E1C09 09/14/2010
15:4:55 Page 409
ceramic tube that houses the lead wires. A hot-film sensor usually consists of a thin (2 mm) platinum
or gold film deposited onto a glass substrate and covered with a high thermal conductivity coating.
The coating acts to electrically insulate the film and offers some mechanical protection. Hot wires
are generally used in electrically nonconducting fluids, while hot films can be used in conducting
fluids or in nonconducting fluids when a more rugged sensor is needed.
Two anemometer bridge operating modes are possible: (1) constant current and (2) constant
resistance. In constant-current operation, a fixed current is passed through the sensor to heat it. The
sensor resistance and therefore its temperature, based on Equation 9.43, are permitted to vary with
the rate of heat transfer between the sensor and its environment. Bridge-deflection voltage provides a
measure of the cooling velocity. The more common mode of operation for velocity measurements is
constant resistance. In constant-resistance operation, the sensor resistance of Equation 9.43 is
originally set by adjusting the bridge balance. The sensor resistance is then maintained constant by
using a differential feedback amplifier to sense small changes in bridge balance, which would be
equivalent to sensing changes in the sensor set-point resistance; that is, the circuit acts as a closed
loop controller using the bridge balance as the error signal. The feedback amplifier rapidly readjusts
the bridge applied voltage, thereby adjusting the sensor current to bring the sensor back to its setpoint resistance and corresponding temperature. Because the current through the sensor varies with
changes in the velocity, the instantaneous power (I
2
R s ) required to maintain this constant
temperature is equivalent to the instantaneous rate of heat transfer from the sensor ( _
Q). In terms
of the instantaneous applied bridge voltage, E, required to maintain a constant sensor resistance, the
velocity is found by the general correlation
E
2
¼ C þ DU
n
ð9:45Þ
where the values of C, D, and n are found by calibration under a fixed sensor and fluid temperature
condition. An electronic or digital linearizing scheme is usually employed to condition the signal by
performing the transformation
E l ¼ K
E
2
À C
D
1=n
ð9:46Þ
such that the measured output from the linearizer, E l , is
E l ¼ KU
ð9:47Þ
where K is found through a static calibration.
For mean velocity measurements, the thermal anemometer is a straightforward device to use. It
has a better usable sensitivity than the pitot-static tube at lower velocities. Multiple velocity
components can be measured by using multiple sensors, each sensor aligned differently to the mean
flow direction and operated by independent anemometer circuits (15,17). Because it has a highfrequency response, fluctuating (dynamic) velocities can be measured. In highly turbulent flows
with root-mean-square (rms) fluctuations of
ffiffiffiffiffi
u 2
p
! 0:1U, signal interpretation can become
complicated, but it has been well investigated (17). Low-frequency fluid temperature fluctuations
can be compensated for by placing resistor R 3 directly adjacent to the sensor and exposed to the flow.
An extensive bibliography of thermal anemometry theory and signal interpretation can be found
elsewhere (18).
In constant temperature mode using a fast-responding differential feedback amplifier, a hotwire system can attain a frequency response that is flat up to 100,000 Hz, which makes it particularly
useful in fluid mechanics turbulence research. However, less expensive and more rugged systems
9.9 Fluid Velocity Measuring Systems 409
15:4:55 Page 409
ceramic tube that houses the lead wires. A hot-film sensor usually consists of a thin (2 mm) platinum
or gold film deposited onto a glass substrate and covered with a high thermal conductivity coating.
The coating acts to electrically insulate the film and offers some mechanical protection. Hot wires
are generally used in electrically nonconducting fluids, while hot films can be used in conducting
fluids or in nonconducting fluids when a more rugged sensor is needed.
Two anemometer bridge operating modes are possible: (1) constant current and (2) constant
resistance. In constant-current operation, a fixed current is passed through the sensor to heat it. The
sensor resistance and therefore its temperature, based on Equation 9.43, are permitted to vary with
the rate of heat transfer between the sensor and its environment. Bridge-deflection voltage provides a
measure of the cooling velocity. The more common mode of operation for velocity measurements is
constant resistance. In constant-resistance operation, the sensor resistance of Equation 9.43 is
originally set by adjusting the bridge balance. The sensor resistance is then maintained constant by
using a differential feedback amplifier to sense small changes in bridge balance, which would be
equivalent to sensing changes in the sensor set-point resistance; that is, the circuit acts as a closed
loop controller using the bridge balance as the error signal. The feedback amplifier rapidly readjusts
the bridge applied voltage, thereby adjusting the sensor current to bring the sensor back to its setpoint resistance and corresponding temperature. Because the current through the sensor varies with
changes in the velocity, the instantaneous power (I
2
R s ) required to maintain this constant
temperature is equivalent to the instantaneous rate of heat transfer from the sensor ( _
Q). In terms
of the instantaneous applied bridge voltage, E, required to maintain a constant sensor resistance, the
velocity is found by the general correlation
E
2
¼ C þ DU
n
ð9:45Þ
where the values of C, D, and n are found by calibration under a fixed sensor and fluid temperature
condition. An electronic or digital linearizing scheme is usually employed to condition the signal by
performing the transformation
E l ¼ K
E
2
À C
D
1=n
ð9:46Þ
such that the measured output from the linearizer, E l , is
E l ¼ KU
ð9:47Þ
where K is found through a static calibration.
For mean velocity measurements, the thermal anemometer is a straightforward device to use. It
has a better usable sensitivity than the pitot-static tube at lower velocities. Multiple velocity
components can be measured by using multiple sensors, each sensor aligned differently to the mean
flow direction and operated by independent anemometer circuits (15,17). Because it has a highfrequency response, fluctuating (dynamic) velocities can be measured. In highly turbulent flows
with root-mean-square (rms) fluctuations of
ffiffiffiffiffi
u 2
p
! 0:1U, signal interpretation can become
complicated, but it has been well investigated (17). Low-frequency fluid temperature fluctuations
can be compensated for by placing resistor R 3 directly adjacent to the sensor and exposed to the flow.
An extensive bibliography of thermal anemometry theory and signal interpretation can be found
elsewhere (18).
In constant temperature mode using a fast-responding differential feedback amplifier, a hotwire system can attain a frequency response that is flat up to 100,000 Hz, which makes it particularly
useful in fluid mechanics turbulence research. However, less expensive and more rugged systems
9.9 Fluid Velocity Measuring Systems 409