From wikipedia:
Aluminium beverage cans are usually recycled by the following method:
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Cans are first divided from municipal waste, usually through an eddy current separator, and cut into small, equally sized pieces to lessen the volume and make it easier for the machines that separate them.
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Pieces are cleaned chemically/mechanically and blocked to minimize oxidation losses when melted. (The surface of aluminium readily oxidizes back into aluminium oxide when exposed to oxygen.[10])
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Blocks are loaded into the furnace and heated to 750 °C ± 100 °C to produce molten aluminium.
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Dross is removed, and the dissolved hydrogen is degassed. (Molten aluminium readily disassociates hydrogen from water vapor and hydrocarbon contaminants.) This is typically done with chlorine and nitrogen gas. Hexachloroethane tablets are normally used as the source for chlorine. Ammonium perchlorate can also be used, as it decomposes mainly into chlorine, nitrogen, and oxygen when heated.
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Samples are taken for spectroscopic analysis. Depending on the final product desired, high-purity aluminium, copper, zinc, manganese, silicon, and/or magnesium is added to alter the molten composition to the proper alloy specification. The top-five aluminium alloys produced are 6061, 7075, 1100, 6063, and 2024.
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The furnace is tapped, the molten aluminium poured out, and the process is repeated again for the next batch. Depending on the end product, it may be cast into ingots, billets, or rods, formed into large slabs for rolling, atomized into powder, sent to an extruder, or transported in its molten state to manufacturing facilities for further processing.
So, if i get this correctly, we need 5 steps:
- To cut the cans in pieces
- To clean & store the aluminum in an environment without O2
- To melt it at ~750 °C
- To separate the product from the dross (maybe we could simplify by ommiting this?)
- Then we got aluminum ingots
From these, only 2 presents a problem, esp. the O2 part.
Maybe a contraption including a vacuum creator and a pressurized chemicals jet will solve it?
I could imagine creating a metal “box” with a tube where the vacuum creator connects, another tube for connecting pressurized chemicals leading to Beck/Arnley’s Fuel injectors so that the chemical agents will clean the material.
The bottom could consist of holes where the chemicals would drain, and be retractable (and manipulated from the exterior) so that the clean material could “fall” into a (still in vacuum) furnace.
Of course the heating of the furnace can happen by using an exterior heat source, like fire (slow), or electric forge or acetylene torch.
Now i feel almost proud for the “invention” 
Thing is that this is almost within a survivor’s ability to craft too. 