Paul,

     In our recent discussion of exhaust pressure, the subject of
     turbocharger sizing came up and it was noted that aircraft engines
     require much bigger turbines and compressors for the power they
     produce -- compared to cars -- because they operate at altitudes
     where the air is thin.

     I thought I?d look into this a little and try to figure out just how
     big a turbocharger might be appropriate for a rotary aircraft
     engine. The turbocharger manufacturers provide compressor maps that
     we can use to pick a turbo. Unfortunately those compressor maps give
     their flow value -- the horizontal axis -- in mass flow, not
     /volume/ flow.

     The compressor does not know or care about the mass of the air it is
     pumping -- it flows the same volume of air, regardless of the air?s
     density. We know that as we go higher the air is less dense, so in
     order to flow a given mass of air, we need a compressor that is able
     too move more volume.

     How much more volume, that is the question? We can figure this out
     quite easily using the ideal gas law. We can then solve for our
     corrected mass flow and use the compressor maps to choose a
     compressor intelligently.

     Let?s say we have a two-rotor engine that is peripheral-ported and
     makes a conservative 230 horsepower at sea level ? the same as a
     Turbo Skylane. Let?s say we want to maintain that power level to 20,
     000 feet -- the service ceiling for the Turbo Skylane. This is a
     reasonable altitude limit for an unpressurized plane and private
     pilot. While planes like the Columbia 400 and the turbocharged
     Mooneys boast a ceiling of 25,000 feet, I really doubt that a lot of
     owner-pilots fly at these heights on a regular basis.

     For the most part, we will be using our turbocharged airplane to fly
     in the mid to low teens, where no oxygen or perhaps a cannula is all
     that is required. At 18,000 feet we need a full mask according to
     regulations.

     The main thing we need to figure out is how big a compressor we will
     need. The turbine is really a subject unto itself, especially for
     the rotary engine, which has a very high-energy exhaust. So I will
     leave out the turbine discussion for now -- but once we know a
     suitable compressor size, at least we will be in the ballpark for
     turbine size too.

     The first thing we need to know is how much air our engine is
     moving. The 13B displaces 605 cubic centimetres per rotor for at
     total of 1310 cc, or 80 cubic inches. It?s /effective/ displacement
     is twice that because each rotor has a combustion event for every
     revolution of the engine shaft, unlike a piston engine where each
     cylinder has a combustion event only every other revolution.

     To figure out flow in cubic feet per minute we multiply displacement
     by rpm and divide by 1728, because that?s how many cubic inches are
     in a cubic foot. So:

                 Flow = 80 ci * 7500 rpm / 1728 = 347 cfm

     This is assuming a volumetric efficiency of 100 percent, which is
     probably what a P-port will deliver.

     Since we have a turbocharger on this engine, let?s say we will run a
     little bit of boost even at sea level, to overcome the engine?s
     pumping losses and make the engine a little more efficient. So let?s
     say we set our takeoff power at 35 inches of mercury on our manifold
     pressure gauge. This is 17.2 pounds per square inch, about 2.5 psi
     above sea level pressure of 14.7 psi.

     The atmospheric pressure on a standard day at 20,000 feet is only
     6.76 psi, so in order to carry a manifold pressure of 35 inches
     mercury (17.2 psi) at that altitude we need to add 10.4 psi of
     boost. (17.2 - 6.76 = 10.4)

     This level of boost will heat up our intake charge somewhat, so in
     order to figure out our mass flow, we need to first figure out the
     charge temperature. We do this using the equation:

                 Tout = Tin + {Tin * [-1 + (Pout / Pin)^0.263] / Efficiency}


     Where:             Tin is air temperature entering the compressor
     (448 R)
                             Tout is air temperature exiting the
     compressor (?)
                             Pin is the ambient pressure (6.76 psi)
                             Pout is the pressure exiting the compressor
     (17.2 psi)
                             Efficiency is the thermal efficiency of the
     compressor. (0.74)
                             Pin/Pout is the compression ratio (2.54)
                             Rankine = Temperature in F + 460

     Today?s compressors have pretty good thermal efficiency as we can
     see from compressor maps, so let?s say our efficiency is 70 percent.


     So we get:        Tout = 448  + {448 * [-1 + (17.2 / 6.76)^0.263] /
     0.70}

                             Tout = 626 R = 166 F

     Our charge temperature is a relatively cool 166 F at 100 percent
     power at 20,000 feet. This is a maximum and we will not likely be
     using 100 percent engine power very much at this altitude, so our
     cruise charge temperatures will be quite a bit lower. We can see
     that there is no need for an intercooler, which will only add
     complexity, cost and probably cost a pressure drop of a couple of
     psi between the compressor outlet and the intake manifold. We can
     also count on a little bit of evaporative cooling from our fuel
     being evaporated at the intake port as well -- a temperature drop in
     the fuel-air charge up to 40 F for gasoline. (I will cover this in
     another post).


     Now that we know the amount of boost we are running at altitude and
     the charge temperature, we have everything we need in order to
     calculate the mass flow, in pounds of air, that our engine needs in
     order to make the required boost.


     We use the ideal gas law:          PV = nRT

     Where:                                     P is the absolute pressure
                                                     V is the volume or
     air flow
                                                     n is the mass in
     lbs. / mole
                                                     R is the gas
     constant (10.73)
                                                     T is the absolute
     temperature in R

     To get pounds of air, we rearrange the equation: n = PV / RT


     A mole of air is 29 lbs, so in order to get mass flow in pounds per
     minute:

     n (lbs/min) = P (psi) * V (cu-ft/min)  * 29 / 10.73 * T (deg R)

     n =  17.2 * 347 * 29 / 10.73 * 626 = 25.75 lbs/min


     This is the actual mass flow our 2-rotor engine needs at 35 inches
     of manifold pressure (17.2 psi) at 20,000 feet: 25.75 pounds per minute.

