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Hot-Wire Anemometry

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					Jordanian – German Winter
       Academy

  Amman, 4-11/ Feb. 2006

    Hot-Wire Anemometry
            HWA


                            0/48
          Discussed Topics
          Definition.   •     Deficiencies and     •
           Features.    •           Limitations.
        Applications.   •   Measurements in 2      •
      Operation and     •    and 3 dimensions.
       Measurement            Data acquisition.    •
           principle.         Steps of a Good      •
       About probes.    •                 HWA.
   Operation Modes.     •          Ending and      •
Governing Equations.    •         Discussions.
         Calibration.   •
                                             1/48
          Hot-wire anemometry is the most •
          common method used to measure
instantaneous fluid velocity. The technique
        ( found in the early 70s by King and
   others) depends on the convective heat
       loss to the surrounding fluid from an
     electrically heated sensing element or
 probe. If only the fluid velocity varies, then
      the heat loss can be interpreted as a
measure of that variable, ( relate heat loss  2/48
                 Features
        • Measures velocities from few cm/s to
                                   supersonic.

  • High temporal resolution: fluctuations up to
                         several hundred kHz.

• High spatial resolution: eddies down to 1 mm
                                        or less.

     • Measures all three velocity components
  simultaneously, and Provides instantaneous
                          velocity information.


                                             3/48
Applications

                         » Aerospace
                       » Automotives
      » Bio-medical & bio-technology
           » Combustion diagnostics
       » Earth science & environmen
       » Fundamental fluid dynamics
       » Hydraulics & hydrodynamics
                  » Mixing processes
 » Processes & chemical engineering
                  » Wind engineering
     » Sprays (atomization of liquids)


                                    4/48
           Principles of operation
 Consider a thin wire mounted •
  to supports and exposed to a
                        velocity U.
      When a current is passed                     Current I               Sensor dimensions:
through wire, heat is generated                                            length ~1 mm
                                                                           diameter ~5 micrometer
   ( I 2 Rw ). In equilibrium, this
 must be balanced by heat loss
    (basically convection) to the
                    surroundings.     Velocity U
                                                                            Wire supports
                                                                            (St.St. needles)

       If the velocity changes, •                     Sensor (thin wire)

      convective heat transfer
    coefficient will change, so
   the wire’s temperature will
change and eventually reach
              a new equilibrium.

                                                                                                    5/48
Principle of operation




                         6/48
          Measurement Principles
                                                                   •
  The control circuit for hot-wire anemometry is in the form of
              a Wheatstone bridge consisting of four electrical
  resistances, one of which is the sensor. When the required
  amount of current is passed through the sensor, the sensor
     is heated to the operating temperature, at which point the
 bridge is balanced. If the flow is increased, the heat transfer
   rate from the sensor to the ambient fluid will increase, and
 the sensor will thereby tend to cool. the accompanying drop
 in the sensor's electrical resistance will upset the balance of
     the bridge. This unbalance is sensed by the high gain DC
      amplifier, which will in turn produce a higher voltage and
    increase the current through the sensor, thereby restoring
       the sensor to its previously balanced condition. The DC
   amplifier provides the necessary negative feedback for the
control of the constant temperature anemometer. The bridge
                                                                7/48
        or amplifier output voltage is, then an indication of flow
                                                         velocity.
Probes




         8/48
                      Probe Types
  Hot film , which is used in    .1
   regions where a hot wire
  probe would quickly break
        such as in water flow
              measurements.


Hot wire , This is the type of   2.
 hot wire that has been used
  for such measurements as
    turbulence levels in wind
        tunnels, flow patterns
   around models and blade
               wakes in radial

               compressors  .
                                      9/48
Hot wire sensor




                  10/48
Hot film sensor




                  11/48
                  Probe selection
    For optimal frequency response, the probe should have as small a       •
                                           thermal inertia as possible.

  Wire length should be as short as possible (spatial resolution;          •
                        want probe length << eddy size)

   Aspect ratio ( L/d ) should be high (to minimize effects of end         •
                                                                 losses)

    Wire should resist oxidation until high temperatures (want to          •
operate wire at high T to get good sensitivity, high signal
                                                      ratio)  to noise

  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

                                                                     12/48
    Modes of operation
Constant Current anemometry (CCA) •
 Constant Temperature anemometry •
                            (CTA)




                               13/48
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




                                   14/48
            Constant Temperature
              Anemometer CTA
Principle:
Sensor resistance
is kept constant by
Servo amplifier

Advantages:
-Easy to use
-High frequency response
-Low noise
-Accepted standard

Disadvantages:
-More complex circuit




                                   15/48
Governing equations I
 Governing Equation:

