I have a home built RepRap with all sides open..
Would there be any advantage to enclosing the print area in acrylic?
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It is hard to tell whether you personally should enclose your printer. However, you asked for the advantages and I will name some of them on which one can base a decision.
A 3D printer enclosure
There are obviously also downsides, as: connected work/money to make it, increased space used for the printer, and, if not well made for that purpose (which it should be), increased difficulty in repairs and maintenance of the printer itself (i.e. to get the printer out of the enclosure).
@kamuro provided an excellent answer, so I'll just try to add by playing devil's advocate.
Possible things to look out for:
People add a "passive heated chamber" when they are printing in ABS. However I personally think the best reason to have a custom chamber is so you can add an air filter. Adding an air filter will reduce your exposure to fine air particulates. It is generally considered a bad idea to breath in particles from plastic.
For PLA you will not want an air chamber. If you want to do an air scrubber they you will need air input to avoid the heat chamber from getting hot.
On that note as we see in the z18, PLA can benefit from an Active heat chamber, but you will have to figure out what the optimal temp is.
Consider the environmental conditions where your printer is.
I have my printer in a garage, where the door is sometimes open, closed, or slightly ajar. This leads to gusts of wind, causing lifting and ruining multiple prints.
I surrounded the printer on three sides with walls made from the original packing foam, and my lifting problems have utterly vanished.
The top and front side are open, so I have a "four sided" box. Heat does not build up, but the variable wind gusts are minimised. Access is slightly reduced, but not a lot.
Ender 3 V2, printing the "Ender" brand of PLA from Creality. Bed is at 55 °C and print head is 200 °C.
If you will be printing PLA, no, or at least not without active cooling of the chamber. PLA's glass transition temperature is sufficiently low that the ambient temperature matters a lot to whether layer N can cool enough before layer N+1 is laid, in order to have a firm surface to extrude against and bond to. This especially matters with overhangs and complex geometry. If you use a heated bed for adhesion, the chamber temperature will tend to reach nearly the bed temperature, keeping your print soft the entire time. In a worst case, it might even cause heat creep and jam the heatbreak. Even if you're not using a heated bed, waste heat from the hotend will warm the chamber somewhat; expect temperatures of at least 35-40 ˚C rather than a (preferred) ambient 19-22 ˚C.