Hot-Wire Anemometry

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Hot-Wire Anemometry

• Purpose
• to measure mean and fluctuating velocities in
  fluid flows

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2
Principles of operation

• Consider a thin wire mounted to supports and
  exposed to a velocity U.
• When a current is passed through wire, heat is
  generated (I2Rw). In equilibrium, this must be
  balanced by heat loss (primarily convective) to
  the surroundings.

• If velocity changes, convective heat transfer
  coefficient will change, wire temperature will
  change and eventually reach a new equilibrium.

3
Governing equation I

• Governing Equation
• E thermal energy stored in wire
• E CwTs
• Cw heat capacity of wire
• W power generated by Joule heating
• W I2 Rw
• recall Rw Rw(Tw)
• H heat transferred to surroundings

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Governing equation II

• Heat transferred to surroundings
• ( convection to fluid
• conduction to supports
• radiation to surroundings)
• Convection Qc Nu A (Tw -Ta)
• Nu h d/kf f (Re, Pr, M, Gr,a ),
• Re r U/m
• Conduction f(Tw , lw , kw, Tsupports)
• Radiation f(Tw4 - Tf4)

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Simplified static analysis I

• For equilibrium conditions the heat storage is
  zero
• and the Joule heating W equals the convective
  heat transfer H
• Assumptions
• Radiation losses small
• Conduction to wire supports small
• Tw uniform over length of sensor
• Velocity impinges normally on wire, and is
  uniform over its entire length, and also small
  compared to sonic speed.
• Fluid temperature and density constant

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Simplified static analysis II
Static heat transfer W H I2Rw
hA(Tw -Ta) I2Rw Nukf/dA(Tw
-Ta) h film coefficient of heat
transfer A heat transfer area d wire
diameter kf heat conductivity of
fluid Nu dimensionless heat transfer
coefficient Forced convection regime, i.e. Re
gtGr1/3 (0.02 in air) and Relt140 Nu A1 B1
Ren A2 B2 Un I2Rw2 E2 (Tw -Ta)(A B
Un) Kings law The voltage drop is used as a
measure of velocity.
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Hot-wire static transfer function

• Velocity sensitivity (Kings law coeff. A 1.51,
  B 0.811, n 0.43)

Output voltage as fct. of velocity
Voltage derivative as fct. of velocity
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Directional response I
Probe coordinate system

• Velocity vector U is decomposed into normal Ux,
  tangential Uy and binormal Uz components.

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Directional response II

• Finite wire (l/d200) response includes yaw and
  pitch sensitivity
• U2eff(a) U2(cos2a k2sin2a) q 0
• U2eff(q ) U2(cos2q h2sin2q ) a 0
• where
• k , h yaw and pitch factors
• a , q angle between wire normal/wire-prong
  plane, respectively, and velocity
  vector
• General response in 3D flows
• U2eff Ux2 k2Uy2 h2Uz2
• Ueff is the effective cooling velocity sensed by
  the wire and deducted from the calibration
  expression, while U is the velocity component
  normal to the wire

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Directional response III

• Typical directional response for hot-wire probe

(From DISA 1971)
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Directional response IV

• Yaw and pitch factors k1 and k2 (or k and h)
  depend on velocity and flow angle

(From Joergensen 1971)
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Probe types I

• Miniature Wire Probes
• Platinum-plated tungsten,
• 5 mm diameter, 1.2 mm length
• Gold-Plated Probes
• 3 mm total wire length,
• 1.25 mm active sensor
• copper ends, gold-plated
• Advantages
• - accurately defined sensing length
• - reduced heat dissipation by the prongs
• - more uniform temperature distribution
• along wire
• - less probe interference to the flow field

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Probe types II

• For optimal frequency response, the probe should
  have as small a thermal inertia as possible.
• Important considerations
• Wire length should be as short as possible
  (spatial resolution want probe length ltlt eddy
  size)
• Aspect ratio (l/d) should be high (to minimise
  effects of end losses)
• Wire should resist oxidation until high
  temperatures (want to operate wire at high T to
  get good sensitivity, high signal to noise
  ratio)
• Temperature coefficient of resistance should be
  high (for high sensitivity, signal to noise
  ratio and frequency response)
• Wires of less than 5 µm diameter cannot be
  drawn with reliable diameters

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Probe types III

• Film Probes
• Thin metal film (nickel) deposited on quartz
• body. Thin quartz layer protects metal film
• against corrosion, wear, physical damage,
• electrical action
• Fiber-Film Probes
• Hybrid - film deposited on a thin
• wire-like quartz rod (fiber) split fiber-film
• probes.

