This assignment is intended to introduce you to the theory of gas turbine propulsion. The theory of the most simple gas turbine aircraft engine, the ideal turbojet, is detailed in the lecture notes and in the appendix of this handout.

In marking this assignment, I am looking for evidence that the students understand clearly the fundamentals of thermodynamics and its implications. Clear argument and concise answers will be rewarded.

Background

A turbojet engine consists of the following components: 

(1-2)  Inlet or "diffuser"   Isentropic deceleration of the air for entry into the engine 

(2-3)  Compressor            Increases the stagnation pressure and stagnation temperature 

(3-4)  Combustor/burner  Adds energy to the flow via the combustion of fuel 

(4-5)  Turbine                    Extracts work from the flow in order to drive the compressor 

(5-9)  Outlet nozzle           accelerates the flow, thus increasing the thrust.  Decreases static  pressure of flow to that of the free stream.  NOTE: can be converging, or converging-diverging nozzle. 

 Questions Format your report such that each numbered item below is repeated in the report, followed by your answer.

1. Derive an equation that determines T_t4 from the measured data.

2. Plot the calculated turbine inlet temperature T_t4 versus engine speed.

3. Are the results for T_t4 reasonable given typical material temperature limits?

4. Derive an equation that determines the exhaust velocity, u₉ from the measured data.

5. Plot u₉ versus engine speed.

6. The exhaust velocity, u₉ reaches values higher than 340 m/s, which is the speed of sound at sea level in the Earth's atmosphere. How are these velocities achieved given that the engine only has a convergent nozzle?

 7. On the same graph, plot the measured and ideal thrust of the engine versus the measured engine speeds.

8. A formula for the specific thrust (and its derivation) is given in the appendix. Re-derive the specific thrust equation for a turbojet whose compressor and turbine have isentropic efficiencies of η_c and η_t respectively

9. What are realistic values of η_c and η_t for the micro turbojet? Using these values and your equation from Q8, recalculate the thrust of the engine, plotting the data on your graph from Q7.

10. How do the theoretical results for thrust (from both Q7 and Q9) compare with the measured data? Comment on the most likely reasons for any differences.