DKA-867-Final

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DKA-867

David Byrd Kristian Lien Austin Sims

Kennesaw State University

SYE 4803

Spring 2016

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Abstract The American Institute of Aeronautics and Astronautics created an engine design competition to be obtained via a student body. The objective was to design an afterburning low bypass turbofan engine to replace the General Electric-J85-5A afterburning turbojet engine used on the Northrop Grumman T-38 Talon trainer jet. The new engine is required to have a lower thrust specific fuel consumption, weight, and improved thrust while maintaining current performance characteristics. By completing multiple parametric analysis, via the AEDsys ONX program, initial values were obtained for the design of the engine. The initial input values of the parametric analysis were based on the given baseline engine. Initially, an inlet had to be designed at the harshest flight condition. The condition given to us was at a Mach number of 1.3. After obtaining a fan inlet Mach low enough not to cause structural damage, the number of fan and high pressure compressor stage had to be found. A low bypass twin spool compressor was selected to reduce the weight and achieve the required thrust. Multiple iterations with various stages were conducted and finalized to be a total of three fan stages and five high pressure compressor stages. The compressor was then designed to allow for both increase in pressure and decrease in flow velocity so that the combustion chamber would not flame out and provide significant efficiency. The combustion chamber was next on the design agenda. A diffuser was developed along with cooling flow and number of nozzles to obtain complete combustion. Both a high pressure and low pressure turbine was then designed based on the given temperature output and power needed to drive both fan and high pressure compressor. An afterburner was then developed to obtain the needed supersonic specification. The afterburner uses both the bypass and core exit streams to increase the propulsive efficiency. In order to produce enough thrust and a high enough exit velocity, a convergent-divergent nozzle was designed. Ultimately, at the takeoff flight condition the nozzle releases a gross thrust of 3,981 pound-force at the exit. Combined with a second engine, this will be sufficient thrust at takeoff for the given aircraft. Upon completion of the engine design, it was found that both takeoff and cruise thrust specific fuel consumption was reduced to: 1.954 pound-mass-per-hour-per-pound-force and 1.807 pound-mass-per-hour-per-pound-force. By maintaining a fan diameter of twenty inches, the overall length was less than 108.1 inches, and the weight without tailpipe was less than 584 pounds; the design criteria was met. Each of these results were found using fifth generation designs and materials.

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Table of Contents

List of Figures ..................................................................................................................................... v

List of Tables ................................................................................................................................... viii

Nomenclature ................................................................................................................................... ix

1 Introduction ...............................................................................................................................1 1.1 Justification.........................................................................................................................1 1.2 Problem Statement .............................................................................................................1

2 Gas Turbine Engine Components .................................................................................................1 2.1 Inlet ....................................................................................................................................2 2.2 Compressor .........................................................................................................................2 2.3 Combustion Chamber ..........................................................................................................3 2.4 Turbine ...............................................................................................................................4 2.5 Afterburner .........................................................................................................................4 2.6 Nozzle .................................................................................................................................4

3 Problem Solving Approach ..........................................................................................................5 3.1 Requirement .......................................................................................................................5 3.2 Gantt Chart .........................................................................................................................7 3.3 Flow Charts .........................................................................................................................7 3.4 Project Management ...........................................................................................................8

3.5 Responsibilities ................................................................................................................9 3.6 Cost Analysis .......................................................................................................................9 3.7 Resources Available & Used .................................................................................................9

4 Results and Discussion .............................................................................................................. 10 4.1 Parametric Analysis ........................................................................................................... 10 4.2 AEDsys Software Analysis .................................................................................................. 13

4.2.1 Inlet ..................................................................................................................................... 14 4.2.2 Fan & Compressor ............................................................................................................... 18 4.2.3 Combustion Chamber ......................................................................................................... 21 4.2.4 Turbine ................................................................................................................................ 26 4.2.5 Afterburner ......................................................................................................................... 31 4.2.6 Nozzle .................................................................................................................................. 32

4.3 Weight Calculation Method ............................................................................................... 34 4.4 Mission Analysis ................................................................................................................ 34 4.5 Results .............................................................................................................................. 35

4.5.1 Compliance Matrix .............................................................................................................. 36 4.5.2 Engine Summary Data ......................................................................................................... 37 4.5.3 Required Detailed Stage and Component Information ...................................................... 39 4.5.4 Velocity Triangles ................................................................................................................ 41

5 Material Selections ................................................................................................................... 45 5.1 Aluminum 2124 Alloy (ρ = 5.29 slug/ft3) ............................................................................. 45 5.2 Titanium 6246 Alloy (ρ = 9.08 slug/ft3) ............................................................................... 46 5.3 Inconel 601 (ρ = 15.6 slug/ft3) ............................................................................................ 47 5.4 Hastelloy X (ρ = 16.0 slug/ft3) ............................................................................................. 48 5.5 Rene’ 80 (ρ = 15.9 slug/ft3) ................................................................................................ 49

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6 Conclusion ................................................................................................................................ 51

7 References ............................................................................................................................... 52

8 Appendix A: Acknowledgements ............................................................................................ 53

9 Appendix B: Contact Information ........................................................................................... 54

10 Appendix C: Reflections ...................................................................................................... 55

11 Appendix D: Initial Values and Requirements ........................................................................ 58 11.1 Inlet .................................................................................................................................. 58 11.2 Fan/Compressor ................................................................................................................ 58 11.3 Combustion Chamber ........................................................................................................ 59 11.4 Turbine ............................................................................................................................. 59 11.5 Afterburner ....................................................................................................................... 60 11.6 Nozzle ............................................................................................................................... 61

12 Appendix E: ONX Parametric Analysis .................................................................................... 64 12.1 Mach 0 and Sea Level ........................................................................................................ 64 12.2 Mach 0.5 and 15,000 feet .................................................................................................. 66 12.3 Mach 0.85 and 35,000 feet ................................................................................................ 68 12.4 Mach 1.3 and 40,000 feet .................................................................................................. 70

13 Appendix F: AEDsys Test Data ............................................................................................... 72 13.1 Inlet .................................................................................................................................. 72 13.2 Fan/Compressor ................................................................................................................ 73

13.2.1 Inlet Guide Vanes ................................................................................................................ 73 13.2.2 Fan/Low Pressure Compressor ........................................................................................... 75 13.2.3 High Pressure Compressor .................................................................................................. 78

13.3 Combustion Chamber ........................................................................................................ 84 13.4 Turbine ............................................................................................................................. 88

13.4.1 High Pressure Turbine ......................................................................................................... 88 13.4.2 Low Pressure Turbine .......................................................................................................... 89 13.4.3 Exit Guide Vanes ................................................................................................................. 90

13.5 Afterburner ....................................................................................................................... 91 13.6 Nozzle ............................................................................................................................... 92

13.6.1 Mach 0................................................................................................................................. 92 13.6.2 Mach 0.5 ............................................................................................................................. 93 13.6.3 Mach 0.85 ........................................................................................................................... 94 13.6.4 Mach 1.3 ............................................................................................................................. 94

13.7 Mission Analysis Results .................................................................................................... 95

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List of Figures Figure 2.1: Cutaway of an Axial-flow Compressor ........................................................................................ 3 Figure 3.1: Gantt Chart for Overall Project ................................................................................................... 7 Figure 3.2: Overall Project Flow Chart .......................................................................................................... 8 Figure 3.3: Flow Chart for Responsibilities ................................................................................................... 9 Figure 4.1: Low Bypass Turbofan Station Numbering................................................................................. 10 Figure 4.2: External compression inlet ....................................................................................................... 14 Figure 4.3: Shock Pressure Recovery for Freestream Mach Number and Number of Oblique Shocks ...... 15 Figure 4.4: Multi Shock Compression for Oswatisch Optimization ............................................................ 15 Figure 4.5: CAD of First Stage Low Pressure Fan Blade .............................................................................. 21 Figure 4.6: Operating regimes .................................................................................................................... 22 Figure 4.7: Geometry of flat-wall diffuser .................................................................................................. 22 Figure 4.8: Geometry of dump diffuser ...................................................................................................... 22 Figure 4.9: Geometry of combined diffuser ............................................................................................... 22 Figure 4.10: CAD of the High Pressure Turbine Blade ................................................................................ 30 Figure 4.11: Turbine Transpiration and Full-Coverage Film Cooling........................................................... 31 Figure 4.12: Geometry of Afterburner ........................................................................................................ 32 Figure 4.13: Flow Patterns in the Afterburner ............................................................................................ 32 Figure 4.14: Principal Features ................................................................................................................... 32 Figure 4.15: Nozzle geometric parameters ................................................................................................. 33 Figure 4.16: Compressor Velocity Triangles................................................................................................ 41 Figure 4.17: Turbine Velocity Triangle ........................................................................................................ 44 Figure 5.1: Effect of Temperature and Exposure Time on Tensile Properties ............................................ 45 Figure 5.2: Creep and Creep-rupture curves at temperatures from 75 to 600˚F for 2124-T851 plate ...... 46 Figure 5.3: Axial Fatigue Properties of α-β forged materials in two heat-treated conditions ................... 46 Figure 5.4: Minimum creep rate at various temperatures and stresses .................................................... 47 Figure 5.5: Fatigue properties of annealed sheet ....................................................................................... 47 Figure 5.6: Creep-deformation curves for plate and bar at temperatures of 1200-1800˚F ....................... 48 Figure 5.7: Fatigue life of plate at various temperatures in air and impure helium at atmospheric pressure

............................................................................................................................................................ 48 Figure 5.8: Effect of elevated temperature on modulus of elasticity ......................................................... 49 Figure 5.9: Creep Strain and creep-rupture at 1400, 1600, and 1800˚F for fully treated cast alloy .......... 49 Figure 5.10: Axial Low Cycle Fatigue behavior at 1200-1800˚F .................................................................. 50 Figure 11.1: Principal Features and Flow Patterns of the Afterburner ....................................................... 60 Figure 11.2: Nozzle Discharge Coefficient: b) Convergent and C-D Nozzle CD max ................................... 61 Figure 11.3: C-D Nozzle Velocity Coefficient ............................................................................................... 62 Figure 11.4: C-D Nozzle Angularity Coefficient ........................................................................................... 63 Figure 12.1: ONX Parametric Analysis Results at M=0 and Sea Level ......................................................... 64 Figure 12.2: Preliminary Engine Performance Analysis at M=0 and Sea Level .......................................... 65 Figure 12.3: ONX Parametric Results at M=0.5 and 15,000 feet ................................................................ 66 Figure 12.4: Preliminary Engine Performance Analysis at M=0.5 and 15,000 feet .................................... 67 Figure 12.5: ONX Parametric Analysis Results M=0.85 and 35,000 feet .................................................... 68 Figure 12.6: Preliminary Engine Performance Analysis at M=0.85 and 35,000 feet .................................. 69 Figure 12.7: ONX Parametric Analysis Results at M=1.3 and 40,000 feet .................................................. 70 Figure 12.8: Preliminary Engine Performance Analysis at M=1.3 and 40,000 feet .................................... 71 Figure 13.1: Inlet Inputs and Results .......................................................................................................... 72 Figure 13.2: Inlet Side View ........................................................................................................................ 73

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Figure 13.3: Inlet Angle Contours ............................................................................................................... 73 Figure 13.4: Low Pressure IGV Results ........................................................................................................ 73 Figure 13.5: Low Pressure IGV Blade Profile ............................................................................................... 74 Figure 13.6: High Pressure IGV Results ....................................................................................................... 74 Figure 13.7: High Pressure IGV Blade Profile .............................................................................................. 74 Figure 13.8: Fan/Low Pressure Compressor Layout ................................................................................... 75 Figure 13.9: Low Pressure Stage 1 Results .................................................................................................. 75 Figure 13.10: Low Pressure Stage 1 Blade Profile ....................................................................................... 76 Figure 13.11: Low Pressure Stage 2 Results ................................................................................................ 76 Figure 13.12: Low Pressure Stage 2 Blade Profiles ..................................................................................... 77 Figure 13.13: Low Pressure Stage 3 Results ................................................................................................ 77 Figure 13.14: Low Pressure Stage 3 Blade Layout ...................................................................................... 78 Figure 13.15: High Pressure Compressor Layout ........................................................................................ 78 Figure 13.16: High Pressure Stage 1 Results ............................................................................................... 79 Figure 13.17: High Pressure Stage 1 Blade Layout...................................................................................... 79 Figure 13.18: High Pressure Stage 2 Results ............................................................................................... 80 Figure 13.19: High Pressure Stage 2 Blade Profile ...................................................................................... 80 Figure 13.20: High Pressure Stage 3 Results ............................................................................................... 81 Figure 13.21: High Pressure Stage 3 Blade Profile ...................................................................................... 81 Figure 13.22: High Pressure Stage 4 Results ............................................................................................... 82 Figure 13.23: High Pressure Stage 4 Blade Profile ...................................................................................... 82 Figure 13.24: High Pressure Stage 5 Results ............................................................................................... 83 Figure 13.25: High Pressure Stage 5 Blade Profile ...................................................................................... 83 Figure 13.26: Data Entry for Combustion Chamber.................................................................................... 84 Figure 13.27: Air Partitioning for Combustion Chamber ............................................................................ 84 Figure 13.28: Diffuser for Combustion Chamber ........................................................................................ 85 Figure 13.29: Primary Zone for Combustion Chamber ............................................................................... 85 Figure 13.30: Secondary Zone for Combustion Chamber ........................................................................... 86 Figure 13.31: Dilution Zone for Combustion Chamber ............................................................................... 86 Figure 13.32: Combustion Chamber Front View......................................................................................... 87 Figure 13.33: Combustion Chamber Side View .......................................................................................... 87 Figure 13.34: Combustion Chamber Plan View .......................................................................................... 88 Figure 13.35: High Pressure Results ............................................................................................................ 88 Figure 13.36: High Pressure Layout ............................................................................................................ 89 Figure 13.37: High Pressure Blade Layout .................................................................................................. 89 Figure 13.38: Low Pressure Results ............................................................................................................ 89 Figure 13.39: Low Pressure Layout ............................................................................................................. 90 Figure 13.40: Low Pressure Blade Layout ................................................................................................... 90 Figure 13.41: Exit Guide Vane Results ........................................................................................................ 90 Figure 13.42: Exit Guide Vane Results ........................................................................................................ 90 Figure 13.43: Data Entry ............................................................................................................................. 91 Figure 13.44: Data Entry ............................................................................................................................. 91 Figure 13.45: Flameholders ........................................................................................................................ 91 Figure 13.46: Side View of Afterburner ...................................................................................................... 92 Figure 13.47: Nozzle Input and Results at Mach 0 ...................................................................................... 92 Figure 13.48: Divergent Angle Contours at Mach 0 .................................................................................... 93 Figure 13.49: Nozzle Side View at Mach 0 .................................................................................................. 93 Figure 13.50: Nozzle Input and Results at Mach 0.5 ................................................................................... 93

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Figure 13.51: Divergent Angle Contours at Mach 0.5 ................................................................................. 93 Figure 13.52: Nozzle Side View at Mach 0.5 ............................................................................................... 93 Figure 13.53: Nozzle Input and Results at Mach 0.85................................................................................. 94 Figure 13.54: Divergent Angle Contours at Mach 0.85 ............................................................................... 94 Figure 13.55: Nozzle Side View at Mach 0.85 ............................................................................................. 94 Figure 13.56: Nozzle Input and Results at Mach 1.3 ................................................................................... 94 Figure 13.57: Divergent Angle Contour at Mach 1.3 .................................................................................. 95 Figure 13.58: Nozzle Side View at Mach 1.3 ............................................................................................... 95 Figure 13.59: Warm-Up Leg ........................................................................................................................ 95 Figure 13.60: Takeoff Accelerate ................................................................................................................ 96 Figure 13.61: Takeoff Rotation ................................................................................................................... 96 Figure 13.62: Horizontal Acceleration ........................................................................................................ 97 Figure 13.63: First Climb and Acceleration ................................................................................................. 97 Figure 13.64: Second Climb and Acceleration ............................................................................................ 98 Figure 13.65: Third Climb and Acceleration ................................................................................................ 98 Figure 13.66: Subsonic Cruise ..................................................................................................................... 99 Figure 13.67: Climb and Accelerate to Supersonic Cruise .......................................................................... 99 Figure 13.68: Supersonic Cruise ................................................................................................................ 100 Figure 13.69: Descend to Subsonic Cruise ................................................................................................ 100 Figure 13.70: Subsonic Cruise ................................................................................................................... 101 Figure 13.71: Descend to Loiter ................................................................................................................ 101 Figure 13.72: Loiter ................................................................................................................................... 102 Figure 13.73: Descend to Land.................................................................................................................. 102 Figure 13.74: Results of Mission ............................................................................................................... 103

