Lecture T10: Stagnation Quantities

I was pleased with the lecture. The performance on the first two PRS (1st, 2nd) questions was quite good. I think that most people understood (physically) why the internal energy of a chunk of gas increases if that chunk of gas stagnates on the surface of a high speed body. The performance on the last PRS question (3rd) was not as good. Some of this was related to difficulty with the terminology--T vs. T1 vs. TT1 vs. Tatm vs. TTatm. This problem is discussed in some detail in the notes. Please review it.

Thanks for the donuts (many students). You are welcome. We will try to make it a semi-regular thing.

Can SP's be due at 9:10 so that we won't miss the deadline if we are 1 minute late? (1 student) No. We would like you to be in class on time and to turn them in on time. This sounds a little harse, but the policy comes from many years experience in Unified. Granting short extensions for unqualified reasons is a slippery slope. It is much easier and more effective to have a very firm deadline. If it is in, it is in. If it is not, it is not.

Responses to 'Muddiest Part of the Lecture Cards'

(57 respondents)

1) Go over Chapter 6 Question #2 again (1 student). Please read the T9 mud responses.

2) If "everything else" is shaft work, how do we tell what part of the work actually goes to spinning the shaft? (1 student) The terminology is confusing. Flow work is p2v2-p1v1. Total work minus flow work is equal to external work. Many times in heat engines, this external work comes about as a result of a shaft spinning a set of blades so the external work is called shaft work. I have re-written the section of the notes to make this clearer. If there was a situation where there were multiple forms of external work (say a shaft and wires delivering electrical power), you would need to be given some additional information to know how much of the external work was accounted for by the different sources.

3) I was confused by the first PRS question. Why is all the work negative? And wouldn't the flow work end up being zero since it's q-s and pv^g=constant? (1 student) The total work and the shaft work are negative because it is a compression process (work done on system). The flow work is positive. The flow work is zero for an isothermal process but not an adiabatic process. For flow work to be zero p2v2=p1v1. There is an extra gamma floating around for the quasi-static adiabatic process. How can you cancel the c expressions of the first PRS problem? (1 student) The problem statement says to neglect changes in kinetic energy.

4) TT versus T1, T2. Why did they randomly replace T2 with TT? (1 student) It wasn't done randomly. If location (2) is a place where the flow is stagnated (so that c2=0) then we call T2 the stagnation temperature and give it the general symbol TT. which stands for "total" or "stagnation" temperature.

5) Stagnation vs. Stagnant (1 student) You didn't listen to what I said carefully. The two words that have similar meanings in common language, but very different meanings in fluids and thermo are "stagnation" and "static".

6) Still confused about stagnation and static quantities and the dependence of stagnation quantities on reference frame. (22 students) Please read over the notes a few times. Also read the discussions I give below. Then ask me more questions--via email, in class, more mud cards, etc.

7) So what you are saying with regards to stagnation temperature is that when something is moving and it stops its temp goes up, and when something is stopped and then it starts moving it goes down? Yes, if that something is a compressible fluid. And the reason the plane's aluminum skin goes up is because with regard to the plane the air is moving towards it (even though it is the plane that is moving) and then stops?? ( 1 student) Yes.

8) How can a particle be accelerated to a given speed without work? How did the chunk of gas in the example get to position (1) if no work was done on it? and related questions (3 students) There is work, but it is flow work, not external work. Remember, our control volume is defined by a set of streamlines. Between the inlet and the outlet of the streamlines the velocity of the flow changes, but it does this without heat transfer and without external work. Remember work is the transfer of energy across a system boundary. It is when it crosses the system boundary that we label and identify it.

9) Stagnation temperature. Is air really not moving on the leading edge of the wing? If this is the only place this happens why does the whole wing heat up? (1 student) Fluids stagnate on every surface they meet. A boundary layer (see discussion above) forms over every surface of the body.

10) Can you explain the case of the engine of the parked aircraft? I am muddy on the subscripts? (1 student) Read the explanation given in the notes. If it is still unclear, please let me know.

