Hi Dave,
Sure had me going for a spell, however, I got out
the equations and believe I can point out a different view
point.
If I understood you correctly, your basic assertion
is that the same mass flow is required for both thin and thick
radiators and since the thicker radiator has a smaller frontal
area it must therefore have a higher velocity air flow to generate
the same mass flow to remove the same heat. Furthermore
the higher velocity also translates into more drag (even with the reduced
frontal area due to the drag being proportional to the square of the
velocity) - but all the above is not necessarily
true.
In fact I found a NACA study where they
looked at the effects of using thicker radiators and I have worked out the
equations on a spreadsheet which I believe sheds some concrete facts on
the old thin Vs Thick debate - but, it is complex and I'll wait a bit
before springing it {:>).
However back to your contention that both
radiators the thin and the thick required the same mass flow to remove the
same amount of heat - it just isn't so and here is why.
First, we have two radiators one is 1" thick and 1
square ft in frontal area, the second one is 1/2 square feet of frontal
area and twice (or more) as thick. Now turning to our trusty
equation for heat rejection and mass flow.
Q = m*Cp*DeltaT is the basic equation that tells us
how much heat we remove for a mass flow "m", a specific heat (air = 0.24)
and temperature increase in the medium (air) or DeltaT.
Taking a specific example of say - 5000 Btu/min
(which is about the amount of heat an NA 13B generates at 175 HP that
needs to be rejected by the coolant). We know the Cp so that leaves
the DeltaT and that is what makes the difference. We have to assume
a DeltaT, lets say 50F (yes, it could easily be different but bear with
me) then we have
m = 5000/(0.24)*(50)/60 = 6.94
lbm/sec of mass flow . and lets say we have a 1
square foot radiator to get rid of that heat. Then the velocity
requires V1 = m/(p1A1) = 6.94 lbm/min/(.0765*1) = 90 ft/sec = 61.36
mph through the 1 square foot radiator. Perhaps a bit higher than
desirable but that's what we get.
Now if I understood you correctly your point
is that the same mass flow is also required for the smaller
radiator (1/2 sq ft) to remove the same amount of heat and therefore since
frontal area is 1/2 the size, the velocity must be double that of
the larger radiator to get the same mass flow and remove the same quantity
of heat. But, it just isn't necessarily so.
Taking the same conditions as before, except this
time I use a DeltaT of 100F (hey! its permitted as I'm using a different
core here{:>) see further discussion on effects of thickness on
DeltaT). Now we have m = 5000/(0.24)*100/60 = 3.47 lbm/sec of mass
flow is required. That is 1/2 of the mass flow required with a
DeltaT of 50F.
Therefore even with 1/2 the frontal area, I can use
the same air velocity as before and remove the same amount of heat with
1/2 the mass flow and with LESS drag because my frontal area is now 1/2
that of the thinner larger radiator and the velocity is the same.
Now you can say I cheated by having a different radiator, but that is
certainly what you would do - as that is what we are discussing are the
relative merits of thinner vs thicker for our application.
But, If you reduce the frontal area of the
radiator, then you must increase the thickness (or add more fins,
turbulators, etc) to increase its Heat transfer coefficient to
continue to reject sufficient heat to the air flow. Therefore,
The air temperature coming out of a thicker radiator is going to be higher
than a thin radiator. The reason is both radiators are flowing at
the same velocity (remember I did used the same velocity for
both radiators), and since the velocity of the flow is the same for both
radiators, the air spends more time (twice, three, four times depending on
the thickness) in the thicker core of the smaller radiator. The
longer duration of the air in the thicker core causes it to be absorb more
heat and be raised to a higher temperature than the thinner radiator,
therefore the higher deltaT (for the same velocity air).
This probably did not/and will not convince you of
the merits of the thicker vs thinner and besides I know your reservations
about my deductive reasoning {:>). So I am working on
understanding fully the Naca study I found that addresses the effect of
thickness on required mass flow and heat rejection. I believe it
would be considered a fairly credible source and will hopefully enable all
to reach their own conclusion. I think its going to blow the socks
off this thick vs thin debate - but, then I've been wrong before
{:>)
Boy, this is fun!!! Sure keeps the old brain
working (hopefully).
Anyhow, Dave, I respectively disagree with your
assertion (see above) {:>)
Best Regards
Ed
----- Original Message -----
Sent: Tuesday, November 13, 2007 9:19
AM
Subject: [FlyRotary] Re: Thick vs Thin was :
Diffuser Configuration Comparison
> David Leonard
wrote:
>> Why is it going slower? BECAUSE YOU HAVE DESIGNED
YOUR THIN RADIATOR SYSTEM
>> DUCTS SUCH THAT AN EQUAL AMOUNT OF
AIR PASSES THROUGH AN EQUAL VOLUME OF
>> RADIATOR AS WOULD OCCUR
ON A THICK RADIATOR SYSTEM. (This is the big if...
>>
system design... but bear with me). ie, equal amount of air, equal
volume
>> of radiator - in the thin radiator system the air will
be flowing more
>> slowly.
>>
>
> I agree with your concept, Dave, but I think you underestimate
the
> difficulty of fitting a large faced radiator into the
physical
> constraints of the area available in a small
airplane. I worked on
> trying to use a large, 1" thick
radiator for a while, and this was in a
> delta planform. I
had comparitively HUGE amounts of volume to work
> with. I
eventually gave up, as there was just no reasonable way to get
> a
duct built around it that would slow the air down. As you increase
> the face area, you increase the size of the duct necessary to
expand the
> air without separation. The best radiator and
duct ever created will be
> useless if we have to leave it on the
ground because it doesn't fit in
> the airplane.
>
> I
think the flow chart for sizing a radiator for our needs should follow
> something like this:
>
> 1) Mark out a space for the
largest volume that you can fit a radiator
> and its associated
ducting into. Insure that routing for the hoses will
> be
convenient, and the ducting can be made something resembling
efficient.
>
> 2) Visit one of the websites like
frigidair.com and find a radiator that
> meets the dimensional
specs you came up with. Or contact Jerry and have
> him make
you one of that size.
>
> 3) If the core volume is less
than 700 cubic inches, add another.
>
> 4) Go fly. If
it is to cool (<160F), choke off the inlet a little. If
>
it is to hot (>200F), fiddle with the ducting.
>
>
--
> Homepage: http://www.flyrotary.com/
>
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