University Thermodynamics- Turbojet

In summary, to calculate the turbine inlet temperature (T4) in a single spool, axial flow turbojet, you will need to use the energy equation and the specific heat capacities of the air. First, calculate T3 using the given information and then use it to calculate T4 using the energy equation.
  • #1
andymarra
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Hello, I am currently revising for a thermodynamics resit exam and I cannot get past a certain part in a turbojet question from a past paper. This is the past paper which I failed a few months ago and still can't understand it. Any help would be appreciated.

A single spool, axial flow turbojet propels an aircraft at a cruise Mach number of 1.8 at
an altitude where the ambient pressure and temperature are 0.116 bar and 216K. The air
mass flow rate through the gas turbine is 20kgs−1, the rate of fuel consumption is 0.2kgs−1
and auxiliary devices take 100kW of power from the turbine. The compressor pressure
ratio is 3.0. The turbojet has component isentropic efficiencies as follows: intake, 0.92;
compressor, 0.93; turbine, 0.94; nozzle, 0.97. Determine the following:

i) Flight speed in ms−1;
(answer Ua = 530ms−1)
ii) Compressor entry temperature and intake pressure ratio;
(answers T2 = 356K, p2/p1= 5.138)
iii) Compressor power;
(answer 2.83MW)
iv) Turbine inlet temperature, and the turbine pressure ratio;
(answers T4 = 923K, p4/p5= 1.915)

Its the turbine inlet temp that I can't work out, i can work out the first parts fine. Basically, I am unsure of how to work out T4 by using the information given in the question.
Any help appreciated!
Regards, Andy
 
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  • #2
To calculate the turbine inlet temperature, you will need to use the information from the question as well as the energy equation. The energy equation states that the change in enthalpy of the air flow is equal to the work done by the turbine plus the power taken away by the auxiliary devices. Assuming ideal isentropic efficiencies for all components and no losses, you can use the following equation to calculate the turbine inlet temperature (T4): T4 = T3 + (h5-h3)/CpWhere Cp is the specific heat capacity at constant pressure of the air. Using the information given in the question, you can then calculate T4. First, calculate T3 using the equation: T3 = T2 * (P3/P2)^((γ-1)/γ)Where γ is the ratio of specific heats. Then calculate h3 and h5 using the equation: h = cv * T + (γ/(γ-1)) * PWhere cv is the specific heat capacity at constant volume of the air. Finally, substitute all the values into the equation above and calculate T4.
 

FAQ: University Thermodynamics- Turbojet

1. What is the purpose of studying thermodynamics in relation to turbojet engines?

The study of thermodynamics is essential for understanding the principles behind how turbojet engines work. This knowledge is used to design, analyze, and improve the performance of these engines. It also helps to identify potential problems and develop solutions to increase efficiency and reduce emissions.

2. How does a turbojet engine use thermodynamics to produce thrust?

A turbojet engine uses the principles of thermodynamics to convert the energy from fuel combustion into mechanical energy, which is then used to power the compressor and turbine. This mechanical energy is then converted into thrust by accelerating the air flowing through the engine, according to Newton's third law of motion.

3. What is the role of entropy in a turbojet engine?

Entropy is a measure of the disorder or randomness in a system. In a turbojet engine, it plays a crucial role in the combustion process by determining the direction and availability of energy transfer. The goal is to minimize entropy to maximize the efficiency of the engine.

4. How does the Second Law of Thermodynamics apply to turbojet engines?

The Second Law of Thermodynamics states that in any energy conversion process, some energy will always be lost as heat. In the case of a turbojet engine, this means that some energy will be lost due to friction and inefficiencies in the conversion of heat into mechanical energy. This law is essential in understanding and improving the efficiency of turbojet engines.

5. What are some common applications of thermodynamics in the design and operation of turbojet engines?

Thermodynamics is used in various aspects of turbojet engine design and operation, such as determining the compression ratio, calculating the specific fuel consumption, and predicting the performance of the engine at different altitudes and speeds. It is also used to analyze the effects of different components and materials on the overall efficiency and performance of the engine.

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