Mixed-Flow Turbofan Engine Model for the Conceptual Design of Sustainable Supersonic Airplanes
Abstract
:1. Introduction
2. Overall Design Methodology
3. Rapid Aircraft Prototyping Tool: ASTRID-H 2.0
4. Propulsion System Modeling
- The flow is, on average, steady and one dimensional.
- The working fluid is modeled as a “half-ideal gas” using Variable Specific Heat (VSH).
- A reference fuel, (JP-4), is adopted.
- The inlet is modeled according to MIL-E-5008B.
- Both turbines provide power to the installed accessories.
- The turbine is cooled by air fractions bled from the high-pressure compressor.
- The constant area mixer is adopted.
- The flow areas are constant at stations 4, 4.5, 6, 16, and 6A.
- The exit area of the nozzle () is adjustable to maintain the exit pressure ratio of the exhaust equal to the external one () or to a selected ratio .
- The area of station 8 remains constant at its reference value.
- The map scaling procedure is adopted.
4.1. Gas Model: Variable Specific Heat (VSH)
- : the universal gas constant of the mixture;
- : the constant pressure specific heat of the mixture;
- : the ratio of the constant specific heat at constant pressure over the constant specific heat at constant volume of the mixture;
- : the speed of sound of the mixture;
- : the temperature of the mixture (if unknown);
- : the enthalpy of the mixture (if unknown);
- : the entropy function;
- : the entropy of the mixture;
- : the reduced pressure of the mixture (if unknown).
4.2. Parametric Analysis
4.3. Emissions Modeling
5. Case Study: Mach 1.5
5.1. On-Design Analysis
5.2. Off-Design Analysis
5.3. Validation
6. Mission Simulation
Emission Estimation
7. Conclusions and Future Work
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ASTRID | Aircraft on-board Systems sizing and TRade-off analysis in Initial Design |
BFFM2 | Boeing Fuel Flow Method 2 |
BPR | By-Pass Ratio |
EICO | Emission Index of Carbon Monoxide |
EIHC | Emission Index of Hydrocarbons |
EINOx | Emission Index of Nitrogen Oxides |
ESATTO | Environmentally Sustainable AircrafT Trajectory and Operations |
GSP | Gas turbine Simulation Program |
ICAO | International Civil Aviation Organization |
IFV | Inverting Flow Valve |
MORE&LESS | MDO and REgulations for Low-boom and Environmentally Sustainable Supersonic aviation |
LTO | Landing and Take-Off |
MTOW | Maximum Take-Off Weight |
NASA | National Aeronautics and Space Administration |
NLR | Netherlands Laboratory Research |
NPSS | Numerical Propulsion System Simulation |
OEW | Operative Empty Weight |
OPR | Overall Pressure Ratio |
TBE | Turbine Bypass Engine |
TIT | Turbine Inlet Temperature |
VCE | Variable Cycle Engine |
VSH | Variable Specific Heat |
Symbols | |
Area | |
Specific heat at constant pressure | |
Polytropic efficiency | |
Uninstalled thrust | |
Fuel-to-air ratio | |
Static enthalpy | |
Fuel heating value | |
Mach number | |
Mass Flow rate Parameter | |
Mass flow rate | |
Pressure | |
Power at take-off | |
Reduced pressure | |
Gas constant | |
Uninstalled thrust specific fuel consumption | |
Temperature or installed thrust | |
Total (or stagnation) temperature | |
Installed Thrust Specific Fuel Consumption | |
Thrust-to-weight ratio | |
Velocity | |
Wing loading | |
Bypass ratio | |
Mixer bypass ratio | |
Bleed air fraction | |
Ratio of specific heats | |
Cooling air #1 mass flow rate | |
Cooling air #2 mass flow rate | |
Efficiency | |
Total pressure ratio | |
Total temperature ratio | |
Entropy function | |
Subscripts | |
Air | |
Burner | |
Compressor | |
High-pressure compressor | |
Low-pressure compressor | |
Fan | |
Mixer | |
Maximum | |
Mechanical, high-pressure spool | |
Mechanical, low-pressure spool | |
Nozzle | |
Products | |
Sea level | |
High-pressure turbine | |
Low-pressure turbine |
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Engine Station Numbering | |
