Jeff Spitzer wrote:

The last few posts about radiator ducts (headers) essentially deal with the
need to understand the dynamic pressure of the incoming flow and how it
affects flow distribution through the core.  This is important whether the
header is feeding perpendicular or parallel or any other angle to the core.

 This is also related to discussions a long time ago about "streamline
diffusers".  Basically the dynamic pressure of the inlet flow follows
newton's second law...it wants to stay in motion and requires a force to
stop or change direction.  If the inlet flow is the same size and direction
as the flow through the core we have no issues.  If the flow must be
re-sized or re-directed, forces must be generated to do this.  These are
pressure forces.  In the case where the inlet flow is perpendicular to the
core, there is no reason for the flow to turn 90 deg and flow through the
core if not for pressure forces to turn it.  The ducts/headers (inlet and
outlet) create these pressure forces.  

If not for the header the flow would
simply flow past the core and never turn.  So, if the header is constant
cross section (non-tapered) what happens?  The flow goes right past the
core for as long as it can and slams into the far end wall.  Once it slams
into the wall pressure is generated (dynamic converted to static) that
forces it to turn and go through the core.  That's a bad scenario because
most of the flow goes through the far end of the core leading to lower
effectiveness.  Also you will see higher pressure drop because the air is
going through a smaller core area, thus moving faster, thus causing higher
pressure drop.  So, how do you make the air go through the core uniformly?
The *inlet and outlet* headers must be shaped such that a uniform pressure
is generated acrosss the face of the core.  The shape of the header is
different for parallel flow/counter flow/flow into open space because both
headers combine to generate the pressure gradient across the core.

The other factor is the ratio of inlet head to radiator head.  I have the
easiest time visualizing this for a non-turning straight in arrangement.
Lets say that the core has a pressure drop of 3 inches water at the
required/desired flow (uniform).  We know this because we hooked it up to a
huge plenum and measured the pressure in the plenum.  The plenum is so huge
that there is essentially no dynamic pressure to be found within.  Now we
want to feed it by blowing through an inlet.  If we have a inlet duct the
same size as the core face then the dynamic head is 1 inch water (cause I
say so) and there is no reason for the air to do anything but flow through
the core uniformly.  

The required 3 inches of water to flow through the
core is mostly supplied by upstream static pressure.  Now say the inlet
duct area is reduced by a factor of 2.  Now the dynamic head is 4
inches...slightly more than the required 3 inches for the core.  We need a
diffuser for two reasons 1) change the size and shape of the inlet flow to
match the core 2) slow it down to 1/2 speed.  We don't need  the diffuser
to recover pressure in this example because we can assume that upstream
there is an infinite supply of static pressure...we're talking about
dynamic pressure.  If we didn't slow or reshape the flow it theoretically
could go straight through 1/2 the core area.  Not really.  If the pressure
drop through the core was 3 inches for full area, it will be 12 inches for
1/2 area (same flow=double velocity=4x pressure drop).  The flow only has 4
inches of dynamic head so it *must* spread out and go through a larger
area.  This is a kind of natural/forced diffusion (also the basis for
streamline diffusers).  It turns out that even when we slow the incoming
flow by 1/2 the *local* static pressure rise is only 1.2 inches water.

This isn't enough to go through the core so the whole flow "backs up" and
is pressed somewhat uniformly through the core even if the inlet diffuser
is pretty lousy (or too short).  Now halve the inlet area again.  Now the
dynamic pressure is 16 inches of water.  If we allow the inlet *jet* to
impact the core face without a diffuser what happens?  The required
pressure to go through 1/4 core is 48 inches water so it doesn't go
straight thru.  But it only takes 12 inches to go through half of the core.

 The equilibrium condition is now met at less than full core area even
without help from upstream static pressure.  In other words, if there is no
diffuser/header or it doesn't work the flow goes through a smaller core
area 'cause it can.  The result is a higher pressure drop (12? vs 3) and
lower heat transfer effectiveness.  So, pay attention to those ducts guys.

Jeff Spitzer

 
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