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List of Tables Table 3.1: Cost Analysis for Engine ............................................................................................................... 9 Table 4.1: Compliance Matrix ..................................................................................................................... 36 Table 4.2: Engine Summary Data ................................................................................................................ 37 Table 4.3: Fan / LP Compressor Flow Station Data ..................................................................................... 37 Table 4.4: HP Compressor Flow Station Data ............................................................................................. 38 Table 4.5: Turbine & Nozzle Flow Data ....................................................................................................... 38 Table 4.6: Additional Information ............................................................................................................... 38 Table 4.7: Fan / Low Pressure Compressor Detailed Data .......................................................................... 39 Table 4.8: High Pressure Compressor Detailed Data .................................................................................. 40 Table 4.9: Turbine Detailed Data ................................................................................................................ 40 Table 4.10: Fan/Low Pressure Compressor ................................................................................................ 42 Table 4.11: High Pressure Compressor ....................................................................................................... 43 Table 4.12: High Pressure Turbine .............................................................................................................. 44 Table 4.13: Low Pressure Turbine ............................................................................................................... 44 Table 11.1: Table of Initial Value for Inlet ................................................................................................... 58 Table 11.2: Table of Requirements for Inlet ............................................................................................... 58 Table 11.3: Initial Values and Requirements for Fan/Compressor ............................................................. 58 Table 11.4: Initial Values and Requirements for Combustion Chamber .................................................... 59 Table 11.5: Initial Values and Requirements for Turbine ........................................................................... 59

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Nomenclature A = Area (in2) AR = Area Ratio a = Speed of Sound (ft/s) B = Blockage Ratio c = Airfoil Chord (in) cp = Specific Heat at Constant Pressure (Btu/lbm-R) D = Diameter (in) ei = Polytropic Efficiency of Component i F = Uninstalled Thrust (lbf) f = Fuel-to-Air Mass Flow Ratio gc = Newton’s Gravitational Constant = 32.174 (lbm-ft)/(lbf-s2) hPR = Heating Value of Fuel = 18400 Btu/(lbm-R) hr = Heat of Rim (in) L = Length (in) M = Mach Number MFP = Mass Flow Parameter

m = Mass Flow Rate (lbm/s) N = Rotational Speed (rpm) NB = Number of Blades NH = Rotational Speed of High-Pressure Spool (rpm) NL = Rotational Speed of Low-Pressure Spool (rpm) P = Pressure (psi) ; Power (hp) Pti = Total Pressure at Station i (psi) q = Dynamic Pressure (psi) R = Gas Constant = 53.34 (ft-lbf)/(lbm-R) for Air r = Radius (in) S = Uninstalled Thrust Specific Fuel Consumption (lbm/h/lbf) S’ = Swirl Number of Primary Air Swirler S = Spacing (in) T = Temperature (R) TSFC = Installed Thrust Specific Fuel Consumption (lbm/h/lbf) Tti = Total Temperature at Station i (R) tBO = Residence Time of Stay Time at Blowout (sec) ts = Residence Time or Stay Time (sec) U = Velocity Component in Direction of Flow (ft/s) u = Axial or Throughflow Velocity (ft/s) V = Velocity (ft/s) V’ = Turbine Reference Velocity (ft/s) v = Tangential Velocity (ft/s) W = Weight (lbm)

Wc = Power Absorbed by the Compressor (hp)

Wt = Power Produced by the Turbine (hp)

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Z = Zweifel Coefficient α = Engine Bypass Ratio; Angle α' = Mixer Bypass Ratio αSW = Off-Axis Turning Angle of Swirler Blades β = Blade Angle γ = Ratio of Specific Heats δt = Exit Deviation of Turbine Blades ε = Combustion Reaction Progress Variable ηi = Adiabatic Efficiency of Component i ηO = Engine Overall Efficiency ηT = Engine Thermal Efficiency ηP = Engine Propulsive Efficiency θi = Dimensionless Total Temperature at Engine Station i πi = Total Pressure Ratio of Component i πr = Isentropic Freestream Recovery Pressure Ratio ρ = Density = 0.0023769 slug/ft3 at sea-level σ = Solidity τi = Total Temperature Ratio of Component i τλ = Enthalpy Ratio of Burner τλAB = Enthalpy Ratio of Afterburner Φ = Cooling Effectiveness Φinlet = Inlet External Loss Coefficient Φnozzle = Nozzle External Loss Coefficient ψ = Turbine Stage Loading Coefficient Ω = Dimensionless Turbine Rotor Speed ω = Angular Velocity (rad/s) ˚Rc = Degree of Reaction for Compressor Stage ˚Rt = Degree of Reaction for Turbine Stage

Subscripts

AB = Afterburner avail = Available b = Burner DZ = Dilution Zone d = Diffuser or Inlet e = Exit; External; Exhaust; Engine f = Fuel; Fan fAB = Fuel at Afterburner h = Hub L = Liner M = Mixer MB = Main Burner m = Mean O = Overall opt = Optimum

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P = Propulsive PR = Products to Reactants PZ = Primary Zone r = Radial Direction ref = Reference rel = Relative req = Required SZ = Secondary Zone s = Stage std = Standard Day Sea Level Property st = Stoichiometric t =Turbine; Total; Tip tH = High-Pressure Turbine tL = Low-Pressure Turbine u = Axial Velocity v = Tangential Velocity 0 → 19 = Station Location (Figure 4.1)

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1 Introduction The purpose of the AIAA Engine Design Competition is to design a low-bypass turbofan engine with afterburner for the Northrop Grumman T-38 aircraft. The engine will be used to decrease the fuel consumption, provide higher thrust, and decrease weight compared to the baseline J85-GE-5A turbojet engine with afterburner already in use. Upon completed design, the low-bypass turbofan engine will replace the afterburning turbojet engine in use. The low-bypass turbofan engine must also be able to accomplish such tasks to emulate a fifth generation aircraft. These include: supersonic speeds of Mach 1.3, cruise speeds of Mach 0.85, wetted fuel consumption less than 2.2 lbm/hr/lbf, and fan diameter less than or equal to 20 inches. The engine must also achieve a minimum take-off thrust of 4000 lbf. Based on an entry-into-service date of 2025, design parameters and limits for the required time will be taken into consideration. Initially, each individual stage of the engine will be designed around the fifth generation aspect of efficiency. Trade studies are to be evaluated in order to obtain an optimized engine mass, fuel burn, fan pressure ratio, bypass ratio, overall pressure ratio, and turbine entry temperature. Upon obtaining the information via parametric analysis, each individual stage will be designed around it. Once the engine is designed, materials will be selected in order to prove the possibilities of temperature, pressure, and cooling throughout each stage. Along with the design of each individual stage of the turbofan engine, an appropriate inlet and nozzle must be designed. It was stated that a 2-ramp, either axisymmetric or 2-dimensional configuration is suggested. Both varieties of inlet will achieve a high enough pressure rise so that the compressor will not surge or stall. The nozzle must also be of the convergent-divergent type. This will allow for both subsonic and supersonic speeds exiting for both wet and dry engine conditions.

1.1 Justification

The American Institute of Aeronautics and Astronautics has set forth the engine design competition in hopes of replacing the in use J85-GE-5A turbojet with afterburner. The J85-GE-5A does not make use of current materials or cooling for the heated components. The hope is to design a low-bypass turbofan with afterburner that allows for a newer selection in material choice as well as cooling methods. The upgrades to the new engine will allow for not only higher thrust but lower fuel consumption. Once the low-bypass turbofan, along with inlet, is designed, the Northrop Grumman T-38 Talon will use it.

1.2 Problem Statement

The American Institute of Aeronautics and Astronautics created an engine design competition to be obtained via a student body. The objective was to design an afterburning low bypass turbofan engine to replace the J85-GE-5A afterburning turbojet engine used on the Northrop Grumman T-38 Talon trainer jet. The new engine is required to have a lower thrust specific fuel consumption, weight, and improved thrust while maintaining current performance characteristics.

2 Gas Turbine Engine Components The compressor, turbine, inlet, nozzle and combustor are the main components of a gas turbine engine. A sub component of a gas turbine engine is the afterburner. Each of the components are described in detail in the following sections.

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2.1 Inlet

The inlet is one of the engine components that directly influences the internal airflow and flow about the aircraft. The inlet interchanges the organized kinetic and random thermal energies of the gas in an essentially adiabatic process. The perfect (no loss) inlet would thus correspond to an isentropic process. The inlet and compressor work hand in hand to give the overall pressure ratio of the engine cycle. The primary purpose of the inlet is to transfer the air required by the engine from freestream conditions to the conditions required at the entrance of the fan or compressor with minimum total pressure loss and flow distortion. The optimum conditions for the air entering the fan or compressor is with uniform flow at a Mach velocity of about 0.5. Since the inlet engine performance depends on the inlet’s installation losses, the inlet should be designed to minimize these. The inlet performance is related to the following characteristics: high total pressure ratio across the diffuser, governable flow matching, good uniformity of flow, low installation drag, acceptable starting and stability, limited signatures (acoustics, radar, and infrared), and minimum weight and cost while adhering to the life and reliability goals. The design and operation of the subsonic and supersonic flight conditions differ significantly because of the characteristics of flow. In the subsonic condition, near-isentropic internal diffusion can easily be achieved and inlet flow rate adjusts to the demand. In contrast, the internal aerodynamic performance of a supersonic inlet is a major challenge to design since efficient and stable supersonic diffusion over a wide range of Mach numbers is very difficult to achieve. In order to capture the required mass flow rate for the engine, varying inlet geometries may be required to minimize the inlet loss and drag and supply stable operation. The main three main supersonic inlet types are: Internal Compression, External Compression, and Mixed Compression. For the purpose of this engine and its given flight conditions, a Two-Ramp External Compression Inlet is designed.

2.2 Compressor

Currently, the axial-flow compressor is the most common types of compressor used. The compressor is designed to increases the pressure of the incoming airflow so that to maximize the efficiency of the combustor. The compressor allows for the volume of air to decrease by increasing the pressure, which means the fuel/air mixture will happen in a smaller volume. There are two main types of compressors which are Centrifugal and Axial.

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Figure 2.1: Cutaway of an Axial-flow Compressor

Axial compressor uses a series of rotating rotor blades and stationary stator blades to pull the air through the compressor. One set of rotor and stator is known as a stage. A cutaway of an axial-flow compressor can be found above in Figure 2.1. In Figure 2.1 part A, from left to right, the first is the rotor, then the stator and the complete compressor. The cross sectional area of an axial compressor decrease in the direction of the air flow. Each stage of the compressor produces a small amount of compression at a high efficiency. Therefore, multiply stages are used consecutively to increase the total pressure ratio.

2.3 Combustion Chamber

The combustor is designed to burn a mixture of fuel and air and to deliver the resulting gases to the turbine at a uniform temperature. The gas temperature must not exceed the allowable structural temperature of the turbine. About one-half of the total volume of air entering the burner mixes with the fuel and burns. The rest of the air, or secondary air, is simply heated or may be thought of as cooling the products of combustion and cooling the burner surfaces. The ratio of total air to fuel varies among the different types of engines from 30 to 60 parts of air to 1 part of fuel by weight. The average ratio in new engine designs is about 40:1, but only 15 parts are used for burning. This is due to the combustion process demanding the number of parts of air to fuel must be within certain limits at a given pressure for combustion to occur. Combustion chambers may be of the can, the annular, or the can-annular type. The annular type is most common in new engine designs. For an acceptable burner design, the pressure loss (as the gases pass through the burner) must be held to a minimum, the combustion efficiency must be high, and there must be no tendency for the burner to flameout. Also, combustion must take place entirely within the burner.

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2.4 Turbine

The turbine extracts kinetic energy from the expanding gases that flow from the combustion chamber. The kinetic energy is then converted to shaft horsepower to drive the compressor and the accessories. Nearly three-fourths of all the energy available from the products of combustion is required to drive the compressor. An axial-flow turbine consists of a turbine wheel rotor and a set of stationary vanes stator. The set of stationary vanes of the turbine is concentric with the axis of the turbine and are set at an angle to form a series of small nozzles that discharge the gases onto the blades of the turbine wheel. The discharge of the gases into the rotor allows the kinetic energy of the gases to be transformed to mechanical shaft power. Like the axial compressor, the axial turbine is usually multi-staged. There are generally fewer turbine stages than compressor stages because in the turbine the pressure is decreasing. The blades of the axial turbine act as airfoils, and the air flow over the airfoil is more favorable in the expansion process. The result is that one stage of turbine can power many compressor stages. Most turbines in jet engines are a combination of impulse and reaction turbines. In the impulse turbine type, the relative discharge velocity of the rotor is the same as the relative inlet velocity because there is no net change in pressure between the rotor inlet and rotor exit. The stator nozzles of the impulse turbine are shaped to form passages that increase the velocity and reduce the pressure of the escaping gases. In the reaction turbine, the relative discharge velocity of the rotor increases and the pressure decreases in the passages between rotor blades. The stator nozzle passages of the reaction turbine merely alter the direction of flow.

2.5 Afterburner

A method of thrust augmentation by burning additional fuel takes place in the afterburner. It is a section of duct between the turbine and exhaust nozzle. The afterburner consists of the duct section, fuel injectors, and flame holders. It is possible to have afterburning because, in the burning section, the combustion products are air-rich. The effect of the afterburning operation is to raise the temperature of the exhaust gases that, when exhausted through the nozzle, will reach a higher exit velocity. It can be seen that afterburning produces large thrust gains at the expense of fuel economy.

2.6 Nozzle

The objective of the nozzle is to boost the velocity of the exhaust gas before exiting the nozzle and to gather and straighten the gas flow. For sizeable values of thrust, the kinetic energy of the expelled gas must be high, which implies a high exit velocity. Overall, the functions of the nozzle can be summarized by the following: 1) Accelerate the flow to a high velocity with minimum total pressure loss, 2) Match exit and atmospheric pressure as closely as desired, 3) Permit afterburner operation without affecting main engine operation (requires a variable throat area nozzle), 4) Allow for cooling of walls if necessary, 5) Mix core and bypass streams of turbofan if necessary, 6) Allow for thrust reversing if desired, 7) Suppress jet noise, radar reflection, and infrared radiation (IR) if desired, 8) Two-dimensional and axis-symmetric nozzles, thrust vector control if desired, and 9) Do all of the previous with minimal cost, weight, and boattail drag while meeting life and reliability goals. Given the nozzle functions described and the engines desired flight condition to achieve a Mach velocity of 1.3, a Convergent-Divergent Nozzle with a varying throat area is chosen nozzle type to be designed.

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3 Problem Solving Approach When beginning the design of the DKA-867 turbofan engine with afterburner, a process had to be adapted. Initially the requirements designated by the customer, engineer, and FAA. Below is a list of each individual’s requirements. Each of these will be revisited as the report progresses.

