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Q1:1. (30 points). Consider an aircraft climbing steadily in the Earth's atmo- sphere with a constant speed of 1100 km/hr. As the aircraft goes to higher altitudes, the temperature of the air changes approximately linearly with elevation at a rate of -6.6 °C/km. Assume that the temperature at sea level is 25 °C. (a) Compute the Mach number of the aircraft when it reaches an altitude of 3000 m. (b) Compute the Mach number of the aircraft when it reaches an altitude of 15000 m. (c) How does the Mach number of the aircraft vary with elevation? At what altitude does the flow around it become sonic?See Answer
Q2:2. (30 points). A fighter jet is traveling with a velocity u = (398 m/s) i + (4.00 m/s) Ĵ+ (51.0 m/s) k relative to the earth. It fires a missile that moves at a velocity of v = (107 m/s) Î + (-10.0 m/s) ĵ + (2.00 m/s) k relative to the fighter jet. If the altitude of the fighter jet is 9000 m: (a) Find the Mach number of the missile an instance after it is fired. (b) Do we have to worry about compressibility effects when analyzing the missile's flight?See Answer
Q3:3. (30 points). You go on vacation and return to find a wind tunnel in your lab is filled with a mystery gas that is either nitrogen (k = 1.400) or helium (k = 1.667). Your colleague has left you a post-it note saying that she determined the temperature to be 293 K, the Mach number to be 1.2, and the wind speed to be 1208 m/s. (a) Which gas fills the wind tunnel? (b) What would the wind speed be if the wind tunnel was filled with the other gas?See Answer
Q4:4. (30 points). A liquid is initially at 30 °C and 1 atm. It is heated to a temperature of 70 °C at a constant pressure. The change in density is -1.804 percent. (a) What is the liquid? (b) What is the change in density if this liquid is compressed to 75 atm at a constant temperature of 30 °C? (c) Is this liquid significantly compressible?See Answer
Q5:Determine: a) πHPс and πLPC b) ec c) Step (time) d) Pt3, Tt3, e) Explain how you determine the change of mass flow rate of the Bleed as function of its Area f) Show all calculations to determine the Pt3 and Tt3 and any other item. g) Explain what is the bleed purpose in this case (show reference in APA v6 or v7 form) h) Show why Mbleed = 1See Answer
Q6:Find and print in table a) Time change by step, bleed Area, m bleed and mass flow rate to combustor for each time step b) Static Temperature at stage 3 for each time step c) Mach number exit of the HPC for each time step Special Homework for 50 points d) Velocity exit of the HPC for each time step e) Plot M3 vs time, and V3 (ft/s) vs time (s) in the same chart with yy axisSee Answer
Q7:Show calculations 1. How to determine that Mbleed is 1. 2. Par Tur Tor Por T₁2, P₁2 3. meore 4. Mach number when bleed is fully closed Mach number when bleed is fully open 5. 6. How you determine the change of the bleed area? Note: number of items is given by the user (n). It can be changed and the program provide the manner to accept any n. y-i Tc = πy where ec is the polytropic efficiency and is around of 88% 92%See Answer
Q8:1 Engine efficiency (25 pts) For a matched engine, the propulsive efficiency is given approximately by 2u Tsp +2u' (1) where Tsp = T/m, is the specific thrust. Using this relation, on a single graph, plot the specific thrust and propulsive efficiency for the systems in Table 1. You may assume a thermal efficiency of 0.4. Put propulsive efficiency on the x axis (from 0 to 1) and specific thrust on the y axis (1 to 5000 m/s). Make this a semilog graph (logarithmic scale on the specific thrust axis). Represent each propulsion system as a filled area between a lower bounding curve and an upper bounding curve. For a fixed thrust, which propulsion system moves the most air mass? The least? System Propellers Turbojets Turbofans (high-bypass) Turbofans (low-bypass) Aircraft velocity (m/s) Overall efficiencies 35 - 200 240 - 600 150 - 300 150 - 600 Table 1: Systems of interest for Problem 2 30% -35% 10% - 25% 15% - 30% 20% - 30%See Answer
Q9:2 Adding bypass to an engine (35 pts) a) Core stage only (10 pts) Compute the propulsive efficiency and spe- cific thrust for a turbojet engine with an exhaust velocity of 450 m/s, an air mass flow rate of 250 kg/s, an exit area of 2 m², and an exit pressure of 35,000 Pa if the aircraft is flying at 200 m/s at an ambient pressure of 30,000 Pa. The fuel fraction is 2.0%. b) with bypass (20 pts) We want to add bypass to this turbojet to adapt it into a turbofan with the original turbojet as a core. The airstream coming from the fan has an exhaust velocity of 250 m/s and its exit pres- sure is matched to the ambient. The flow rate ingested by the fan m, is related to the air passing through the core me by m = 3me, where 3 is the bypass ratio. i) Efficiency (15 pts) Given that the heat of reaction of the fuel used by the engine is 43 MJ/kg, plot its thermal efficiency, propulsive effi- ciency, and total efficiency as a function of bypass ratio over 3 € [0, 15]. Render all efficiencies on the same plot. ii) Thrust (5 pts) Plot the specific thrust and thrust specific fuel con- sumption as a function of bypass ratio over 3 € [0, 15]. Render both on the same plot (multiple y axes). c) Comparison (5 pts) Based on your results, for which applications would we want to use a high-bypass turbofan? A low-bypass turbofan? Justify your answer.See Answer