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Probe types IV

• X-probes for 2D flows
• 2 sensors perpendicular to each other. Measures
  within 45o.
• Split-fiber probes for 2D flows
• 2 film sensors opposite each other on a quartz
  cylinder. Measures within 90o.
• Tri-axial probes for 3D flows
• 3 sensors in an orthogonal system. Measures
  within 70o cone.

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Hints to select the right probe

• Use wire probes whenever possible
• ü relatively inexpensive
• ü better frequency response
• ü can be repaired
• Use film probes for rough environments
• ü more rugged
• ü worse frequency response
• ü cannot be repaired
• ü electrically insulated
• ü protected against mechanical and chemical
  action

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Modes of anemometer operation
Constant Current (CCA) Constant Temperature
(CTA)
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Constant current anemometer CCA

• Principle
• Current through
• sensor is kept
• constant
• Advantages
• - High frequency
• response
• Disadvantages
• - Difficult to use
• - Output decreases with velocity
• - Risk of probe burnout

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Constant Temperature Anemometer CTA I

• Principle
• Sensor resistance
• is kept constant by
• servo amplifier
• Advantages
• - Easy to use
• - High frequency
• response
• - Low noise
• - Accepted standard
• Disadvantages
• - More complex circuit

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Constant temperature anemometer CTA II

• 3-channel StreamLine with Tri-axial wire probe
  55P91

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Modes of operation, CTA I

• Wire resistance can be
• written as
• Rw Ro(1a o(Tw-To))
• Rw wire hot resistance
• Ro wire resistance at To
• a o temp.coeff. of resistance
• Tw wire temperature
• To reference temperature
• Define OVERHEAT RATIO as
• a (Rw-Ro)/Ro a o(Tw-T0)
• Set DECADE overheat resistor as RD (1a)Rw

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Modes of operation, CTA II

• The voltage across wire is given by
• E2 I2Rw2 Rw(Rw - Ra)(A1 B1Un)
• or as Rw is kept constant by the servoloop
• E2 A BUn
• Note following comments
• to CTA and to CCA
• - Response is non-linear
• - CCA output decreases
• - CTA output increases
• - Sensitivity decreases
• with increasing U

CTA output as fct. of U
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Dynamic response, CCA I

• Hot-wire Probes
• For analysis of wire dynamic response, governing
  equation includes the term due to thermal energy
  storage within the wire
• W H dE/dt
• The equation then becomes a differential
  equation
• I2Rw (Rw-Ra)(ABUn) Cw(dTw/dt)
• or expressing Tw in terms of Rw
• I2Rw (Rw-Ra)(ABUn) Cw/a oRo(dRw/dt)
• Cw heat capacity of the wire
• ao temperature coeff. of resistance of the
  wire

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Dynamic response, CCA II

• Hot-wire Probes
• The first-order differential equation is
  characterised by a single time constant t
• t Cw/(aoRo(ABU n)
• The normalised transfer function can be expressed
  as
• Hwire(f) 1/(1jf/fcp)
• Where fcp is the frequency at which the amplitude
  damping is 3dB (50 amplitude reduction) and the
  phase lag is 45o.
• Frequency limit can be calculated from the time
  constant
• fcp 1/2pt

