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> Ed,
>
> The most the rejected heat could
change in this case
> is 300%. You made a 300% change in thickness
which
> results in a 300% change in wetted surface area.
Hi Ron,
The heat rejection was 283%,
so a bit less than the 300% thickness - how valid? Well, that is why I
posted this to the list. What should the heat rejection be?? That is
what I am after. If there is a well-known correlation between radiator
characteristics and heat rejection - what are they.
If I look at K&W (page 266) they
show the heat transfer Coefficient Kh for turbulent flow in a core as Kh=
1/ 2*L/D*0.316*(Re)^(-1/4). Re being proportional to Mass flow
velocity. So If I look at this equation it would appear that heat transfer
goes up proportional to the thickness (L) and decreases as the diameter of
the tubes hydraulic diameter (D) gets larger. It appears that as the
velocity (mass flow) decreases the Reynolds number goes down, as it goes down
the 4th root of it decreases it even more and then in the denominator it makes
Kh coefficient higher all implying more heat transfer per unit thickness of the
core.
But, then I could be misinterpreting the
factors in the coefficient, but I do not see any factor in the equation that
would indicate this heat transfer coefficient changes as the air flows through
the core. But clearly the decreasing deltaT causing the
last part of the thicker's core surface area to be less effective in
transferring heat to the air - but, how less? Does it decrease other
than linearly?
> Your number will be lower for a couple
reasons:
>
> 1) Decreased mass flow (5% in your
case)
I guess I did not make it clear. But,
in calculating the heat removal, I used the mass flow for the thicker radiator
which was down by 5% - in other words the mass flow used to calculate the heat
removal for the 4" thick rad was decreased by 5%. So I think that kept the
apples with the apples, at least in this case {:>).
> 2) Boundary layer thickness grows as you go
deeper
> into the radiator. The last 1" of radiator will never
> be
as effective as the first 1".
I agree, the boundary layer thickness grows
and the deltaT decreases both which decrease the heat transfer - but, I'm
uncertain as to what extent. But, There is still metal transferring heat
to the air even if it is less effective. As I mentioned, I have looked for
reports/experiments that would provide a better handle on what thickness does or
does not do. There do not seem to be a whole lot around explicitedly
addressing that question, although almost all the Naca reports on
radiators are referring to radiators that are quick thick by our
standards.
If you look at their charts in the
back of the report, they are plotting effectiveness with radiators from 4" to
16". The equations they/I used are based on imperical data so I don't
have an answer other than they did an experiment and reported the results.
Perhaps the answer is buried in the report and I simply don't have sufficient
understand to recognize it or interpret it correctly.
> I know your equations accounted for (1) but not
sure
> about (2). I haven't checked your reference.
Certainly needs to be check by
someone. I am not interested in leading anybody astray - I don't get as
many beers when I do that {:>). I'm the first to admit a severely
limited understanding of this stuff, but I think there are questions regarding
these areas (certainly is in my mind) that folks like you can bring clarity
to. Besides that, I could easily have
screwed up these equations in the spreadsheet - but, I did check against their
examples and think they are OK.
> The drag increase of 58% sounds way too low. You
> increased
surface area by 300%. Unless mass flow
> decreased a lot (it didn't) or
drag coefficient
> dropped a lot (it shouldn't), then this can't
be
> right.
Well, there is no change in frontal area between the
radiators, so the old 1/2pV^2*A drag factor remains essentially the same for
all - discounting the small 5% decrease in mass flow which would (by
itself) help decrease the frontal drag some. So the question is would the
increase in skin friction be proportional to the increased internal surface area
( I would presume it is)? And if it is? Then what is the absolute amount
of drag per square inch based on. Is the internal core
drag a small part or a large part of the overall core drag.????
I know - it probably depends........ {:>)
I know the pressure drop across a radiator is composed
of 4 parts. The initial decrease in flow area (open area/frontal area),
the Ventura Contracta effect as the airflow contracts inside the tube entrance,
the friction drag caused by the viscocity of the air and the tube skin (also a
function of hydraulic diameter), the pressure change as it exits the core tubes
. How does it compare to frontal drag?
I imagine it depends on the type of core.
Cores with a few large diameter tubes would probably have less skin drag than
one with a number of smaller diameter tubes.
I can send you a copy of the report if you have any
trouble finding it on the web.
Thanks again, Ron, for your insight and
comments.
Ed
> Ron > > --- Ed Anderson < eanderson@carolina.rr.com>
wrote:
>
>> But in any case, assuming I did not screw
up
>> someplace, here are the results I got when I changed
>>
only the thickness of the radiator on drag, mass
>> flow and heat
removal:
>> 1. The Drag (R) went from 4.28 lbf/ft2 to 6.77
>>
lbf/ft2 or a 58% increase presumably due to wall
>>
friction
>>
>> 2. The Mass flow (M) decreased from
12.33
>> lbm/ft^2/sec to 11.705 or a 5.13 % decrease
>>
>> 3. The Heat Rejected(Q) increased from 6.1707
>> HP/100F
to 23.66 HP/100F for a 283% increase
>
>
> --
>
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