3.1 Requirement

The customer requirements are defined as followed: • Max Speed: Mach 1.3 @ 40,000 ft • Cruise Speed: Mach 0.85 @ 30,000 ft • Loiter Speed: Mach 0.5 @ 15,000 ft, for 30 mins. • Service Ceiling: 51,000 ft • Range: 1,500 nmi • Maximum Takeoff Weight: 12,000 lbm • Power plant: 2x Low-Bypass Turbofan • Fan Diameter ≤ 20” • Use of Convergent-Divergent Nozzle

The engineer requirements are defined as followed:

Intake o Inlet optimized for all flight conditions, while being able perform at aircraft Mach speeds

of 1.3. o Material: Aluminum 2124 Alloy

Fan o Material: Titanium 6246 Alloy o Airfoil: NACA65A010

Compressor o Design: twin spool with maximum of 9 stages o Material: Titanium 6246 alloy o Airfoil: NACA65A010

Combustion Chamber o Fuel: JP-8 o Design: Double Annular o Material:

Inconel 601 for liner, diffuser, igniters, and containment rings Hastelloy X for structural parts

o Cooling Air used to protect material o Maximum of two igniters

Turbine o Design: 2 Stage Axial Flow o Material: Rene’ 80 o Airfoils: C4 and/or T6 o Cooling and/or coating used o Calculations taken assuming no exit swirl

Afterburner o Cooling Air used to protect material o Material:

6

Inconel 601 for liner, diffuser, igniters, and containment rings Hastelloy X for structural parts

Nozzle o Nozzle optimized for all flight conditions, including aircraft Mach speeds of 1.3. o Variable Exhaust o Material: Hastelloy X

The FAA requirements are defined as followed:

Stress analysis must be performed showing design safety margin of each rotor, spacer, and rotor shaft

Each operating condition be obtained without inducing excessive stress in any engine part or aircraft structure do to vibrations

Applicant must establish by test and/or validated analysis that all static parts subject to significant gas pressure loads for a stabilized period of one minute will not:

o Exhibit permanent distortion beyond serviceable limits of 1.1 times maximum working pressure

o Exhibit fracture or burst when subjected to 1.15 times the maximum possible pressure

At each operating condition, engine may not cause surge or stall to the extent that flameout, structural failure, over-temperature, or failure of the engine to recover power

Engine must supply bleed air without adverse effect on the engine, excluding thrust or power output, at conditions up to the discharge flow conditions

Each engine must be equipped with an ignition system for starting the engine on ground and in flight. An electric ignition system must have at least two igniters and two separate secondary electric circuits

For more in depth aircraft engine design certification approvals refer to FAA guidelines found in the References:

o Part 21 – Certification Procedures for Products and Parts o Part 33 – Airworthiness Standards: Aircraft Engines o Part 34 – Fuel Venting and Exhaust Emission Requirements for Turbine Engine Powered

Airplanes o Part 36 – Noise Standards: Aircraft Type and Airworthiness Certification

7

3.2 Gantt Chart

The use of a schedule of goals was initially made and continuously revised based on the needs stated in the previous section. These goals were put into a Gantt chart to maintain a visually stable appearance. As seen in the figure below, most goals were met by the date required. In order to help with the completion of the project in an orderly manner, each assignment is color coded. As seen below, green is labeled for easiest, yellow for moderate, and red for difficult.

Figure 3.1: Gantt Chart for Overall Project

3.3 Flow Charts

Once the Gantt chart was completed, each individual component had to be broken down into a design process. Within each component of an engine, there are necessities for which designing will be allowed. The breakdown of what will be calculated at each station is listed below. It can be seen that certain aspects require more attention. The flow chart below can be compared to the Gantt chart in order to see the progress made during the project.

8

Figure 3.2: Overall Project Flow Chart

3.4 Project Management

From the beginning of the project, the group had made a more than conscientious effort to be organized and adhere to a schedule. Since the first half of the Spring 2016 semester, the group met at the same time every Wednesday night and Sunday morning, in addition to the class time designated for the project on Tuesdays. Upon the start of the meetings, the work that had been done since the last meeting was discussed. Then the team decided on what needed to be done while at the current meeting. Finally, at the end of each meeting, work was divvied out to each member that would need to be done before the next meeting. Unique to the Sunday meetings, a list of questions would be made to ask Mentor and Advisor Dr. Adeel Khalid during the designated project class time. These steps of information sharing and work reviews helped to keep a constant understanding of what was going on with the project as a group and for each individual as it progressed. A group communication application, GroupMe, was implemented in order for all the members to communicate together. Similarly, a Microsoft OneDrive shared folder was made so that all files, documents, and programs were accessible to each member and constantly updated. Along with having access to the files, all members could even collaborate in real time on any Microsoft Office program file. The utilization of this program was one of the most effective and productive elements used throughout the project. Lastly, each member of the group was given the responsibility of designing two of the 6 different components: Austin) Inlet and Nozzle; David) Compressor and Afterburner; and Kristian) Turbine and Main Burner. While each member worked on their respective engine components, constant communication was made in order to make sure each entity would work efficiently together in the installed condition. Ultimately, every group member found themselves managing one element of the project or another.

DKA-867

Intake

Nacelle

Engine

Fan

Blade Design

Sizing

Compressor

Blade Design

# of Stages

𝜋𝐶

Combustor

Annular

Temperatures

Turbine

Blade Design

Cooling/Coating

# of Stages

Nozzle

Convergent/ Divergent

Afterburner

Design

9

3.5 Responsibilities

Below is a diagram of the responsibilities given to each of the group members. Each of these designations are tailored to the individuals’ knowledge and strengths.

Figure 3.3: Flow Chart for Responsibilities

3.6 Cost Analysis

Inflations models were used to calculate the current and future cost of the General Electric J85 turbojet engines, as seen in Table 3.1. The cost for a pair of J85 turbojet engine in 2025 will be over 2 million dollars. The amount of money spent on a turbojet engine compared to the total cost of the aircraft averages to 25%.

Table 3.1: Cost Analysis for Engine

Total Cost Engine Cost Percent of

engine cost

Cost per Unit Jet (1961) $756,000.00 $189,000.00 25.00%

Cost per Unit Jet (2015) $5,990,497.57 $1,497,624.39 25.00%

Cost per Unit Jet (2025) $8,050,727.94 $2,012,681.99 25.00%

3.7 Resources Available & Used

• EOP Software • AEDsys Software • SOLIDWORKS

Dr. Adeel Khalid

Advisor

David Byrd

CAD Engineer

CAD & Simulations

Report

Aerodynamics

Kristian Lien

Technical Expert

Calculations

Analysis

Research

Austin Sims

Project Manager

Software

Manufacturing

Propulsions

10

• Expanded Technology Inc. Machine Shop • Delta TechOps • “Elements of Propulsion- Gas Turbines & Rockets” [1] • “Aircraft Engine Design Second Edition” [2]

4 Results and Discussion The use of parametric analysis for a real engine was the first process in designing a low bypass turbofan engine. Once the values of the parametric analysis were finalized, AEDsys program was used to design each component of the turbofan engine. In the following sections, 4.1 & 4.2, the parametric calculations and the AEDsys design are describe in great detail. For reference, Figure 4.1 is a cross section of low bypass turbofan engine with the station number locations.

Figure 4.1: Low Bypass Turbofan Station Numbering

4.1 Parametric Analysis

In order to compare the results of the given baseline turbojet engine to the newly developed low bypass turbofan engine, a mathematical approach was initially considered. An analysis of a real engine required a multitude of equations to be used. By applying the inputs of the turbojet with afterburner to a mixed-flow low bypass turbofan with afterburner at each flight condition needed for the aircraft. Equations (1 – 45), listed below, can be used as an initial analysis for a mixed-flow low bypass turbofan with afterburner. To simplify the process, the ONX program provided by AEDsys is used to do the parametric analysis calculations. The results can be found in Appendix 12. After completing the analysis, a comparison between both engines can be made. The fan pressure ratio and polytrophic efficiency of the fan were initially assumed based on statistical data found in previous low bypass turbofan engines. Through multiple iterations, the fan parameters can be finalized in order [2] to achieve the needed fuel consumption and thrust.

Rc =γc − 1

γccpc

(1)

Rt =γt − 1

γtcpt

(2)

RAB =γAB − 1

γABcAB

(3)

a0 = √γcRcgcT0

(4)

11

V0 = a0M0

(5)

τr = 1 +γc − 1

2M02

(6)

πr = τrγc γc−1⁄

(7)

ηr = 1 for M0 ≤ 1

(8)

ηr = 1 − 0.075(M0 − 1)1.35 for M0 > 1

(9)

πd = πdmaxηr

(10)

τλ =cptTt4

cpcT0

(11)

τλAB =cpABTt7

cpcT0

(12)

τc = πc(γc−1) (γcec)⁄

(13)

τf = πf(γc−1) (γcef)⁄

(14)

f =τλ − τrτc

ηbhPR (cpcT0)⁄ − τλ

(15)

α =ηm(1 + f)(τλ τr⁄ ){1 − [πf (πcπb)⁄ ](γt−1)ec γt⁄ } − (τc − 1)

τf − 1

(16)

τt = 1 −1

ηm(1 + f)

τrτλ[τc − 1 + α(τf − 1)]

(17)

πt = τtγt [(γt−1)et]⁄

(18)

𝑃𝑡16𝑃𝑡6

=𝜋𝑓

𝜋𝑐𝜋𝑏𝜋𝑡

(19)

𝑀16 = √2

𝛾𝑐 − 1{[𝑃𝑡16𝑃𝑡6

(1 +𝛾𝑡 − 1

2𝑀62)

𝛾𝑡 (𝛾𝑡−1)⁄

]

(𝛾𝑐−1) 𝛾𝑐⁄

− 1}

(20)

𝛼′ =𝛼

1 + 𝑓

(21)

𝑐𝑝6𝐴 =𝑐𝑝𝑡 + 𝛼′𝑐𝑝𝑐1 + 𝛼′

(22)

12

𝑅6𝐴 =𝑅𝑡 + 𝛼′𝑅𝑐1 + 𝛼′

(23)

𝛾6𝐴 =𝑐𝑝6𝐴

𝑐𝑝6𝐴 − 𝑅6𝐴

(24)

𝑇𝑡16𝑇𝑡6

=𝑇0𝜏𝑟𝜏𝑓

𝑇𝑡4𝜏𝑡

(25)

𝜏𝑀 =𝑐𝑝𝑡𝑐𝑝6𝐴

1 + 𝛼′(𝑐𝑝𝑐 𝑐𝑝𝑡)⁄ (𝑇𝑡16 𝑇𝑡6)⁄

1 + 𝛼′

(26)

𝜑(𝑀6, 𝛾6) =𝑀62{1 + [(𝛾𝑡 − 1) 2⁄ ]𝑀6

2}

(1 + 𝛾𝑡𝑀62)2

(27)

𝜑(𝑀16, 𝛾16) =𝑀162 {1 + [(𝛾𝑐 − 1) 2⁄ ]𝑀16

2 }

(1 + 𝛾𝑐𝑀162 )2

(28)

𝛷 =

[

1 + 𝛼′

1

√𝜑(𝑀6, 𝛾6)+ 𝛼′√

𝑅𝑐𝛾𝑡𝑅𝑡𝛾𝑐

𝑇𝑡16 𝑇𝑡6⁄𝜑(𝑀16, 𝛾16)]

2

𝑅6𝐴𝛾𝑡𝑅𝑡𝛾6𝐴

𝜏𝑀

(29)

𝑀6𝐴 = √2𝛷

1 − 2𝛾6𝐴𝛷 +√1 − 2(𝛾6𝐴 + 1)𝛷

(30)

𝐴16𝐴6

=𝛼′√𝑇𝑡16 𝑇𝑡6⁄

𝑀16𝑀6

√𝛾𝑐𝑅𝑡𝛾𝑡𝑅𝑐

1 + [(𝛾𝑐 − 1) 2]⁄ 𝑀162

1 + [(𝛾𝑡 − 1) 2]⁄ 𝑀62

(31)

𝜋𝑀 𝑖𝑑𝑒𝑎𝑙 =(1 + 𝛼′)√𝜏𝑀1 + 𝐴16 𝐴6⁄

𝑀𝐹𝑃(𝑀6, 𝛾𝑡 , 𝑅𝑡)

𝑀𝐹𝑃(𝑀6𝐴, 𝛾6𝐴, 𝑅6𝐴)

(32)

𝜋𝑀 = 𝜋𝑀 𝑚𝑎𝑥𝜋𝑀 𝑖𝑑𝑒𝑎𝑙

(33)

𝑃𝑡9𝑃9

=𝑃0𝑃9𝜋𝑟𝜋𝑑𝜋𝑐𝜋𝑏𝜋𝑡𝜋𝑀𝜋𝐴𝐵𝜋𝑛

(34)

Afterburner off: 𝑐𝑝9 = 𝑐𝑝6𝐴 𝑅9 = 𝑅6𝐴 𝛾9 = 𝛾6𝐴 𝑓𝐴𝐵 = 0

13

𝑇9𝑇0=

𝑇𝑡4𝜏𝑡𝜏𝑀 𝑇0⁄

(𝑃𝑡9 𝑃9)⁄ (𝛾9−1) 𝛾9⁄

(35)

Afterburner on: 𝑐𝑝9 = 𝑐𝐴𝐵 𝑅9 = 𝑅𝐴𝐵 𝛾9 = 𝛾𝐴𝐵

𝑓𝐴𝐵 = (1 +𝑓

1 + 𝛼)𝜏𝜆𝐴𝐵 − (𝑐𝑝6𝐴 𝑐𝑝𝑡⁄ )𝜏𝜆𝜏𝑡𝜏𝑀

𝜂𝐴𝐵ℎ𝑃𝑅 (𝑐𝑝𝑐𝑇0) − 𝜏𝜆𝐴𝐵⁄

(36)

𝑇9𝑇0=

𝑇𝑡7 𝑇0⁄

(𝑃𝑡9 𝑃9)⁄ (𝛾9−1) 𝛾9⁄

(37)

Continue:

𝑀9 = √2

𝛾9 − 1[(𝑃𝑡9𝑃9)(𝛾9−1) 𝛾9⁄

− 1]

(38)

𝑉9𝑎0

= 𝑀9√𝛾9𝑅9𝑇9𝛾𝑐𝑅𝑐𝑇0

(39)

𝑓𝑂 =𝑓

1 + 𝛼+ 𝑓𝐴𝐵

(40)

𝐹

��0=𝑎0𝑔𝑐[(1 + 𝑓𝑂)

𝑉9𝑎0−𝑀0 + (1 + 𝑓𝑂)

𝑅9𝑅𝑐

𝑇9 𝑇0⁄

𝑉9 𝑎0⁄

1 − 𝑃0 𝑃9⁄

𝛾𝑐]

(41)

𝑆 =𝑓𝑂

𝐹 ��0⁄

(42)

𝜂𝑃 =2𝑔𝑐𝑉0(𝐹 ��0)⁄

𝑎02[(1 + 𝑓𝑂)(𝑉9 𝑎0)⁄ 2 −𝑀0

2]

(43)

𝜂𝑇 =𝑎02[(1 + 𝑓𝑂)(𝑉9 𝑎0)⁄ 2 −𝑀0

2]

2𝑔𝑐𝑓𝑂ℎ𝑃𝑅

(44)

𝜂𝑂 = 𝜂𝑃𝜂𝑇

(45)

4.2 AEDsys Software Analysis

When utilizing the AEDsys software provided, each individual stage must be calculated prior. By utilizing the processes given by “Aircraft Engine Design” [1] book, the needed results can be found. Upon finding these results, certain numbers can be placed in each stage of the AEDsys software. Once each stage is filled in, the entire engine can be analyzed. The analysis will thus prove if the calculated results will provide an engine suitable for the T-38 aircraft. Below are the given requirements and steps needed to accomplish the task.

14

4.2.1 Inlet The INLET program of the AEDsys software is used to design a 2-D External Compression Inlet. Below in Figure 4.2 an example of external compression inlet is given from Mattingly’s Aircraft Engine Design [2]. The inlet is designed for the desired maximum Mach velocity and flight condition. Before the inlet design and calculations can be made the Inlet program asks for the following inputs: a chosen number of oblique shocks, and their ramp angles (in degrees) relative to the Upstream Velocity Vector, the Free Stream Mach Number, the Ratio of Specific Heats, the Corrected Mass Flow (lbm/s) or Area 0 (ft2), and lastly the desired Inlet Height-to-Width Ratio. Upon the completion of entering the inputs the user can press the Design Calc button to return a sketch and dimensions of the design inlet. Additionally, the calculated performance results across each oblique shock, an internal normal shock, and total change across the shocks is returned.

Figure 4.2: External compression inlet

From the results a contour plot may be designed by pressing the Contours button. A window will emerge asking the user to choose the desired x-axis and y-axis variables with the ability to select the variable minimum and maximum values for each, the number of calculations to be made up to a max of 100, and then a button to calculate the points for the plot contour data. Once these points are calculated the user has a choice between having a standard black and white plot or a color plot to be made. Using the contour plot, one can estimate the optimum values of either variable relative to the Inlet Total Pressures (Pts/Pt0) described by the legend on the right side of the window. Refer to Appendix E for results of the INLET program. Similarly refer to Appendix D: inlet inputs and requirements tables for Capture Area Estimations.

