I made a few very conservative educated guesses about the conditions inside the exhaust pipe. These can be easily verified by measurement's which is the next step.

Gas velocity in the 3 inch diameter exhaust pipe is assumed to be 1000 FPS or 681 MPH. A variable nozzle would increase that at the expense of some back
pressure.

Air density in the pipe is assumed to be half sea level or .0013 for the MPH constant. That affects the dynamic pressure directly. Not to be confused with static pressure.

I assumed the lift coefficients on the blades was 1.5.

There were 31 blades at about one inch apart. It is possible to build
a turbine with blades much closer together so that is going to affect the
results directly.

Bottom line I estimated  37 HP from the turbine at 11,000 RPM which is slightly over 12.3% more power from a 300 HP P-port rotary no increase in fuel burn. This would be about the same for a BSFC improvement. NASA in a paper study with a super charged rotary obtained 80 HP additional. The DD15 diesel turbo compound
obtained 11% and diesel's have much less waste energy in the exhaust.

The actual results are going to vary according to the real numbers. There are a  lot of factors here. This is probably a good turbine to start with.

I think the theory and calculation method is good. We will not know the actual numbers until we build the hardware and test it. I think this method will get us in the ball park. I won't bore everybody with the equations so if you want
them let me know.

Paul Lamar

Paul,

I think we can get into mass flow with HP, BSFC and air/fuel ratio.

let's assume a 360 hp rotary on 75% cruise, BSFC as 0,45 lb/HPh, A/F as
leaned to 1:16.

75% cruise is 275 hp, 122 lb/h. Converting that to grams/sec = 15,3
grams/sec fuel flow. Air/fuel was 16:1, so required air is 245 grams/sec.

Air density on 15 deg C, std. pressure, is 1,225 kg/m3.
That translates to 1,225 grams/litre. So our intake air volume is 200
litres/sec. That translates to 414 CFM.

So, a 360 hp rotary on 75% with 0,45 lb/HPh BSFC and 16:1 A/F gives:

Mass flow: 15,3 (fuel) + 245 (air) = 260 grams/sec or 0,574 lb/sec.
Intake air volume: 200 ltr/sec or 414 CFM

That agrees quite nicely on (3-rotor equivalent) 4 ltr engine table
value - on 6500 rpm/80% VE/ 14:1 A/F  = 350 CFM.

Putting that on kinetic energy equation gives us:

305 m/s^2 * 0,26 kg/sec * 0,5 = 12 kJ/sec = 12 kW = 16,1 HP = 4,5%
340 m/s^2 * 0,26 kg/sec * 0,5 = 15 kJ/sec = 15 kW = 20,1 HP = 5,6%
380 m/s^2 * 0,26 kg/sec * 0,5 = 19 kJ/sec = 19 kW = 25,1 HP = 7,0%

Percents as against 360 SHP. And this is total kinetic energy, before
conversion.

Thus, in order to have 20% power recovery, gas speed should be at least
643 m/s, ie. 2.5 Mach... not happening.

Something's not right here. As much as i can see, mass flow should be
quite right, but total energy and it's recovery should be calculated
some other way...

This is quite basic case, so there must be a myriad of calculated
examples on textbooks..

Hot gas should have stored energy as kinetic, heat and pressure. Any
ideas? I'll give up for now, need to sleep...

Cheers,

Petri

Correction: 1700 F / 1200 K exhaust gas has the speed of sound as:
T^0,5 * 20,05 = V (m/s) that gives 1200^0,5 * 20,05 = 695 m/s.
So 695 m/s is 0.93 Mach, not 2.5...

Cheers,

Petri

Good thing you did not go directly to bed :)
695 meters per second is  2.042 mach. One heck
of a lot of HP that would be.

Mass flow speed is not necessarily the speed of sound.
A pressure wave in the pipe will travel at the speed
of sound super imposed on the average flow speed.
That was covered in this book.

Scientific Design of Exhaust and Intake Systems. Philip H. Smith
and John C. Morrison Published by Robert Bentley. ISBN 0-8376-0309-9

There is a lot of good exhaust info in the book. Here are four samples.

Paul Lamar

Petri,

Getting back to rotaries. do you want to give calculating the exhaust velocity
another try?

I think we can build this into the flywheel and make the bell housing the muffler.

Paul Lamar

Hi Paul,

I think we can approach this from other direction. We can quite safely
say that rotary engine puts 33% of fuel energy on exhaust gas's temp,
kinetic and pressure energy - plus or minus 9%.

Since we got 15,3 grams/sec of 42 Mj/Kg (42 Kj/g) fuel, we got
643 kJ/sec. That's 643 kilowatts, ie. 861 SAE BHP. 33% of that is 284
HP... that's almost 80% of 360 hp shaft horsepower.

Conversion efficiency is another matter then. NASA paper talked about
initial 12% of SHP recovery efficiency, and possibly 20% when impulse
effects are fully utilised. I think we can also assume that gasoline
burning 20B has quite much higher exhaust energy than "pseudo-diesel" SCORE.

So, if NASA got 20%, we can probably get that too from higher energy
flow we have on 13B/20B.

That would give us BSFC's as 0,44 -> 0,35 - right on diesel BSFC range.


Regarding the placement of compound turbine, putting it on front of
engine would create a cooling problem. eg. A357 aluminium should be kept
under 200 C to retain it's strength. Maybe if 900 C turbine casing could
be isolated well enough from bell housing...

Putting another speed reduction planetary gear on driveshaft wouldn't be
too difficult. That way we can get away with a smaller disc that fits
inside extended bell housing with thermal insulation.

Fabricating the turbine disc isn't easy, but i don't think it's an
overwhelming task. It will require high-precision superalloy investment
casting to make proper channeling for blade cooling air. To protect
superalloy components like magnesium from evaporation, melt should be
kept on inert gas and preferably on overpressure. That's doable.


Unfortunately - or fortunately, i have my hands and schedule pretty
packed right now. I'm making test bars from A357/AC-42200 to find out
how much tensile strength i can get on our faculty's test foundry. High
quality ceramic mold, effective melt purification, non-turbulent casting
and careful heat treatment are basic requirements to get aerospace-grade
castings done - and that requires testing, and testing, and...

Why bother?? - when succesful, i can do anything i like :)
I think that's the position we all wish to be! So i think this effort is
very much worthwile.

I think that mastering the casting process is the key to the real
manufacturing. Of course, one can just mill out the billets, but that's
not nearly as cost-effective.

Cheers,

Petri