Page 405 - Mechatronics with Experiments

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JWST499-c06
JWST499-Cetinkunt
SENSORS 391 254mm×178mm
Tungsten wire

u
FIGURE 6.63: Hot wire anemometer for flow
rate measurement using the thermal heat
transfer principle.

This relationship is used in the hot wire anemometer. A tiny probe with a tunsgten
wire (length in the range of 1 to 10 mm and diameter in the range of 1 to 15 μm) is placed
in the flow field. The resistance of the tungsten probe is proportional to its temperature.
R = R (T ) (6.186)
w
w
w
As a current is passed through the tungsten wire, heat is transferred from the wire to
the fluid.
̇ H = R ⋅ i 2 (6.187)
w
The heat transfer rate depends both on the temperature difference and fluid speed. The
tungsten wire current is controlled in such a way that its temperature (and hence resistance)
is held constant. The amount of heat transferred can be estimated from the current and
resistance measurements on the sensor. Assuming that the fluid temperature is also constant
(or measured separately by a temperature sensor), we can calculate the flow speed. In other
words, K , K is known in advance. We assume that the fluid temperate is also known, T .
1
0
f
Then, we control the current through the tungsten wire in order to control its temperature,
2
T , and while achieving that we measure ̇ H = R ⋅ i , the heat rate it generates. Hence, we
w
w
can calculate the fluid speed u, from which the flow rate can be estimated.
Example applications of a thermal flow rate sensor are shown in Figure 6.64, which
operate based on the “hot film anomometer” principle. The principle is that a flowing gas
transfers heat from a heated probe and the heat transfer rate is proportional to the flow rate
of gas. Then, if a sensor head is heated in a controlled way, we can determine the gas flow
rate based on how much heat is lost.
6.10.5 Mass Flow Rate Sensors: Coriolis Flow Meters
The coriolis flow meter measures the mass flow rate as opposed to the volume flow rate.
Therefore, it is not sensitive to temperature, pressure, or viscosity variation in the fluid
flow. The sensor includes a U-shaped tube, a magnetically excited base which excites the
U-shaped tube at a fixed frequency, that is around 80 Hz (Figure 6.65). The interaction
between the inertial force of the incoming fluid in one arm of the U-shaped tube and the
vibration of the tube creates a force in perpendicular direction to the direction of flow and
the direction of the tube vibration. The forces acting on the two sides of the U-shaped tube
are in opposite directions, which creates a twist torque around the tube. The twist torque,
hence the twist angle of the tube, is proportional to the mass flow rate of the fluid.
The frequency of the twist is the same as the frequency of the tube’s base oscillation.
The output of the twisting motion is measured as an oscillating angular displacement. The
magnitude of the twisting oscillations is proportional to the flow rate.