NOTES
OVERVIEW OF FLOW DIAGNOSTICS
Lecture G1:General Issues in Flow Diagnostics
Purpose of Flow Diagnostics
1. Discover the nature of flow phenomena ("What's happening?")
2. Test hypotheses ("If this is an acoustic wave, then
the delay between the pressure fluctuations at points A and B should correspond
to the time of travel of a sound wave, as opposed to some other mechanism.
Does it?")
3. Get accurate, unambiguous, quantitative measurements,
which enable new technology.
4. Develop ideas to control flow phenomena
5. "code validation".
The experimenter's discipline involves 3 areas:
a. Diagnostics to see what is happening.
b. Analysis to quantify it and reduce uncertainty
c. Interpretation to reveal the implications of what has
been seen.
There are no "routine experiments". If it is routine, its
no longer an "experiment". Thus, even those who believe that wind tunnels
are run to "validate CFD codes" eventually discover that the validation
is a routine process only until the first real experiment is performed.
Features of Flow Diagnostics
1. Multidisciplinary: (i) we can use all the help we
can get to find clues to what is really happening. (ii) new ideas come
up all the time, enabling new capabilities. Examples: condenser microphone
for pressure measurement, laser, video imaging, Charge-Coupled Devices,
MEMS (Micro-Electro-Mechanical Systems)
2. Search for simplicity: we aim for the simplest and
cheapest technique which is accurate enough, and safe. Note: "Smart" is
better than "Sophisticated and Expensive".
3. Constant interchange between science and practical
innovation.
Some Basic Concepts
Sensitivity:
a) Does our sensing device sense what we want it to sense?
b) How much of a change do we see in the sensor output for a given
change in the "input" property?
Partial Sensitivity:
Example: consider a hot-film constant-temperature anemometer
sensor, which you used to measure velocity fluctuations in AE3010. The
calibration of the
Bridge Voltage E vs. flow velocity U was:
Actually,
E**2 = A + C *(Ts - Ta) *(Re)**n
where
A and C are constants (in reality they both include some
weak dependence on temperature),
Ts is the temperature of the sensor (which we keep constant
by changing the current through the sensor using feedback control),
Ta is the temperature of the fluid (air)
Re is Reynolds number of the flow over the sensor, which
is a long, thin cylinder.
U is the flow velocity ahead of the sensor
Re = (fluid density)*(U)*(Diameter of the sensor) / (absolute
viscosity)
As long as Ta remains constant, and far away from Ts, we
can say that the sensor is an anemometer: it is primarily sensitive to
velocity fluctuations. The sensitivity increases as (Ts -Ta) increases.
However, if Ta is close to Ts, the sensor is primarily sensitive to temperature
fluctuations: this is the principle of the Resistance Temperature
Detector, or RTD.
Homework:
Find the partial sensitivity of
an anemometer sensor to temperature and velocity, in terms of the mean
Bridge voltage E and the constant C, for 2 cases:
Case 1: Ts = 250deg. C, Ta = 25
deg. C, U = 40m/s, 1 atmosphere air pressure, sensor diameter 50 micrometers.
Case 2: All else same as above,
but Ta = 210 deg.
Precision vs. Accuracy
Precision is just the opposite of vagueness.
You can state something precise to 6 decimal places, but it need not be
accurate. An example was cited by Dr. Norman Augustine ("Augustine's
Laws") about the uncertainty faced by those who develop budgets for large
organizations. It goes something like this:
Each year a Three-year Budget Projection is made, down
to the cents (say, $4,639,237,563,327. 47). It has to be this precise,
or the Committees which vote on the budget would slash it on the
argument that the planners did not do their homework thoroughly in preparing
the numbers. Every year, the projection from last year changes in
the first three significant figures, as large amounts are added or subtracted,
but the cents remain unchanged: say, $5,339,237,563,327.47). This Law has
been used by many people for diverse purposes, few of them kind. One general
conclusion from this is:
"never express results to more significant figures than
you know". That is, the above budget would havve been just as well expressed
as "around $5,000,000,000,000." If you measured the distance from home
to school using your car's Tip Odometer, and got 23.65 miles by interpolating
the last digit carefully, this does not mean that you know the actual distance
down to the last hundredths of a mile: next time you repeat the measurement,
you might get 23.9, depending on how many times you changed lanes on the
Interstate. So it might be wisest to say that the distance is 24 miles.
There is no merit in being imprecise, though: you should
state things to the precision to which they are known. For example,
if you measure every day, and record your readings down to the 10th of
a mile, after a few days you will see that the average distance is 23.6
miles, with the deviation being no more than 0.3 miles either way. Now
you have a better, and significant, measurement than if you had thrown
away the decimal place every time you measured. Five years (that's 2500
trips) later, when you have to defend your distance measurement to the
IRS, you might save a few dollars because you took the trouble to obtain
careful, and statistically significant, samples.
A better example is where intermediate measurements are used in the
process of developing a result. You can round off the final result; but
if you round off results at every step along the way, you might accumulate
so much error that your final answer becomes meaningless.
Accuracy includes numerical precision, but also
includes consideration of whether the figure stated is actually right and
reliable.
