Lecture T8: The Brayton Cycle and the Steady Flow Energy Equation


General comments

The lecture focused on 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. We concluded this part of the lecture with a PRS question designed to reinforce the thermodynamic representation of the various pocesses occuring in an engine.

Gas turbine engines are pretty bitchin' (1 student) You are correct.

Responses to 'Muddiest Part of the Lecture Cards'

(47 respondents out of 63 students)

1) q2-3 = cp (T3-T2): Why T3-T2 instead of T2 - T3? and the same question for Q4-1?(2 students) It should match our sign convention. That is, it should give a positive number if heat is added to the system (T3 >T2).

2) How do you get Qin and Qout? (1 student) Using the first law for the process steps involving heat transfer. Why does Wcycle=Qin + Qout? (1 student). Because it is a cycle so the net work must balance the net heat flow.

3) I am confused how you determine whether a process is going to be adiabatic, isothermal or isobaric. (1 student) It depends on the behavior of the device being modeled. In general, I will specifiy this or try to give you enough information to make an informed judgement.

4) When using the du and dh first law equations what do we do if neither the pressure nor the volume are constant? (1 student) Then you will have to integrate either pdv (if using the internal energy equation) or vdp (if using the form of the equation with enthalpy), just like we did for the isothermal work expression. For a constant pressure process is dh=delq? (1 student) Yes.

5)What exactly is a turbine? (4 students) There is some confusion about the terms. A gas turbine engine is the whole engine. The turbine is a set of rotating and stationary airfoils that extract work from the flow (we will learn how this is done in the spring). In a gas turbine engine, the turbine is used to drive the compressor (they are connected by a shaft).

6) What does the combustor do? (1 student) It converts chemical energy to thermal energy (adding heat to the flow).

7) wcycle=function of (p2/p1 or T2/T1) and efficiency = function of (T2/T1), are these just for a Brayton cycle. (1 student) Yes. Why is the efficiency only based on temperature when the equation is simplified? It seems kind of odd that T is the only thing it depends on. (2 students) Odd but true, at least for ideal cycles. For real cycles it depends on many other parameters. What is a nominal cycle efficiency for a gas turbine? (1 student) You will calculate this on the homework. The ideal efficiency is around 50%. Real efficiencies are about half to 2/3rds of this. Why is wcycle = delta-hcycle? (1 student) This is only true for a Brayton cycle.

8) Efficiency is unitless right? Yes. In the enthalpy derivation, where did the pdv go? (1 student) It canceled with the work term, leaving vdp as shown in the notes.

9) How do you figure the Q and W by just looking at the p-v diagram? (1 student) If the volume goes up, the work is positive. If the volume goes down, it is negative. Heat transfer to and from the system can be determined then either from applying the first law or by comparing the thermodynamic process curve to a line of zero heat transfer (an adiabat). If the process crosses over adiabats, the heat is being transferred. Depending on the direction it is going, you can determine whether heat is added or removed.

10) I am still confused about finding the work in an adiabatic expansion or compression. Are the volume, pressure and temperature all changing? (1 student) Yes they are (as shown in the notes).

11) It seems that from 2-3 (in the Brayton cycle) there would be a small increase in pressure needed as a force to drive the turbine. ... could you approximately label where the work for the compressor is done on the 3-4 process? (1 student) The pressure actually drops about 5% through the combustor (although we model it as constant pressure). What is required to drive the turbine is a high speed flow (i.e. converting internal energy into kinetic energy with a nozzle). We will learn about this in the spring. Relative to the second question, it is possible to label the part of the 3-4 process that accounts for the compressor work -- the shaft work has to be equal to the shaft work from the compressor -- you will do this as part of a homework assignment.

12) Can you go over what the thermodynamic functions of the various components are? (1 student) This is described briefly in the notes. If you would like to discuss it in more detail, please see me.

13) In terms of equations, how do we get from the first law in terms of du to the first law in terms of dh? (1 student) This is described in the notes.

14) How do we know for sure that in a gas turbine engine, our system (which is the gas) in its last stages, bequeaths more of its energy to the vehicle that to the atmosphere? (1 student) You don't know for sure. It is possible to design a poorly performing gas turbine where the work extracted in the turbine is not enough to power the compressor (so in order to keep it running it needs additional work input--like a continuously running starter). This is called "not closing the cycle". On the very first microengines we are building we are in danger of not closing the cycle (the performance of the individual components is so poor).

15) How can work be done by the gas after expulsion from the engine? (3 students) Good question. From the perspective of the engine, it continuously receives cold gas in the inlet and continuously expels hot gas in the exhaust.The work done during constant pressure heating or cooling is what is called "flow work" rather than "shaft work". It is the work the flow does against the atmosphere in compressing or expanding. So where the work appears in nature is that the gas that comes out of the engine occupies a larger volume than the gas that comes into the engine. So there is some net displacement of volume at constant pressure (i.e. work). Why is work positive from step 4 to step 1? (1 student) The work is negative. The system (the chunk of gas) gets smaller.

16) Why (on the cycle diagram) is the work for the compressor at constant pressure? (1 student) It isn't. The combustor is constant pressure. The compressor is quasi-static, adiabatic compression.

17) For the power plant, how can you get chilled water from a hot exhaust? (1 student) This is described at http://cogen.mit.edu.

18) Since the compression and expansion in jet engines is adiabatic, does this mean that the waste heat absorbed by the engine is all from the burning, or is the adiabatic label just an idealization? (1 student) Compared to the energy flows in a gas turbine engine, the energy absorbed by the structure itself is very small, but this comes from a variety of sources (compressor, turbine, combustor, outside air, etc.).

19) To change the ratio of work done compressing the gas to work received in the turbine, the fan blade pitch is changed, right? Or do you use more turbines? (1 student) The turbine is connected to the compressor with a shaft, so the ratio of the work is one. However, if you want to extract additional workin excess of that used to drive the compressor, a second turbine (a power turbine) can be used.

20) The language throws off of what combustion turbine and so forth do, should just call it by processes. (1 student) I am not sure I understand your point, but part of learning about thermodynamics and propulsion is learning the common terminology (even if it is sometimes confusing).

21) The problem set took me a long time to do...are we going to do problems that will take that much time in the future? (1 student) We collect and take action on the average of the "time spent" data. However, there are always high time and low time students. The assignments will be of similar magnitude in the future (unless the average time spent creeps up). If you are spending a lot of time, please see me early in the week and I can help walk you through the problems to ease the time crunch.

22) Why are the images of the equations on the site so small? (1 student) Because I converted them from a Word document with out going through and re-scaling them. Sometime, I will pay somebody to do this.

23) No mud (11 students). Good.