# 03-a-ConceptionAeroPropulsion1.pdf

2 de Jun de 2023
1 de 14

### 03-a-ConceptionAeroPropulsion1.pdf

• 1. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Low BPR turbofan/jet pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 1 ■1. Which sort of power generator? > Piston engine will be too much inertia to accelerate supersonic in a short time > Piston engine will save fuel consumption, but its big size, then wider surface, will significantly impact the aircraft drag & mass, implying more engine power  In fine as much fuel burn as gas generator as FB = SFC x PW > Electrical engine, with batteries, in such a hot environment as afterburning jet engine shall not be the best reliability option > The most intuitive choice is the gas generator  Small sizing  Low mass & inertia for good acceleration ■2. Fan thermodynamics > Assume Mach 0.8 flight at sea level > Assume some quite high fan pressure ratio at 2.0 > P2/T2 are also gas generator inlet conditions Station Pt (Pa) Tt (K) Ambiant Pamb/Tamb 100000 300 1bar, 27°C Fan inlet P1/T1 142961 332 Pt=Pamb + 1/2 rho V² , Tt/Tamb=(Pt/Pamb)^((gamma-1)/gamma) Fan outlet P2/T2 285922 413 FPR=2, if adiabatic : T2ad/T1=FPR^(0.4/1.4) , as efficiency 0.9 : (T2-T1) = (T2ad-T1)/0.9 Nozzle Ve (m/s) = 571 Ve = sqrt((P2-Pamb)/0.5rho), to determine rho : Ps=Pamb, Ts/T2=(Pamb/P2)^(0.4/1.4)
• 2. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Low BPR turbofan/jet pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 2 ■3. Gas generator thermodynamics > Gas generator first part is compressor > Assuming ~25 OPR (overall pressure ration = Pcombustion/P1)  GG compressor shall have a 9 pressure ratio > Choose the inlet turbine temperature  1450K enables uncooled turbine rotor  Cooled one could reach 1700K to 1900K > Fuel/Air ratio : FAR = [ Cp_air x (T4-T3) ] / FHV ~ 2% << 14%  => there is still enough oxygen for afterburning ■4. Fan turbine & primary nozzle > Here we have to choose BPR to determine the fan turbine power.  T5-T6 = (BPR+1) x (T2-T1) / turbine_efficiency > I will assume a 1 BPR Station Pt (Pa) Tt (K) GG inlet P2/T2 285922 413 Combustion inlet P3/T3 2573298 960 0.85 efficiency : (T2-T1) = (T2ad-T1)/0.85 Combustion outlet P4/T4 2521832 1800 T4 = 1450K for uncooled turbine (1700 to 1850K for cooled turbines) ; 2% pressure drop HP Turbine outlet T5/P5 709704 1192 0.9 efficiency : (T4-T5) = (T3-T2)/0.9 ; T5ad = T4-0.9*(T4-T5) = T4-T3+T2 HP Turbine outlet T5/P5 709704 1192 0.9 efficiency : (T4-T5) = (T3-T2)/0.9 ; T5ad = T4-0.9*(T4-T5) = T4-T3+T2 LP turbine outlet T6/P6 426104 1013 0.9 efficiency : (T5-T6) = (T2-T1).(1+1)/0.9 Cold nozzle Ve (m/s) = 1119 Ve = sqrt((P6-Pamb)/0.5rho), to determine rho : Ps=Pamb, Ts/T6=(Pamb/P6)^(0.4/1.4)
• 3. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Low BPR turbofan/jet pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 3 ■Specific thrust of this engine, M0.8 no afterburning T/q = 1 / (1+BPR) x Ve_afterburning + BPR / (1+BPR) x Ve_fan – V0 T/q = 559.5 + 285.5 – 272 = 573 N/kg Eta_prop = 2 x T x V / [ BPR/(BPR+1) Ve_fan² + 1/(BPR+1) VE_nozzle² -V0² ] Eta_prop = 2 x T x 0.8 x 340 / [ 0.5 x 1119² + 0.5 x 571² - 272² ] ~ 44% Station Pt (Pa) Tt (K) Ambiant Pamb/Tamb 100000 300 Fan inlet P1/T1 142961 332 Fan outlet P2/T2 285922 413 Nozzle Ve (m/s) = 571 Station Pt (Pa) Tt (K) GG inlet P2/T2 285922 413 Combustion inlet P3/T3 2573298 960 Combustion outlet P4/T4 2521832 1800 HP Turbine outlet T5/P5 709704 1192 LP turbine outlet T6/P6 426104 1013 Cold nozzle Ve (m/s) = 1119 cold 573 44% M0.8 T/q (kN/kg) Etaprop
• 4. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 4 ■1. Sizing the propeller 2 formulas for Propeller choice : > J = V0/(N.D) – speed coefficient  V0 = airplane speed (m/s)  N = propeller rotation speed (rev/s)  D = diameter (m) > Ct = F/(rho.N².D4)  F = propeller traction (N)  Rho = air density (kg/m³)  N = propeller rotation speed (rev/s)  D = diameter (m) 2 specifications : > Thrust > Airplane speed at key points, as cruise & take-off
• 5. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 5 ■2. Find some propeller maps Ct, Efficiency (h) characteristics function of J factor and propeller pitch
