Lecture G2: Survey of Flow Diagnostic Techniques


 

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Examples of Physical Phenomena Used in Flow Diagnostics

The field of diagnostics is somewhat like that of crime solving: we will use any and all clues to obtain information, and bring in expertise from any discipline as needed.
 

1. Temperature Measurement

 

a. Thermocouples

Principle: Thermoelectric emf (electromotive force). If you take wires of two different materials (usually metal), join them at both ends, and place the two junctions at different temperatures, a voltage will be generated between the two arms. Generally, the voltage increases with increasing (T-Tc).

Features:

1. Very reliable technique, used for many decades, well understood.

2. Insensitive to other flow properties such as pressure or velocity.

3. Pure metal combinations such as Platinum / Platimum with 10% Rhodium (Type S thermocouple) exhibit very linear relations between voltage and temperature difference: approximately 1 millivolt per 100 degrees Celsius.

3. Low voltage, generally in millivolts: needs amplification. Susceptible to electronic noise. The long wires pick up extraneous signals.

4. Response depends on the mass, volume and thermal conductivity of the junction, and the rate of convective heat transfer, which in turn depends on the speed (actually, Nusselt Number) of the flow. This may be far too slow to pick up the true fluctuations of temperature in the flow, especially in flames

where D is junction spherical diameter, k is thermal conductivity, and U is flow speed.

5. Response behavior is approximately that of a first-order system.

6. Metals exhibit the thermoelectric emf property: thermocouples can be used in flames because the melting point is quite high.

7. May catalyze chemical reactions, thereby changing the environment which is to be measured.
 
 
 
Thermocouple properties (From Omega Engg. Temperature Measurement Handbook)
Type
Metal
(+) 
Metal
(-)
Standard Color Code
+ -
Ohms per double foot 20AWG
Seebeck Coefficient S (microvolts per Deg. C @ Temperature of Deg. C
Deg. C Standard Wire Error
NBS Specified Material Range (deg. C)
B
Platinum-6% Rhodium
Platinum-30% Rhodium
-
0.2
6 @ 600
4.4-8.6
0 to 1820
E
Nickel-10% Chromium
Constantan
Violet Red
0.71
58.5 @0
1.7-4.4
-270 to 1000
J
Iron
Constantan
White Red
0.36
50.2@0
1.1-2.9
-210 to 760
K
Nickel-10% Chromium
Nickel
Yellow Red
0.59
39.4@0
1.1-2.9
-270 to 1372
N (AWG14)
Nicrosil
Nisil
-
-
39@600
-
0 to 1300
N (AWG28)
Nicrosil
Nisil
26.2@0
-270 to 400
R
Platinum-13% Rhodium
Platinum
-
0.19
11.5@600
1.4-3.8
-50 to 1768
S
Platinum-10% Rhodium
Platinum
0.19
10.3@600
1.4-3.8
-50 to 1768
T
Copper 
Constantan
Blue Red
0.30
38 @ 0
0.8 - 2.9
-270 to 400
W-Re
Tungsten-5%Rhenium
Tungsten-26%Rhenium
-
19.5@600
-
0 to 2320
 

Notes:
1. Type B is double-valued below 42 deg. C - curve fit is specified only above 130 deg. C.
2. Material range is specified for AWG8, and decreases with decreasing wire size. This may be because high-termperature environments also contain large temperature fluctuations, so that spikes of very high temperature are encountered. These short pulses (such as a flame front) take thin wires beyond their melting points, while leaving thicker wires well below the melting point. Also, as wire diameter decreases, the surface area per unit mass of wire increases, so effects such as catalysis and oxidation become more severe.

3. W-Re (Tungsten-Rhenium) is believed to be susceptible to being oxidized in flames: can't be used reliably in lean flames. Tungsten wire is also quite britttle.
 

 

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b. Resistance Temperature Detector (RTD)

Many materials exhibit the property that their electrical resistance increases with temperature.  . The proportionality constant is called the "temperature coefficient of resistance". It is indeed a constant (meaning resistance is linear with temperature) for materials such as platinum. Thus, a sensor of such material can be used as one element of a Wheatstone Bridge, just as in a hot-film anemometer. Note that for a hot-film (or hot-wire) anemometer,

, with n being close to 0.5. The subscripts `s' and `flow' indicate conditions of the sensor and the flow of interest, respectively. The "constant" A has to do with instrument particulars like bias voltages, and the errors due to nonlinearities not modeled in the above relation. It is usually determined by calibration as the intercept of the line relating the square of voltage to the flow parameters. The "constant" B includes the conductivity of the sensor material, and some of the properties of the fluid in the flow of interest, as well as particulars of the circuit being used. The coefficient n comes from the relation between Reynolds number and Nusselt number, which determines convective heat transfer.