         E = thermal energy stored in wire
            E = CwTs
           Cw = heat capacity of wire

         W = power generated by heating
          W = I² Rw

           recall Rw = Rw(Tw)

         H = heat transferred to surroundings




                                                16/48
      Governing equations II
• Heat transferred to surroundings

                  ( convection to fluid
H = sum off       + conduction to supports
                  + radiation to surroundings)

         Convection       Qc = Nu · A · (Tw -Ta)
                          Nu = h ·d/kf = f (Re, Pr, M, Gr,α),
                          Re = ρU/μ


         Conduction        f (Tw , lw , kw, Tsupports)

         Radiation                   f (Tw - Tf   )




                                                                17/48
    Simplified static analysis I
For equilibrium conditions the heat storage is zero:
                 dE
                    O        W  H
                 dt
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

                                                                18/48
     Simplified static analysis II
                                                  Static heat transfer :    •
                                                                            •
     W=H           I ² Rw = hA(Tw -Ta)        I²Rw = Nu kf/dA( Tw -Ta)      •
                        film coefficient of heat transfer       =   h       •
                                      heat transfer area        =   A       •
                                           wire diameter        =   d       •
                              heat conductivity of fluid        =   kf      •
                dimensionless heat transfer coefficient         = Nu        •

Forced convection regime, i.e. Re > Gr^(1/3 ) (0.02 in air) and Re<140      •

                                     Nu = A1 + B1 · Re ⁿ= A2+ B2 · U ⁿ      •
         “King’s law”               I ² Rw ² = E² = (Tw -Ta)(A + B · U ⁿ)   •

        Then the voltage drop is used as a measure of velocity.



                                                                     19/48
     Heat transfer from Probe

  Convective heat transfer Q from a wire is a •
      function of the velocity U, the wire over-
         temperature Tw –T0 and the physical
     properties of the fluid. The basic relation
between Q and U for a wire placed normal to
 the flow was suggested by L.V. King (1914).
              In its simplest form it suggests :

where Aw is the wire surface area and h
     transfer coefficient, which are the heat
calibration constants A       merged into the
                                       and B.
                                                20/48
Hot-wire static transfer function
  Velocity sensitivity (King’s law coeff. A = 1.51, B = 0.811, n = 0.43)


                       2,4


                       2,2
             E volts




                        2


                       1,8


                       1,6
                             5   10   15   20   25   30   35   40
                                           U m /s




                       Output voltage as fct. of velocity
                                                                           21/48
    HOT-WIRE CALIBRATION

                 The hot-wire responds according to King’s Law:            •


where E is the voltage across the wire, u is the velocity of the flow normal
                                                             to the wire.

   A, B, and n are constants. You may assume n = 0.5, this is common for
  hot-wire probes. A can be found by measuring the voltage on the hot
              wire with no flow, i.e. for u = 0, so A = E^2 as we can see.
     Make sure there is no flow, any small draft is significant. The HWLAB
          software operating in calibration mode will give you a voltage.

         Once you know A, you can measure the wire voltage for a known
flow velocity and then determine B from King’s law, were B = (E ^2 – A)/ U
                                                                    ⁿ)
                                                                         22/48
Calibration curve




                    23/48
Problem sources
 contamination I
     Most common sources: •
            dust particles-
                       dirt-
               oil vapors-
               chemicals-
                       Effects: •
      - Probe Change flow
sensitivity of the sensor (DC
   drift of calibration curve)
        Reduce frequency -
                  response
                 What to do: •
          Clean the sensor-         24/48
               Recalibrate-
           Problem Sources
         Probe contamination II
        Drift due to particle •                         20
        contamination in air




                                  (Um-Uact)/Uact*100%
5 m Wire, 70 m Fiber and
                                                        10


  1.2 mm Steel Clad Probes                               0
                                                                                                 w ire

                                                        -10                                      fiber

                                                                                                 steel-clad
                                                        -20
                                                              0   10   20   30    40   50
                                                                       U (m /s)                  Poly. (steel-
                                                                                                 clad)
                                                                                                 Poly. (fiber)
                                                                                        (From Jorgensen, 1977)



 - Wire and fiber exposed to unfiltered air at 40 m/s for 40 hours
 - Steel Clad probe exposed to outdoor conditions 3 months during
 winter conditions


                                                                                                           25/48
        Problem Sources
     Probe contamination III
Drift due to particle contamination in water •
  Output voltage decreases with increasing dirt
                                      deposits
                             10
       % voltage reduction




                                                                            theory
                              1                                             fiber
                                                                            w edge



                             0,1
                               0,001     0,01      0,1          1
                                  Dirt thicknes versus sensor
                                           diameter, e/D
                                                           (From Morrow and Kline 1971)   26/48
    Problem Sources
 Probe contamination IV
 - slight effect of dirt on heat transfer were heat
                            transfer may increase !