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Dynamic response, CCA III

• Hot-wire Probes
• Frequency response of film-probes is mainly
  determined by the thermal properties of the
  backing material (substrate).
• The time constant for film-probes becomes
• t (R/R0)2F2rsCsks/(ABUn)2
• rs substrate density
• Cs substrate heat capacity
• ks substrate heat conductivity
• and the normalised transfer function becomes
• Hfilm(f) 1/(1(jf/fcp)0.5)

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Dynamic response, CCA IV

• Dynamic characteristic may be described by the
  response to
• - Step change in velocity or
• - Sinusoidal velocity variation

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Dynamic response, CCA V

• The hot-wire response characteristic is specified
  by
• 
  
  
• For a 5 µm wire probe in CCA mode t 0.005s,
  typically.
• (Frequency response can be improved by
  compensation circuit)

(From P.E. Nielsen and C.G. Rasmussen, 1966)
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Dynamic response, CTA I

• CTA keeps the wire at constant temperature, hence
  the effect of thermal inertia is greatly reduced
• Time constant is reduced to
• t CTA t CCA/(2aSRw)
• where
• a overheat ratio
• S amplifier gain
• Rw wire hot resistance
• Frequency limit
• fc defined as -3dB amplitude
• damping

(From Blackwelder 1981)
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Dynamic response, CTA II

• Typical frequency response of 5 mm wire probe
  (Amplitude damping and Phase lag)
• Phase lag is reduced by frequency dependent gain
  (-1.2 dB/octave)

(From Dantec MT)
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Velocity calibration (Static cal.)

• Despite extensive work, no universal expression
  to describe heat transfer from hot wires and
  films exist.
• For all actual measurements, direct calibration
  of the anemometer is necessary.

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Velocity calibration (Static cal.) II

• Calibration in gases (example low turbulent free
  jet)
• Velocity is determined from
• isentropic expansion
• Po/P (1(g -1)/2M 2)g /(g- -1)
• a0 (g RT0 )0.5
• a ao/(1(g -1)/2M 2)0.5
• U Ma

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Velocity calibration (Static cal.) III

• Film probes in water
• - Using a free jet of liquid issuing from the
  bottom of a container
• - Towing the probe at a known velocity in
  still liquid
• - Using a submerged jet

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Typical calibration curve

• Wire probe calibration with curve fit errors
• Curve fit (velocity U as function of output
  voltage E)
• U C0 C1E C2E2 C3E3 C4E4

(Obtained with Dantec 90H01/02)Calibrator)
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Dynamic calibration/tuning I

• Direct method
• Need a flow in which sinusoidal velocity
  variations of known amplitude are superimposed on
  a constant mean velocity
• - Microwave simulation of turbulence (lt500 Hz)
• - Sound field simulation of turbulence (gt500
  Hz)
• - Vibrating the probe in a laminar flow
  (lt1000Hz)
• All methods are difficult and are restricted to
  low frequencies.

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Dynamic calibration/tuning II

• Indirect method, SINUS TEST
• Subject the sensor to an electric sine wave
  which simulates an instantaneous change in
  velocity and analyse the amplitude response.

Typical Wire probe response
Typical Fiber probe response
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Dynamic calibration/tuning III

• Indirect method SQUARE WAVE TEST
• Subject the sensor to an electric sine wave
  which simulates an instantaneous change in
  velocity and analyse the shape of the anemometer
  output

(From Bruun 1995)
For a wire probe (1-order probe response)
Frequency limit (- 3dB damping) fc 1/1.3 t
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Dynamic calibration

• Conclusion
• Indirect methods are the only ones applicable in
  practice.
• Sinus test necessary for determination of
  frequency limit for fiber and film probes.
• Square wave test determines frequency limits for
  wire probes. Time taken by the anemometer to
  rebalance itself is used as a measure of its
  frequency response.
• Square wave test is primarily used for checking
  dynamic stability of CTA at high velocities.
• Indirect methods cannot simulate effect of
  thermal boundary layers around sensor (which
  reduces the frequency response).

