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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