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, u_{9} from the measured data.
5. Plot u_{9} versus engine speed.
6. The exhaust velocity, u_{9} 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.