Jeff Spitzer wrote:
Did you ever see the cookbooks by Jan Roskam on airplane design? For those
that haven't they comprise about 14 volumes and take a whole shelf on the
bookshelf. That's what it takes to give a decent description related to
"layout design" of a new transport or fighter aircraft. A full
dissertation on cooling system design would be
waste of time if not 500+ pages. Even giving a good description on how to
detail a singular solution (like if you already selected a P51 style,
placement, etc) would not be trivial.
I took the time a few years ago to respond as follows in
rec.aviation.homebuilt:
"Bruce A. Frank" writes:
As for proper sizing of the radiator, companys such as Griffin and Ron
Davis Racing have had years of experience with development of the
correctly sized radiator. When you supply them with the parameters of
operation, displacement, Horse Power and vehicle speed they can usually
draw from their stock to meet our needs. The speeds at which we fly are
in the same range as the racing cars for which these companys supply
radiators.
I have used Ron Davis once in the past and found that he could not supply
me with the information that I needed to my satisfaction. What I asked was
for heat rejection vs. (airflow) pressure drop for a given core face area.
He did not have this. It was more like what Bruce said where Ron said
"...well, this ## x ## radiator cools a Nascar Grand National car making
500 hp at 150+ MPH..." or something to that effect. That's good info to
have. But it does not answer the question. The reason why it's so
important to know with good accuracy the required pressure drop is because
_that_is_the_only_way_ you can design a proper inlet and outlet system.
The scenario goes something like this:
-First pick a critical design condition, this is usually hot day climb at
full power. You need to know:
-Indicated Airspeed
-Heat rejection (usually BTU's equivalent to output power)
-Atmospheric conditions
-Next pick airframe locations for inlet and outlet. This is important
because it will be needed before other design parameters can be addressed.
It has been mentioned before "don't put your outlet in a high pressure
area". This is a good idea but shouldn't be a drop dead factor. The best
place for an inlet is right behind the propeller (duh!) This is because
total pressure available there is:
-Free stream total pressure
+Prop induced velocity head
+Prop static pressure rise
A relatively simple propeller analysis formula can give guesstimates for
the second two and I hope everyone knows how to get the first.
-From these chosen locations and conditions we can establish a pressure
differential that we have to work with. I don't have time to work up a big
example so let's just guess that for a 100 mph climb you get about 6" of
water if the inlets are in the normal location and the exit is at the
bottom of the firewall.
-Your next choice is how to use that 6". If your chosen core needs 6" to
reject adequate heat, you have very little choice. You effectively have to
put a inlet lip on the sucker and hang it out the side of the Cowl. You
cannot reduce the outlet size and need 100% efficiency in the inlet. A
better choice is to use a core that uses say 3" of back pressure. (Note
that this is at least twice conventional automotive practice) Then you
have 3" left over to work with to make everything smaller. In the end,
you need to know:
-Pressure differential of cooler
-Air mass flow through cooler for associated pressure drop.
-Next, you set up a tradeoff with where and how you place the cooler. The
common scenario may be to duct air from an inlet on the front of the cowl.
If this duct is small, it may have significant losses from inlet to cooler.
You also have to decide how (where/when) you will diffuse the air that
will pass through the cooler. For instance, if you cannot possibly squeeze
more than a 3" duct around the engine to the cooler, then there is
positively no benefit in making your inlets any bigger. So, you go through
each component step by step keeping a tally of pressure usage. Things to
consider include:
-External diffusion amount
-Inlet loss
-Internal diffuser efficiency and/or effectiveness
-Inlet duct losses
-(core pressure drop)
-Outlet duct losses
-Now you can design your outlet. Your outlet size will be that which uses
up all residual pressure based on previous discussion. Usually, the outlet
will be designed as a "nozzle" and depending on entrance efficiency will
turn substantially all remaining pressure into velocity. Then, knowing
velocity and mass flow leaving the exit, it can be sized.
-Finally, you rework the numbers considering max level flight speed, full
power. At this condition your heat rejection will be identical to the
climb case but you will have substantially more pressure to deal with. So,
as we all know, you reduce the size of the outlet until a pressure balance
is achieved. i.e. outlet velocity goes up and area goes down...same outlet
mass flow, much increased back pressure. Note that for same mass flow all
other components of cooling ducting will be identical. So, if you've made
it this far deciding how much cowl flap motion you need is very simple.
(BTW, don't forget about leaks if it applies, you might be surprised how
much flow can go through a loose fitting cowl flange)
In regards to my previous statement about needing data on coolers, it still
stands. If anyone out there has data as to pressure drop and heat
rejection for a type of cooler it would be very useful. In writing this I
realized that I would also have to have duct design info in order to
reverse engineer mass flow from empirical data. Note that data of heat
rejection and flight condition even including inlet and outlet sizes will
not fully characterize a heat exchanger sufficiently for the above
analysis. There must be enough info to get mass flow. One good way to do
this would be to measure temps before and after the HX. Then from an
assumed heat rejection based on power you could get within about 5% on mass
flow based on air temp rise.
Let me say that without good HX design data, the process may be a little
trial and error. But I think the above methodology shows how a resourceful
homebuilder could "develop" a good system.
-Start with some assumptions
-Design an overall system
-Fly and measure pressure differential and temp rise (maybe some other
pressures to if its complex ductwork)
-If it's not cooling adequately, you'll at least know where to work first
and can avoid the common "just make the inlet bigger" scenario.
Jeff Spitzer
Thanks Jeff. That's a good start.
A couple of questions. What is the maximum rate of increase in
the duct cross sectional area as a function of the duct length?
Is this a linear function or some other function? In other words is the
air velocity change linear or accelerated.
Same questions for the exit duct?
Paul Lamar
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