15

The following equations, charts, and figures from the paper, “Preliminary Design of a 2D Supersonic Inlet to Maximize Total Pressure Recover,” [3] are used as a reference to the Inlet program results:

Figure 4.3: Shock Pressure Recovery for Freestream Mach Number and Number of Oblique Shocks

Figure 4.4: Multi Shock Compression for Oswatisch Optimization

𝑀1 sin𝜃1 = 𝑀2 sin 𝜃2 = ⋯ = 𝑀𝑛−1 sin𝜃𝑛−1

(46)

Mach number and Turning Angle Calculations across each Oblique Shock (Ramp)

𝑀12 =

(𝛾 − 1)2𝑀04𝑠𝑖𝑛2𝜃1 − 4(𝑀0

2𝑠𝑖𝑛2𝜃1 − 1)(𝛾𝑀02𝑠𝑖𝑛2𝜃1 + 1)

[2𝛾𝑀02𝑠𝑖𝑛2𝜃1 − (𝛾 + 1)][(𝛾 − 1)𝑀0

2𝑠𝑖𝑛2𝜃1 + 2]

(47)

16

tan 𝛿1 =2𝑐𝑜𝑡𝜃1(𝑀0

2𝑠𝑖𝑛2𝜃1 − 1)

2 +𝑀02(𝛾 + 1 − 2𝑠𝑖𝑛2𝜃1)

(48)

𝑀22 =

(𝛾 − 1)2𝑀14𝑠𝑖𝑛2𝜃2 − 4(𝑀1

2𝑠𝑖𝑛2𝜃2 − 1)(𝛾𝑀12𝑠𝑖𝑛2𝜃2 + 1)

[2𝛾𝑀12𝑠𝑖𝑛2𝜃2 − (𝛾 + 1)][(𝛾 − 1)𝑀1

2𝑠𝑖𝑛2𝜃2 + 2]

(49)

tan 𝛿2 =2𝑐𝑜𝑡𝜃2(𝑀1

2𝑠𝑖𝑛2𝜃2 − 1)

2 +𝑀12(𝛾 + 1 − 2𝑠𝑖𝑛2𝜃2)

(50)

Applying the optimum criteria from Eq. (4.46):

𝑀0 sin 𝜃1 = 𝑀1 sin𝜃2

(51)

M2 is assumed to be equal to M3_up, and M3 _up will be a given input parameter, therefore M2 is known.

𝑀2 = 𝑀3_𝑢𝑝

(52)

Since M3_up is given, M3, the Mach number just after the normal shock, is calculated by the normal shock equation:

𝑀32 =

(𝛾 − 1)𝑀32_𝑢𝑝 + 2

2𝛾𝑀32_𝑢𝑝 − (𝛾 − 1)

(53)

In order to calculate M4, assume that M5 and hub-tip ratio h_t is given based on engine data. Assuming the duct diameter is constant from 4 to 5, we have the following relation for the

airflow areas:

𝐴4𝐴5

=1

1 − ℎ_𝑡2

(54)

𝐴4𝐴5

=

𝐴4𝐴∗⁄

𝐴5𝐴∗⁄

(55)

According to the Area-Mach number relation, we have:

(𝐴5𝐴∗)2

=1

𝑀52 [

2

𝛾 − 1(1 +

𝛾 − 1

2𝑀52)]

𝛾+1𝛾−1

(56)

(𝐴4𝐴∗)2

=1

𝑀42 [

2

𝛾 − 1(1 +

𝛾 − 1

2𝑀42)]

𝛾+1𝛾−1

(57)

With M5 known and using Eq. (54-58), the equation solving for M4 is derived.

17

𝑀4 =

√ 2

𝛾 + 1

𝛾+1𝛾−1

(𝐴5𝐴∗)2

−2

𝛾 + 1

𝛾+1𝛾−1

−1

(58)

For the 2 oblique shocks, the total pressure across each oblique shock is calculated as the following:

𝑃𝑅𝑖 = [(𝛾 + 1)𝑀𝑖−1

2 (sin𝜃𝑖)2

(𝛾 − 1)𝑀𝑖−12 (sin𝜃𝑖)

2 + 2]

𝛾𝛾−1

[(𝛾 + 1)

2𝛾𝑀𝑖−12 (sin𝜃𝑖)

2 − (𝛾 − 1)]

1𝛾−1

, 𝑖 = 1 − 2

(59)

The total pressure ratio across the normal shock is calculated by the following:

𝑃𝑅3 = [(𝛾 + 1)𝑀3

2_𝑢𝑝

(𝛾 − 1)𝑀32𝑢𝑝+ 2

]

𝛾𝛾−1

[(𝛾 − 1)

2𝛾𝑀32𝑢𝑝− (𝛾 − 1)

]

1𝛾−1

(60)

From the subsonic diffuser, assume the total temperature is constant, then according to the equation flow function, we have:

𝑃𝑅_𝑆𝑢𝑏 =𝑃𝑡4𝑃𝑡3

=1

𝐴𝑅43

𝑊𝑓𝑓3

𝑊𝑓𝑓4

(61)

The flow function values Wff3 and Wff4 are determined by statics temperatures t3 and t4, and the Mach numbers M3 and M4.

Based on Borda-Carnot loss equation, the following equation is derived with correction factors:

𝑃𝑡4𝑃𝑡3

= 1 − 𝐾𝑀𝑡ℎ𝐾𝑑 (1 −1

𝐴𝑅43)2 𝛾

2𝑀32

(1 +𝛾 − 12 𝑀3

2)

𝛾𝛾−1

(62)

The coefficient KMth accounts for friction loss and Kd accounts for expansion loss. With the values found, then the values of PR4 and AR43 are determined by solving Eq. (61) and

(62) simultaneously.

The total pressure recovery is then calculated as following:

𝑇𝑃𝑅 =∏𝑃𝑅𝑖 × 𝑃𝑅_𝑠𝑢𝑏

3

𝑖=1

(63)

18

Φ𝑖𝑛𝑙𝑒𝑡 =

(𝐴0𝑖 𝑟𝑒𝑠𝐴0 𝑟𝑒𝑞

− 1) {𝑀0 − (2

𝛾 + 1 +𝛾 − 1𝛾 + 1𝑀0

2)

12}

𝐹𝑔𝑐 (��0𝑎0)⁄

(64)

4.2.2 Fan & Compressor One of the first steps in designing a gas turbine engine is to design the compressor. The turbine, combustion chamber, and afterburner design are greatly determined by the outputs of the compressor. Using the method describe in “Elements of Propulsion” [1], below is a list of the equations that were used to calculate the initial values of each stage of the compressor. Each calculation had to be repeated for the number of stages that were chosen for the compressor. The desired number of stages for a compressor are determined by the designer preference, output required, and weight desired for the entire turbofan engine. Certain inputs are initially assumed and later altered based on the designer’s preference in stage loading, degree of reaction, stage efficiency, blade radius, blade solidity, and number of blades per stage. These inputs include: M1, α1, α3, u2/u1, φcr, and φcs; to view typical initial guesses, see Table 11.2 located in the Appendix D. The equations can also be used to determine the velocity triangles at each compressor stage. The mass flow parameter can be calculated using the GASTAB program provided with the AEDSYS software. Air flow through an axial-flow compressor is naturally three-dimensional, which makes it extremely hard to comprehend and analyze the flow. To simplify the design process, a two-dimensional flow field is used. The sum of the two flow fields will give the total flow field. The two different coordinate systems are used to describe the flow, Absolute (V = absolute velocity) is fixed to the compressor housing and the relative (VR = relative velocity) is fixed to the rotating blades.

𝑇1 =𝑇𝑡1

1 + (𝛾 − 12 )𝑀1

2

(65)

𝑎1 = √𝛾𝑅𝑔𝑐𝑇1

(66)

𝑉1 = 𝑀1𝑎1

(67)

𝑢1 = 𝑉1 cos 𝛼1

(68)

𝜐1 = 𝑉1 sin 𝛼1

(69)

𝑃1 =𝑃𝑡1

[1 + (𝛾 − 12 )𝑀1

2]𝛾𝛾−1

(70)

MFP(M1)

𝐴1 = ��√𝑇𝑡1

𝑃𝑡1(cos 𝛼1)𝑀𝐹𝑃(𝑀1)

(71)

19

𝜐1𝑅 = 𝜔𝑟 − 𝜐1

(72)

𝛽1 = tan−1𝜐1𝑅𝑢1

(73)

𝑉1𝑅 = √𝑢12 + 𝜐1𝑅

2

(74)

𝑀1𝑅 =𝑉1𝑅𝑎1

(75)

𝑇𝑡1𝑅 = 𝑇1(1 +𝛾 − 1

2𝑀1𝑅2 )

(76)

𝑃𝑡1𝑅 = 𝑃1(𝑇𝑡1𝑅𝑇1

)𝛾

(𝛾−1)

(77)

𝑃𝑡2𝑅 = 𝑃𝑡1𝑅(𝑃𝑡2𝑅𝑃𝑡1𝑅

)

(78)

𝑇𝑡2𝑅 = 𝑇𝑡1𝑅

(79)

𝑇𝑡2 = 𝑇𝑡1 + ∆𝑇𝑡

(80)

tan 𝛽2 =1

1.1[tan𝛽2 −

𝑔𝑐𝑐𝑝

𝜔𝑟𝑢1(𝑇𝑡2 − 𝑇𝑡1)

(81)

𝑢2 =𝑢2𝑢1𝑢1

(82)

𝜐2𝑅 = 𝑢2 tan𝛽2

(83)

𝑉2𝑅 = √𝑢22 + 𝜐2𝑅

2

(84)

𝜐2 = 𝜔𝑟 − 𝜐2𝑅

(85)

𝛼2 = tan−1𝜐2𝑢2

(86)

𝑉2 = √𝑢22 + 𝜐2

2

(87)

𝑇2 = 𝑇𝑡2 −𝑉22

2𝑔𝑐𝑐𝑝

(88)

𝑃2 = 𝑃𝑡2𝑅(𝑇2𝑇𝑡2𝑅

)𝛾𝛾−1

(89)

20


(90)

𝑀2 =𝑉2𝑎2

(91)

𝑀2𝑅 =𝑉2𝑅𝑎2

(92)

𝑃𝑡2 = 𝑃2(𝑇𝑡2𝑇2)𝛾𝛾−1

(93)

MFP(M2)

𝐴2 =��√𝑇𝑡2

𝑃𝑡2(cos𝛼2)𝑀𝐹𝑃(𝑀2)

(94)

𝑇𝑡3 = 𝑇𝑡2 = 𝑇𝑡1 + ∆𝑇𝑡

(95)

𝑇3 =𝑇𝑡3

1 + (𝛾 − 12 )𝑀3

2

(96)

𝑃𝑡3 = 𝑃𝑡2(𝑃𝑡3𝑃3)

(97)

𝑃3 = 𝑃𝑡3(𝑇3𝑇𝑡3)𝛾𝛾−1

(98)


(99)

𝑉3 = 𝑀3𝑎3

(100)

𝑢3 = 𝑉3 cos 𝛼3

(101)

𝜐3 = 𝑉3 sin 𝛼3

(102)

𝐴3 =��√𝑇𝑡3

𝑃𝑡3(cos𝛼3)𝑀𝐹𝑃(𝑀3)

(103)

°𝑅𝑐 =𝑇2 − 𝑇1𝑇3 − 𝑇1

(104)

𝐷𝑟 = 1 −𝑉2𝑅𝑉1𝑅

+|𝜐1𝑅 − 𝜐2𝑅|

2𝜎𝑉2

(105)

𝐷𝑠 = 1 −𝑉3𝑉2+|𝜐2 − 𝜐3|

2𝜎𝑉2

(106)

21

𝜂𝑆 =ln(𝑃𝑡3 𝑃𝑡1)⁄

𝛾−1𝛾 − 1

(𝑇𝑡3 𝑇𝑡1) − 1⁄

(107)

𝑒𝑐 =𝛾 − 1

𝛾

ln(𝑃𝑡3 𝑃𝑡1)⁄

ln (𝑇𝑡3 𝑇𝑡1)⁄

(108)

𝜓 =𝑔𝑐𝑐𝑝∆𝑇𝑡(𝜔𝑟)2

(109)

Φ =𝑢1𝜔𝑟

(110)

After completing these calculations for each desired stage, the values can be placed in program COMPR form the AEDsys. The COMPR program computes a more detailed analysis of each stage in the compressor. All output data from the COMPR can be found in Appendix 13.2. Keep in mind that these inputs will be altered to the designer’s needed specifications and include: (c/h)s, (c/h)r, σs, and σr. It is important to know that the number of blades are typically calculated based on the tip solidity and that a solidity of 1 should be chosen for an optimum stage. COMPR will help determine the number of blades for the stator and rotor in each stage. The output data form COMPR was use to generate a 3 dimensional CAD model with the help of SOLIDWORKS shown if Figure 4.5.

Figure 4.5: CAD of First Stage Low Pressure Fan Blade

4.2.3 Combustion Chamber Once the high pressure compressor and turbine are completed, the combustion chamber (main burner) analysis can begin. The resulting radii for the compressor final stage and turbine first stage will be needed in order to obtain values for the combustion chamber layout. Typically, the outer radius of the turbine first stage will be used as the outer radius of the main burner. The program MAINBRN from the AEDsys software is used to finalize the results for the calculations made from equations (111 - 158) below. Before starting the design method, one must take into considerations the requirements and ranges of a

22

combustion chamber. To view the optimal ranges as well as the requirements, Table 11.4 can be viewed in the Appendix. In the design of the main burner, there are three typical diffusers that can be used in the MAINBRN program. The three types of diffusers are: flat-wall, dump, and combined. For the combined diffuser, typically two to three streams are used in a flat-wall that discharges into a dump. To view the operating regimes of these three diffusers as well as the geometries, see the figures below. The diffuser is used to slow down the air before entering the primary zone, this is to ensure complete combustion as well as reduce the chances of flame-out. For initial design, the equations below will only take into consideration the flat-wall. Although used for initial design, the combined diffuser typically provides better results but the diffuser selection will be based on the designer.

Figure 4.6: Operating regimes

Figure 4.7: Geometry of flat-wall diffuser

Figure 4.8: Geometry of dump diffuser

Figure 4.9: Geometry of combined diffuser

After leaving the diffuser, the air is then mixed with fuel and ignited in the primary zone. Due to the extreme temperatures, liner cooling will be used to maintain stability of the material in the main burner. Upon leaving, the combusted gas will enter the secondary zone and dilution zone where the air will be

23

cooled to a point that will allow the turbine to maintain stability. To begin the initial design, follow the equations listed below.