---|---|
0 | Fan upstream or freestream |
1 | Inlet or diffuser entry |
2 | Inlet or diffuser exit, fan entry, low-pressure compressor entry |
13 | Fan exit |
2.5 | Low-pressure compressor exit, high-pressure compressor entry |
3 | High-pressure compressor exit |
3.1 | Burner entry |
4 | Burner exit |
4.1 | Nozzle vane entry Coolant mixer 1 entry High-pressure turbine entry |
4.4 | High-pressure turbine exit Modeled coolant mixer entry |
4.5 | Coolant mixer 2 exit Low-pressure turbine entry |
5 | Low-pressure turbine exit |
6 | Core stream mixer entry |
16 | Fan bypass stream mixer entry |
6A | Mixer entry Afterburner entry |
7 | Afterburner exit Exhaust nozzle entry |
8 | Exhaust nozzle throat |
9 | Exhaust nozzle exit |
Air Alone | Fuels | |
---|---|---|
A0 | ||
A1 | ||
A2 | ||
A3 | ||
A4 | ||
A5 | ||
A6 | ||
A7 | ||
[Btu/lbm] | ||
[Btu/(lbm °R)] |
Parametric Cycle Analysis (Input Variables) | |
---|---|
Flight parameters | |
Gas properties | |
Fuel heating value | |
Components (pressure ratios, efficiencies) | |
Design choices |
Parametric Cycle Analysis Inputs | ||
---|---|---|
Parameter | Symbol | Value |
Inlet pressure ratio | 0.995 | |
Burner pressure ratio | 0.96 | |
Nozzle pressure ratio | 0.98 | |
Mixer pressure ratio | 0.96 | |
Burner efficiency | 0.995 | |
Mechanical efficiency LP spool | 0.99 | |
Mechanical efficiency HP spool | 0.99 | |
Fan polytropic efficiency | 0.89 | |
LP compressor polytropic efficiency | 0.9 | |
HP compressor polytropic efficiency | 0.9 | |
HP turbine polytropic efficiency | 0.89 | |
LP turbine polytropic efficiency | 0.89 | |
Max turbine inlet temperature (TIT) | 2000 K | |
Afterburner exit temperature | 2200 K | |
Pressure ratio at nozzle exit | 1.00 | |
Mixer inlet Mach number | 0.5 | |
Fuel heating value | 43.260 MJ/Kg |
Aircraft High-Level Requirements | |
---|---|
Parameter | Value |
Payload | 1320 kg |
Mach @cruise | 1.5 |
Range | km |
Sonic boom | |
Fuel | Biofuel |
Design Data | |
---|---|
Parameter | Value |
T/W | 0.32 |
W/Sw | 320 kg/ |
MTOW | 39,283 kg |
OEW | 19,048 kg |
Sw | 112 |
Length | 44 m |
Wingspan | 14 m |
Propulsion System Requirements | |
---|---|
Parameter | Value |
Number of engines | 2 |
Inlet diameter | 1.10 m |
Mach @on-design | 1.5 |
Altitude @on-design | 16 km |
Required Thrust @on-design | 62 kN |
On-Design Results | ||
---|---|---|
Parameter | Symbol | Value |
Compressor pressure ratio | 30 | |
Fan pressure ratio | 4.5 | |
LP compressor ratio | 5 | |
HP compressor ratio | 6 | |
By-Pass Ratio (BPR) | 0.7 | |
Turbine Inlet Temperature (TIT) | 2000 K | |
Air mass flow rate | 82 kg/s | |
Core mixer Mach number | 0.5 | |
Fuel heating value | 43.260 MJ/kg | |
Cooling fractions | 6.38% | |
Power extraction | 240 kW | |
Uninstalled thrust | 68 kN | |
Specific fuel consumption | 25.2 mg/Ns |
Parameter | GSP 11 | Engine Model | Absolute Error | Relative Error |
---|---|---|---|---|
Thrust | 11.48 | 11.54 | 0.06 | 0.52% |
TSFC | 0.0538 | 0.0541 | 0.0003 | 0.51% |
Fuel flow | 0.0172 | 0.0174 | 0.002 | 1.01% |
Mixer exit area | 0.200 | 0.198 | 0.002 | 1.00% |
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Piccirillo, G.; Gregorio, A.; Fusaro, R.; Ferretto, D.; Viola, N. Mixed-Flow Turbofan Engine Model for the Conceptual Design of Sustainable Supersonic Airplanes. Aerospace 2024, 11, 740. https://doi.org/10.3390/aerospace11090740
Piccirillo G, Gregorio A, Fusaro R, Ferretto D, Viola N. Mixed-Flow Turbofan Engine Model for the Conceptual Design of Sustainable Supersonic Airplanes. Aerospace. 2024; 11(9):740. https://doi.org/10.3390/aerospace11090740
Chicago/Turabian StylePiccirillo, Grazia, Antonio Gregorio, Roberta Fusaro, Davide Ferretto, and Nicole Viola. 2024. "Mixed-Flow Turbofan Engine Model for the Conceptual Design of Sustainable Supersonic Airplanes" Aerospace 11, no. 9: 740. https://doi.org/10.3390/aerospace11090740