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THE UNIVERSITY OF ADELAIDE AEROSPACE PROPULSION MECH ENG 4106/7053 Assignment 2 Instructions: 

Assignment is due by 5pm Friday 3rd May 2019.

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Assignments are to be submitted online on Canvas.

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This assignment is to be done individually. (i.e., no collaboration). By submitting your assignment you are agreeing to the following: I declare that all material in this assessment is my own work except where there is clear acknowledgement and reference to the work of others. I have read the University Policy Statement on Plagiarism, Collusion and Related Forms of Cheating. I give permission for my assessment work to be reproduced and submitted to other academic staff for the purposes of assessment and to be copied, submitted and retained in a form suitable for electronic checking of plagiarism.

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All relevant workings must be shown. Marks may be deducted for work that is poorly presented. Any problems that require a derivation or equation formulation will include marks for how clearly you’ve set out and explained your derivations.

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Each problem must be started on a new page and must be neatly set out and clearly explained.

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For problems with MATLAB coding, you must attach your Matlab code to your solutions as well as your resultant graphs. You must type your student ID number in both the first line of your Matlab code and the title of your graphs. Failure to adhere to these instructions may result in zero marks awarded for the entire problem. All Matlab codes/graphs must be accompanied by clear written explanations of your workings.

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Late assignments will be penalised at 10% per day late. Late assignments will not be accepted more than one week after the due date.

Q1. [10 marks] Consider the thermal and propulsive efficiencies of an afterburning turbojet: 𝜂 =

()  [( / )  ] 

𝜂 = (

 /󰇗

)  [( / )  ]

Derive these expressions, stating any assumptions.

Q2. Consider an afterburning turbojet cruising at Mach 1.5 at 11km altitude with an engine inlet that slows the flow to Mach 0.5. The engine has a compressor ratio of 18, a turbine-entry temperature of T4 = 1500K and an afterburner exit temperature of T7 = 1900K. The jet uses fuel with a heating value of 42.8MJ/kg. This afterburning turbojet engine can be analysed either using a quasi-1D aerothermodynamic analysis or by idealising it as a Brayton cycle with reheat. Additional heat is added subsequent to the low pressure turbine (which drives the compressor), increasing the temperature from T5 to T7. Power from the cycle is then extracted from a low pressure turbine (or a nozzle), lowering the temperature to T9. (a) [12 marks] Carry out a quasi-1D aero-thermodynamic analysis of the engine assuming perfect expansion of the exhaust gases, ideal performance of all components, and constant mass flow and specific heats throughout the engine. Calculate the specific thrust, thrust specific fuel consumption, thermal efficiency, and propulsive efficiency. (b) [3 marks] If the engine is instead analysed as an ideal Brayton cycle with reheat, show that the thermal efficiency is given by: 𝜂 =

𝑇 − 𝑇 𝑇 − 𝑇

(c) [7 marks] Show that the thermal efficiency of part (b) can be expressed in terms of the design constraints T4/T2, T7/T2, and the compressor pressure ration PR as:

𝜂 =

1 1− 󰇡 󰇢 𝑃𝑅

 

1 −

 𝑃𝑅 

𝑇 1 − 𝑇

𝑇 − 1   𝑇





(d) [3 marks] Calculate the thermal efficiency of the engine using the Brayton cycle with reheat expression derived in part (c). (e) [5 marks] The aero-thermodynamic analysis and Brayton cycle are both ideal processes, so why do they not produce the same thermal efficiencies? If T2 in the expression derived in (c) were set to T0 and PR were set to P3 / P0, would the values be closer? Why / why not?

Q3. [8 marks] The ideal turbofan that we analysed during class assumed separate exhaust streams. However, there are some installations in which it is more suitable to duct the core and by-pass flow through a common exit nozzle (i.e., mix them prior to exhaust).

Assuming that the mixer has constant area, that there is no sidewall friction, that the basic ideal cycle assumptions can be applied, and that the total pressure of the exhaust can be calculated by considering the bypass stream, derive the specific thrust, 𝐹/(𝑚󰇗 + 𝑚󰇗 ) for the mixed exhaust stream turbofan as a function of 𝑎 , 𝛾, 𝛼, 𝜏 , 𝜏 , 𝜏 , 𝜏 , 𝑀 𝑎𝑛𝑑 𝑃 /𝑃󰆒 in its simplest form. Clearly show each step of the ideal cycle analysis required to do this. You do not need to express 𝜏 as function of 𝜏 , 𝜏 , 𝜏 , 𝜏 . End of assignment...