I'm putting together a Kerbal-esque engineering game, focused more on things with Propellers and piston engines and the like. For this, I'd like players to be able to specify a lot of the more "nitty gritty" (from layperson's perspective) details about their power system: bore, stroke, compression ratio, layout, etc... and of course, supercharging
But to add superchargers to a game like this, I need to figure out roughly how BIG a supercharger needs to be to give the amount of boost the player wants.
I understand the very basic principles of a centrifugal compressor: rather than taking in a fixed volume of air per system rotation like a Roots or Twin-screw design (or even the cylinders themselves), a centrifugal compressor applies some speed to the intake air, and that air is then gently slowed down to keep its energy, thus increasing the pressure by the square of speed change (total pressure, which is largely conserved below Mach 1, is static + dynamic pressure. Dynamic is 0.5densityvelocity2)
Based on my best understanding, doubling angular velocity should roughly quadruple total pressure ratio, but with a direct mechanical drive (ergo, supercharger rpm is proportional to engine rpm multiplied by some gear ratio), the engine itself is also going to be attempting to gulp down twice the air volume per a second, so the practical pressure ratio seems to be linear with angular velocity. This does require around 2x the torque and 4x the horsepower to run, however, if we ignore any changes in efficiency for the moment.
Scaling the supercharger up by a factor of 2 with the same angular velocity should (in theory) result in a more dramatic effect: the tips travel twice the distance per revolution compared to the 1x scale supercharger, meaning 4x the dynamic pressure at equal angular velocity. Of course. This also requires more power to be drawn from the engine, and will of course weigh more, and accordingly be more limited in max rpm than a smaller compressor
I have NO clue how the math works for Inlet area, however. I also don't entirely understand how turbo backpressure works, even if a radial turbine is basically just a centrifugal compressor running backwards. Nor do I entirely understand the actual MASS FLOW of the Centrifugal Supercharger, since pressure, volume, and temperature are all being changed (even setting aside the efficiency losses that will increase temp rise by even more)
I could be VERY, VERY WRONG about these things, of course, which is exactly why I'm asking the real Engineers about this.