Constructing the Engine-Thrust Curves In this assignment, we will learn how the engine-thrust curves are constructed. Using the parameters provided in the table on the next page: (a) For an arbitrary flight speed, Ugo, write an expression for the inlet mass flowrate, ma in terms of the ambient pressure, Poe, ambient temperature, T., flight Mach number, M, and characteristic engine area, Aengine. Justify any assumption(s) that you have made in this calculation. (b) Determine the formulae for all total temperature, Ton, and total pressure, Pon; where the subscripts refers to the n-th state inside the engine. Write all total conditions as a ratio to the ambient conditions (i.e., Ton/T., and Pon/Poe). NOTE: You may assume "zero velocity condition" everywhere inside the engine. (c) Express the exit Mach number, Me, exit temperature, Te, and generated thrust, Fthrust as functions of the turbine outlet conditions found in (b). NOTE: You may assume that the engine outlet is perfectly expanded. (d) Draw the engine-thrust curves in terms of M., normalized thrust, Fthrust/P. Aengine, and normalized fuel consumption rate, mjquv/Po. AengineU. for an operation at lcp,max. Consider only M. [0.1, 0.8) and mig = [0.5, 5] kg/s. Refer to Lecture #8.2 for an example of the plot. NOTE: The overall pressure ratio, PR, of the compressor can be modelled as: PR = [1 + Matage (- 1) Mip] Nutare? 7-1 where Muip is the compressor tip Mach number given by Utip/220; where compressor speed speed is Utip = Dengine.cp/2 and ambient speed-of-sound is a = VYRT.. The use of a computational program here is highly encouraged. (e) At M = 0.5 and normalized fuel consumption rate of 5, determine the corresponding overall efficiency, 1 of the engine. 00 Flow Properties max Adiabatic constant 1.4 [-] Specific gas constant 287 (J/kg/K] Specific heat capacity Cp 1000.5 [J/kg/K] Turbojet Engine Specifications Characteristic engine diameter Dengine 3 [m] Maximum compressor RPM NCP, 266.7 [rad/s) Number of compressor stages 10 Compressor stage efficiency stage 0.15 ] Compressor isentropic efficiency TCP 0.98 Combustor total pressure loss IICB 0.95 Fuel heating value 9HV 40 [MJ/kg) Turbine isentropic efficiency Тргв 0.98 [-] Notage I III NOTE: With y and C being listed as constants here, the assumption of calorically perfect gas is implied. In addition, consider a flying altitude of halt = 9.1 km.
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