Q10:3 Control volume analysis (40 pts) In lecture, we derived an expression for thrust using a control volume whose left edge was upstream of the engine intake and whose right edge was at the exit plane. Now consider a control volume (depicted in Figure 2), where the left edge is at the intake and whose right edge is far downstream of the engine outlet. Ambient air moving at speed u relative to the aircraft slows down and compresses as it moves into the inflow duct of the engine. We measure the state and velocity of the air at station i, inside the inlet, and at station d. some distance downstream where the pressure phas returned to atmospheric AEROSP 335 (Winter 2024) AEROSP 335 (Winter 2024) "₂ Pa A₂ 44, P A₁ 2 "₂ Pa = Pa A₂ Jorns Jormes Figure 1: Engine diagram for problem 3 pressure på. The fuel fraction of the engine is f. Use this control volume to answer the following questions: a) (15 pts) Write down the integral form of conservation of momentum in this control volume. Label all terms. b) (15 pts) Starting from your answer in part (a), derive an expression for the thrust in terms of ui, ud. Pi, Pa, Ai, f, and ma. c) (10 pts) Compare your result to the expression we derived in class. Why do you think we use the expression derived in class rather than the one from part (b)?See Answer
Q11:1. A non-afterburning turbojet is being designed for operation at an altitude of 15 km and a Mach number of 1.8. The maximum stagnation temperature at the inlet of the turbine is 1500 K. The fuel is a jet fuel having a LHV of 43124 kJ/kg and fat is 0.06. The following efficiencies apply at this Mach number: na = 0.9 nc = 0.9 nb = 0.98 Tb = 0.97 nt = 0.92 nn = 0.98 Use a gamma value of 1.4 up to the burner, and a value of 1.3 for the rest of the engine. Assume R is 0.287 kJ/kgK throughout the engine. Plot the specific thrust, TSFC, nth, np and no as a function of rc, the total pressure ratio across the compressor. Is there an optimum rc that minimizes TSFC? Is there an optimum re that maximizes specific thrust? Consider a range of rc from 2 to 60. Assume the exhaust is ideally expanded. Also plot the nozzle area ratio as a function of rc. 2. Add an afterburner to the above situation. The maximum stagnation temperature downstream of the afterburner is 2000 K. The afterburner combustion efficiency nab is 0.95 and the total pressure ratio is rab is 0.97. All other efficiencies remain the same. Use a gamma value of 1.4 up to the primary burner, and a value of 1.3 for the rest of the engine. Assume R is 0.287 kJ/kgK throughout the engine. Plot the specific thrust, TSFC, nth, np and no as a function of r, the total pressure ratio across the compressor. Consider a range of re from 2 to 60. Assume the exhaust is ideally expanded. Also plot the nozzle area ratio as a function of rc. Comment on the changes that occur due to the addition of the afterburner (i.e. compare the plots to that of problem 1). Note that the overall fuel-to-air ratio can not exceed the stoichiometric value (fb+fab<fst).See Answer
Q12:1. (50 Points) Design the angular orientations of a 4 stage axial compressor that generates a total compression ratio = 9. Assume that the axial velocity has the constant magnitude of 277 m/s. The rotor is designed at the nominal radius of 0.8 m and constant rotation rate of 5000 rpm. Static properties of the fluid before the first stator are 250 K and 88 kPa with standard specific heat ratio of 1.4. The first element is a stator (inlet guide vane) that turns the flow 8°. Select the subsequent angles for the remaining stages to achieve the necessary to ±4% accuracy. Provide the following in your analysis: (a) Velocity triangles drawn to scale for each stator-rotor stage (b) The degree of reaction determined by the angles you designed (50% is not required) (c) The static and total properties of the fluid as a function of stage position (d) The total work done by the compressor as a result of the design Extra Credit: (20 Points) If you consider the entire blade length from 0.65 <r<0.95 m, draw a three dimensional model of the blade used in middle stage rotor-stator pair. In other words, as the radius changes, the angle of deflection will adjust to still maintain the compression ratio.See Answer
