Rotax 914 cooling and cowling ruminations

Maximum power output (Rotax OM) 84.5 kW
Consumption at maximum power (Rotax OM) 33 l/h, i.e. 9.17 ml/s.
Gasoline represents 35 kJ of energy per ml.
Power consumption is therefore 9.17 x 35 = 321 kW
Efficiency is 26.3%.

Maximum cruise power output (Rotax OM) 73.5 kW
Consumption at maximum cruise power (Rotax OM) is 27.2 l/h, i.e. 7.56 ml/s.
Power consumption is 264 kW
Efficiency is 27.8%.

75% cruise power output (Rotax OM) 55.1 kW
Consumption at 75% cruise power (Rotax OM) is 20.4 l/h, i.e. 5.67 ml/s.
Power consumption is 198 kW
Efficiency is 27.8%.

Combustion is probably a few percent from complete in all cases 
At maximum power a few percent more (enrichment solenoid). 
Probably at least some 10 to 15 potential kW are not produced at maximum power
Total heat production to be removed is then estimated at 321 - 84.5 - 12.5 =  223 kW.

Rotax heat removal prescription for maximum power operation (84.5 kW)
Remove 45 kW as follows:
30 kW through cooling radiator
9 kW through oil radiator
6 kW from cylinder barrel fins

Under the cowling.
As the engine and exhaust system heat up they radiate more heat.
Stefan-Boltzmann says: about 5 / 10^11 x T^4 kW/m^2, T in Kelvin.
A little table - T in Kelvin ('F) and corresponding radiation flux in kW/m^2 - :
300 (80'F)  0.4
400 (260'F) 1.3
500 (440'F) 3.1
600 (620'F)  6.5
700 (800'F) 12.0
800 (980'F) 20.5
900 (1160'F) 32.8
1000 (1340'F) 50.0
1100 (1520'F) 73.2
1200 (1700'F) 103.7

Estimate of 1000K area (4 primary exhaust pipes): 0.10 m2
Radiated heat: 5.0 kW
Estimate of 800K area (muffler, turbo): 0.15 m2
Radiated heat: 3.0 kW
Assume the under cowling air temperature held at 500K
Counterflux from environment: 0.25 x 3.1 = 0.8 kW
Net heat flow estimate: 5.0 + 3.0 - 0.5 = 7.2 kW
The final number is very sensitive to temperature and size of the hottest areas.

Say another 7 kW to be removed from under the cowling.
Total now 45 + 7 = 52 kW.
The remaining 171 kW or so then leaves with the exhaust gasses.
More than half - and a good thing too, but what a waste.

Tony Bingelis rule of thumb:
For an aircooled engine provide 0.35 square inches of air inlet per rated engine HP.
That is 2.25 cm^2 per kW.
Assuming similar cooling requirements for the Rotax 914;
also assuming similar efficiency for direct and indirect - via liquid - air cooling:
Total inlet area for Rotax: 84.5 x 2.25 = 190 cm^2 (diameter 15.6 cm)
Of which:
cooling radiator 30/52 x 190 = 109.6 cm^2 (diameter 11.8 cm, or 5.5 cm x 20 cm, or 4.3 cm x 25 cm)
oil radiator 9/52 x 190 = 32.9 cm^2 (diameter 6.5 cm, or 1.6 cm x 20 cm, or 1.3 cm x 25 cm)
cylinder barrel fins 6/52 x 190 = 21.9 cm^2 (diameter 5.3 cm)
rest of cowling 7/52 x 190 = 25.6 cm^2 (diameter 5.7 cm)

And the air outlet to be "larger" than the inlet.

Exhaust augmenter as described by Frans Veldman.
Diameter 8 cm, area 50.3 cm2
Exhaust diameter is 4 cm. area 20.4 cm2
Leaves a 29.9 cm2 (equivalent diameter 6.2 cm) cowling air outlet size
With forced extraction action

Cooling design attempt. To be updated with new insights.

1. cowling heat removal 6 + 7 = 13 kW
1.1. cowling hermetically sealed except for intended openings
1.2. inlets
1.2.1.  5.3 cm front hole and Rotax 1 to 4 guide to cylinder barrels *)
1.2.2.  air filter plenum circular leak around airfilter to turbo minimal *)
1.2.3.  propeller shaft circular leak minimal or remove *)
1.2.4.  5 cm front hole general purpose *)
1.3. outlets
1.3.1.  exhaust augmenter port side
1.3.2.  bottom cowl flap starboard side, possibly open mostly for max climb *)

2. central liquid cooling radiator duct 30 kW
2.a. inlet 4.3 cm x 25 cm
2.b. bottom outlet flap max opening 8 cm x 25 cm (flap 32 cm long)
2.c. hermetically sealing 
2.d. flap with thermostat say 70 - 100 'C, manual emergency override

3. oil cooler on port footwell (Rotax allows if mounted connections up) 9 kW
3.a. front hole 6 cm
3.b. port side outlet flap max opening 6 cm x 6 cm (flap 24 cm long)
3.c. hermetically sealing 
3.d. flap with thermostat say 100 - 110 'C, manual emergency override

4. engine electrics box on starboard footwell < 0.5 kW
4.a. hermetically sealed
4.b. inlet air plenum roof riser 1 cm x 15 cm (oil cooler to port side)
4.c. outlet starboard gills
4.d. to contain:
4.d.1. TCU
4.d.2. wastegate servo (single plane cable bend desired)
4.d.3. regulator
4.d.4. capacitor
4.d.5. engine sensors box
4.d.6. any relays and fuses and ...

5. intercooler, decide later, make agree with 4
- must remove about 1 kW per 10 'C of cooling effect
- a lot for low delta-T air-to-air and iffy airflow
- I wonder at effectiveness

( 9.17 ml gasoline per second with mass 6.5 g
requires about 100 g of air per second (for AFR 15)
with volume about 70 l at sea level pressure (close enough)
volumetric heat capacity of air 1.3 J/l per K (close enough)
we require 100 J/s per K or 1 kW per 10 K
)

*) not so sure