Note: In the Wheatstone Bridge above, the sensor resistance Rs is kept constant by changing the voltage E (and hence the current through the circuit) in response to unbalances fed back from "e". The other resistances are set up to adjust the current range. The resistance R1 is generally a variable resistance in a constant-temperature anemometer circuit. If R2 and R3 are equal (a 1:1 Bridge), then setting R1 to desired value of operating resistance has the effect of increasing the current until the sensor resistance reaches a value Rs equal to R1.

In the above relation, if the temperature difference (the quantity within parentheses) is large compared to the fluctuations in temperature, then the device is primarily sensitive to velocity fluctuations. Even here, note that the device is directly proportional to temperature fluctuations, but only proportional to the square root of velocity, so the hot-wire anemometer works well as an anemometer only if temperature is really constant.
 

 

When the temperature difference is approximately zero (i.e., the sensor temperature is essentially the same as the flow temperature, sensitivity to velocity fluctuations is essentially zero. However, temperature fluctuations do cause voltage fluctuations, and so the device becomes a thermometer. Materials used for RTD applications are generally those with a high value of the temperature coefficient of resistance. Often, these materials are nonmetallic, and are linear temperature sensors only over a limited range of temperature. RTDs are used for control applications over relatively small ranges (a few degrees C) at low to moderate temperatures. By making the sensor a thin film, the frequency response can be made very fast, since a thin film has a very high surface area for heat transfer, per unit mass.

 

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c. Rayleigh Scattering Thermometry

When light of wavelength much greater than molecular size falls of molecules, it is scattered in all directions without change in wavelength. The scattered intensity is approximately the same in all directions. The actual scattering process is discussed in detail elsewhere. Different types of molecules have different "scattering cross-sections" for the same light wavelength, so the scattering intensity depends on :
a) the incident laser beam intensity
b) the molecular cross-section

c) the number of molecules per unit volume in the laser beam.
 

If we take care to get a uniform laser beam profile within a small volume (usually achieved by collimating and focusing the beam), limit the scattering to that coming from a very small segment of the focal volume (using a slit and a receiving lens in front of the collecting pinhole), then the received light intensity depends on the density of the gas, and its composition. If the gas concentration does not vary much over time, then the fluctuations in the received signal can be directly related to density. If the static pressure is constant, then the fluctuations can be inversely related to temperature. This is used in pre-mixed turbulent flames, where the temperature fluctuates from near the reactant temperature (say 300K) to the flame temperature (say 2100K), a factor of 7. The fluctuations in concentration and pressure are not nearly so large, so Rayleigh scattering can be used as an excellent temperature sensor.

, or  . For small changes, the linearized version is:
 
 

, or e' = -kT'

Its advantages are:

a) non-intrusive: no mechanical probe.

b) very fast response: the scattering is "elastic", meaning that there is no appreciable delay between incident and scattered light. The sensing occurs at the speed of light, so the response is determined by the response of the photomultiplier and associated electronic circuits. These are usually good for frequencies well into the hundreds of MegaHertz.

Disadvantages are:

a) the difficulty of keeping the incident light intensity stable in light intensity, beam shape and direction . Lasers do flicker a lot unless expensive precautions are taken. Light-stabilizing and beam-pointing control systems are used, and the laser cooling and input current are carefully regulated.

b) any dust particle going through the beam scatters orders of magnitude more light in the Mie scattering regime, drowning the Rayleigh scattering signal, and generally sending the photomultiplier into a daze, with the circuits saturating and overloading.

This problem is generally reduced by keeping the flow as clean as possible, using filters etc., and by using "gating" circuits which shut off the photomultiplier when the light starts rising above some threshold level.

c) when problems (a) and (b) are minimized, the accuracy at the low-temperature limit is limited by "dark current", the electronic noise from the photomultiplier when there is no laser light falling on it. The dark current is due to the emission of electrons due to random thermal motion. This is minimized by keeping the photomultiplier cooled using liquid nitrogen or other cryogenic means.

 

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