Diffuser:

𝐴𝑅 =𝐴3.2𝐴3.1

(111)

𝜂𝐷 =𝜂𝐷𝑚𝐴𝑅

2(1 − [𝐴3.1 𝐴𝑚⁄ ]2) + 2(𝐴𝑅[𝐴3.1 𝐴𝑚⁄ ] − 1)

𝐴𝑅2 − 1

(112)

(𝛥𝑃𝑡𝑞1)𝐷

= (1 −1

𝐴𝑅2) (1 − 𝜂𝐷)

(113)

𝜋𝐷 = 1 −(∆𝑃𝑡 𝑞1⁄ )𝐷

1 + 2 𝛾𝑀3.12⁄

(114)

𝐴𝑚 = 𝜂𝐷𝑚(𝐴𝑅)𝐴3.1

(115)

𝐿 = 𝐻3.1 (𝑟𝑚3.1𝑟𝑚3.2

)𝐴𝑅 − 1

2 tan4.5𝑑𝑒𝑔

(116)

∆𝑥 = √𝐿2 − (𝑟3.1 − 𝑟3.2)2

(117)

Air Partitioning:

𝜑4 =��𝑓𝑀𝐵

𝑓𝑠𝑡��3.1

(118)

∆𝑇𝑚𝑎𝑥 =𝑇𝑡4 − 𝑇3.1

𝜑4

(119)

𝜑𝑆𝑍 =𝑇𝑔 − 𝑇3.1

∆𝑇𝑚𝑎𝑥

(120)

𝜑𝑃𝑍 =𝜑𝑆𝑍휀𝑃𝑍

(121)

𝜇𝑃𝑍 =𝜑4𝜑𝑃𝑍

(122)

𝜇𝑆𝑍 =𝜑4𝜑𝑆𝑍

−𝜑4𝜑𝑃𝑍

(123)

𝑇𝑔 = 𝑇𝑡3.1 + 𝜑𝑃𝑍휀𝑃𝑍∆𝑇𝑚𝑎𝑥

(124)

𝛷 =𝑇𝑔 − 𝑇𝑚

𝑇𝑔 − 𝑇3.1

(125)

24

For Film Cooling:

𝜇𝑐 =1

6(𝑇𝑔 − 𝑇𝑚

𝑇𝑚 − 𝑇3.1)

(126)

For Transpiration or Effusion Cooling:

𝜇𝑐 =1

25(𝑇𝑔 − 𝑇𝑚

𝑇𝑚 − 𝑇3.1)

(127)

𝜇𝐷𝑍 = 1 − (𝜇𝑃𝑍 + 𝜇𝑆𝑍 + 𝜇𝑐)

(128)

Dome and Liner:

(∆𝑃𝑡𝑞𝑟)𝑀𝐵

=𝑃𝑡3.2 − 𝑃𝑡4𝑃𝑡3.2 − 𝑃3.2

(129)

��𝐴

��𝑟= 𝜇𝑆𝑍 + 𝜇𝐷𝑍

(130)

𝛼𝑜𝑝𝑡 = 1 − (��𝐴

��𝑟)2 3⁄

(∆𝑃𝑡𝑞𝑟)𝑀𝐵

−1 3⁄

(131)

𝐻𝐿 = 𝛼𝑜𝑝𝑡𝐻𝑟

(132)

Total Pressure Loss:

𝜏𝑃𝑍 =𝑇𝑔

𝑇𝑡3.2

(133)

(∆𝑃𝑡𝑞𝑟)𝑚𝑖𝑛

= (𝜇𝑃𝑍𝛼𝑜𝑝𝑡

)

2

𝜏𝑃𝑍(2𝜏𝑃𝑍 − 1)

(134)

Primary Zone:

𝑉𝑗 = 𝑈𝑟√(∆𝑃𝑡𝑞𝑟)𝑀𝐵

(135)

𝐶𝐷90° = {0.64 𝑓𝑜𝑟 𝑝𝑙𝑎𝑖𝑛 ℎ𝑜𝑙𝑒𝑠

0.81 𝑓𝑜𝑟 𝑝𝑙𝑢𝑛𝑔𝑒𝑑 ℎ𝑜𝑙𝑒𝑠

(136)

𝑟𝑡 = √𝑟ℎ2 +

��𝑃𝑍 − 3��𝑓𝑀𝐵

𝑁𝑛𝑜𝑧𝜋𝐶𝐷90° cos 𝛼𝑠𝑤(𝐴𝑟��𝑟) (∆𝑃𝑡𝑞𝑟)𝑀𝐵

−1 2⁄

(137)

𝑆′ =2

3tan𝛼𝑠𝑤 [

1 − (𝑟ℎ 𝑟𝑡⁄ )3

1 − (𝑟ℎ 𝑟𝑡⁄ )2]

(138)

𝐴𝑆𝑊 = 𝜋(𝑟𝑡2 − 𝑟ℎ

2)

(139)

𝐿𝑃𝑍 = 2𝑆′𝑟𝑡

(140)

25

Secondary Zone: 𝑞𝑗

𝑞𝑟=∆𝑃𝑡𝑞𝑟

(141)

𝑞𝐴𝑞𝑟= (

𝜇𝑆𝑍 + 𝜇𝐷𝑍1 − 𝛼𝑜𝑝𝑡

)

2

(142)

𝑞𝐿𝑞𝑟= 𝜏𝑃𝑍 (

𝜇𝑃𝑍𝛼𝑜𝑝𝑡

)

2

(143)

𝑌𝑚𝑎𝑥𝑑𝑗

= 1.15√𝑞𝑗

𝑞𝑟

𝑞𝑟𝑞𝐿(1 −

𝑞𝐴𝑞𝑟

𝑞𝑟𝑞𝑗)

(144)

𝑑𝑗 =1

4𝐻𝐿 (


)

−1

(145)

𝑁ℎ𝑆𝑍 = 𝜇𝑆𝑍 (4𝐴𝑟

𝜋𝑑𝑗2)𝑈𝑟𝑉𝑗

(146)

sin𝜃 = √1 −𝑞𝐴𝑞𝑟

𝑞𝑟𝑞𝑗

(147)

𝑑ℎ =𝑑𝑗

√𝐶𝐷90° sin𝜃

(148)

𝐿𝑆𝑍 = 2𝐻𝐿

(149)

Dilution Zone: 𝑞𝐴𝑞𝑟= (

𝜇𝐷𝑍1 − 𝛼

)2

(150)

𝑞𝐿𝑞𝑟=𝑞𝑆𝑍𝑞𝑟

= 𝜏𝑃𝑍 (𝜇𝑃𝑍 + 𝜇𝑆𝑍

𝛼)2

(151)


= 1.15√𝑞𝑗

𝑞𝑟

𝑞𝑟𝑞𝐿(1 −

𝑞𝐴𝑞𝑟

𝑞𝑟𝑞𝑗)

(152)

𝑑𝑗 =1

3𝐻𝐿 (


)

−1

(153)

sin𝜃 = √1 −𝑞𝐴𝑞𝑟

𝑞𝑟𝑞𝑗

(154)

26

𝑑ℎ =𝑑𝑗

√𝐶𝐷90° sin𝜃

(155)

𝑁ℎ𝐷𝑍 = 𝜇𝐷𝑍 (4𝐴𝑟

𝜋𝑑𝑗2)𝑈𝑟𝑉𝑗

(156)

𝐿𝐷𝑍 = 1.5𝐻𝐿

(157)

Total Length: 𝐿𝐿 = 𝐿𝑃𝑍 + 𝐿𝑆𝑍 + 𝐿𝐷𝑍

(158)

4.2.4 Turbine Upon completing the initial calculations for the compressor, the turbine calculations can be started. Based on the number of high pressure and low pressure stages of both the fan and compressor will determine the number of stages in the turbine. The high pressure turbine(s) will power the high pressure compressor stages, the low pressure turbine(s) will power both the low pressure compressor and fan stages. The decision on the number of stages for both high and low pressure turbines will be based upon weight, designer preference, stage loading, and power needed to drive the compressor. Once the designer achieves desired results, the turbine calculations will be completed. Below is a list of equations (159 - 192) for calculating the mean-radius stage for stator and rotor flow with losses. The equations can also be used to determine the velocity triangles at each turbine stage. Certain inputs are initially assumed and later altered based on the designer’s preference in stage loading, degree of reaction, stage efficiency, blade radius, blade solidity, and number of blades per stage. These inputs include: M2, α1, α3, u3/u2, φt stator, and φt rotor; to view typical initial guesses, see Table 11.5 located in the Appendix. It is important to keep in mind that M2 must be supersonic at the first turbine stage in order to obtained choked flow but should not cause M3 to be greater than 0.9. It is also important to note that a desirable multistage design would have the total temperature difference distributed evenly among each stage. Within each stage, the total temperature at station two will equal that of station one (i.e. Tt1 = Tt2). It can also be seen that the stage loading should remain between 1.4 and 2 for modern aircraft engines. For simplicity of design, α1 will remain the same throughout each stage of the turbine.

𝑇1 =𝑇𝑡1

1 + [(𝛾 − 1)/2]𝑀12

(159)

𝑉1 = √2𝑔𝑐𝑐𝑝𝑇𝑡1

1 + 2 [(𝛾 − 1)𝑀12]⁄

(160)

𝑢1 = 𝑉1 cos𝛼1

(161)

𝑣1 = 𝑉1 sin𝛼1

(162)

𝑇2 =𝑇𝑡2

1 + [(𝛾 − 1) 2⁄ ]𝑀22

(163)

27

𝑉2 = √2𝑔𝑐𝑐𝑝𝑇𝑡2

1 + 2 [(𝛾 − 1)𝑀22]⁄

(164)

𝜓 =𝑔𝑐𝑐𝑝(𝑇𝑡1 − 𝑇𝑡3)

(𝜔𝑟)2

(165)

𝛼2 = sin−1(𝜓

𝜔𝑟𝑉2) − (

𝑢3𝑢2tan𝛼3)√1 + (

𝑢3𝑢2tan𝛼3)

2− (𝜓

𝜔𝑟𝑉2)2

1 + (𝑢3𝑢2tan𝛼3)

2

(166)


(167)


(168)

𝛷 =𝑢2𝜔𝑟

(169)

𝑉3 =𝑢3𝑢2

cos𝛼2cos𝛼3

(170)


(171)


(172)

°𝑅𝑡 = 1 −1

2𝜓(𝑉2𝜔𝑟)2

[1 − (𝑢3 cos 𝛼2𝑢2 cos 𝛼3

)2

]

(173)

𝑇3 = 𝑇2 − °𝑅𝑡(𝑇𝑡1 − 𝑇𝑡3)

(174)

𝑀3 = 𝑀2

𝑉3𝑉2√𝑇2𝑇3

(175)

𝑀2𝑅 = 𝑀2√cos2 𝛼2 + (sin𝛼2 −

𝜔𝑟

𝑉2)2

(176)

𝑀3𝑅 = 𝑀3√cos2 𝛼3 + (sin𝛼3 −

𝜔𝑟

𝑉3)2

(177)

𝑇𝑡3𝑅 = 𝑇𝑡2𝑅 = 𝑇𝑡3 +𝑉32

2𝑔𝑐𝑐𝑝[cos2 𝛼3 + (sin𝛼3 +

𝜔𝑟

𝑉3)2

− 1]

(178)

28

𝜏𝑠 =𝑇𝑡3𝑇𝑡1

(179)

𝑍𝑠𝑐𝑥𝑠

= (2 cos2 𝛼2) (tan𝛼1 +𝑢2𝑢1tan𝛼2) (

𝑢1𝑢2)2

(180)

𝛽2 = tan−1𝑣2 −𝜔𝑟

𝑢2

(181)

𝛽3 = tan−1𝑣3 +𝜔𝑟

𝑢3

(182)

𝑍𝑟𝑐𝑥𝑠

= (2 cos2 𝛽3) (tan𝛽2 +𝑢3𝑢2tan 𝛽3)(

𝑢2𝑢3)2

(183)

𝑃1 = 𝑃𝑡1 (𝑇1𝑇𝑡1)𝛾 (𝛾−1)⁄

(184)

𝑃𝑡2 =𝑃𝑡1

1 + 𝜑𝑡 𝑠𝑡𝑎𝑡𝑜𝑟[1 − (𝑇2 𝑇𝑡2⁄ )𝛾 (𝛾−1)⁄ ]

(185)

𝑃2 = 𝑃𝑡2 (𝑇2𝑇𝑡2)𝛾 (𝛾−1)⁄

(186)

𝑃𝑡2𝑅 = 𝑃2 (𝑇𝑡2𝑅𝑇2

)𝛾 (𝛾−1)⁄

(187)

𝑃𝑡3𝑅 =𝑃𝑡2𝑅

1 + 𝜑𝑡 𝑟𝑜𝑡𝑜𝑟[1 − (𝑇3 𝑇𝑡3𝑅⁄ )𝛾 (𝛾−1)⁄ ]

d

(188)

𝑃3 = 𝑃𝑡3𝑅 (𝑇3𝑇𝑡3𝑅

)𝛾 (𝛾−1)⁄

(189)

𝑃𝑡3 = 𝑃3 (𝑇𝑡3𝑇3)𝛾 (𝛾−1)⁄

(190)

𝜋𝑠 =𝑃𝑡3𝑃𝑡1

(191)

𝜂𝑠 =1 − 𝜏𝑠

1 − 𝜋𝑠(𝛾−1) 𝛾⁄

(192)

After completing the calculations for each desired stage; the flow annulus area, radii, and number of blades can be calculated for each stator and rotor. Below is a list of equations (193 - 211) that allow for completion of the calculation process. Upon completing the calculations, the values found can be placed

29

in the AEDSYS software using the TURBN program. Before beginning the calculations, it should be known that the Zweifel coefficient shall remain close to 1 for an optimum stage. Along with this, the chord/height ratio shall remain between 0.3 and 1. As stated before, initial inputs will be assumed and typical assumed inputs can be seen in the Appendix. These inputs will be altered to the designer’s needed specifications and include: (c/h)s, (c/h)r, Zs, Zr, σs, and σr. The assumed solidities will be made for the hub, mean, and tip of the blades. It is important to know that the number of blades are typically calculated based on the tip solidity. The mass flow parameter can be calculated using the GASTAB program provided with the AEDSYS software.

Station 1 and 2R:

𝐴1 =��√𝑇𝑡1

𝑃𝑡1𝑀𝐹𝑃(𝑀1)(cos 𝛼1)

(193)

ℎ1 =𝐴12𝜋𝑟𝑚

= 𝑟𝑡1 − 𝑟ℎ1

(194)

𝑣1ℎ = 𝑣1𝑚 = 𝑣1𝑡 = 0

(195)

Station 2 and 3R:

𝐴2 =��√𝑇𝑡2

𝑃𝑡2𝑀𝐹𝑃(𝑀2)(cos 𝛼2)

(196)

ℎ2 =𝐴22𝜋𝑟𝑚

= 𝑟𝑡2 − 𝑟ℎ2

(197)

𝑣2ℎ = 𝑣2𝑚𝑟𝑚𝑟2ℎ

(198)

𝛼2ℎ = tan−1𝑣2ℎ𝑢2

(199)

𝑣2𝑡 = 𝑣2𝑚𝑟𝑚𝑟2𝑡

(200)

𝛼2𝑡 = tan−1𝑣2𝑡𝑢2

(201)

𝑐 =𝑐

ℎ

ℎ1 + ℎ22

(202)

𝑍𝑠,𝑟 (𝑐𝑥𝑠)𝑚,ℎ,𝑡

= (2 cos2 𝛼2𝑚,2ℎ,2𝑡) (tan𝛼2𝑚,2ℎ,2𝑡 +𝑢2𝑢1tan𝛼2𝑚,2ℎ,2𝑡)(

𝑢1𝑢2)2

(203)

(𝑐𝑥𝑠)𝑚,ℎ,𝑡

=𝑍𝑠,𝑟 (

𝑐𝑥𝑠 )𝑚,ℎ,𝑡𝑍𝑠,𝑟

(204)

𝛾1𝑚,1ℎ,1𝑡 = 𝛼1𝑚,1ℎ,1𝑡 = 0 (205)

30

𝛾2𝑚,2ℎ,2𝑡 =𝛾1𝑚,1ℎ,1𝑡 + 8√𝜎𝑚,ℎ,𝑡𝛼2𝑚,2ℎ,2𝑡

8√𝜎𝑚,ℎ,𝑡 − 1

(206)

𝜃2𝑚,2ℎ,2𝑡 =𝛾2𝑚,2ℎ,2𝑡 − 𝛾1𝑚,1ℎ,1𝑡

2

(207)

𝜎𝑚,ℎ,𝑡 =(𝑐𝑥 𝑠⁄ )𝑚,ℎ,𝑡cos 𝜃𝑚,ℎ,𝑡

(208)

𝑠𝑚,ℎ,𝑡 =𝜎𝑚,ℎ,𝑡𝑐

(209)

𝑐𝑥 = 𝑠𝑚,ℎ,𝑡𝜎𝑚,ℎ,𝑡 cos𝜃2𝑚,2ℎ,2𝑡

(210)

𝑁𝑏 = 2(𝜋𝑟2𝑚,2ℎ,2𝑡𝜎𝑚,ℎ,𝑡

𝑐)

(211)

As seen above, equations (193 - 211) can be used to find the number of blades for the mean, hub, and tip of each station in the turbine. Typically, if the number of blades is any decimal then it will be rounded up to the nearest whole number. This will be the total number of blades for each station of each turbine stage. The values obtained can now be placed in the TURBN program. Once the values were found for the turbine section, a computer aided drawing was made to represent the first stage rotor blade. The model, using SOLIDWORKS, can be viewed below in Figure 4.10 to obtain an idea of what will be expected in the final design process. It can be seen that the turbine blade is much smaller than the compressor blades. The reason for this is that the turbine blades are more numerous for both stator and rotor to obtain the needed power. Due to the relatively weaker programming power of the student edition of SOLIDWORKS and insufficient time, the cooling qualities of the CAD model were not added. Figure 4.11 can be seen below the CAD model to obtain an understanding of the cooling used in the turbine.

Figure 4.10: CAD of the High Pressure Turbine Blade

31

Figure 4.11: Turbine Transpiration and Full-Coverage Film Cooling

4.2.5 Afterburner After the main turbofan engine components have been completed, the design of the afterburner can begin. The output data of the TURBN and the ONX programs can be used for the input data to the AFTRBRN program. The design of an afterburner generally follows the design of the combustion chamber. The following inputs are need for the AFTRBRN program: total pressure, total temperature, Mach number, gas flow, and outer radius. It is important to note, that the outer radius of the afterburner typical does not exceed the maximum outer radius of the engine. The geometry of the afterburner can be seen in Figure 4.12. The afterburner fuel flow at station 6.1 can be found with the ONX program, as well as the total pressure and temperature a station 7. A crucial design aspect of the afterburner is the time at blowout (tBO). The tBO must be obtained from the AEDsys software program KINTEX. The follow requirements for KINTEX are the pressure, temperature, composition of the approach gas stream, and afterburner fuel flow rate. Once all of the pervious information is enter into TURBN, the number of spray / vee-gutter rings can be determined. The position of the spray / vee-gutter rings can be seen in Figure 4.13 and Figure 4.14. To make sure that the afterburner functions properly, the number of spray / vee-gutter rings should be less than 15. To meet the desired performance, 10 spray / vee-gutter rings were chosen. Figure 13.46 shows the layout of the completed afterburner.

