Hot-wire Anemometry

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Hot-wire Anemometry

• P M V Subbarao
• Professor
• Mechanical Engineering Department

True Measurement of High frequency Velocity
Variations..
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Theory of operation

• Fundamentally, a hot wire makes use of the
  principle of convective heat transfer from a
  heated surface being dependent upon the flow
  conditions passing over it.

• The maximum temperature of the sensor is
  maintained at a nominally constant value of 1.7
  times the fluid temperature.
• For a given sensor geometry, the steady state
  temperature distribution is a function of the
  cooling velocity.

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Wire Temperature Distribution
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Thermal model of sensor

• A hot-wire uses a 1 mm active region of 5 µm
  tungsten filament with 50 µm copper plated
  support stubs.
• The unplated tungsten is referred to as the
  active portion of the sensor.
• The x-coordinate for the sensor is shown from the
  centre of the wire.

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Heat balance for an incremental element
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This can be simplified to give the general hot
wire equation
if radiation is neglected. The constants are
given by
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Time Constant of Hot-wire
Rwire
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Frequency of Hot-wire Anemometer
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Schematic of Constant Current Anemometer
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Schematic of Constant Temperature Anemometer
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CTA

• The constant temperature anemometer uses a
  feedback amplifier to maintain the average wire
  temperature and wire resistance constant i.e.,
  dTw/ dt 0, within the capability of the
  amplifier.
• The practical upper frequency limit for a CTA is
  the frequency at which the feedback amplifier
  becomes unstable.
• A third anemometer, presently under development,
  is the constant voltage anemometer.
• This anemometer is based on the alterations of an
  operational amplifier circuit and does not have a
  bridge circuit.

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Frequency Response of CTA
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Steady state solution

• The general steady state solution to Equation,
  assuming that b1gt0, is found by applying the
  boundary condition and defining the mean wire
  temperature

The non-dimensional steady state wire temperature
distribution is then
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A heat balance can then be performed over the
whole wire, assuming that the flow conditions are
uniform over the wire
The two heat transfer components can be found
from the flow conditions and the wire temperature
distribution
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to give a steady state heat transfer equation
where the corrected heat transfer coefficient is
given by
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If the Biot number is larger than approximately
3, as is usually the case, in terms of Nusselt
number this approximates to
giving the steady state calibration equation
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PROBE PRE-CALIBRATION PROCEDURE

• Once a probe is constructed and mode of operation
  is selected, the following procedure should
  ensure accurate and reliable measurements.
• First, the probe should be operated at the
  maximum q and Tw that will be used during the
  proposed test.
• This is done to pre-stress and pre-heat the wire
  to ensure that no additional strain will be
  imposed on the wire during the test that could
  alter its resistance.
• For supersonic and high subsonic flows, the wires
  should also be checked for strain gaging, that
  is, stresses generated in the wire due to its
  vibration.
• During this pre-testing many wires will fail due
  to faulty wires or manufacturing techniques.
• But it is better that the wires fail in
  pre-testing rather than during an actual test.

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In practice, hot-wires are calibrated in the
form of u f (E). rather than the more
conventional form of E f (u). The constant To
and r version of King's law for a CTA is
When expressed as u f (E) gives
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VELOCITY CALIBRATION, CURVE FITTING

• Calibration establishes a relation between the
  CTA output and the flow velocity.
• It is performed by exposing the probe to a set of
  known velocities, U, and then record the
  voltages, E.
• A curve fit through the points (E,U) represents
  the transfer function to be used when converting
  data records from voltages into velocities.
• Calibration may either be carried out in a
  dedicated probe calibrator, which normally is a
  free jet, or in a wind-tunnel with for example a
  pitot-static tube as the velocity reference.
• It is important to keep track of the temperature
  during calibration.
• If it varies from calibration to measurement, it
  may be necessary to correct the CTA data records
  for temperature variations.