     If we simply take that 25.75 lbs/min and look at compressor maps we
     will end up choosing one that is too small because those maps are
     using mass flow at sea level and at a particular temperature. In
     order to flow 25 pounds of air at 20,000 feet is going to take much
     more air volume going through the compressor -- so a large
     compressor is needed.

     What we need to do is correct our mass flow to the altitude we are
     interested in. We do that using the formula:

                 Corrected Flow = Actual Flow * (Tin / Tmap)^0.5 / Pin / Psl

     Where:        Tmap is the temperature used in the compressor map in R

     Let?s assume the turbo manufacturer has used 85 F as the reference
     temperature for the map, so we add 85 to 460 to get 545 R. (Turbo
     makers usually use a hotter day temperature in these maps so as to
     be on the safe side in terms of flow -- the hotter day will result
     in lower air density).

     So we get:

     Corrected Flow = 25.75 * (448 / 545 )^0.5 / (6.76 / 14.7) = 50.76

     Our mass flow corrected for altitude and temperature is nearly
     double our actual mass flow -- 50.76 pounds per minute. To be
     precise, 50.76 pounds would be the sea level mass of the /volume/ of
     air we are moving through the compressor at 20,000 ft. It sounds
     confusing, because turbochargers pump volume not mass, so we must go
     through these calculations to use those compressor maps.

     So the bottom line is that we need a pretty big compressor to move
     50 pounds of air per minute, double the size that we would choose
     for the same engine if we were using it in a car.

     If we look at a couple of compressor maps, we see that the Garrett
     T04E with 40 trim is nowhere near big enough -- the most it can
     handle is only about 35 lbs/min. The biggest in this series, T04E
     with 60 trim is barely marginal. At 50 lbs/min and 2.5 pressure
     ratio, we would be to the right of the choke line. Still, since
     we?re not going to run the engine at 100 percent at our service
     ceiling, this compressor might do the job.

     A better choice would be the T04B series. The T04B 60-1 trim looks
     pretty good, as does the T04B H-3 trim. Another good choice would be
     the T61.

     I don?t know what the stock Mazda turbo map looks like, but I would
     guess it is designed for a mass flow of about 20 lbs/min which is
     way too small. It should never even be attempted in aircraft use.

     I?ve also included a map for the Rotrex centrifugal supercharger
     model C30-94, which Doug Fir is using. The flow is given in metric
     units, kilograms per second -- our 50.76 lbs/min equals 0.383
     kg/sec. We can see that this is a good size for the two-rotor engine
     and will give 75 percent efficiency at our compression ratio of 2.5.
     Good choice Doug.

     Now all we have to do is choose the right turbine?


     Regards,

     Gordon.

      Ah so that is the hard part. Boost at altitude has not
been a problem with the 2nd gen  stock turbo.  The problem with the
stock turbo is over speed. As soon as you remove the car exhaust
system back pressure you pick up several psi of boost at SL to about 8.
So the manifold pressure is now about 46 inch of HG at SL. The stock turbine
has more than enough HP to do this. The stock compressor is also
big enough to do this.  Hugh Macinnis has a simple formula
in his book Turbo Chargers in the chapter on altitude performance.
A turbo charger will gain RPM at the rate of 2% per 1000 feet.

So far the guys have been unable to increase the waste gate
flow enough to prevent the turbo charger from over speeding
at full throttle at altitude. Obviously if no exhaust gas was
getting to the turbine this would not be happening.

The flapper valve is restricted from opening more than
about 20 degrees due to the interference with the back cover.
Dave Leonard has removed the flapper valve entirely and
the stock turbo is still generating too much boost and over
speeding. There is a lot of kinetic energy in the rotary
exhaust. Others have opened up the hole with a slot
between the two stock waste gate holes.

Nobody to my knowledge has removed
the flapper valve AND greatly increased the area of
the by pass passage at the same time. Also nobody to
my knowledge has installed a turbo tachometer to know
precisely  what RPM the turbo is actually achieving.
If you don't know that you are just fooling around
in the dark.

Evidence from the failed turbines suggest over speeding.
Basically what is happening is the A/R of the turbine
scroll is too small. It is somewhat less than one. What
that means is the nozzle area squirting exhaust gas at the
turbine is too small and it is speeding up the exhaust gas
velocity too much. The turbine is spinning too fast with
more than enough torque and HP to spin the compressor.


Changing out the turbo for a larger turbo has its drawbacks.
The TO4 does not have a built in waste gate. That means you
have to buy one and find an exhaust manifold that will accommodate
it. Then too the stock turbo is water cooled and the plumbing is
there. Nice to have a water cooled turbo. This is an extra cost
option on the TO4. The other thing is the oil supply and drain
back plumbing would have to be redone if a TO4 was installed.
Another nice feature of the stock turbo charger is a very
compact installation.

What appears to work is a larger compressor that gives
the same boost at a lower turbine RPM and with less throttle
opening.

The problem boils down to improving the stock waste gate.

IMHO what needs to be done is further improvement to the stock
waste gate aerodynamics which IMHO will solve the problem. It is
the cheapest solution to the problem and you can still have your
boost when you need it.

I'll upload a bunch of pictures with the next message.