Lecture T7: Heat Engines: The Otto Cycle & The Brayton Cycle


General comments

The lecture focused on applying the thermodynamic tools we have been discussing to estimating the performance (work and efficiency) of heat engines. We will only model ideal performance in this class (no friction, no unrestrained expansion, no heat loss where it isn't desired, etc.). In 16.050 you will develop higher fidelity models that take account of these effects. After concluding the discussion of the Otto cycle, we did one PRS problem which was designed to show that different engines will be represented by different thermodynamic processes. This will affect the work output and the efficiency.

Then we discussed the Brayton cycle as a model for the thermodynamic processes a small chunk of gas experiences when passing through a gas turbine engine. As with the Otto cycle, we used the following solution process: a) identify thermodynamic processes to represent the behavior, b) plot the processes on a p-v diagram, c) identify the flows of heat and work for each leg of the cycle, d) calculate the net work for the cycle and the efficiency, and e) re-write these expressions in terms of common design parameters. The Brayton cycle provides an example of two convenient short cuts. The first is using the net flow of heat instead of calculating the net work (since the two are equal for a cyclic process). The second is using the first law written in terms of enthalpy to evaluate changes for constant pressure processes.

After working through these two examples I described some of the features and pieces and part of the CFM56 engine. It is not expected that you will absorb all of these details which we will have the opportunity to spend more time on in the spring semester. Foir now just remember the basics of the operation of a gas turbine engine: adiabatic compression with a set of spinning blade rows, constant pressure heat addition in a combustor, adiabatic expansion in the turbine (which drives the compressor), and further expansion in the exhaust nozzle, then in the atmosphere, constant pressure cooling.

I thought I had enough copies of the engine diagram, but I did not. For those who did not get a copy, here is a .pdf file for the CFM56 cross-sections.

Responses to 'Muddiest Part of the Lecture Cards'

(52 respondents out of 68 students in class)

1) Is the heating and cooling (legs 2-3 and 4-1) in the IC engine and the gas turbine the same as Qin and Qout? (1 student) Yes, since the other legs in the two cycles are adiabatic. But in other cycles, heat may be transferred on more than two legs.

2) Is the pressure ratio P * r where r=v1/v2? -- and related questions (2 students) No. The pressure ratio is p2/p1 (used for Brayton cycles). The compression ratio is v1/v2 (used for Otto cycles).

3)Please define design parameters? (1 student) These are simply useful quantities that are related more directly to design features than T's and p's may be. For example, typical design parameters for a gas turbine are the mass flow through the engine, the compressor pressure ratio and the peak temperature in the cycle.

4) I did miss out on a few points about what each part of the engine does. Where can I find this info best presented? --and related questions (3 students) We will talk about it more in lecture (and you will see it repeated on the homework). For additional reading, I recommend Hill and Peterson (Fundamentals of Jet Propulsion), on reserve in the library. There is also a great book by Rolls-Royce called The Jet Engine. I am not sure if the library has this on reserve or not, but I will check.

5)Why is Q>0 for a constant pressure expansion? (1 student) You can show this with the first law, or you can tell by looking at a p-v diagram by whether the process has a steeper or shallower slop than an adiabat (line of no heat transfer). If the slope is shallower then heat is added, if steeper then the heat is removed.

6) How do you go from the Brayton cycle efficiency in terms of T1/T2 to the expression in terms of the pressure ratio? -- and related questions (3 students). Start by substituting pv^g=constant then use the ideal gas law. The steps are shown in the notes.

7) Who makes the hollow blades? (1 student) Typically the same companies that make the engines (e.g. Pratt & Whitney, General Electric Aircraft Engines, and Rolls-Royce).

8) Does the afterburner use combustion again? --and related questions. (3 students) Yes it does, lots of it. In the afterburner, additional fuel is sprayed into the flow and then burned (increasing the internal energy of the gas). The increased internal energy is then converted to increased kinetic energy in the exhaust nozzle, producing a large increase in thrust. This would be modeled as a second constant pressure heating leg part way through the expansion process.

9) How does the shroud of cool air around the blades in the high temperature flow affect engine performance? (1 student) There is a large penalty in complexity, cost and some detriments to efficiency. But these negative effects are more than outweighed by the positive effects of being able to run the cycle hotter (more work per unit mass flow, higher compression ratios, etc.), as evidenced by the wide use of such cooling schemes in modern gas turbine engines.

10) What is the temperature change for an adiabatic process? (1 student) For an adiabatic process, q = 0, but the temperature will change if there is any work done (Du=-w for a q-s adiabatic process).

11) What stage is air taken from to cool the turbine? (1 student) Typically from the last stage for cooling the first turbine stage (since the pressures are similar. For later stages in the turbine where the pressure is lower, the cooling air can be taken from earlier stages in the compressor.

12) Can I assume Qcycle/Qin = thermal efficiency for all processes? (1 student) Not for all processes, but for all cycles, yes. Only for a cycle (a closed loop on a thermodynamic diagram) does Wcycle=Qcycle (since Du = 0).

13) Why is the diesel cycle better modeled with a constant pressure heat addition? (1 student)

14) Where can I see a more dynamic or visual demonstration of a gas turbine engine? (1 student) An airplane? Just kidding. I will see if I can find a good video to show if we have time in one of the later recitations.

15) It would be helpful to have more practice problems. I would also like a quick summary of the tools (equations) we have and what they are for. (1 student) I will try to do both in recitation.

16) What is the relationship between pressure ratios (or compression ratios) and efficiency? (1 student) These are given in the notes for the Brayton and Otto cycles.

17) What does it take to start an engine? (1 student) Most gas turbine engines are started by a geared shaft powered by a very small gas turbine called an APU (auxillery power unit).

18)In general, does every engine cycle start off with a quasi-static adiabatic expansion? (1 student) No. Just the two we have looked at.

19) Does q=cpDT for any constant pressure adiabatic process? (1 student) No. Just the one involving an ideal gas.

20) How does dp go to zero in the cycle analysis even though there is a change in pressure for two legs? (1 student) I only set dp=0 for the two constant pressure legs.

21) No mud (24 students). Very good.