                                                             effect :

low velocity indication, for increased surface vs. insulating effect    •
                                                       High Velocity,   •
    - more contact with particles especially in laminar flow, were
                               turbulent flow has a “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
                                                                    27/48
Further Problem Sources
  Bubbles in Liquids I
                               Drift due to bubbles in water •




                                       (From C.G.Rasmussen 1967)

 In liquids, dissolved gases form bubbles on sensor, resulting in:
                                       - reduced heat transfer
                                   - downward calibration drift
                                                                   28/48
          Bubbles in Liquids II
                                 e
                 Effect of bubbling on : •
                      portion of typical
     calibration curve ( noised signal )
             Bubble size depends on : •
                     surface tension-
                   overheating ratio-
                             velocity-
                         Precautions : •
                    Use low overheat-
Let liquid stand before use         -
                                     155     175              195 cm/sec

Don’t allow liquid to mix with air    -
                                             (From C.G.Rasmussen 1967)
                        Clean sensor-


                                                                    29/48
Stability in Liquid Measurements

                 Fiber probe operated stable in water •




          - De-ionized water (reduces algae growth)
                                             (From Bruun 1996)


            - Filtration ( should be better than 2 m)
 - Keeping water temperature constant (within 0.1oC) 30/48
                   Eddy shedding I
•   Eddy shedding from cylindrical sensors
Occurs at Re ~50




                                                              (From Eckelmann 1975)
* Select small sensor diameters/ Low-pass filter for signal

                                                                                      31/48
                   Eddy shedding II
•   Vibrations from prongs and probe supports:
    - Probe prongs may vibrate due to there own shedding or
      due to induced vibrations from the surroundings via the probe
      support ( effects of resonance and vortices ).
    - Prongs have natural frequencies from 8 to 20 kHz
    Always use stiff and rigid probe mounts.




                                                                32/48
              Temperature Variations I
•   Fluctuating fluid temperature
Heat transfer from the probe is proportional to the temperature
  difference between fluid and sensor.
                           E2 = (Tw-Ta)(A + B·Un)
    As (Ta ) varies:
    - heat transfer changes
    - fluid properties change
    Air measurements:
    - limited effect at high overheating ratio
    - changes in fluid properties are small
    Liquid measurements effected more, because of:
    - lower overheats
    - stronger effects of T change on fluid properties


                                                                  33/48
                       Temperature Variations II
• Anemometer output depends on both velocity and
 temperature

     Hot-wire calibrations at diff. temperatures          Relative velocity error for 1C temp. increase




                                                                                                                (From Joergensen and Morot1998)
   2,4                                                    -1,5
   2,3
                                                   T=20   -1,7
   2,2
   2,1                                             T=25   -1,9
   2,0
                                                   T=30   -2,1
   1,9                                                                                             Tdiff=10 C
   1,8                                             T=35   -2,3
   1,7                                             T=40   -2,5
   1,6
   1,5                                                    -2,7
         5   10   15   20   25   30   35   40                    0   10    20     30      40




When ambient temperature increases the velocity is found to be
low if not corrected for.                                                                                 34/48
          Temperature Variations III
Film probe calibrated at different temperatures




                                                  35/48
            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.




                                                                   36/48
          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




     U = U1·cos1 + U2·cos2
   U = U1·cos1 + U2·cos2
   V = U1·sin1 - U2·sin2
                          )·(cos(90 -  ))2 = k12 are U22
             Ucal12·(1+k12coordinate1systemU12 +found by solving:
where U1 and U2 in wire 2
   V = U1·sin 1 - U2·sin
                Ucal1 ·(1+k1 )·(cos(90 - 1)) = k1 U1 + U2
                    2      2              2    2   2     2


               Ucal2 2·(1+k22 )·(cos(90 - 22)) = U1 +2 k2 2U2
                    2       2                  2    2     2 2
                                                 2
                Ucal2 ·(1+k2 )·(cos(90 - 2)) = U1 + k2 U2            37/48
                   Measurements in 2D Flows II

•    Directional calibration provides the coefficients k1 and k2


                              Uc1,Uc2 vs. Angle                                                K1,K2 vs. Angle
       34.68                                                            3.000



       29.14                                                            0.600



       23.59                                                            0.200
    Uc1,Uc2                                                          K1,K2

       18.04                                                            -0.200



       12.49                                                            -0.600



       6.945                                                            -1.000
          -40.00    -24.00   -8.000      8.000    24.00   40.00             -40.00   -24.00   -8.000       8.000   24.00   40.00
                                Angle (deg)                                                       Angle (deg)