11) I am unclear as to why the leading edge of the wing heats up in the first example, then later you said temperature drops over the wing causing the condensation trails. How can it get hotter and colder at the same time? (1 student) This is a very good question. It does get hotter and colder at the same time. Just not in the same place. The flow very close to the body gets hotter, the flow farther from the body gets cooler. You need to know a little more about fluids before the answer is clear. There are two different processes going on. The first is like the example of the engine sitting motionless on the ground drawing in air--the (static) temperature and (static) pressure drop. The second is like the example of the skin temperature of a supersonic airplane being significantly elevated above the ambient atmospheric temperature. In the first case, no energy is added to the flow; energy is just converted from internal energy to kinetic energy. In the second case, energy is added to the flow. Now let us discuss why this happens.

PROCESS 1:When a body moves through a fluid it creates a disturbance. That is, it changes the velocity, pressure and temperature of the flow around it. It tells the flow "Get out of my way, I am coming through!" This disturbance is felt some distance away from the body (a distance of about two times the characteristic physical dimension of the body). You can think of this like the bow wave in front of a boat, the water starts to move out of the way before the boat gets there. This information is transmitted upstream of the body at the speed of sound. So for a supersonic body (one traveling faster than the speed of sound), the flow doesn't know to get out of the way sometimes until the body has passed (it happens when the shockwave passes through the region of flow). There is no external work done in causing the flow to move (there can be flow work). So the total energy of the flow is the same. When it moves to get out of the way, the kinetic energy must come from somewhere. It comes from the internal energy (or more appropriately, the enthalpy since stagnation enthalpy is the conserved quantity for these processes) and thus the temperature and pressure are reduced.

PROCESS 2: For the flow very close to the body (within an inch or so of the surface for a large airplane), the body adds energy to the flow. That is it pulls it along with it. We discussed this in lecture T1 and in a PRS question. Some number of molecules very close to the surface of the body stick to the body. They in turn pull on the particles next to them. This is exactly the same mechanism by which honey sticks to a spoon. The more viscous the fluid, the stickier it is and the more molecules get pulled along with the body (compare how much honey sticks to a spoon--to how much water sticks to a spoon--to how much air sticks to a spoon). What develops is something called a boundary layer. So the velocity very near the surface of the body looks like the sketch shown below. The thickness of the boundary layer depends on how viscous the fluid is, on how fast the body is moving, and on the distance from the leading edge of the body. The boundary layer is thicker the more viscous the fluid is, thinner the faster the body is moving, and thicker the longer the distance from the leading edge. By dimensional analysis you can see that the thickness of the boundary layer is proportional to sqrt(nx/c) where n is the kinematic viscosity (units=m^2/s), x is the distance from the leading edge of the body and c is the speed of the body. So to cause the flow to stagnate on a body (move at the same speed as the body) kinetic energy must be added, thus raising the total energy of the flow.

12) With the engine, why doesn't the flow stagnate on the blades of the compressor? (1 student) It does.

13) I was just wondering if when you breathe in it feels cold because you are adding kinetic energy to the air and decreasing internal energy, or is it just because of the temperature difference between your mouth and the air? (1 student) Breathing in is similar to the gas turbine engine problem. The stagnation tempereature on your tounge is the same as the temperature in the atmosphere (this of course can be different from your body temperature). It feels colder when you breathe in (versus when you open your mouth without breathing) because the moving flow increases the rate of heat transfer from your tounge. This is why you blow on icecream to warm it up faster and why you blow on soup to cool it off faster.

14) What causes contrails to form and what causes "bridges to freeze before the road"? (1 student) Contrail form because one of the primary products of hydrocarbon combustion is water. So airplanes leave a trail of water behind them (which sometimes condenses depending on the local temperature of the atmosphere). Bridges freeze before roads, because they are not in contact with the ground (which can have significant thermal inertia and thus cool at a slower rate).

15) No mud (13 students). Good.