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Disturbing effects (problem sources)

• Anemometer system makes use of heat transfer from
  the probe
• Qc Nu A (Tw -Ta)
• Nu h d/kf f (Re, Pr, M, Gr,a ),
• Anything which changes this heat transfer (other
  than the flow variable being measured) is a
  PROBLEM SOURCE!
• Unsystematic effects (contamination, air bubbles
  in water, probe vibrations, etc.)
• Systematic effects (ambient temperature changes,
  solid wall proximity, eddy shedding from
  cylindrical sensors etc.)

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Problem sourcesProbe contamination I

• Most common sources
• - dust particles
• - dirt
• - oil vapours
• - chemicals
• Effects
• - Change flow sensitivity of sensor (DC drift
  of calibration curve)
• - Reduce frequency response
• Cure
• - Clean the sensor
• - Recalibrate

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Problem SourcesProbe contamination II

• Drift due to particle contamination in air
• 5 mm Wire, 70 mm Fiber and 1.2 mm SteelClad
  Probes

(From Jorgensen, 1977)
Wire and fiber exposed to unfiltered air at 40
m/s in 40 hours Steel Clad probe exposed to
outdoor conditions 3 months during winter
conditions
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Problem SourcesProbe contamination IV

• Low Velocity
• - slight effect of dirt on heat transfer
• - heat transfer may even increase!
• - effect of increased surface vs. insulating
  effect
• High Velocity
• - more contact with particles
• - bigger problem in laminar flow
• - turbulent flow has cleaning effect
• Influence of dirt INCREASES as wire diameter
  DECREASES
• Deposition of chemicals INCREASES as wire
  temperature INCREASES
• FILTER THE FLOW, CLEAN SENSOR AND RECALIBRATE!

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Problem SourcesProbe contamination III

• Drift due to particle contamination in water
• Output voltage decreases with increasing dirt
  deposit

(From Morrow and Kline 1971)
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Problem SourcesBubbles in Liquids I

• Drift due to bubbles in water
• In liquids, dissolved gases form bubbles on
  sensor, resulting in
• - reduced heat transfer
• - downward calibration drift

(From C.G.Rasmussen 1967)
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Problem SourcesBubbles in Liquids II

• Effect of bubbling on
• portion of typical
• calibration curve
• Bubble size depends on
• - surface tension
• - overheat ratio
• - velocity
• Precautions
• - Use low overheat!
• - Let liquid stand before use!
  
• - Dont allow liquid to cascade in air!
  
• - Clean sensor!

(From C.G.Rasmussen 1967)
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Problem Sources (solved) Stability in Liquid
Measurements

• Fiber probe operated stable in water
• - De-ionised water (reduces algae growth)
• - Filtration (better than 2 mm)
• - Keeping water temperature constant (within
  0.1oC)

(From Bruun 1996)
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Problem sourcesEddy shedding I

• Eddy shedding from cylindrical sensors
• Occurs at Re 50
• Select small sensor diameters/ Low pass filter
  the signal

(From Eckelmann 1975)
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Problem SourcesEddy shedding II

• Vibrations from prongs and probe supports
• - Probe prongs may vibrate due to eddy
  shedding from them or due induced vibrations
  from the surroundings via the probe support.
• - Prongs have natural frequencies from 8 to 20
  kHz
• Always use stiff and rigid probe mounts.

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Problem SourcesTemperature Variations I

• Fluctuating fluid temperature
• Heat transfer from the probe is proportional to
  the temperature difference between fluid and
  sensor.
• E2 (Tw-Ta)(A BUn)
• As Ta varies
• - heat transfer changes
• - fluid properties change
• Air measurements
• - limited effect at high overheat ratio
• - changes in fluid properties are small
• Liquid measurements effected more, because of
• - lower overheats
• - stronger effects of T change on fluid
  properties

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Problem SourcesTemperature Variations II

• Anemometer output depends on both velocity and
  temperature
• When ambient temperature increases the velocity
  is measured too low, if not corrected for.