Frequency Response
The sensitivity (output per unit input) of a a device may depend on the
rate of change of the input. This is most conveniently expressed in terms
of "frequency response": sensitivity as a function of frequency. Excellent
frequency response means that the sensitivity does not vary with frequency
at all over the range of frequencies likely to be present in the input
signal. This being the case, one does not have to worry about frequency
response.
Usually, one does not have this luxury, and has to calibrate
the frequency response in detail. The results may look something like one
of the curves shown above; hopefully more like the "good" one than the
"poor" one. Such curves are shown with sound amplifiers and other stereo
equipment. The specification is cited as "flat response to beyond 25KHz",
or "3dB point at 30KHz". The assumption is that we don't care what happpens
beyond 18KHz, because our ears, battered by the 120dB noise levels
on the highway or the 140dB Music level in a rock concert, have long since
lost the ability to discern anything beyond 18KHz. So, for us, "flat
to 20KHz" is the same as "ideal".
For measurement purposes, the frequency response function
is a big deal, and there's more to it than sketching color plots showing
flat response. The frequency response function is the transfer function
between input and output, expressed in the frequency domain. It is
a complex function of frequency: the magnitude of the frequency response
is the magnitude of the sensitivity, and the phase is the amount by which
the output lags the input at each frequency. What is shown above is merely
the magnitude. Let's look at that function again:
In the figure, you see that the phase is shown as a linear
function of frequency: It increases along a straight line to +180 degrees,
then suddenly switches to -180 degrees.
Why?
Expressing this function in the frequency domain has some
benefits. The Fast Fourier Transform algorithm (more on this under the
Digital Signal Processing lectures) makes it convenient to transform samples
of signals into the frequency domain. In the frequency domain, one can
simply divide the signal sample by the frequency response function to get
what the signal would have been, had it been sampled using a sensor with
infinitely flat frequency response. It is usually possible to rig up a
calibration experiment to determine the frequency response of a sensor.
Active vs Passive Diagnostics
Example: You want to capture a photograph of a cat with its claws out.
You can do it by passive diagnositcs: wait, with camera focused, until
the cat decides to sharpen its claws against the furniture (Power-up the
camera when the cat wakes up, yawns and stretches), or use active diagnostics:
tweak its tail, or dangle a set of keys in front of it.
In flows, an example of passive diagnostics is where you receive the
light from a flame and analze its frequency content. Active Diagnostics
would be where you excite molecular transitions in the fluid using a high-power
laser, and then capture the radiation released as the molecules relax to
equilibrium.
Types of Data Analysis
1. Sense phenomena
2.
Discover trends
a) change in the mean
b) change in the frequency and amplitude of fluctuation
3. Find "Statistics": mean, root-mean-square, histogram, etc. This is
in cases where we cannot use the detailed, full information.
4. Detailed quantitative analysis: time trace of pressure in a shock
tube, for example.
What did we learn in Lecture 1?
Did we waste all our time chatting about the Federal
budget and the commute on I-85 and cats? Let's see:
1. A cooled-film anemometer sensor
was used in the 1970s to make measurements in rocket exhausts. It worked
on the same principle as a hot-film, i.e., a temperature difference between
the flow and sensor resulted in heat transfer, which changed with flow
conditions. The difference is that the flow in this case might be at a
temperature of several hundred, or even a couple of thousand, degrees K,
far above the survival range of the sensor. So the sensor in this case
is a thin film of platinum or gold, coated (perhaps one molecule thick)
on the surface of a tube made of electrically non-conducting materal. The
tube has cold water flowing at a high rate; in fact in later versions of
the probe, the water would just shoot out into the environment under high
pressure, some distance downstream along the tube from the sensor.
The water flow rate had to be kept
high enough that the sensor, with no electrical current applied, would
stay cool. Now the sensor is heated using the current through a Wheatstone
bridge under feedback control of its resistance, just as in the case of
the hot-wire anemometer. In this case the anemometer circuit had to be
pretty hefty, with much larger current capability than the bridge used
for the hot-wire.
So, at steady state, the heat transfer
from the flow would be a function of the Nusselt number and the temperature
difference. When the velocity or temperature fluctuated, the heat transfer
would fluctuate, and the current was immediately adjusted by the feedback
circuit to keep the sensor resistance constant. From the expressions discussed
above, construct partial sensitivities (voltage change per m/s change in
velocity, voltage change per N/m**2 change in pressure, and voltage change
per degree change in temperature), for the following conditions:
A = 5.
C = whatever gives a net
bridge voltage of 10 volts when the conditions are as given below.
T sensor = 250K
T flow = 1000K
U = 10m/s
P = 1 atmosphere, Standard Day,
sea-level.
2. You are comparing two stereo
receivers. Everything else appears to be the same, so you are goind to
buy the one with the better frequency response. Model A quotes: "flat to
10KHz; 1.5dB per octave roll-off beyond that". Model B quotes: 3dB point
is 20KHz, 3dB per octave roll-off beyond that. You do care what happens
up to 22KHz, but not beyond. Which is better, and why?
Click
here to go to Lecture G2