Q13:2. (50 Points) Explore the Pratt & Whitney F135 low-bypass turbofan engine with after- burner that powers the F-35 Lightning. Determine the stage compression ratios, turbine inlet temperatures, and potential efficiencies to achieve 191 kN of thrust as a result of exit velocity with afterburner when at subsonic flow at Mach 0.95 at 18,000 feet altitude. Consider the alternative performance at Mach 2.2 following an oblique shock around a 0 = 22° deflection angle. How does the system compare when at efficiency versus high performance? Extra Credit: (20 Points) Compare the F135 engine to other military aircraft engines to conduct similar performance characteristics.See Answer
Q14:3. (50 Points) A 787 Dreamliner is designed for Mach 0.77 flight at an altitude of 8.8 km with two turbofans each with inlet diameter of 2.65 m. The core compression ratio is 11 with variable efficiency ne. The turbine inlet temperature after the combustor is 1350° C and has a variable turbine efficiency nt. The fan has a compression ratio 2.8 and bypass ratio a = 4.5. Assume the quantity of fuel added is 1.6%, constant specific heat, determine the following as a function of variable ranges 0.66 and 0.77 0.96: (a) Total temperature at after each turbomachinery component (b) Exit velocities of both the core and the fan 0.92 (c) Thrust force generated by the engine assuming full expansion of the nozzles P = Po (d) Specific thrust (e) Thrust specific fuel consumption Use the combination of idealized and efficiency ratios to determine which of the adjust- ment variables has the greatest impact on each of the parameters calculated? Extra Credit: (20 Points) Explore performance characteristics as a function of altitude. How does the change of properties for the inlet flow affect the performance away from operational design?See Answer
Q15:4. (50 Points) Investigate the flight characteristics of the Cessna Citation aircraft. Given the wing span dimensional length as well as tapering chord length when either the NACA 2412 or the NASA/Langley 0213 airfoils are used. Evaluate the angle of attack of the wings attached to the fuselage when at straight and level flight 22,000 feet. Compare the performance during take off and landing (different angles of attack) in the range of environments at DeKalb Taylor Municipal Airport (i.e. super hot or super cold days). At what climb rate could the Citation have some concern about reaching stall condition and lose lift? Extra Credit: (20 Points) Confirm the scaling of the airfoil lift and drag performance as the same shapes could be used on larger aircraft like the Embraer E135/145 or Airbus A320.See Answer
Q16:1. A non-afterburning turbojet is being designed for operation at an altitude of 15 km and a Mach number of 1.8. The maximum stagnation temperature at the inlet of the turbine is 1500 K. The fuel is a jet fuel having a LHV of 43124 kJ/kg and fst is 0.06. The following efficiencies apply at this Mach number: nd = 0.9 nc = 0.9 nb = 0.98 rb = 0.97 nt = 0.92 Vn = 0.98 Use a gamma value of 1.4 up to the burner, and a value of 1.3 for the rest of the engine. Assume R is 0.287 kJ/kgK throughout the engine. Plot the specific thrust, TSFC, th, np and no as a function of rc, the total pressure ratio across the compressor. Is there an optimum rc that minimizes TSFC? Is there an optimum rc that maximizes specific thrust? Consider a range of rc from 2 to 60. Assume the exhaust is ideally expanded. Also plot the nozzle area ratio as a function of r.See Answer
Q17:2. Add an afterburner to the above situation. The maximum stagnation temperature downstream of the afterburner is 2000 K. The afterburner combustion efficiency nab is 0.95 and the total pressure ratio is rab is 0.97. All other efficiencies remain the same. Use a gamma value of 1.4 up to the primary burner, and a value of 1.3 for the rest of the engine. Assume R is 0.287 kJ/kgK throughout the engine. Plot the specific thrust, TSFC, nth, np and no as a function of rc, the total pressure ratio across the compressor. Consider a range of rc from 2 to 60. Assume the exhaust is ideally expanded. Also plot the nozzle area ratio as a function of rc. Comment on the changes that occur due to the addition of the afterburner (i.e. compare the plots to that of problem 1). Note that the overall fuel-to-air ratio can not exceed the stoichiometric value (f+fab<fst).See Answer
Q18: The jet engines of an aircraft produce amaximum thrust, Tmax that is proportional to density:9 Tmax= The wing surface area of the aircraft is 71 m².What zero lift coefficient of drag, CDO will the aircraft have if its absolute ceiling is atan altitude of 10 km and its maximum cruisespeed is 199 m s¹ at an altitude of 8 km?See Answer
Q19: A propeller-driven aircraft has a maximum endurance of 14.1 hours when flying according to cruise climb conditions. What is the range of the flight if the aircraft's speed is 68 m s™¹, the propeller efficiency is 0.85 and the specific fuel consumption is 10-7 kg W-¹ s-¹? The answer should have units of km.See Answer
Q20: 2. Briefly explain the following concepts (a) Wetted aspect ratio (b) Rubber-engine sizing (c) Mission profile (d) Thrust matchingSee Answer

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