32

Figure 4.12: Geometry of Afterburner

Figure 4.13: Flow Patterns in the Afterburner

Figure 4.14: Principal Features

4.2.6 Nozzle The NOZZLE program from the AEDsys software is used for designing a One-Dimension/Two-Dimensional Circular Convergent-Divergent Nozzle. Due to customer requirements and a more accurate representation of a real nozzle, only a two-dimensional convergent-divergent nozzle was designed for the project. Initially the inputs required by the program are as follows: mass flow rate, total pressure at station 8, total temperature at station 8, ration of specific heats, gas constant, static pressure at station 0 or freestream, the area ratio of area at 9 divided by the area at 8 (A9/A8), the convergent angle (degrees), the divergent angle (degrees), and the diameter at station 7 (inches). The values can be found from the results via ONX and AED Engine Cycle Deck Component Interfaces at each flight condition. The only disclaimer is when using the results from the component interfaces; stages 7, 8, and 9 are considered wet. In order to compensate for the entrance of the nozzle, conditional values are assumed when the engine is dry. Additionally, nozzle’s convergent-divergent angles are optimized for maximum amount gross thrust actual with the diameter at 7 being constant. Once the inputs are entered, the design results can be calculated. A color contour plot of Divergent Angle vs A9/A8, a sketch of the nozzle’s dimensions, and performance values are returned. The contour plot shows the optimal divergent angle relative to gross thrust constant, Cfg. Below in Figure (4.15) and Equations (212 - 224) are used by the NOZZLE program for the output calculations. For examples of the inputs into the program and the results produced, refer to Appendix E: Test Data. A general guide to the values for which the CD Max, the CV, and the CA of the nozzle configurations can be seen in Figures 11.2, 11.3, and 11.4 of Appendix D.

33

Figure 4.15: Nozzle geometric parameters

𝐶𝑓𝑔 = 𝐹𝑔 𝑎𝑐𝑡𝑢𝑎𝑙 𝐹𝑔 𝑖𝑑𝑒𝑎𝑙⁄

(212)

𝐶𝐷 = ��8 ��8𝑖⁄

(213)

𝐶𝐷 =��8

��8𝑖=𝜌8𝑉8𝐴8𝜌8𝑉8𝐴8𝑒

=𝐴8𝐴8𝑒

=𝑃𝑡8𝑃𝑡7

(214)

𝐶𝑉 = 𝑉9 𝑉9𝑖⁄

(215)

𝐶𝐴 =1

��∫ cos𝛼𝑗 𝑑��

(216)

𝐶𝑓𝑔 𝑝𝑒𝑎𝑘 = 𝐶𝑉𝐶𝐴

(217)

𝐴

𝐴∗|9𝑖=

𝐴9𝐶𝐷𝐴8

(218)

𝑉9𝑖 = √𝑅𝑔𝑐𝑇𝑡8√2𝛾

𝛾 − 1{1 − (

𝑃9𝑖𝑃𝑡9𝑖

)(𝛾−1) 𝛾⁄

}

(219)

34

𝐶𝑓𝑔 =𝐶𝑓𝑔 𝑝𝑒𝑎𝑘��7 𝑉9𝑖 𝑔𝑐⁄ + (𝑃9𝑖 − 𝑃0)𝐴9

��7𝑉𝑠 𝑔𝑐⁄

(220)

𝐹𝑔 = 𝐶𝑓𝑔 𝑝𝑒𝑎𝑘��7 𝑉9𝑖 𝑔𝑐⁄ + (𝑃9𝑖 − 𝑃0)𝐴9

(221)

𝐶𝑉 =𝑉9𝑉9𝑖

= √1 − (𝑃9 𝑃𝑡9⁄ )(𝛾−1) 𝛾⁄

1 − (𝑃9𝑖 𝑃𝑡8⁄ )(𝛾−1) 𝛾⁄

(222)

𝑃9𝑃𝑡9

= {1 − 𝐶𝑉2 [1 − (

𝑃9𝑖𝑃𝑡8

)(𝛾−1) 𝛾⁄

]}

𝛾 (𝛾−1)⁄

(223)

𝜋𝑛 =𝑃𝑡9𝑃𝑡8

= 𝐶𝐷𝐴 𝐴∗⁄ |9𝐴9 𝐴8⁄

(224)

4.3 Weight Calculation Method

Due to the fact that the DKA-867 is in the preliminary stage of design, a preliminary weight estimation was made for both the engine with and without a tailpipe. For a more in depth look as to what the exact weight of the engine will be based on dimensioning and material choice, a CAD model will need to be made. The CAD model will allow for a material selection for each individualized component of the engine. Once labeled and completed, the weight of each component may be found. Although, a CAD model will only give a valid comparison to an actual low-bypass turbofan engine. The only way to truly know the actual weight of the engine is to create a prototype model that uses equivalent density materials or the same materials stated below in the materials section of this report. For the case of the DKA-867, the preliminary weight calculation can be made via equation (225) found below. This will be used to find the weight of the engine with the afterburning section. To find the weight without afterburner, comparisons of afterburners with similar dimensions of the one used in the DKA-867 low-bypass turbofan with afterburner were used. Using an average of the afterburner weights found, the weight was then subtracted from the weight found using the equation below. It can be seen that both the thrust and Mach number used in the equation are the maximum allotted by the engine.

𝑊 = 0.063𝑇1.1𝑀0.25𝑒(−0.81 𝐵𝑃𝑅) (225)

4.4 Mission Analysis

The analysis of each mission needed for the Northrop Grumman T-38 Talon was determined using the AEDsys software provided by “Aircraft Engine Design Second Edition” [2]. Upon completing the ONX parametric analysis provided, a document will be saved with the results. Using these results, a mission analysis can be done. To begin the analysis, the completed parametric analysis must be uploaded to the AEDsys main program software. Once uploaded, the aircraft and engine type must be chosen based on the needs of the designer. This will allow for a more realistic output when selecting the needed mission. These can be selected by going to the ‘Aircraft Drag’ and ‘Engine’ tabs found on the task bar. To state how many engines will be used in flight, the ‘Cycle Deck’ button can be opened under the ‘Engine’ tab. Next, the ‘Mission’ button should be clicked, which will open a second screen that is used to determine a given operation.

35

Initially, the box displaying the aircraft performance and sizing can be filled out. This will allow for the engine test to be run with the aircraft for which it is designed for. The thrust found from the NOZZLE program output, wing area, and design takeoff weight will be filled in to update the aircraft model. Once filled in, the ‘Empty Weight Model’ button can be pressed to estimate the empty weight of the aircraft. Along with the atmospheric conditions updated, the mission choice can now be created. The ‘Number of Mission Legs’ box will now be filled in to complete the inputs before the program can be ran. Certain legs can either be added or subtracted from the box in order to determine the overall mission required. For each leg created, an altered name can be used to display a more in depth understanding. Within each leg of the mission, certain aspects can be altered. A few examples of these are: Mach number, altitude, temperature, time, and distance. It is important to keep in mind exactly what the purpose of the aircraft is used for when determining the mission legs needed. For the case of the T-38 Talon; a subsonic cruise, supersonic burst, and loiter are a few of the key components used in the analysis. To view the mission legs and results found for the T-38 using the DKA-867 low-bypass turbofan engine with afterburner at each leg, Appendix 13 can be viewed. Once the input data is filled in, the ‘Calculate’ button can be clicked to view the results. Each leg will then provide a list of results ranging from thrust output to TSFC. These results can also be viewed by clicking ‘Summary’ upon the completion of the calculations. The summary data provided gives a brief overview of each segment previously mentioned. Although not entirely accurate, the mission analysis of the AEDsys main program will provide for an acceptable preliminary design. It can be seen that the landing weight of the aircraft must be slightly larger than the empty weight calculated previously in order to prove the validity of the results.

4.5 Results

Once the calculations were completed for each station and the mission requirements, the results had to be studied. It can be seen in the tables below that each individual requirement set forth by AIAA was met. By obtaining these results, it can be seen that the DKA-867 will be an excellent replacement for the J85-GE-5A engine in current use.

36

4.5.1 Compliance Matrix

Table 4.1: Compliance Matrix

General characteristics

Wing area (ft2) 170

Max. take-off weight (lbm) 12000

Takeoff-Thrust (lbf) 8014

Design Afterburning Thrust (lbf) 3446

Performance

Maximum speed Mach 1.3

Cruise speed Mach 0.85

Mission Fuel Burn (lbs) 3488

Cruise TSFC (lbm/h/lbf) 1.002

Takeoff TSFC (lbm/hr/lbf) 1.673

Engine Weight w/o tailpipe (lbs) 407.07

Engine Weight w/ tailpipe (lbs) 517.07

Engine Length w/o tailpipe (in.) 49.12

Engine Length w/ tailpipe (in.) 102.02

Fan Diameter (in.) 20

37

4.5.2 Engine Summary Data Table 4.2: Engine Summary Data

Summary Data

Design MN 0.85

Design Altitude (ft) 35000

Design Fan Mass Flow (lbm/s) 51

Design Gross Thrust (lbf) 2050

Design Bypass Ratio 0.22

Design Net Thrust (lbf) 1597

Design Afterburning Net Thrust (lbf) 3446

Design TSFC (lbm/h/lbf) 1.002

Design Overall Pressure Ratio 6.947

Design T4.1 (R) 2000

Design Engine Pressure Ratio 2.232

Design Fan / LPC Pressure Ratio 1.850

Design Chargeable Cooling Flow #1 5%

Design Chargeable Cooling Flow #2 5%

Design Adiabatic Efficiency for HP Turbine 0.9058

Design Adiabatic Efficiency for LP Turbine 0.9123

Design Polytropic Efficiency for Fan/LP Compressor 0.89

Design Polytropic Efficiency for HP Compressor 0.90

Design HP Shaft RPM 18,812

Design LP Shaft RPM 11,077

Table 4.3: Fan / LP Compressor Flow Station Data

Flow Station Data

IGV

Fan / LP Compressor Bypass

Stage 1 Stage 2 Stage 3

Inflow (lbm/s) 51 51 51 51 9.20

Corrected Inflow (lbm/s)

49.40 49.40 49.40 49.40 5.31

Inflow Total Pressure (psi)

14.70 14.70 18.33 22.49 27.22

Inflow Total Temperature (R)

486.70 486.70 522.00 542.20 592.60

Inflow Fuel-air-Ratio N/A N/A N/A N/A N/A

Inflow Mach # 0.5 0.4 0.386 0.373 0.343

Inflow Area (in^2) 314.16 269.93 230.90 199.96 58.89

Pressure Loss/Rise Across Component

1 1.247 1.227 1.210 1

38

Table 4.4: HP Compressor Flow Station Data

IGV

HP Compressor Combustion Chamber Stage 1 Stage 2 Stage 3 Stage 4 Stage 5

Inflow (lbm/s) 41.80 41.80 41.80 41.80 41.80 41.80 36.48

Corrected Inflow (lbm/s)

24.12 24.12 24.12 24.12 24.12 24.12 28.28

Inflow Total Pressure (psi)

27.22 27.22 37.32 49.62 64.44 82 102.5

Inflow Total Temperature (R)

592.60 592.6 654.2 715.9 777.5 839.1 900.8

Inflow Fuel-air-Ratio N/A N/A N/A N/A N/A N/A 0.0355

Inflow Mach # 0.35 0.5 0.475 0.453 0.434 0.417 0.386

Inflow Area (in^2) 130.07 133.66 106.38 86.69 71.92 60.58 25.595


1 1.371 1.330 1.299 1.272 1.250 0.930

Table 4.5: Turbine & Nozzle Flow Data

HP Turbine LP Turbine EGV Afterburner Nozzle

Inflow (lbm/s) 40.62 42.71 42.71 50.89 53.13

Corrected Inflow (lbm/s) 12.11 26.62 36.58 34.409 49.040

Inflow Total Pressure (psi) 94.97 42.83 30.37 32.8 31.522

Inflow Total Temperature (R) 1924 1711 1625.5 1492 2500

Inflow Fuel-air-Ratio N/A N/A N/A 0.0236 N/A

Inflow Mach # 0.4 0.474 0.4546 0.416 0.324

Inflow Area (in^2) 60.28 115.81 165.39 177.12 307.872


0.451 0.709 0.998 0.998 0.999

Table 4.6: Additional Information

Additional Information

Design HP Shaft Off-take Power (hp) 5016.859

Design LP Shaft Off-take Power (hp) 2105.101

Design Customer Bleed Flow 1%

39

4.5.3 Required Detailed Stage and Component Information Table 4.7: Fan / Low Pressure Compressor Detailed Data

Compressor

Fan / Low Pressure

Stage 1 Stage 2 Stage 3

Rotor Stator Rotor Stator Rotor Stator

Lieblein Diffusion Factor 0.3865 0.4851 0.3892 0.4819 0.4103 0.4900

De Haller Number 0.669 0.652 0.674 0.672 0.6632 0.6825

Stage Loading 0.4799 0.4115 0.3782

Flow Coefficient 0.5432 0.503 0.4822

Hub-to-Tip Ratio 0.375 0.4329 0.5000 0.5385 0.5806 0.6012

Number of Blades 19 22 25 28 31 33

Solidity 1.1 1.1 1.1

Pitch (in.) 2.436 2.125 1.9427 1.7709 1.6300 1.5245

Chord (in.) 2.680 2.388 2.137 1.948 1.793 1.677

Aspect Ratio 3.571 N/A 2.538 N/A 2.4320 N/A

Taper Ratio 0.9999 0.9999 0.9999

Tip Speed (rad/s) 1160

Stagger Angle (deg) N/A 34.485 N/A 41.160 N/A 44.495

Blade metal angles (deg) 50.57 18.40 53.73 28.59 55.38 33.61

Degree of Reaction 0.7328 0.7098 0.6866

Mach Numbers 0.4 0.604 0.386 0.565 0.373 0.538

40

Table 4.8: High Pressure Compressor Detailed Data

Compressor

High Pressure

Stage 1 Stage 2 Stage 3 Stage 4 Stage 5

Rotor Stator Rotor Stator Rotor Stator Rotor Stator Rotor Stator

Lieblein Diffusion Factor

0.3982 0.4818 0.4311 0.4954 0.4335 4936 0.4345 0.4914 0.4483 0.4947

De Haller Number 0.6554 0.6671 0.6768 0.6828 0.6789 0.6841 0.6837 0.6870 0.6891 0.6899

Stage Loading 0.3444 0.3019 0.2986 0.2914 0.2838

Flow Coefficient 0.3957 0.3705 0.3684 0.3640 0.3592

Hub-to-Tip Ratio 0.5788 0.6284 0.6863 0.7105 0.7397 0.7613 0.7831 0.8008 0.8280 0.8303

Number of Blades 26 31 36 40 45 50 55 61 66 72

Solidity 1.000 1.000 1.000 1.000 1.000

Pitch (in.) 1.585 1.371 1.199 1.080 0.973 0.881 0.800 0.729 0.688 0.618

Chord (in.) 1.585 1.371 1.199 1.080 0.973 0.881 0.800 0.729 0.688 0.618

Aspect Ratio 2.9823 N/A 2.5353 N/A 2.3333 N/A 2.0120 N/A 1.8289 N/A

Taper Ratio 1.000 1.000 1.000 1.000 1.000

Tip Speed (rad/s) 1970

Stagger Angle (deg) N/A 44.84 N/A 50.335 N/A 50.765 N/A 51.675 N/A 52.625

Blade metal angles (deg)

56.66 33.02 59.42 41.25 59.64 41.89 60.12 43.23 60.63 44.62

Degree of Reaction 0.6597 0.6211 0.6052 0.5936 0.5785

Mach Numbers 0.500 0.732 0.475 0.680 0.453 0.648 0.434 0.619 0.417 0.593

Table 4.9: Turbine Detailed Data

Turbine High Pressure Low Pressure

Stator Rotor Stator Rotor

Zweifel Coefficient 1.00 1.00 0.65 1.50

Taper Ratio 0.999 0.999

Stage Work 1.993 2.304

Stage Pressure Ratio 0.451 0.709

Degree of Reaction 0.383 0.305

Aspect Ratio N/A 2.495 N/A 3.333

AN^2 (in2-rpm2) 4.124 x 1010 1.844 x 1010

Number of Blades 42 93 86 53

Chord (in) 1.091 0.979 0.985 1.363 Blade Metal Angles (deg) 53.69 50.63 38.52 41.15

Mach numbers 1.2 0.747 0.9 0.643

Tip speed 1970 rad/s 1160 rad/s

Flow Coefficient 0.721 1.456

Stage Work Split 71.78% 28.22%

Pitch (in) 1.130 2.247 2.090 1.783

Cooling Flow Details Transpiration and Full-Coverage Film Cooling

Film Cooling

mailto:AN%5E@

41

4.5.4 Velocity Triangles To help understand the flow through the compressor and the turbine, velocity triangles are used to describe the flow. Tangential velocity, absolute velocity, and relative velocity are what make up the three sides of the velocity triangle. The diagram shows the absolute velocities entering and leaving the guide vanes, stator, and rotor. In additions, the entering and leaving of the relative velocity (subscript R) and the tangential velocity in association to the rotor. This can be seen in Figure 4.16 & 4.17. The axial velocity component is assumed to be constant in the velocity triangle diagram. The following sections show the results of the velocity triangle for each stage in the compressor and in the turbine.