                                       (Obtained with Dantec Dynamics’ 55P51 X-probe and 55H01/H02 Calibrator)
                                                                                                                   38/48
       Measurements in 3D Flows I

TRIAXIAL PROBES (measures within a 70o cone around axis):



                                               z

                                   3
                                         35°              x

                                                       Probe stem
                                   55°


                               1
                                   35°
                                          45°

                                                   2




                                                                    39/48
         Measurements in 3D Flows II

•   Velocity decomposition into the (U,V,W) probe coordinate system
              U = U1·cos54.74 + U2·cos54.74 + U3·cos54.74
              V = -U1·cos45 - U2·cos135 + U3·cos90
              W = -U1·cos114.09 - U2·cos114.09 - U3·cos35.26
where U1 , U2 and U3 in wire coordinate system are found by solving:
              U1cal ·(1+k1 +h1 ) ·cos 35.264= k1 ·U1 + U2 + h1 ·U3
                   2      2   2      2           2   2    2     2  2

              U2cal ·(1+k2 +h2 )·cos 35.264 = h2 ·U1 + k2 ·U2 + U3
                   2      2   2     2             2   2   2   2     2

              U3cal ·(1+k3 +h3 )·cos 35.264 = U1 + h3 ·U2 + k3 ·U3
                   2      2   2     2             2     2  2     2  2


left hand sides are effective cooling velocities. Yaw and pitch
coefficients are determined by directional calibration.


                                                       * Measurements taken for previous situation




                                                                                      40/48
                                                 Measurements in 3D Flows III

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

                            5                                                                                                      0,15
                                                                                        Umeas




                                                                                                        Meas. - Act. vel. , m/ s
Vel ocity comp onent, m/s




                            4                                                                                                      0,10
                                                                                        Vmeas
                            3
                                                                                        Wmeas                                      0,05
                                                                                                                                                                          Up-Uact
                            2                                                           Res,meas                                   0,00                                   Vp-Vact
                            1                                                           Uact
                                                                                                                                   -0,05                                  Wp-Wact
                            0                                                           Vact
                                                                                        Wact                                       -0,10
                            -1
                                                                                        Res,act                                    -0,15
                            -2
                                                                                                                                           0   60   120 180 240 300 360
                                 0   30 60 90 120 150 180 210 240 270 300 330 360
                                                    Roll angle.                                                                                       Roll angle


                                                                            (Obtained with Dantec Dynamics’ Tri-axial probe 55P91 and 55H01/02 Calibrator)




                                                                                                                                                                           41/48
Measurement at Varying Temperature
     Temperature 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
                                                                        0.5
           E          = ((T       -T         )/(T       -T         ))         E
               corr           w        ref          w        acq                  acq.


    -This gives under-compensation of approximately 0.4%/ C in velocity.

    Improved correction:
                                                                   0.5(1±m)
                 Ecorr = ((Tw- Tref)/(Tw- Tacq))                                  Eacq.
    Selecting proper m (m = 0.2 typically for wire probe at a = 0.8)
    improves compensation to better than ±0.05%/C.
                                                                                          42/48
Measurement at Varying Temperature
     Temperature Correction II
•   Temperature correction in liquids may require correction
    of power constants A and B:

                                      (1±m)                      0.2
         Acorr = (((Tw-To)/(Tw-Tacq))        ·(kf0/kf1)·(Prf0/Prf1) ·A0
                                     (1±m)
         Bcorr = ((Tw-To)/(Tw-Tacq)) ·
                                      0.33        f0/f1)n·B0
                 (kf0/kf1)·(Prf0/Prf1) ·( f1/ f0)n·(

* In this case the voltage is not corrected




                                                                          43/48
          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 a number of samples




                                                  44/48
                  Data acquisition II

A/D boards convert analogue signals into digital information (numbers),
They have the following main characteristics:

•   Resolution:
    - Minimum 12 bits (~1-2 mV depending on range)
•   Sampling rate:
    - Minimum 100 kHz (allows 3D probes to be sampled with
    approximately 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)



                                                               45/48
            Data acquisition III
                 Sample rates 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 minimum 2
                              times integral time scale.
    Number of samples should be sufficient to provide •
 stable statistics (often several thousand samples are
                                               required)
Proper choice requires some knowledge about flow’s •
                                                  nature
It is recommended to try to make autocorrelation and •
                                                     46/48
            power spectra first, as basis for the choice
                       CTA Anemometry
Steps 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



                                                                         47/48
Thank you for •
   listening…


            48/48

				
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