**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.

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.

5)* What exactly is a turbine?*
(4 students) There is some confusion about the terms. A

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.

8) * Efficiency is unitless
right?* Yes.

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).

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.