**General comments**

The lecture reviewed the material presented in T12 regarding stagnation properties, and then continued with four different example problems (one, two , three, four). Each of these illustrates the basics of the frame dependence of the stagnation quantities. Please read over the explanations of these problems. Remember, the following points. 1) You can only apply the steady flow energy equation in a reference frame where the flow appears as steady. 2) Flows stagnate on surfaces. 3)If two points are not moving relative to one-another (i.e. they are in the same reference frame), and the flow moves from one point to another without heat addition or external work, then the total enthalpy is constant and the stagnation temperatures at the two points are the same. 4) If a flow moves without heat addition or external work, the enthalpy is reduced ( and the temperature along with it) as the kinetic energy is increased (because total enthalpy is constant). 5) If a reference frame is moving relative to a stationary frame, flows that stagnate in the moving frame have a higher stagnation temperature (the stagnation or total enthalpy in the moving frame is higher).

**Responses to 'Muddiest Part of the Lecture Cards'**

(33 respondents out of 64 students in class)

1) * General fuzziness about frame dependency,
unclear about 3 PRS at end, and related questions*. (30 students
more or less) You have a lot of company. We will work on this more in recitation.
I will make a few comments below and answer a few of the specific questions
which I think may be particularly enlightening.

**First,** the rotor
blade and supersonic
airplane examples (they are the same case--instead of blades spinning around,
think of tiny supersonic airplanes spinning around in the engine). There are
two ways to think about the problems. First, in the reference frame of the blade
or the airplane. They see flow coming at them with kinetic energy associated
with the moving flow, and with an internal energy (or more appropriately enthalpy)
associated with its temperature far away in the atmosphere. When the flow is
stagnated on the blade, both of these sum into the stagnation enthalpy. Thus
the temperature is higher than the ambient temperature. The second way to look
at it is in the fixed reference frame (not moving with respect to the atmosphere).
In this case the flow has some stagnation temperature as it comes in the inlet
which is equal to the ambient atmospheric temperature. Then the blade or airplane
comes along and the fluid sticks to the blade or airplane (work is done on the
fluid particle) gaining kinetic energy. Thus the total or stagnation temperature
on the surface of the blade is greater than the stagnation temperature the flow
had when coming in the inlet. But this is an unsteady problem (the blades and
the airplane are moving), so you can only think about it this way conceptually
-- you can't apply the steady flow energy equation in this frame. You need to
apply the steady flow energy equation in a reference frame where the flow is
steady.

**Second**, the wind-tunnel
model example and the engine
sitting on the ground example (they are the same case-- the flow starts
out stagnant someplace and moves to a new location with no heat or external
work where it stagnates again on a surface -- either the wall of the engine
inlet or the model. The two reference frames are the same with no relative motion,
therefore the stagnation temperature is the same.) Why
didn't the model get hotter just as the skin of the airplane? Isn't it just
backwards, air is moving instead of the body? It did get hotter--hotter
than the static temperature of the freestream. This is the same thing that happened
with the supersonic airplane, except the static temperatures were different.
In the wind-tunnel, the freestream flow is very cold (when it is moving at M=2.5).
When it is stagnated on the model it reaches its stagnation temperature. The
whole process (from stagnated flow in the high pressure cylinders, to moving
flow in the pipes and wind-tunnel, and back to stagnated flow on the surface
of the wind-tunnel model) can be approximated as adiabatic and there is no external
work, and the model and the high pressure cylinders are motionless with respect
to one another. Therefore the stagnation temperature is constant. Enthaly (cpT)
is just traded for kinetic energy (c^2/2) as the flow accelerates and decelerates.
So as the flow moves faster, its static temperature drops. As the flow moves
slower, its static temperature increases.

2)** So
just to clarify, T1 is the temperature I would measure if I placed a thermometer
somewhere in space and TT1 is the temperature that the chunk of air attains
under the conditions specified by stagnation?** (1 student) Sort
of. Your statement is correct except for the thermometer part. If you place
a thermometer in the flow you always get the stagnation temperature (as long
as q and ws are zero) since the flow always stagnates on the surface of the
thermometer. However, if you measured the temperature with a non-intrusive laser-based
method, you would get T1, the static temperature.

3) ** After
an aircraft wing is heated by passing airflow as the result of stagnation, is
there any cooling effect from the lower temperature of the passing airflow as
well? **(1 student) No the wing reaches the temperature of the
fluid which stagnates on its surface (to first approximation, in general there
is a small amount of heat transfer to the flow which does not fully stagnate
and this changes the surface temperature). Relative to the air in the atmosphere
after the airplane flies through, the airflow that doesn't have work put into
it (that is outside the viscous boundary layer) retains its stagnation temperature
(that of the atmosphere). But the flow that is heated by the passage of the
airplane does mix with the flow around it and the temperature wake gradually
dissapates through this process of mixing and the process of thermal conduction.

4) * If air comes in contact with a
moving wing, it picks up heat and kinetic energy. How can stagnation enthalpy
be constant if T goes up and c goes up.?* (1 student)

5)**
Does the air stuck to the blade or wing
get hotter or does the blade get hotter?** (1 student) They both
get hotter.

6) * How does the relationship for stagnation
and static pressure relate to Bernoulli's equation and what is Bernoulli's equation?*
(1 student) You will learn more about this in fluids soon. You don't need to
know about it for the thermo part of the course.

7) * No mud* (3 students).
Good.