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.
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.
, 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.
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.