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Polynomial curve fitting Plot U as function of
Ecorr Create a polynomial trend line in 4th order
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Measurement of Multi-dimensional Flow
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X-probe calibration procedure
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DIRECTIONAL CALIBRATION

• Directional calibration of multi-sensor probes
  provides the individual directional sensitivity
  coefficients (yaw factor k and pitch-factor h)
  for the sensors, which are used to decompose
  calibration velocities into velocity components.
• X-array probes
• The yaw coefficients, k1 and k2, are used in
  order to decompose the calibration velocities
  Ucal1 and Ucal2 from an X-probe into the U and V
  components.
• Directional calibration of X-probes requires a
  rotation unit, where the probe can be rotated on
  an axis through the crossing point of the wires
  perpendicular to the wire plane.
• Calculation of the yaw coefficients requires that
  a probe coordinate system is defined with respect
  to the wires, and that the probe has been
  calibrated against velocity.

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X-Probe
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X-probe decomposition into velocity components U
and V

• Calculate the calibration velocities Ucal1 and
  Ucal2 using the linearisation functions for
  sensor 1 and 2.
• Decomposition with yaw coefficients k1 and k2
• Calculate the velocities U1 and U2 in the
  wire-coordinate system (1,2) defined by the
  sensors using the two equations

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which gives
Calculate the velocities U and V in the probe
coordinate system (X,Y) from
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Tri-axial probes

• The directional sensitivity of tri-axial probes
  is characterised by both a yaw and a pitch
  coefficient, k and h, for each sensor.
• Calibration of tri-axial probes requires a
  holder, where the probe axis (X-direction) can be
  tilted with respect to the flow and thereafter
  rotated 360 around its axis.
• Proper evaluation of the coefficient requires
  that a probe coordinate system is defined with
  respect to the sensor-orientation.
• Directional calibration is made on the basis of a
  velocity calibration.

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Tri-axial probe calibration procedure
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Tri-axial probe decomposition into velocity
components U, V and W

• In a 3-D flows measured with a Tri-axial probe
  the calibration velocities are used together with
  the yaw and pitch coefficients k2 and h2 to
  calculate the three velocity components U, V and
  W in the probe coordinate system (X,Y,Z).
• The yaw and pitch coefficients for the three
  sensors may be the manufacturers default values,
  or if higher accuracy is required they are
  determined by directional calibration of the
  individual sensors.

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Calculate the calibration velocities Ucal1 ,
Ucal2 and Ucal3 using the linearisation functions
for sensor 1, 2 and 3. Calculate the velocities
U1 , U2 and U3 in the wire-coordinate system
(1,2,3) defined by the sensors using the three
equations
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With the k20.0225 and , h21.04 default values
for a tri-axial wire probe, the velocities U1, U2
and U3 in the wire coordinate system becomes
Calculate the U, V and W in the probe coordinate
system
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Time averaged Navier Stokes Equation
For all the Three Momentum Equations, turbulent
stress tensor
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2.Eddy Viscosity models
For 2-D incompressible boundary layer equation
or
Momentum Equation,
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(b) ONE-EQUATION MODELS
Turbulence Kinetic Energy
Mean Strain Rate
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(c) TWO-EQUATION MODELS
Turbulence K.E.
Dissipation Rate
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Measurement of Turbulence
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Two simultaneous velocity time series provide
cross-moments (basis for Reynolds shear stresses)
and higher order cross moments (lateral transport
quantities), when they are acquired at the same
point. If they are acquired at different points
they provide spatial correlations, which carries
information about typical length scales in the
flow.
Reynolds shear stresses
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Lateral transport quantities
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Sensor type selection

• Wire sensors
• Miniature wires
• First choice for applications in air flows with
  turbulence intensities up to 5-10. They have
  the highest frequency response. They can be
  repaired and are the most affordable sensor type.
• Gold-plated wires
• For applications in air flows with turbulence
  intensities up to 20-25. Frequency response is
  inferior to miniature wires. They can be
  repaired.
• Fibre-film sensors
• Thin-quartz coating For applications in air.
  Frequency response is inferior to wires. They
  are more rugged than wire sensors and can be used
  in less clean air. They can be repaired.

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• Heavy-quartz coating
• For applications in water. They can be repaired.
  Film-sensors
• Thin-quartz coating For applications in air at
  moderate-to-low fluctuation frequencies.
• They are the most rugged CTA probe type and can
  be used in less clean air than fibre-sensors.
  They normally cannot be repaired.
• Heavy-quartz coating
• For applications in water. They are more rugged
  than fibre-sensors. They cannot normally be
  repaired.