4.5.4.1 Fan/Compressor

Figure 4.16: Compressor Velocity Triangles

42

Table 4.10: Fan/Low Pressure Compressor

Station 1 1R 2R 2 3

Hub Mean Tip Mean Mean Hub Mean Tip Hub Mean Tip

α (deg)

48.87 32.00 23.25 - - 67.39 56.45 46.09 43.14 32.00 25.11

43.14 32.00 25.11 - - 63.63 55.28 47.28 40.38 32.00 26.28

40.38 32.00 26.28 - - 61.95 54.64 48.44 39.13 32.00 26.89

β (deg)

- 50.57 18.40 - -

- 53.73 28.59 - -

- 55.38 33.61 - -

u (ft/s)

361.1 361.1 361.1 361.1 361.1

361.1 361.1 361.1 361.1 361.1

361.1 361.1 361.1 361.1 361.1

v (ft/s)

413.5 225.6 155.1 439.1 120.1 866.9 544.6 375.1 338.4 225.6 169.2

338.4 225.6 169.2 492.2 196.8 728.3 521.0 392.4 307.1 225.6 178.3

307.1 225.6 178.3 523.1 240.0 677.6 508.8 407.3 293.8 225.6 183.1

V (ft/s)

549.0 425.8 393.0 568.5 380.5 939.1 653.4 520.7 494.9 425.8 398.8

494.9 425.8 398.8 610.4 411.2 812.9 633.9 533.2 474.0 425.8 402.7

474.0 425.8 402.7 635.6 433.5 767.8 623.9 544.3 465.5 425.8 404.9

43

Table 4.11: High Pressure Compressor

Station 1 1R 2R 2 3

Hub Mean Tip Mean Mean Hub Mean Tip Hub Mean Tip

α (deg)

53.94 45.20 38.49 - - 66.95 61.96 55.94 51.05 45.20 40.33

51.05 45.20 40.33 - - 65.42 61.24 57.25 49.83 45.20 41.21

49.83 45.20 41.21 - - 64.44 61.18 57.83 48.90 45.20 41.92

48.90 45.20 41.92 - - 63.66 61.05 58.26 48.20 45.20 42.48

48.20 45.20 42.48 - - 63.21 60.91 58.70 47.74 45.20 42.86

β (deg)

- 56.66 33.02 - -

- 59.42 41.25 - -

- 59.64 41.89 - -

- 60.12 43.23 - -

- 60.63 44.62 - -

u (ft/s)

410.3 410.3 410.3 410.3 410.3

410.3 410.3 410.3 410.3 410.3

410.3 410.3 410.3 410.3 410.3

410.3 410.3 410.3 410.3 410.3

410.3 410.3 410.3 410.3 410.3

v (ft/s)

563.4 413.1 326.2 623.7 266.7 964.3 770.2 606.8 507.6 413.1 348.3

507.6 413.1 348.3 694.2 359.8 896.8 747.5 637.7 486.0 413.1 359.3

486.0 413.1 359.3 700.4 367.9 857.9 745.6 652.2 470.2 413.1 368.4

470.2 413.1 368.4 714.1 385.7 828.5 741.6 663.2 458.8 413.1 375.7

458.8 413.1 375.7 729.0 404.8 812.5 737.3 674.9 451.5 413.1 380.8

V (ft/s)

696.9 582.2 524.1 746.6 489.3 1048.0 872.7 732.5 652.7 582.2 538.2

652.7 582.2 538.2 806.3 545.7 986.2 852.7 758.3 636.0 582.2 545.3

636.0 582.2 545.3 811.7 551.1 950.9 851.0 770.5 624.0 582.2 551.4

624.0 582.2 551.4 823.6 563.1 924.5 847.5 779.9 615.5 582.2 556.3

615.5 582.2 556.3 836.5 576.4 910.2 843.8 789.8 610.1 582.2 559.7

44

4.5.4.2 Turbine

Figure 4.17: Turbine Velocity Triangle

Table 4.12: High Pressure Turbine

Station 1 2 2R 3R 3

Hub Mean Tip Hub Mean Tip Mean Mean Hub Mean Tip

α (deg) 0.00 0.00 0.00 74.21 70.00 66.01 - - 0.96 0.76 0.63

β (deg) - - 53.69 50.63 -

u (ft/s) 789 789 789 764 764 764 764 878 878 878 878

v (ft/s) 0 0 0 2700 2098 1716 1039 1071 15 12 10

V (ft/s) 789 789 789 2806 2233 1878 1290 1385 878 878 878

Table 4.13: Low Pressure Turbine

Station 1 2 2R 3R 3

Hub Mean Tip Hub Mean Tip Mean Mean Hub Mean Tip

α (deg) 0.00 0.00 0.00 64.33 56.00 49.03 - - 9.21 6.33 4.82

β (deg) - - 38.52 41.15 -

u (ft/s) 879 879 879 908 908 908 908 817 817 817 817

v (ft/s) 0 0 0 1889 1346 1046 723 714 133 91 69

V (ft/s) 879 879 879 2096 1624 1385 1160 1085 828 822 820

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5 Material Selections Below is a list of materials that will be used in the design of the DKA-867 engine. The materials have been found via the “Aircraft Engine Design Second Edition” [2] in the Reference section. Each has a brief description of the capabilities along with the properties and components associated as they relate to aircraft engines. Most of the materials have been recently developed and have proved to excel in the components listed within the sections. It is highly advised for the engine developer to use these materials when finalizing the design of the DKA-867.

5.1 Aluminum 2124 Alloy (ρ = 5.29 slug/ft3)

This is one of a series of premium aluminum alloys that were developed as a result of studies into the micro mechanisms of fracture in high-strength aluminum compositions. Normally, the alloy is produced in a plate with a thickness ranging up to six inches. It can be seen in Figure 5.1 below the traditional yield and ultimate tensile strength data for Aluminum 2124. The figure will allow for a non-conservative design to be considered because of the fact that the part could undergo permanent deformation during the exposure time.

Figure 5.1: Effect of Temperature and Exposure Time on Tensile Properties

It is actually preferable to base designs on creep and creep-rupture data. The values for these can be determined by using Figure 5.2. For common practice, an allowance of less than 1% creep during the life of the part. As seen in the figure, Al 2124 is seldom used above 400˚F. From the figure, it should be noted that reductions will be made to results because of the cyclic stress, uncertainties in load calculations, property variations, and safety margins. Based on the properties seen in the figures and recently stated, the inlet and nacelle will be using Al 2124.

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Figure 5.2: Creep and Creep-rupture curves at temperatures from 75 to 600˚F for 2124-T851 plate

5.2 Titanium 6246 Alloy (ρ = 9.08 slug/ft3)

This alloy was designed to combine long-time, elevated-temperature strength characteristics with markedly improved short-time strength properties at both room and elevated temperatures. It is intended for use in forging for intermediate-temperature-range sections of gas turbine engines, particularly in stator and rotor airfoil components of the fan and compressor. Ti-6246 is recommended for gas turbine applications up to 750˚F. Figure 5.3 below can be seen to compare the allowable stress based on the needed temperature applications based on 1% creep for 1000 hours. It can also be seen that Ti-6246 allows for regulated cyclic stress. It also has a poor fracture toughness and is very susceptible to minor damage. Therefore, it is recommended to use a damage-tolerant processed version of Ti-6246.

Figure 5.3: Axial Fatigue Properties of α-β forged materials in two heat-treated conditions

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5.3 Inconel 601 (ρ = 15.6 slug/ft3)

This is a general-purpose alloy for applications requiring resistance to both heat and corrosion at temperatures up to about 2100˚F. It has been used in burner liners, diffuser assemblies, containment rings, exhaust liners, and burner igniters. The data shown in Figure 5.4 below can be used to compare the stresses based on a 1% creep rate. In contrast to the titanium alloy listed above, Inconel 601 retains much of its room temperature strength well beyond 1000˚F. Figure 5.5, seen below, also displays that it has more than adequate fatigue strength when considering vibrations. Due to these properties, it is suggested that most components of the combustion chamber and afterburner use Inconel 601.

Figure 5.4: Minimum creep rate at various temperatures and stresses

Figure 5.5: Fatigue properties of annealed sheet

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5.4 Hastelloy X (ρ = 16.0 slug/ft3)

This is a nickel-base superalloy with good oxidation resistance at temperatures up to 2200˚F. It has been used in jet engine exhaust nozzles, afterburner components, and structural parts in the burner and turbine components. By referring to Figure 5.6 below, the stresses can be found at certain temperatures based on the amount of creep allowable for the component.

Figure 5.6: Creep-deformation curves for plate and bar at temperatures of 1200-1800˚F

Because Hastelloy X is generally used in situations where only low-cycle fatigue caused by pressure or thermal cycles matters, its fatigue characteristics are presented in terms of strain range rather than stress range. It can be seen in Figure 5.7 below how the material will react in cycles of use.

Figure 5.7: Fatigue life of plate at various temperatures in air and impure helium at atmospheric pressure

The modulus of elasticity given in Figure 5.8 below can also be used to obtain the thermal stress calculation involved. Note that in the 1200-1600˚F range, the modulus of elasticity is approximately 20

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million psi. Consequently, the stress corresponding to a 1% strain range equates approximately to 200,000 psi. This makes it evident that such materials can tolerate only a small fraction of a percent strain.

Figure 5.8: Effect of elevated temperature on modulus of elasticity

5.5 Rene’ 80 (ρ = 15.9 slug/ft3)

This is a cast, precipitation-hardenable, nickel-base superalloy. It has excellent creep-rupture strength up to 1900˚F, combined with good elevated temperature ductility and superior hot corrosion resistance. The main use of Rene’ 80 is in investment-vacuum-cast turbine stator and rotor airfoils, which are coated for any jet engine application. Using the 1% creep deformation at the 1000-hour criterion, Figure 5.9 below reveals that Rene 80’ has a remarkably high tensile stress capability.

Figure 5.9: Creep Strain and creep-rupture at 1400, 1600, and 1800˚F for fully treated cast alloy

Alternating stress conditions are often important in cooled turbine rotor airfoils, which are usually cantilevered and subject to the aerodynamic buffeting that produces vibratory loads. It is especially

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important to avoid resonance between a regular upstream disturbance and a natural frequency of the rotor airfoils. Thermal stresses can cause low-cycle fatigue failure if the limits given in Figure 5.10 are reached. This means that cooled airfoils must be designed with the greatest care so that no local areas of large thermal stress are created at any time during the normal engine operation. In particular, it can be readily seen that a thin airfoil “skin” with a large temperature difference between coolant and mainstream will not last long.

Figure 5.10: Axial Low Cycle Fatigue behavior at 1200-1800˚F

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6 Conclusion Upon completion of the DKA-867 components, it was found that the engine had achieved each objective set out by AIAA. To begin, the thrust of the newly designed low-bypass turbofan is able to achieve the needed thrusts for takeoff, loiter, cruise, and supersonic burst at each given flight condition. The thrusts acquired is also higher than that defined by the baseline turbojet engine. Fuel consumption was also lowered for each individual flight condition. The maximum defined fuel consumption was lowered well beyond the point needed for both wet and dry conditions. This allows for a highly efficient engine to be used on the T-38 Talon. With this comes a lowered cost of flight. The next two requirements set out by AIAA was to stay within certain dimensions and weight for the engine without the afterburning section. The dimensions for both the length of engine less afterburner and fan diameter were kept within the specifications. In fact, the length of the engine is smaller than that of the baseline turbojet engine. Due to the smaller length, the engine weight has also been lowered compared to the baseline turbojet engine. It can be seen that the DKA-867 afterburning low-bypass turbofan engine will be more efficient for any flight condition of the T-38. Therefore, the DKA-867 will offer an excellent substitute for the already in use J85-GE-5A afterburning turbojet engine. Since the low-bypass turbofan engine is shorter than the turbojet, an easy swap can be made. An inlet for the DKA-867 has been made based on the specifications required by AIAA. Although the engine can be easily added to the T-38, the alternate design of the inlet will cause for a new nacelle design which will need to be replaced on the T-38 as well. Upgrades have also been made to the material choice in each component of the DKA-867. The new material choice will also cause an increase in engine cost. The engine will be able to have less maintenance hours due to the increased stress and creep tolerances. Along with cooling to be used in the turbine blades, combustion chamber, and afterburner, the engine will be able to last many more hours than the baseline turbojet engine. To finalize the design of the DKA-867 afterburning low-bypass turbofan engine results, a complete computational fluid dynamic, finite element analysis, and physical testing of a prototype engine must be made. Due to time restraints and being outside the scope of this project, such results were not found. By using each individual test, the validity of the results using the AEDsys software can be found. Upon completion of the tests previously mentioned, FAA regulations must be taken into consideration. When calculating the design of each component of the DKA-867, the regulations have been taken into consideration. The design calculations may not always prove to be as precise as actual testing. Therefore, a list of the regulations for FAA can be found by following the websites listed in the References section of this report. After completion of each test and obtaining authorization from FAA, the engine will then be ready for flight.

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7 References

[1] J. D. Mattingly, Elements of Propulsion: Gas Turbines and Rockets, 1st Edition ed., J. A. Schetz, Ed., Reston, Virginia: AmericanInstituteof Aeronauticsand Astronautics,Inc., 2006.

[2] J. D. Mattingly, Aircraft Engine Design, 2nd Edition ed., J. S. Przemieniecki, Ed., Reston , VA: American Institute of Aeronautics and Astronautics , 2002.

[3] H. R. &. D. Mavris, "Preliminary Design of a 2D SUpersonic Inlet to Maximize Total Pressure Recovery".

[4] J. L. Kerrebrock, Aircraft Engines and Gas Turbines, Massachusetts: The Alpine Press Inc. , 1977.

[5] C. W. Smith, Aircraft Gas Turbines, New York : John Wiley & Sons , 1956.

[6] FAA, "14 CFR Parts Applicable to Engines & Propellers," 22 March 2016. [Online]. Available: https://www.faa.gov/aircraft/air_cert/design_approvals/engine_prop/engine_prop_regs/regs/ . [Accessed 10 April 2016].

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8 Appendix A: Acknowledgements We would like to thank multiple people in aiding us complete this project in an orderly and timely manner. To begin, our advisor and mentor Dr. Adeel Khalid has been with us every step of the way. We would like to thank him for taking time out of his schedule in order to help us succeed. He has spent time reviewing the calculations and pointing us in the correct direction when it seemed there was none. His expertise in engine design has been of great use when questions were posed. Along with Dr. Khalid, a series of videos posted by Agent Jay-Z have been of great help in understanding the component design. With his videos, many of the unknowns were able to be known. He currently works in a turbine engine repair shop and develops movies of the incoming engines. By dissecting each component, we have been able to visually understand the geometry. Finally, the staff at Starbucks off of highway 120 has been of great courtesy. They have consistently allowed us to use their space in aid of completing our project. Along with this, they have offered free coffee and questioning of our project. Without them being open, we would not have been able to meet at sometimes in-opportune hours of the morning and night.

