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homew#6 - AAE 439 Homework#6 D u e D ate O ctober 2 2 2 0 0...

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Unformatted text preview: AAE 439 Homework #6 D u e D ate: O ctober 2 2 , 2 0 0 8 O ct. 3 1 , 2 0 0 8 NAME: Problem 1: A supersonic wind tunnel is designed to produce flow in the test section at Mach 2.4 at standard atmospheric conditions. Calculate: a.) Exit-to-throat area ratio of the nozzle. b.) Reservoir pressure and temperature. Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 2: Problem 6 The reservoir pressure of a supersonic wind tunnel is 5 atm. At static pressure probe is moved along the center–line of the nozzle, taking measurements at various stations. For the following probe measurements, calculate the local Mach number and area ratio: a.) 4 atm b.) 2.64 atm c.) 0.5 atm Problem 7 Problem 8 Problem 9 TOTAL Problem 3: A rocket engine burns hydrogen and oxygen. Parameters in the combustions chamber and exit conditions are given as follows: Pressure: p0 = 25 atm Temperature: T0 = 3,517 K Molecular Weight: M = 16 kg kmol Spec. Heat Ratio: γ = 1.22 Exit Pressure: pe = 2.174⋅10–2 atm Throat Area: A* = 0.4 m2 Assuming a calorically perfect gas, calculate: a.) Exit Mach number, b.) Exit velocity, c.) Mass flow through the nozzle, d.) Exit area. Problem 4: Consider a rocket engine burning hydrogen and oxygen. The combustion chamber temperature and pressure are 4,000 K and 15 atm, respectively. The exit pressure is 1.174⋅10–2 atm. Calculate the Mach number at the exit. Assume that γ =1.52=const. and that R=519.6 J/(kg K). Homework #6 AAE 439 D u e D ate: O ctober 2 2 , 2 0 0 8 O ct. 3 1 , 2 0 0 8 NAME: Problem 5: Consider the flow of a working fluid through a convergent-divergent nozzle. The reservoir pressure and temperature are 10 atm and 300 K, respectively. The nozzle has two locations where A/A* = 6. At each location, calculate M, p, T and v. Problem 6: Analyze a rocket nozzle with the internal aeroynamic contour given by: r = 2.54 + 0.435 x − 0.001437 x2 − 0.000102145 x 3 x ≤ 25.4 where r (in cm) is the radial distance to the nozzle wall and x (in cm) is the axial distance measured from the throat. Suppose that the stagnation quantities feeding the nozzle are: p0 = 3.5 MPa Stagnation Pressure: Stagnation Temperature: T0 = 3, 000 °K Molecular Weight: M = 12 kg kmol a.) What is the nozzle expansion ratio? b.) What mass flow rate is traveling through the nozzle? c.) Write a computer code to solve for Mach number, static pressure and static temperature in the nozzle assuming choked flow. Use Newton’s Method (Tangent Method) or other to solve the nonlinear Mach number/area ratio relationship. Plot the following quantities assuming γ =1.1 and γ =1.3: i. Nozzle contour, ii. Mach number variation as a function of x, iii. Static temperature variation as a function of x, iv. Static pressure variation as a function of x, v. Velocity variation as a function of x. d.) Attach a listing of your code from Part c.) e.) What would the ambient (back) pressure have to be to invalidate the assumption of choked flow? Problem 7: A small projectile propulsion system is designed for shooting practice at sea–level conditions. The geometry is given in the schematic below. Further the design specifies parameters as follows: Chamber pressure: 70 atm, Exhaust gas velocity with a specific heat ratio: 1.2. Characteristic exhaust velocity of 1000 m/s, AAE 439 Homework #6 D u e D ate: O ctober 2 2 , 2 0 0 8 O ct. 3 1 , 2 0 0 8 NAME: Payload delivered to target: 10 kg, Propellant mass fraction: 0.8, Propellant mass: 30 kg. a.) How much thrust does the propulsion system deliver? b.) How much ∆v will it achieve during horizontal flight, if you assume drag losses (during horizontal flight), which amount to 10% of gravity losses for a vertical flight? A* = 14 cm 2 Ae = 98 cm 2 Problem 8: Consider the performance of a solid-propellant rocket under conditions that change with time. The stagnation temperature is constant at 3,000 °K. The stagnation pressure changes slowly with time: p0 = 20 − 0.04 t 0 < t < 100 for p0 in MPa and t in seconds. The nozzle has an area ratio of 5 and a throat area of 0.3 m2. It exhausts into a vacuum. The fluid man be considered to have γ =1.4 and a molecular weight of M = 20 kg kmol . How do the following vary with time: a.) Exhaust Velocity, b.) Mass Flow Rate, c.) Thrust? Problem 9: A rocket engine is designed for optimal expansion at sea level. The pressure in the combustion chamber is 7 MPa and the temperature is 2,800 K. The working fluid is an exotic oxidizer/fuel combination whose molecular weight is 11 kg/kmol and γ = 1.2 . The exit diameter is 2.5 m. a.) Determine thrust at design conditions. b.) Determine ambient pressure for a thrust increase of 5%. c.) Determine thrust generated in vacuum. ...
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