I have three round cardboard mailing tubes of various lengths. 49" 30" and 17" all from things that I have bought or ordered over the years and came in the mail. They all have plastic plugs in the ends and I cover the "bottom" one with tape to keep it in place and to keep them from breaking out. The larger one is about 2-1/2" or 3" O.D.
I just stand them on end and store all my dowels, according to the length in each one, in a corner.
I would recommend that if you don't have any mailing tubes, see if you can find some plastic pipe and plug the ends with some wood cut round and fit snugly.
Rog
PS I would check with a UPS or FEDEX shipping station and see if they have any low cost mailing tubes available.