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9 Appendix B: Contact Information

David Byrd Email: [email protected] Phone: (678) 447-4729

Kristian Lien Email: [email protected] Phone: (678) 777-3761

Austin Sims Email: [email protected] Phone: (678) 296-5514

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10 Appendix C: Reflections

David Byrd: This project has been the most challenging yet interesting task of my college career. I have always had a love for engines and trying to make them more powerful. When AIAA posed a competition to design a low-bypass turbofan engine using a baseline turbojet engine, I knew this was the project for me. Fortunately, I found two other people with the same passion for air, fuel, and power. The three of us set out to design the best low bypass engine we could as well as furthering our understanding of gas turbine engine. Upon starting the project, I decided that I would take on the responsibility of designing the compressor and the afterburner. Little did I know how complex and vital the compressor was to the entire engine. With the use of “Aircraft Engine Design Second Edition” [2] and “Elements of Propulsions: Gas Turbines and Rockets” [1] books, I was able to increase my knowledge of the in-depth calculations for each stage of the compressor. Using the process found in both books, I generated an Excel spreadsheet for each stage of the compressor. This task turned into a considerable greater undertaking. Even though the Excel spreadsheet did not work the way anticipated, it did increase my understanding of the relationship with the values in the compressor. I took most of the values found in the Excel spreadsheet and input the into COMPR program. The output data allowed me to double check my initial calculations and provided other critical data for the compressor. After main iterations of the Excel spreadsheet and the COMPR program, the compressor was finally completed. One of the major disadvantages of designing the afterburner, was the lack of useful resources. “Aircraft Engine Design Second Edition” [2] used a combination of ONX, GASTAB, AFTRBRN program to design the afterburner. I initial started an Excel Spreadsheet, but reverted to the process describe in “Aircraft Engine Design Second Edition” [2] book due to absence of information. However, the process in the book was not the easiest to follow, but did produce excellent results. This Project has been a great challenge to me while sheading knowledge of the complexity of a gas turbine engine. I would like to thank Dr. Adeel Khalid for his time teaching and a growing my love of the aerospace engineering.

Kristian Lien: Upon beginning the engine design project, I knew it would be a great challenge. It soon became one of the hardest things I had done in school but also my greatest success. Upon taking the Aircraft Propulsion class, I knew that my calling would be to design engines for a living. To challenge that goal, my group and I decided to design a propulsive system for our Aeronautics Senior Design Project. Luckily, AIAA had posed a competition to design a low-bypass turbofan engine using a baseline turbojet engine. This helped in the ease of knowing what to expect for results as well as comparison purposes. In beginning the project, each component had to be designated to each group member. I had decided to design the turbine as well as the combustion chamber. Initially, I knew that the design of both would be quite perplexing. To obtain more knowledge about each individual system, much research and reading was done. By using both the “Aircraft Engine Design Second Edition” [2] and “Elements of Propulsions: Gas Turbines and Rockets” [1] books, much new knowledge was obtained on either subject. To begin, the turbine had to be developed. Using the equations found in each book, an Excel spreadsheet was created. The results of the spreadsheet created little success but helped with an understanding of how each input value could determine the resulting flow through the turbine. After weeks of

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manipulation, the TURBN program was used to finalize the design. It took many iterations using the program to achieve the needed results for each stage but proved to be easier than the spreadsheet. Upon obtaining values of the turbine size, the combustion chamber then needed to be designed. As seen in the turbine, an excel spreadsheet was created to visualize and understand the complexity of the combustion chamber. After many revisions, the MAINBRN program was used to finalize the design of the combustion chamber. The manipulation of the diffuser and primary zone seemed to pose the greatest difficulty. Through many iterations, a desired size, number of secondary and dilution zone holes, and temperatures were obtained. Once completing the designs, a time for reflection on accomplishments was needed. It was stated that a huge learning curve was needed for both the understanding of component design and program use. Luckily, the books my group and I had used aided in both. It took countless hours of reading chapters to fully understand the preliminary design of the turbine and combustion chamber. It took even longer to appreciate how much each individual component affects the others. As stated previously, many iterations were made to obtain desired goals. Occasionally, when the components neared completion, it was found that other components in the engine needed to be reassessed. This caused a new design needed for both combustion chamber and turbine. The overall design posed a great challenge but allowed for my dream to become an engine designer to reach a new height. Understanding the complexity of each engine stage allowed for a greater sense of accomplishment as an individual. With the help of our advisor/mentor Dr. Adeel Khalid and the books written by Jack D. Mattingly, a higher appreciation of propulsive systems was accomplished.

Austin Sims: The decision to take on this project is something I do not regret. In my mechanical and aeronautical engineering studies, my proficiency relative to thermodynamics and heat transfer has been one of my weaknesses. Knowing this, I chose to see this as an opportunity to not only challenge me but to better myself as engineer. One thing I have learned in my studies is that with enough work and determination I can do just about anything. Sure enough once getting into the project my previous knowledge learned and experiences with preliminary engine design in my classes helped guide me along the way. The engine components I chose to design for this project included the 2-Ramp External Compression Inlet with a Diffuser and the Convergent-Divergent Nozzle. Initially I knew that a great deal of work and effort went in to the development of these two elements. What I learned very quickly is that it’s one thing to design the sections individually, but it’s another to design them so that they are optimally in tune with the entire engine. This can be seen considering one of my main references used for this project is an entire paper on the optimization of a 2-D ramped external compression inlet. For the purposes and general scope of this project the designs of my components include a fixed geometry for the inlet and the optimized convergent-divergent angles of the nozzle for only the aircraft’s main flight conditions. In cases like the F-14 and the Concorde their inlet and nozzle geometries vary relative to the aircraft’s different flight conditions midflight. Ultimately there is an unlimited number of combinations in which the geometries can be arranged for every possible flight condition. Recognizing the true scope of the project as a preliminary engine design, much of my information and influence for design came from the use of two of my textbooks by Jack D. Mattingly: “Aircraft Engine Design, Second Edition” and “Elements of Propulsion: Gas Turbines and Rockets.” Using these resources helped me to organize a better plan of attack and more efficiently determine the best possible results and performance of the engine components while minimizing their vast complexities that could be investigated.

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In correlation with the text resources, the use of the AEDsys software and its INLET and NOZZLE programs helped to expedite the process of calculating the design performance and component sizing of each component. Additionally, the computations based on a given mission leg could be completed in order to enhance the comprehensive performance of each component. The fundamental results found for the inlet were the total pressure recovery, the eventual velocity at the fan face, and the capture area sizing suitable for obtaining the mass flow rate required by the engine. Similarly, the significant products of the nozzle include the gross thrust actual produced at exit, the exit velocity of the air flow, and pressure matching at the nozzles exit. Considering these aspects of the design, the losses and flow separation are supposed to be limited. After experiencing the intricacies in the research, design, and development required by this project I learned a great deal about myself. At first it seemed as if taking on this project would be virtually impossible given the groups initial knowledge of the subject and time limitations of a heavy class load. In the end tenacity and not accepting nothing less than success prevailed. I will be able use this experience in the future as a baseline of what I should expect myself being able to accomplish. As student at the end of my college career this has helped me to boost my confidence and resolve when faced with adversity. Furthermore, the knowledge gained from my studies, my mentor/advisor Dr. Adeel Khalid, and this project will be a strong foundation for me as I embark onto my professional career and future endeavors.

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11 Appendix D: Initial Values and Requirements 11.1 Inlet

Table 11.1: Table of Initial Value for Inlet

Initial Values

Selected Shock System Required Selected Resulting

M0 ηR As/A0i A0 (ft2) A0i (ft2) As (ft2) A1 (ft2) As (ft2) A0i (ft2) Fgcm0a0

φinlet

1.0 1.0000 1.0000 2.874 3.012 3.012 4.000 3.203 3.203 3.500 0.0000

1.1 0.9989 0.9995 2.896 3.046 3.045 4.000 3.203 3.205 3.522 0.0025

1.2 0.9928 0.9990 2.944 3.109 3.106 4.000 3.203 3.206 3.542 0.0041

1.3 0.9972 0.9453 3.062 3.246 3.068 4.000 6.203 3.388 3.560 0.0073

1.4 0.9896 0.9290 3.179 3.382 3.142 4.000 3.203 3.447 3.576 0.0076

1.5 0.9947 0.8635 3.372 3.640 3.124 4.000 3.203 3.732 3.590 0.0111

Table 11.2: Table of Requirements for Inlet

Requirements

Inlet Requirements Based on Engine Performance Cycle Analysis Calculations

Inlet Area Modified for Safety Margin and Boundary Layer Bleed

M0 ηR spec A0 spec (ft2) A0 spec + 4% (ft2) A0t spec (ft^2)

1.0 1.0000 2.874 2.989 3.012

1.1 0.9966 2.889 3.005 3.039

1.2 0.9915 2.940 3.058 3.105

1.3 0.9852 3.025 3.146 3.207

1.4 0.9782 3.142 3.268 3.343

1.5 0.9706 3.290 3.422 3.514

11.2 Fan/Compressor Table 11.3: Initial Values and Requirements for Fan/Compressor

Initial Values Requirements

Low Pressure/Fan High Pressure Low Pressure/Fan High Pressure

M1 = M3 60˚F ≤ ΔTt per stage ≤ 100˚F 60˚F ≤ ΔTt per stage ≤ 90˚F

α1 = α1 = 40 deg 1.5 ≤ πc for one stage ≤ 2.0 0.90 ≤ Hub/tip at exit ≤ 0.92

u2/u1 = 1.1 2.0 ≤ πc for two stage ≤ 3.5 1300 ft/s ≤ Vrim exit ≤ 1500 ft/s

Φcr = 0.09 3.5 ≤ πc for three stage ≤ 4.5 1700 R ≤ Max Texit ≤ 1800 R

Φcs = 0.03 0.50 ≤ DF ≤ 0.55

σ = 1.0 1400 ft/s ≤ Vtip ≤ 1500 ft/s

c/h = 0.5

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11.3 Combustion Chamber Table 11.4: Initial Values and Requirements for Combustion Chamber


ηDm = 0.9 0.2 ≤ φ ≤ 1.0

θ = 5 deg 0.6 ≤ S' ≤ 1

ε = 1 35 deg ≤ αSW ≤ 50 deg

Tm = 2500 R 3000 R ≤ Tg ≤ 3420 R

rh = 0.5 in φPZ ≥ 0.8

αSW = 45 deg εPZ ≈ 0.7

ri ≥ 0.5 in.

11.4 Turbine Table 11.5: Initial Values and Requirements for Turbine


High Pressure Low Pressure High Pressure Low Pressure

M2 = 1.1 M2 = 0.9 4x1010 in2-rpm2 ≤ AN2 ≤

4x1010 in2-rpm2 N/A

α1 = 0 deg 1.4 ≤ Ψ ≤ 2.0 Ψ ≤ 2.4

u3/u2 = 0.9 0.4 ≤ M3 ≤ 0.5

φt stator = 0.06 0 deg ≤ α3 ≤ 40 deg

φt rotor = 0.15 0.3 ≤ c/h ≤ 1.0

Z = 1.0 Best performance : 60 deg ≤ α2 ≤ 70 deg

c/h = 1.0 Mean radius (rm) stays consitient

σ = 1.0

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11.5 Afterburner

Figure 11.1: Principal Features and Flow Patterns of the Afterburner

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11.6 Nozzle

Figure 11.2: Nozzle Discharge Coefficient: b) Convergent and C-D Nozzle CD max

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Figure 11.3: C-D Nozzle Velocity Coefficient

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Figure 11.4: C-D Nozzle Angularity Coefficient

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12 Appendix E: ONX Parametric Analysis

12.1 Mach 0 and Sea Level

Figure 12.1: ONX Parametric Analysis Results at M=0 and Sea Level

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Figure 12.2: Preliminary Engine Performance Analysis at M=0 and Sea Level

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12.2 Mach 0.5 and 15,000 feet

Figure 12.3: ONX Parametric Results at M=0.5 and 15,000 feet

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Figure 12.4: Preliminary Engine Performance Analysis at M=0.5 and 15,000 feet

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12.3 Mach 0.85 and 35,000 feet

Figure 12.5: ONX Parametric Analysis Results M=0.85 and 35,000 feet

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12.4 Mach 1.3 and 40,000 feet

Figure 12.7: ONX Parametric Analysis Results at M=1.3 and 40,000 feet

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13 Appendix F: AEDsys Test Data

13.1 Inlet

Figure 13.1: Inlet Inputs and Results

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Figure 13.2: Inlet Side View

Figure 13.3: Inlet Angle Contours

13.2 Fan/Compressor

13.2.1 Inlet Guide Vanes

13.2.1.1 Low Pressure

Figure 13.4: Low Pressure IGV Results

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Figure 13.5: Low Pressure IGV Blade Profile

13.2.1.2 High Pressure

Figure 13.6: High Pressure IGV Results

Figure 13.7: High Pressure IGV Blade Profile

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13.2.2 Fan/Low Pressure Compressor

Figure 13.8: Fan/Low Pressure Compressor Layout

13.2.2.1 Stage One

Figure 13.9: Low Pressure Stage 1 Results

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Figure 13.10: Low Pressure Stage 1 Blade Profile

13.2.2.2 Stage Two


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Figure 13.12: Low Pressure Stage 2 Blade Profiles

13.2.2.3 Stage Three


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Figure 13.14: Low Pressure Stage 3 Blade Layout

13.2.3 High Pressure Compressor

Figure 13.15: High Pressure Compressor Layout

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13.2.3.1 Stage One

Figure 13.16: High Pressure Stage 1 Results

Figure 13.17: High Pressure Stage 1 Blade Layout

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13.2.3.2 Stage Two


Figure 13.19: High Pressure Stage 2 Blade Profile

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13.2.3.3 Stage Three



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13.2.3.4 Stage Four



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13.2.3.5 Stage Five



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13.3 Combustion Chamber

Figure 13.26: Data Entry for Combustion Chamber

Figure 13.27: Air Partitioning for Combustion Chamber

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Figure 13.28: Diffuser for Combustion Chamber

Figure 13.29: Primary Zone for Combustion Chamber

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Figure 13.30: Secondary Zone for Combustion Chamber

Figure 13.31: Dilution Zone for Combustion Chamber

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Figure 13.32: Combustion Chamber Front View

Figure 13.33: Combustion Chamber Side View

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Figure 13.34: Combustion Chamber Plan View

13.4 Turbine

13.4.1 High Pressure Turbine

Figure 13.35: High Pressure Results

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Figure 13.36: High Pressure Layout

Figure 13.37: High Pressure Blade Layout

13.4.2 Low Pressure Turbine

Figure 13.38: Low Pressure Results

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Figure 13.39: Low Pressure Layout

Figure 13.40: Low Pressure Blade Layout

13.4.3 Exit Guide Vanes

Figure 13.41: Exit Guide Vane Results

Figure 13.42: Exit Guide Vane Results

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13.5 Afterburner

Figure 13.43: Data Entry

Figure 13.44: Data Entry

Figure 13.45: Flameholders

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Figure 13.46: Side View of Afterburner

13.6 Nozzle

13.6.1 Mach 0

Figure 13.47: Nozzle Input and Results at Mach 0

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Figure 13.48: Divergent Angle Contours at Mach 0

Figure 13.49: Nozzle Side View at Mach 0

13.6.2 Mach 0.5

Figure 13.50: Nozzle Input and Results at Mach 0.5

Figure 13.51: Divergent Angle Contours at Mach 0.5

Figure 13.52: Nozzle Side View at Mach 0.5

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13.6.3 Mach 0.85


Figure 13.54: Divergent Angle Contours at Mach 0.85


13.6.4 Mach 1.3


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Figure 13.57: Divergent Angle Contour at Mach 1.3


13.7 Mission Analysis Results

Figure 13.59: Warm-Up Leg

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Figure 13.60: Takeoff Accelerate

Figure 13.61: Takeoff Rotation

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Figure 13.62: Horizontal Acceleration

Figure 13.63: First Climb and Acceleration

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Figure 13.64: Second Climb and Acceleration

Figure 13.65: Third Climb and Acceleration

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Figure 13.66: Subsonic Cruise

Figure 13.67: Climb and Accelerate to Supersonic Cruise

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Figure 13.68: Supersonic Cruise

Figure 13.69: Descend to Subsonic Cruise

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Figure 13.70: Subsonic Cruise

Figure 13.71: Descend to Loiter

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Figure 13.72: Loiter

Figure 13.73: Descend to Land

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Figure 13.74: Results of Mission

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