• 6. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 6 ■3. Specification As example (pure imagination), let’s take > Cruise is 1kN traction at 100m/s (~200knts) @ 4500m, ISA > Take-off is 5kN traction at 70m/s (~140knts) @ 0m, ISA ■4. Propeller diameter first guess Choose propeller diameter >D = V0/(N.J) => for a typical 2000RPM propeller, Diameter is here 3/J meters >Let’s start with a 2m propeller, J=1.5 >Best efficiency is for 35° pitch,and then Ct = 0.06
• 7. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 7 ■5. Propeller cruise pitch Get necessary traction coefficient at cruise for choosen J ratio >Here, J = 1.5 => D = 2m >Ct = F/(rho.N².D4) = 0.072 F = 1kN, D = 2m, N = 2000/60 rev/s Rho = P0/(Rair.T0) = 0.78kg/m³ ○ Rair = 287.05 ○ P0 = 57.7kPa @ 4500m, ISA ○ T0 = 258.5K @4500m, ISA >Pitch ~36° ■6. Control propeller efficiency From Ct & J factors, look for propeller efficiency for the dedicated pitch value >Here, h ~ hmax >J = 1.5 was a good choice for cruise operating point
• 8. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 8 ■7. Propeller take-off pitch Get necessary traction coefficient at take-off >J = V/(N.D) = 1.1 V = 70m/s, D = 2m, N = 2000/60 rev/s >Ct = F/(rho.N².D4) = 0.230 F = 5kN Rho = P0/(Rair.T0) = 1.23kg/m³ ○ Rair = 287.05 ○ P0 = 101.3kPa @ 0m, ISA ○ T0 = 288.2K @ 0m, ISA >! Ct > Ct max (~0.18) ! Speed or diameter is too low
• 9. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 9 ■8. Adapt take-off rotation speed A safer traction coefficient would be Ct = 0.15 >N² = F/(rho.Ct.D4) = 1693 rev/s >=> N ~ 2470 RPM We can increase take-off propeller speed by 25% vs. cruise to reach the traction specification >J factor value is now 0.84, & pitch is 32° But efficiency is poor (~0.65) To reach better efficiency at take-off, we need >To decrease the pitch >Or to increase the J factor
• 10. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 10 ■9. Iterate on propeller sizing To decrease take-off pitch, we need to decrease J factor >Increase propeller diameter Proportional to 1/J >In the same time, it will decrease the needed Ct Proportionnal to J4 Change cruise J factor from 1.5 to 1.4 (diameter reaches 2.1m) >Cuise Ct coefficient changes from 0.72 to 0.055 >Take-off J factor moves from 0.84 to 0.78 >And associated Ct coeff. from 0.15 to 0.11 Resulting cruise pitch is 32° with still >.8 efficiency And take-off pitch is now 25° only and efficiency reaches 0.75
• 11. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 11 ■10. Define engine power needed Look for power coefficient for both cruise and take-off Read the diagram using known J & pitch values from 9. >Cruise : J = 1.4 & pitch = 32° Cp value is ~0.09 >Take-off : J = 0.78 & pitch = 25° Cp value is ~0.11 Then you get the propeller power thanks to the formula PW = Cp.rho.N³.D6 Cruise power = 55kW Take-off power = 206kW
• 12. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 12 ■11. Which operating point is engine sizing point? Available engine power is varying with altitude >To compare all altitude powers we correct to 0m ISA conditions 𝑃𝑊 𝑐𝑜𝑟𝑟 = 𝑃𝑊 . 101325𝑃𝑎 . 288.15𝐾 𝑃0 . 𝑇0 In this example >Take-off power of 206kW @ 0m, ISA leads to Pwcorr = 206kW >Cruise power of 55kW @ 4500m, ISA leads to Pwcorr = 101kW >Take-off power of 206kW is sizing the engine
• 13. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 13 ■12. Last, find the engine ! 206kW engine (276 horse power) is needed by the propeller >Don’t forget to consider ~10% installation losses on the engine >Looking for 300shp engine For such power, solution will probably be turbine engine But some piston engine would still be available Seems one solution exists 
• 14. This document and the information therein are the property of Safran. They must not be copied or communicated to a third party without the prior written authorization of Safran Turboprop pre-design Safran name of the activity / Date / Department (menu "Insert / Header and footer") 14 ■13. And very last, find the propeller ! Available manufacturers are depending the size & power >For such power, solution could be found by MT-Propellers or Hartzell for example >You can check your pre-design 2700RPM @ 350 HP ○ We got 2500 for 300 HP ○ Not so bad  78”” diameter ~1.98m ○ We got 2.1m ○ Not so bad, still  Here is a possible solution 