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Ok folks,
Been developing a bit more
understanding (I hope) of the cooling science/art/mystery - still a long
ways to go, but finally understood a bit more about ducts and diffusers and
why you want to use a diffuser (where possible) in front of an heat
exchanger.
What's a duct and what's a
diffuser?
A duct can be though of as an
airpath with no change in its cross sectional
area.
A diffuser on the other hand
has an airpath that goes from a smaller to larger cross-sectional area
or the area diverges (as they say).
_____
/
/
____ /
_________________
----------------->
Diffuser --------------------->
Duct
_____ __________________
\
\
\_______
Clearly the constant cross section duct is
easier to build so why would you want the complication of making a varying
cross-section diffuser. Note: The terms Duct and Diffuser are sometimes used
interchangeably - so it can get a bit confusing when reading. But,
for our purposes a duct is with unchanging cross-sectional
area.
Well, it took me a while to understand what all the
math meant in real world terms regarding a diffuser (assuming that I now have it
correct).
A subsonic diffuser does one principal
thing - it slows down the velocity of the air mass entering it.
So? you say. (when I want all the cooling airmass I can get) Why should I want
to slow down the air? Well, because its good for your cooling and your
airspeed.
Yep! that what it ultimately boils down to and why
you want a diffuser rather than just a duct.
Don't ask me (yet) how to go about designing the
diffuser you need at this point, but here is what happens in a nut shell.
What the diffuser does is transform the kinetic and pressure energy of the
airstream. With the cross section area diverging (getting larger),
the air pressure increases, the air density increases, the temperature increases
(but not much) and the velocity decreases. The following is my attempt to
explain how this happens.
Explanation of
Diffuser
Picture a tube of air created by drawing a circle
of area Ai (your cooling inlet) through the air at 120 MPH (176 ft/sec) for one
second. That is then the air mass entering your inlet of area Ai for
your Diffuser of area Ae (the large divergent end). The tube of air is 176 ft
long (Li) with an area of Ai which is the same as saying the volume is Ai*Li or
since Li =Vi (for one second), we can say the volume is Ai*Vi. This is the
volume of air that flows into the diffuser section with cross-section area of Ae
= 3*Ai (remember to be a diffuser, the outlet area has to be larger than
the inlet area) but where the velocity of the airmass has dropped to
velocity Ve (where Ve = 1/10*Vi nothing is 100% efficient so there will be some
residue velocity left)
Some
terms
Inlet (small
area) Diffuser
(large area)
Vi (Velocity ft/sec)
Ve (velocity remaining
in diffuser (always some))
Li = Vi/(1 sec)
Le (length of large area)
Ai = Area of Tube
(ft^2)
Ae (area of large
section)
pi = air density
(Lbm/ft^2)
pe (air density in diffuser)
Mass = (Lbm)
Kinetic Energy Ke =
BTU
Consider a air mass flowing at a velocity
Vi through the inlet of area Ai to a diffuser for one second of
flow. This volume of air is Ai*Vi, taking the density (pi -air density
0.0076lbm/ft^3 -not PIE)) of this air mass, one can calculate the mass flow =
pi*Ai*Vi. Mass flow through the system does not change
(subsonic velocity assumed) !!!!
Now have this mass flow be decelerated to Ve (where
Ve=1/10*Vi - a good value for a good diffuser) by a diffuser of area Ae
placed at the end of the inlet. Assume that the area Ae is 3 times larger
than the inlet area Ai or Ae = 3*Ai. Consider what this
means:
1. Since the mass flow must remain constant
through the ducts then pi*Ai*Vi = pe*Ae*Ve. However we know that area Ae
is 3 times larger than Ai, which means the product of pe*Ve must be smaller
by a factor of 1/3 to maintain the mass flow equation balance. In reality,
we know that Ve is also less as the basic function of a diffuser is
to decelerate an airflow. This then means that the density pe must
increase. Actually the density pe, the pressure Pe and the temperature Te
all increase as a results of converting the kinetic energy of the mass flow into
dynamic pressure and increased density within the smaller volume of the
diffuser.
2. It t may seem counterintuitive to have the
pressure and density increase when the area is increased. Most would
predict that the density and pressure would decrease with an increase in
area. This is indeed what would happen in a closed system. However,
a diffuser with air mass flow into and out of is an open system and the airmass
flow continuously brings energy and air mass into the system (diffuser)
3. Consider this: You have a volume of air Li
Long travelling at speed Vi (think of a long tube of air) with the kinetic
energy of= m*1/2piVi^2. This energy is for the column Li long.
