Calculating Combustion Energy for Turbojet and Turbofan Engines

[vincentryan]

How to determine the amount of combustion energy to provide the thrust in turbojet and turbofan engine?



and in the following example
How much of combustion Energy is Provided for the thrust?

A jet aircraft moves with a velocity of 200 m/s where the air temperature is 20°C and the pressure is 101 kPa. The inlet and exit areas of the turbojet engine of the aircraft are 1 m2 and 0.6 m2, respectively. It is known that the exit jet nozzle velocity is 1522 m/s (from lab calculation) if the exhaust gases expand to 101 kPa at a temperature of 1,000°C. The mass flow rates of the inlet and exhaust flow are 240 kg/s and 252 kg/s, respectively. As a thermal engineer, your task is to (a) determine if the temperature of the exhaust gases is too high for the turbine blades as they exit from the combustion chamber. (b) Determine the amount of combustion energy necessary to provide the thrust. The maximum tolerable temperature of the blades is 3,000 K. It is known that the pressure ratio of the multi-stage compressor is 8 to 1.

Assumptions and simplifications:
neglect all losses and irreversibilities. All processes are isentropic.
Neglect all kinetic energy components except at the inlet and the nozzle.
Air and fuel mixture behaves as an ideal gas and has the same thermal properties as the air.
All shaft works produced by the turbine are used to drive the compressor.
Air (& mixture) has a constant CP=1 kJ/kg.K, and k=1.4

 

[Navin A S]

.(a) The theoretical temperature of the exhaust gases is 1000°C. This is below the maximum tolerable temperature of 3,000 K, so the temperature of the exhaust gases is not too high for the turbine blades.(b) The amount of combustion energy necessary to provide the thrust can be calculated using the following equation: Thrust (F) = m_dot * (V_exit - V_inlet) + 0.5 * (P_exit * A_exit – P_inlet * A_inlet)where m_dot is the mass flow rate, V_exit and V_inlet are the exit and inlet velocities, A_exit and A_inlet are the exit and inlet areas, and P_exit and P_inlet are the exit and inlet pressures. Substituting the given values:F = 240 kg/s * (1522 m/s - 200 m/s) + 0.5 * (101 kPa * 0.6 m2 - 101 kPa * 1 m2)F = 119,904 N The amount of combustion energy necessary to provide the thrust is119,904 N * (1522 m/s - 200 m/s) = 1.65 x 10^7 J