Most research facilities that I am aware of require an application to show what science you are doing and what you are attempting. They then pool all the applications and select the ones that are 'most promising' - and dole out "free" time but not unlimited. One facility, Jeulich (in Germany) has it's process documented - http://www.fz-juelich.de/ias/jsc/EN/Expertise/SimLab/prep_access.html
If you can strike up a collaboration with faculty at a Canadian university, there are many facilities available through Compute Canada. (We have a category of access which is has an application/review process, but there is still lots of "buffet" style access.) I'm happy to help.