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AAE 372 Spring 2008 Final Exam (Open Book) May 2 nd , Friday, 8:00-10:00 AM, ARMS 1010 Name:____________ 1. n-Propys alcohol (C 3 H 7 OH) is combined with air at stoichiometric condition. Write the governing chemical equation for the process in the space below. (10 pts) 2. Axial compressors and turbines use a “cascade” of “stages”, with each stage composed of a rotor/stator blade pair. In a compressor, the rotor blades do work on the gas flowing through each stage and thereby increase the pressure from one stage to the next. In a turbine, the gas flowing through each stage does work on the rotor blades, with the result that the pressure decreases from each stage to the next. In both cases, the blade shapes and blade orientations in each stage of the cascade must be properly designed to avoid boundary layer separation from the blade surfaces, which would lead to large irreversibility and thus poor efficiency. Assume the stage configuration shown below has been proposed to you as a design for a high-efficiency compressor. Describe clearly why or why not this design is a good idea. Be as specific as possible, and present velocity triangles to support your reasoning. (15 pts) 1
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AAE 372 Sample Final Exam

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AAE 372 Sample Final Exam
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Page 1: AAE 372 Sample Final Exam

AAE 372 Spring 2008Final Exam (Open Book)

May 2nd, Friday, 8:00-10:00 AM, ARMS 1010

Name:____________

1. n-Propys alcohol (C3H7OH) is combined with air at stoichiometric condition. Write the governing chemical equation for the process in the space below. (10 pts)

2. Axial compressors and turbines use a “cascade” of “stages”, with each stage composed of a rotor/stator blade pair. In a compressor, the rotor blades do work on the gas flowing through each stage and thereby increase the pressure from one stage to the next. In a turbine, the gas flowing through each stage does work on the rotor blades, with the result that the pressure decreases from each stage to the next. In both cases, the blade shapes and blade orientations in each stage of the cascade must be properly designed to avoid boundary layer separation from the blade surfaces, which would lead to large irreversibility and thus poor efficiency.

Assume the stage configuration shown below has been proposed to you as a design for a high-efficiency compressor. Describe clearly why or why not this design is a good idea. Be as specific as possible, and present velocity triangles to support your reasoning. (15 pts)

3. In an axial compressor, location 1 is upstream of the rotor blade and location 2 is downstream of the rotor: (25 pts)

c1 = magnitude of velocity vector, with respect to engine = 122 m/sw1 = magnitude of velocity vector, with respect to rotor = 222 m/sc2 = magnitude of velocity vector, with respect to engine = 235 m/s

Assume: c1Z = c2Z as we did in class. 1 = 25 degrees is the angle between vector c1 and the compressor axis, as we defined in class.

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Page 2: AAE 372 Sample Final Exam

a) Determine the work done, per kilogram of air that passes through the engine.

b) Determine the pressure ratio for the stage (p03/p01) if the stage efficiency is 0.90 and T01 is 400 K.

c) Determine the RPM of the engine if the mean radius of the rotor blade is 15 cm.

d) Draw the stator blade that is upstream of this stage and draw an arrow to indicate whether it should be rotated in the clockwise or counterclockwise direction.

4. Hot gases from the combustor enter the single stage turbine shown above. You may assume that the axial velocity remains constant across the entire stage and that all flow angles are coincident with blade angles. In addition, since this is a single stage device, we desire the absolute rotor exit velocity to be entirely in the axial direction in order to maximize thrust. For these assumptions, determine: (25 pts)

a) The absolute velocity exiting the nozzles (C2)

b) The rotor speed, U, which gives optimal flow entering the rotor at the angle show in the figure below.

c) The rotor exit angle, 3

d) The degree of reaction of this turbine stage.

5. Consider the ideal turbofan engine with perfectly expanded nozzles in the sketch below. Instrumentation provides the pressure, temperature, and massflow at locations shown in the sketch. Designers are considering installing an afterburner in the fan duct to enhance thrust. Assuming the afterburner is off, determine: (25 pts)

a) Flight Mach number and velocity

b) Fan thrust

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Page 3: AAE 372 Sample Final Exam

c) We wish to augment fan thrust by 25% through the use of the afterburner in the fan duct. Determine the fuel flowrate required to accomplish this task assuming a perfectly expanded nozzle and a fuel heating value of 18, 600 Btu/lbm.

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Solutions:1.

2.

This is an extremely bad design. The relative flow velocity approaching the rotor, namely w1, is at a very poor angle of attack relative to the rotor blades, which would certainly cause massive flow separation to occur on the concave side of the rotor blades. Similarly the velocity seen by the stator blades, namely c2, also is at a very poor angle of attack relative to the stator blades, which would cause massive flow separation to occur on the concave side of the stator blades. The total pressure losses resulting from such massive flow separation would give extremely poor compressor performance.

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