. The crock sat in a shallow pan of water and she would ladle water over the crock from time to time. The evaporation kept the items cooler than room temp, but not cold. She was fortunate to have a decent spring house to help extend the shelf life of certain food items, and a root cellar for less temperature sensitive goods. She also kept drinking water in an evaporative crock so that it was refreshingly cool.

There are some small units designed to keep vaccines cool in areas without electricity for refrigeration. I'm not real familiar with them but I believe they work on the absorptive system, much like a propane frig. The problem here is that they are small and pricey. I don't think they could store many jars of pickles. And I don't know what sort of heat source they are designed to work off of.

100+ years ago there was this ...

The grandparents lived through four  'refrigeration eras':

1. A perforated metal meat safe that would be hung from the ceiling with a tray of water on top and draped with a cloth. The breeze kept things cool in the subtropical climate.
2. A meat safe with a big block of ice in it had a similar effect - an 'Ice Man' would deliver it, like a milkman or baker once did.
3. A kerosene fridge - small pilot flame heated pipe work that contained ammonia and thus chilled the space. These are still available and also run on LPG.
4. Typical electric fridge.

I like the idea of the kerosene fridge because it's widely available and not all that environmentally unfriendly - it can come from a variety of sources.

It can also be operated via a solar panel and battery setup.