Question 2 You are an engineer working in the propulsion team for a supersonic civil transport aircraft driven by a turbojet engine, where you have oversight of the design for the engine intake and the exhaust nozzle, indicated in Figure Q2a. The turbojet engine can operate when provided with air flow in the Mach number range, 0.60 to 0.80. You are asked to analyse a condition where the aircraft is flying at 472 m/s at an altitude of 14,000 m. For all parts of the question, you can assume that the flow path of air through the engine has a circular cross section. (a) normal shock 472 m/s A B (b) intake engine altitude: 14,000 m D exhaust nozzle→ exit to atmosphere 472 m/s 50 m/s B diameter: DE = 0.30 m EX diameter: DF = 0.66 m Figure Q2: Propulsion system for a supersonic aircraft. F a) When the aircraft is at an altitude of 14,000 m, use the International Standard Atmosphere in the Module Data Book to state the local air pressure and tempera- ture. Thus show that the aircraft speed of 472 m/s corresponds to a Mach number of 1.60. b) In the frame of reference of the aircraft, what are the static pressure and tem- perature ahead of the intake (point A)? What are the stagnation pressure and temperature at this point? c) The intake is designed to produce a normal shock wave ahead of its entrance during supersonic operation, similar to a Pitot tube (it is therefore called a Pitot intake). State the Mach number of the flow ahead of the shock wave (point A). Thus, calculate the Mach number of the flow after the shock wave (point B). d) Use the normal shock tables in the Module Data Book to calculate the static pressure and temperature after the shock wave (point B). Also determine the stagnation pressure and temperature at this location. e) The intake duct has a diameter of 0.75 m and its walls can be approximated as adiabatic and frictionless. Comment on whether the Mach number of the flow arriving at the engine (point C) is within the specified operational range. What is the mass flow rate supplied to the engine? f) The certification requirements for the engine requires it to continue to function when subject to a sudden change in upstream conditions, which causes the shock wave to enter the intake duct and start moving downstream at 50 m/s, as shown in Figure Q2b. What is the new Mach number of the incoming flow in the reference frame of the shock wave? g) In the scenario described by Figure Q2b, what is the Mach number of the flow arriving at the engine (point C), as defined in the reference frame of the aircraft. Is this within the specified operational range? h) The flow exiting the engine (point D) has a stagnation pressure of 900 kPa. It then passes through the exhaust nozzle shown in Figure Q2a. The flow at the nozzle throat (point E) is choked and there are no shock waves within the interior of the nozzle duct. By using the duct diameters specified in Figure Q2c, calculate the exit Mach number and therefore determine the static pressure at the nozzle exit (point F). i) By comparing the static pressure to the local atmospheric pressure (which you determined in part (a)) sketch the flow pattern immediately outside the nozzle. Provide an explanation for this flow pattern in two or three sentences.