Now when the air enters the increased area Ae, the velocity has decreased to
Ve. So we have a volume = Ae*Le. Recall that Ae was = 3*Ai however Le is
1/10*Li (because Length of tube is equal to the velocity divided by time (1
second in this case), so Le is effectively Ve at 1 sec). Therefore we have
the same amount of kinetic and pressure energy that had previously occupied an
volume of Ai*Li, but now it occupies a lesser volume of
Ae*Le.
( I know, I know my duct is not 17.6 ft
long (Le = 1/10Li = 1/10*176 ft = 17.6ft. But that is for 1 second of flow
after diffusion. Even at Ve=1/10Vi, my airflow would actually undergo the
continous diffusion process -the amount of time it takes for the denser airmass
to flow through my diffusers larger area- (approx 6" in length) would be =
0.5ft/17.6 ft/sec = .0028 sec. So you don't need a diffuser
length of 1/10 your Vi as the diffuser is continously processing the
airmass as it flow in and out of it (it does it Very,very fast
{:>)).
So the airmass that now occupies Ae = 3*Ai and Le =
1/10Li (because we assumed the diffuser decelerated the Vi to 1/10Vi = Ve (and
for 1 sec timing Le = Ve) so Volume Ae*Le = 3*Ai*1/10*Li = 3/10*Ai*Li.
Again the diffuser volume AeLe = 3/10AiLi volume.
So the volume the 1 second of airmass
occupies after being processed by the diffuser only 3/10ths (in this example)
of the original volume it previously occupied in the 176 ft long tube of
air.
4. So with the original column's airmass now
in a volume 1/3 the original size, we can see why the pressure, density
and temperature increases in the diffuser. Its because all the kinetic and
pressure energy of the original airflow (and its air molecules) now
occupies a volume only 3/10's as large as it once did.
5. Therefore in summary, the density,
pressure and temperature all increase and the airflow velocity decrease in a
subsonic diffuser (you can check this in plenty of references).
Additional notes of interest: Duct vs
Diffuser. So, Ok, fine a diffuser is magic, but so what? Here is
the so-what!
Both a duct and diffuser act as a container for the
air flow. However, the duct does not reduce the velocity of the
air as does a diffuser (Note: There is some reduction due to side wall
friction and turbulence in a duct (but that is loss energy and not
recoverable) but nowwhere near the reduction of airflow velocity cause by a
diffuser).
If the radiator were unshrouded, then while
some airflow would continue to go through the center, much of the air at the
outer edges would flow around the sides of the radiator as the path of least
resistance. Both the duct and diffuser acts as a container. If a
radiator were abutted to the end of duct the air trapped in the duct would tend
to flow through the radiator (at a higher velocity, with more turbulence and
energy loss) than the air out of a diffuser. So both diffuser and
duct prevent this from happening. So "even-stephen" so far as containing the air
flow goes - they both do it..
You could just make a duct to contain the
airflow (to prevent it from spilling around the edges of the radiator) much as a
diffuser would do. However, there is yet another factor that
favors the diffuser. Drag is directly proportion to the
frontal area of the radiator. However, drag is also proportional
to the square of the velocity of the air flow through that radiator
area. So higher velocity through the radiator (say from a duct) causes
more drag than just making your radiator larger . But, you say
- if I slow down the air velocity (as a diffuser does) , I'll impede
cooling. Well, not quite.
While a diffuser does slow down the air
velocity, it does not slow down the airmass flow which
remains constant (less velocity - but more density and area).
Remember it is the air mass quantity not the velocity that cools. So
velocity has slowed but air density has increased such that the airmass flowing
through the radiator is essentially the same (there is some loss) as
originally entered the inlet.
So we get the same air mass for
cooling but with much less drag due to the
slower velocity of the air flowing through the radiator after a diffuser
(Remember the mass flow through a diffuser system and radiator does not change
from one end to the other - can't make mass disappear). Note, this is
one reason that if you do have less than perfect sealing of your diffuser to
your radiator that your cooling effectiveness loss will be much higher than you
would think. The air pressure is higher and the air is denser, both of
which contribute to a relative large airmass loss even though fairly small
holes.
Less drag would still be true even if we had
to made the radiator area larger to compensate from some of the pressure
unrecovered (nothing is 100% efficient) as the increase in area to
compensate does not produce as much drag effect as a higher velocity air flow
would. So by slowing the air velocity, we get better cooling and less drag
than just using a duct would do for us.
So in summary you want a diffuser and not a
duct for your cooling system because you get better cooling and less
drag
Well, thats what I think I've learned - so those of
you with aerodynamic backgrounds, how about hopping in an correcting
me.
Now, when (if?_I can just get the design parameters
figured out, I will provide that for you consideration.
Still recoverying from being forced stuff with food
on Thrusday.
.
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