4. You are responsible for the design of the convergent nozzle for a turbojet engine fitted to a civil aircraft, as shown in Figure Q4. During operation at an altitude of 10,000 m, the aircraft flies at 300 m/s and the flow exhausts to atmosphere, where the pressure is 26.5 kPa and the temperature is 223 K. In this question, you should treat the flow as quasi-one-dimensional and inviscid. a) The radius of the nozzle satisfies the equation R(x) = 2-0.44x² where both x and R are expressed in metres. What is the area ratio between the nozzle inlet (x = 0.0 m) and the nozzle exit (x = 1.5 m)? b) The turbine exit temperature is the stagnation temperature, To = 400 K, of the flow in the nozzle. Similarly, the turbine exit pressure is the stagnation pressure, Po, of the flow in the nozzle. When the turbine exit pressure is 35 kPa, what is the Mach number at the nozzle exit? c) In a different scenario, the turbine exit pressure is 70 kPa. What is the Mach number of the flow at the nozzle exit? Also determine the Mach number at the nozzle inlet. d) The turbo-machinery team within the company have asked you to specify what exit pressure of the turbines results in perfectly expanded flow, with minimal expansion and compression waves outside the nozzle. What is this turbine exit pressure? p=26.5 kPa T=223 K capture streamtube 100 m combustion compressor chamber turbine nozzle nozzle nozzle inlet. exit. x=0.0 m x=1.5 m Figure Q4: Diagram of turbojet engine p=26.5 kPa T=223 K

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question 4d

4.
You are responsible for the design of the convergent nozzle for a
turbojet engine fitted to a civil aircraft, as shown in Figure Q4. During
operation at an altitude of 10,000 m, the aircraft flies at 300 m/s and the
flow exhausts to atmosphere, where the pressure is 26.5 kPa and the
temperature is 223 K. In this question, you should treat the flow as
quasi-one-dimensional and inviscid.
a) The radius of the nozzle satisfies the equation R(x) = 2-0.44x²
where both x and R are expressed in metres. What is the area ratio
between the nozzle inlet (x = 0.0 m) and the nozzle exit (x = 1.5 m)?
b) The turbine exit temperature is the stagnation temperature, To = 400 K,
of the flow in the nozzle. Similarly, the turbine exit pressure is the
stagnation pressure, Po, of the flow in the nozzle. When the turbine exit
pressure is 35 kPa, what is the Mach number at the nozzle exit?
c) In a different scenario, the turbine exit pressure is 70 kPa. What is the
Mach number of the flow at the nozzle exit? Also determine the Mach
number at the nozzle inlet.
d) The turbo-machinery team within the company have asked you to
specify what exit pressure of the turbines results in perfectly expanded
flow, with minimal expansion and compression waves outside the
nozzle. What is this turbine exit pressure?
p=26.5 kPa
T=223 K
capture
streamtube
100 m
combustion
compressor chamber turbine nozzle
nozzle
nozzle
inlet.
exit.
x=0.0 m
x=1.5 m
Figure Q4: Diagram of turbojet engine
p=26.5 kPa
T=223 K
Transcribed Image Text:4. You are responsible for the design of the convergent nozzle for a turbojet engine fitted to a civil aircraft, as shown in Figure Q4. During operation at an altitude of 10,000 m, the aircraft flies at 300 m/s and the flow exhausts to atmosphere, where the pressure is 26.5 kPa and the temperature is 223 K. In this question, you should treat the flow as quasi-one-dimensional and inviscid. a) The radius of the nozzle satisfies the equation R(x) = 2-0.44x² where both x and R are expressed in metres. What is the area ratio between the nozzle inlet (x = 0.0 m) and the nozzle exit (x = 1.5 m)? b) The turbine exit temperature is the stagnation temperature, To = 400 K, of the flow in the nozzle. Similarly, the turbine exit pressure is the stagnation pressure, Po, of the flow in the nozzle. When the turbine exit pressure is 35 kPa, what is the Mach number at the nozzle exit? c) In a different scenario, the turbine exit pressure is 70 kPa. What is the Mach number of the flow at the nozzle exit? Also determine the Mach number at the nozzle inlet. d) The turbo-machinery team within the company have asked you to specify what exit pressure of the turbines results in perfectly expanded flow, with minimal expansion and compression waves outside the nozzle. What is this turbine exit pressure? p=26.5 kPa T=223 K capture streamtube 100 m combustion compressor chamber turbine nozzle nozzle nozzle inlet. exit. x=0.0 m x=1.5 m Figure Q4: Diagram of turbojet engine p=26.5 kPa T=223 K
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