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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/
> Archive
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