Assuming that selecting your inlet
opening size controls mass flow is incomplete. It is the total
pressure loss for the entire duct (and core) which combined with the available
freestream kinetic energy (due to velocity) that determines mass
flow.
I can make changes to any of the intake, diffuser, core, and outlet and make
changes in the mass flow - so its not just the inlet.
Then I compute the required opening area
of my ram scoop based on the velocity of the incoming air; the speed of the
airplane at the design point; generally a fast climb. Area x velocity = mass
flow rate. The ram scoop is not necessarily 100% efficient, so add maybe 10%
to the area. Now, yes, that is incomplete; but on first order, unless I
do something wrong that causes the scoop to spill air (like poor diffuser
design or too thick a radiator), then it is complete - that is the mass flow
rate. Only changes I make that cause air to spill around the scoop is
going to change that; so on this macro view I can ignore the details of the diffuser
of which you are more expert than I.
Now if I have a well designed diffuser
with an area ratio of say about 4+ I know that the pressure recovery will be
greater than the pressure drop through the rad, so all that air is going
through. Right? Well; here is where we have to start thinking about both the
thickness and the density of the core because the pressure drop through the
core must be less than the amount of pressure recovery – and is why I say
that talking thickness without specifying core density and diffuser ratio is 'incomplete'
because they depend on one another.
But back to fist order; given the
conditions of adequate pressure recovery the flow rate is fixed.
2nd regarding the deltaT
"swap" I made:
I do not agree that you need to compare on the basis of sam
e mass flow or deltaT - the only factor that really
matters is that the needed heat be removed. There are a large
combinations of mass flow and deltaT that will remove X amount of heat. True, but:
The design point heat load is fixed, the
mass flow rate is fixed; therefore the delta T is fixed (see formula used for
computing the the flow rate in the first place.)
Now, given these conditions; we can look
at thick vs thin. We can have a large frontal area, slow velocity through
the core, and have pressure left over for accelerating the air back toward free
stream (along with the heat energy that we pick up which gives velocity by
expansion); or we can make the core thicker up to the limit of the pressure
recovery that we have achieved; and have no remaining pressure at the core exit.
But keep in mind that the have a fixed scoop area for the speed we designed
for; and the frontal area of the rad is the other area in the diffuser ratio;
so making the rad smaller and thicker both cut into the available pressure
recovery. When we reach that limit where we have used all the available
pressure recovery; we have no pressure left over to accelerate the air back to
something closer to that at which it came in.
Because of the effects of the velocity
on heat transfer, as well as pressure drop, there does happen to be a rad
pressure drop (thickness) that results in minimum drag – just as there is
a corresponding delta T that results in minimum mass of the core (all other
things equal; i.e., properly designed).
Now the big caveat - It is clear here
that to take advantage of the less pressure drop in the thin rad to reduce
drag, we have to have an exit configuration that efficiently re-accelerates the
air. If not, or if we going to release the exit air into the free stream
at a negligibly small velocity, then it's a different ball game. Then
from a drag standpoint there may be little difference, and that using a
radiator thickness (pressure drop) that exhausts the pressure recovery, may be
the way to go for fitting into a confined space.
So there ya go; cooling system design in
a nutshell; minus all the magicJ
.
Al G