(From Joergensen and Morot1998)
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Problem Sources Temperature Variations III
Film probe calibrated at different temperatures
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Problem Sources Temperature Variations IV

• To deal with temperature variations
• Keep the wire temperature fixed (no overheat
  adjustment), measure the temperature along and
  correct anemometer voltage prior to conversion
• Keep the overheat constant either manually, or
  automatically using a second compensating sensor.
• Calibrate over the range of expected temperature
  and monitor simultaneously velocity and
  temperature fluctuations.

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Measurements in 2D Flows I

• X-ARRAY PROBES (measures within 45o with respect
  to probe axis)
• Velocity decomposition into the (U,V) probe
  coordinate system
• where U1 and U2 in wire coordinate system are
  found by solving

53
Measurements in 2D Flows II

• Directional calibration provides yaw
  coefficients k1 and k2

(Obtained with Dantec 55P51 X-probe and 55H01/H02
Calibrator)
54
Measurements in 3D Flows I
TRIAXIAL PROBES (measures within 70o cone around
probe axis)
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Measurements in 3D Flows II

• Velocity decomposition into the (U,V,W) probe
  coordinate system
• where U1 , U2 and U3 in wire coordinate system
  are found by solving
• left hand sides are effective cooling
  velocities. Yaw and pitch coefficients are
  determined by directional calibration.

56
Measurements in 3D Flows III

• U, V and W measured by Triaxial probe, when
  rotated around its axis. Inclination between flow
  and probe axis is 20o.

(Obtained with Dantec Tri-axial probe 55P91 and
55H01/02 Calibrator)
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Measurement at Varying TemperatureTemperature
Correction I

• Recommended temperature correction
• Keep sensor temperature constant, measure
  temperature and correct voltages or calibration
  constants.
• I) Output Voltage is corrected before conversion
  into velocity

- This gives under-compensation of approx. 0.4/C
in velocity.
Improved correction
Selecting proper m (m 0.2 typically for wire
probe at a 0.8) improves compensation to better
than 0.05/C.
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Measurement at Varying Temperature Temperature
Correction II

• Temperature correction in liquids may require
  correction of power law constants A and B
• In this case the voltage is not corrected

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Data acquisition I

• Data acquisition, conversion and reduction
• Requires digital processing based on
• Selection of proper A/D board
• Signal conditioning
• Proper sampling rate and number of samples

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Data acquisition II
A/D boards convert analogue signals into digital
information (numbers) They have following main
characteristics

• Resolution
• - Min. 12 bit (1-2 mV depending on range)
• Sampling rate
• - Min. 100 kHz (allows 3D probes to be sampled
  with approx. 30 kHz per sensor)
• Simultaneous sampling
• - Recommended (if not sampled simultaneously
  there will be phase lag between sensors of 2-
  and 3D probes)
• External triggering
• Recommended (allows sampling to be started by
  external event)

61
Data acquisition III

• Signal Conditioning of anemometer output
• Increases the AC part of the anemometer output
  and improves resolution
• EG(t) G(E(t) - Eoff )
• Allows filtering of anemometer
• - Low pass filtering is recommended
• - High pass filtering may cause phase distortion
  of the signal

(From Bruun 1995)
62
Data acquisition IV

• Sample rate and number of samples
• Time domain statistics (spectra) require sampling
  2 times the highest frequency in the flow
• Amplitude domain statistics (moments) require
  uncorrelated samples. Sampling interval min. 2
  times integral time scale.
• Number of samples shall be sufficient to provide
  stable statistics (often several thousand samples
  are required)
• Proper choice requires some knowledge about the
  flow aforehand
• It is recommended to try to make autocorrelation
  and power spectra at first as basis for the choice

63
CTA AnemometrySteps needed to get good
measurements

• Get an idea of the flow (velocity range,
  dimensions, frequency)
• Select right probe and anemometer configuration
• Select proper A/D board
• Perform set-up (hardware set-up, velocity
  calibration, directional calibration)
• Make a first rough verification of the
  assumptions about the flow
• Define experiment (traverse, sampling frequency
  and number of samples)
• Perform the experiment
• Reduce the data (moments, spectra, correlations)
• Evaluate results
• Recalibrate to make sure that the
  anemometer/probe has not drifted