Question

Air enters the diffuser of a ramjet engine at 22 kPa, 228 K and a velocity of 920 m/s, decelerating to a negligible velocity at the point at which heat is added. Using cold airstandard analysis with constant specific heats at 300K, determine the following if the exit pressure is 22 kPa and heat is added at 750 kJ per kg of air:
(a) The pressure at the diffuser exit, in kPa.

(b) The velocity at the nozzle exit, in m/s.

(c) If the fuel used requires a temperature of 900K to auto-ignite, is the craft moving fast enough to use this fuel? If not, what minimum speed must it be moving such that the air temperature after compression will ignite the fuel?

Answer 1

Solution :-

Given - V_a = 920 m/s, T_i = 228 K, P_i = 22 KPa

Q = 22KJ/Kg

a) Calculation:- let

Now we can calculate Match Number for entering position of air as follows -

V_a = M_a

_{^{Substituting all the values and we get-}}

M_a = 920 /302.67

M_a = 3.03 approx 3

Now we can calculate the exit pressure at diffuser by-

Substituting all the values and we get -

P_o = P_i /0.0272

P_o = 808.8 KPa

The pressure at the exit of diffuser is 808.8 KPa.

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b) Calculation:- Exit velocity of Nozzle -

Match number at nozzle exit -

Substituting all the values and we get -

M_e = 0.47

exit velocity, V_e = M_e

V_e = 230 m/s

The exit velocity at nozzle is 230 m/s.

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c) In a Ramjet engine at 900 K the auto ignite fuel will affect the efficiency of engine, because Ramjet engine requires the mixture of air and fuel.

the minimum speed can be calculated by -

V = M_e

V = 282.6 m/s

Velocity of engien at temperature 900K is 282.6 m/s.