Hey London,
"Would it be sensible to cool after the TC and then cool again after the SC?"
That would not be sensible, that would be a must on a compound set-up unless your feeding a big bad tractorpulling diesel which is throttle-fueled
think of ramming 90degreesC of compressed air into the second compressor to compres it even further buy ratio 1.5, the volume gets far smaller the Mass goes up and heat is generated, and lots of it to get the Mass flux even higher for the same volume of air you need to cool it down, if you're only IC would be after the turbo and that would be 100% efficient you'd still be feeding the engine with 90dC+ (200dF+) airtemp which at that presure ratio would melt a piston in seconds.
let's asume 1500hp is wanted and we go by GM's rule that for every 100hp you'd need about 150CFm of air.
15X150=2250CFm of air
delta T is 90-20= 70 degrees (20 = ambient temp)
ideal law of gasses says (the rulebook) 90 degrees air has a density of 0.969 kg/m^3 so I'll recalculate all CfeetM's to CmeterM
2250CFm=63.712 CMm
we're trying to find M * T *cP = ???kj of energy stored
Mass of the air is 63.712 * 0.969 = 61.736 KG of air per Minute
Delta T = 70
rulebook cP for air is 1
so there is { 61.736 * 70 * 1 }= 4321.6 KiloJoule of heat energy stored in the amount of air needed,
TWICE because first the turbo get's this temp and after that the SC will do the same again.
4321.6Kj : 60sec = 72KW of power per charging stage
so Yes intercoolers are very very important for this sort of set-up.
in fact this calculation is the simplyfied version because when temp goes down presure ratio will also slightly go down Nasa has so nice maths info of this fenomenon called isentropic expansion.
here it is (just click through the safety screen it works)
https://www.grc.nasa.gov/WWW/K-12/////airplane/compexp.html
so Now I'm off going to get some coffee since it's only 6:30 over here.
for the charge air water coolers after the SC, when it's finished I'll post the pics, still in solidworks drawing stage.
regards Thomas