An aircraft is operating at an altitude of 20,000 feet (6.1 km) where the ambien

Question

An aircraft is operating at an altitude of 20,000 feet (6.1 km) where the ambient pressure is

46.5 kPa. The engine nozzle exit (exit area A7=0.116m2) is choked (M7=1, with ?7=1.33) and

the pressure and temperature at the nozzle exit are p7=62.1kPa and T7=810.8 K. Assume

that R=287 J/kg-K throughout the engine. Determine the following:

a) The force exerted on the engine due to the exhaust gases alone (i.e. neglect m0u0).

b) The percentage this force (from (a)) that is due to the pressure imbalance at the nozzle

exit.

c) The exit mass flow rate.

d) The

Explanation / Answer

Static temperature at nozzle exit (given) = 810.8 K

Speed of sound at nozzle exit = sqrt(gamma*R*T)

= sqrt(1.33*287*810.8)

= 556.32 m/sec

As, exit mach number is 1

So, exit velocity = 1 * 556.32 = 556.32 m/sec

Density of air at exit = P / (RT) = (62.1*10^3) / (287*810.8) = 0.2668 Kg/m^3

Mass flow pew second= density*velocity*area = 0.2668*556.32*0.116 = 17.22 Kg/sec

Thrust due to exhaust gases alone = 17.22*556.32

= 9580.83 N

Pressure thrust = exit area*(exit pressure - ambient pressure)

= 0.116*[(62.1*10^3) - (46.5*10^3)]

= 1809.6 N

% of pressure thrust = 1809.6/9580.83 = 0.188 = 18.88 %

Ram drag = mo*uo = 17.22*167.64

= 2886.76 N

Net thrust = Exhaust gas thrust + pressure thrust - Ram drag

= 9580.83 + 1809.6 - 2886.76

= 8503.67 N

Thrust power produced = thrust*uo

= 8503.67*167.64

= 1425555.2 watts

= 1425.5 kW

Propulsive efficiency = thrust power / change in KE of air

= 1425555.2 / 0.5*17.22*(556.32^2 - 167.64^2)

= 0.588 or 58.8%

mass of fuel burned = f * mass of air

= 0.02*17.22

= 0.344 Kg/sec

Thermal efficiency = change in KE of air / Heat inpiut

= 0.5*17.22*(556.32^2 - 167.64^2) / (0.344*44000000)

= 0.16 or 16%

Reason for low thermal efficiency is that the nozzle is underexpanded.

Overall efficiency = Propulsive efficiency * Thermal efficiency

= 0.588*0.16

= 0.0941 or 9.41%

Specific Impulse = Total thrust / mass flow rate

= 8503.67 / 17.22

= 493.82 N/Kgsec

TSFC = mass of fuel/Thrust

= 0.344/8503.67

= 4.045*10^-5 Kg/Nsec

= 0.145 Kg/Nhr

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