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George, here you are getting into something we have not
discussed in depth.
Two equations/laws of fluid dynamics are involved.
Bernoulli's equation and an equation called the law of continuity.
This equation relates to the fact that you don't create or lose mass in the
duct, so the mass flow is a constant everywhere in the duct. The mass flow
is frequently shown as the product of air density*cross section area*air
velocity = mass flow or simply p*A*V
The equation goes something like this, the
p1A1V1 (mass flow at point 1) = p2A2V2
(mass flow at point 2). Since the air is normally considered to act like
it is incompressible at the lower speeds we are talking about, that means
the density p1= p2, so we can drop them from the equation
for this explanation.
That leaves us with A1V1 = A2V2 or the
product of the area and velocity at point 1 is equal to the area and velocity at
point 2 in the duct. Now if A1 = A2 then V1
has to equal V2 for the two sides of the
equation to be equal. But, what if A2 = 2* A1
or the cross section area of point 2 is made twice the cross section area
of point 1. Then if A2 = 2*A1, we can substitute
2*A1 for A2 in the equation and we have the
following.
Taking A1V1 = A2V2 and substituting we
have A1*V1 = (2*A1)*V2. So what does that tell us
about the air velocity at point 2 now that we have doubled the cross section
area there?
Well solving the equation for the new V2, We can call the
new velocity at point 2 V2n (for V2 new) with
V2o being the old velocity at point 2.
So we have V2n =
A1V2o/(2*A1) Now we can cancelled the A1
in the numerator and denominator on right side of the equation
leaving
V2n =
V2o/2 This shows us that the new
velocity at point 2, V2n is 1/2 the old velocity
(V2o) at point 2 or V2n =
0.5V2o
So what this says is the velocity starts changing
(slowing in this case and the pressure increasing ) as
soon as the cross section area A2 starts to increase from A1. The
process continues until the area stops expanding (or the kinetic energy of the
moving air has all been converted to a static pressure increase) and that
is where the process is finished as the duct/diffuser has expanded to its
maximum area. Actually, this process happens with both nozzles and
diffusers just the opposite way. Its derived from the Bernoulli equation
and the continuity law.
So if you had a duct whose cross section area continued to
expand for a distance of 2" or 20" or 200" then theoretically the
pressure would continue to build and the velocity to decrease until all of the
kinetic energy of the moving air has been converted to pressure increase.
This is all theoretical, there are losses and turbulence and etc, that makes a
difference, but you get the ideal. It depends on your specific diffuser
dimensions.
Think of it this way, George, some wind tunnels have
diffuser which expand over 10's of feet while some microscopic cooling systems
have diffusers measured in 10th's of an inch.
Now aren't you sorry you asked
{:>)?
Ed
----- Original Message -----
Sent: Friday, November 09, 2007 4:52
PM
Subject: [FlyRotary] Re: Total,duct,
Ambient or Velocity????
Ed and Al,
This is all good info me, it either confirms,
clarifies or informs.
The straw concept is a timely reminder of
pressure differentials, a good example IMHO.
One thing I would really love to know is - at
what point in the inlet duct does the dynamic flow change to static pressure.
I would assume this would vary with different shaped ducts and different
dynamic flow ( airflow speed).
Your opinions on this or guesstimates ie 1",
2" or 3" from the face of the rad, would be of great interest to
me.
George (down under)
Hi Al,
Not picky - some good points as always . Yes, I
agree, generalization does have its pit falls, but on the
other hand I think they can help promote a conceptual understanding
which can be refined (through study and experiments) to meet a particular
situation. As we know, cooling airflow is attempting to balance
conflicting aerodynamic and thermodynamic principles.
I also agree that much of this stuff
addresses the "Perfect theoretical duct" out of necessity as there is
only one perfect duct but many, many implementations
that fall short of perfect. So its more of a conceptual
goal to be aimed for - it may never be achieved,
but provides at least guidelines. But,this is
just my opinion of course.
Actually, I disagree, you can not "suck" air though
anything. You may create a partial pressure difference with the fan,
but it is the higher pressure air on the other end of the duct that pushes
or "blows" air through the duct into the area of lower pressure
{:>) .
But, semantics aside, yes, I agree, lower exit
pressure is what you are after and that does not always equate to larger
exit duct area. In fact, if the air heated by the core flows through a
nozzle it might even produce thrust and lower exit pressure using a
smaller exit. But, in general, I still believe that in most of our
cases, we are short of the level of duct design that would reliably permit
that. What we need is someone to invest in one of those $$$$ Computer
Fluid Flow software programs and see what they would reveal.
Ed
----- Original Message -----
Sent: Friday, November 09, 2007 1:09
AM
Subject: [FlyRotary] Re: Total,duct,
Ambient or Velocity????
It would
seem "reasonable" that a low pressure area at the exit will help
flow through a duct - no argument on that point. What the report
appeared to say is that the after a certain point opening the exit area
wider does not appear to have any additional benefit. (Exit “area” and exit “pressure” are not interchangeable
terms)
That if the duct is capable of "using up" all of the kinetic
energy in your air flow by obstructions, pressure drops and friction
losses then enlarging the exit does not necessarily add to the
flow.
Remember you can
not suck air through a duct, you can only blow it through. (Of course you can suck air through a
duct – I do it after (and sometimes before) every flight with the fan I
have on the back side of the radiator) So in effect if the
straw is pinched you can "suck" on it all you want but it won't increase
flow {:>).
If I understood
the report, it appears that enlarging the exit area beyond the
frontal area of your core provides little if any additional benefit.
That does not mean cowl flaps never work or provide benefit. In fact
it appears that the better your duct, the more benefit the cowl
flaps appear to have, the worst your duct, the lesser benefit - just the
opposite of what you might think.
Ed;
Don’t mean to
be picky, but some of these generalities are making me
nervousJ. These
things are applicable only when the duct/diffuser is operating at max
efficiency – which is rarely the case.
Lot’s of good
info.
Thanks. You’re right; it’s some kind of magic, and you don’t know
for sure until you built it and try it.
Al
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