A jet engine for a supersonic transport (SST) propels the airplane at Mach 3 at an altitude of 50,000 ft where the temperature i
s 217°K and the ambient pressure is 0.115 atm. The maximum temperature that the advanced turbine blades can handle is 1900°K. The engine operates at a compressor pressure ratio that allows the engine to achieve maximum work. The temperature at the entrance to the compressor is 595.7K. Assume that γ = 1.4 and Cp = 1004 J/kg-°K throughout the engine. If the engine inlet isentropically slows down the incoming freestream air such that the Mach number of the flow just upstream of the compressor is 0.3,
a) How many stages should the aircraft engine compressor have if the compression pressure ratio of each stage is 1.2? b) Please plot the cycle on a T-s diagram labeling only the temperature at each point? c) What is the thermal efficiency of the engine? d) What is the absolute highest possible thermal efficiency one can expect from a machine operating within the range of temperatures involved in this problem? e) What is the amount of heat per unit mass of working fluid that is needed to be generated by the combustion of fuel in the engine burner?
a) How many stages should the aircraft engine compressor have if the compression pressure ratio of each stage is 1.2? b) Please plot the cycle on a T-s diagram labeling only the temperature at each point? c) What is the thermal efficiency of the engine? d) What is the absolute highest possible thermal efficiency one can expect from a machine operating within the range of temperatures involved in this problem? e) What is the amount of heat per unit mass of working fluid that is needed to be generated by the combustion of fuel in the engine burner?
1 answer:
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Answer:
The answer is as given in the explanation.
Explanation:
The 1st thing to notice is the assumptions required. Thus as the diameter of the cylinder and the wind tunnel are given such that the difference is of the orders of the magnitude thus the assumptions as given below are validated.
- Flow is entirely laminar, there's no boundary layer release.
- Flow is streamlined, ie, it follows the geometrical path imposed by the curvature.
By D'alembert's paradox, "The net pressure drag exerted on a circular cylinder that moves in an inviscid fluid of large extent is identically zero".Just in the surface of the cylinder, the velocity profile can be given in the next equation:
And the pressure P on the surface of cylinder is given by Bernoulli's equation along the streamline through that point:
where P_∞ is Pressure at stagnation point, U is the velocity given, ρ is the density of the fluid (in this case air) and θ is the angle measured from the center of cylinder to the adjacent point where your pressure point will be determine.
