TitleTitle

Jordanian – German Winter AcademyJordanian – German Winter Academy

Amman, 4-11/ Feb. 2006Amman, 4-11/ Feb. 2006

Hot Wire AnemometryHot Wire Anemometry

Hot wire anemometry is the most common Hot wire anemometry is the most common method used to measure instantaneous fluid method used to measure instantaneous fluid velocity. The technique depends on the velocity. The technique depends on the convective heat loss to the surrounding fluid convective heat loss to the surrounding fluid from an electrically heated sensing element or from an electrically heated sensing element or probe. If only the fluid velocity varies, then the probe. If only the fluid velocity varies, then the heat loss can be interpreted as a measure of that heat loss can be interpreted as a measure of that variable.variable.

FeaturesFeatures

FeaturesFeatures• Measures velocities from a few cm/s • Measures velocities from a few cm/s to supersonicto supersonic• High temporal resolution: fluctuations • High temporal resolution: fluctuations up to several hundred kHzup to several hundred kHz• High spatial resolution: eddies down • High spatial resolution: eddies down to 1 mm or lessto 1 mm or less• Measures all three velocity • Measures all three velocity components simultaneouslycomponents simultaneously• Provides instantaneous velocity • Provides instantaneous velocity information information

ApplicationApplication ::

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Principles of operationPrinciples of operation Consider a thin wire Consider a thin wire

mounted to supports and mounted to supports and exposed to a velocity exposed to a velocity UU..

When a current is passed When a current is passed through wire, heat is through wire, heat is generated (generated (II22RRww). In ). In equilibrium, this must be equilibrium, this must be balanced by heat loss balanced by heat loss (primarily convective) to the (primarily convective) to the surroundings.surroundings.

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

Velocity U

C urrent I

Sensor (th in w ire)

Sensor d im ensions:length ~1 m mdiam eter ~5 m icrom eter

W ire supports (S t.S t. needles)

Principle f operationPrinciple f operation

Measurement PrinciplesMeasurement Principles

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

ProbesProbes

Probe TypesProbe Types1.1. Hot film , Hot film , which is used in which is used in

regions where a hot wire regions where a hot wire probe would quickly break probe would quickly break such as in water flow such as in water flow measurements.measurements.

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

compressorscompressors..

Hot wire sensorHot wire sensor

Hot film sensorHot film sensor

Probe selection Probe selection For optimal frequency response, the probe should have as For optimal frequency response, the probe should have as

small a thermal inertia as possible.small a thermal inertia as possible.

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

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

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

Temperature coefficient of resistance should be high Temperature coefficient of resistance should be high (for high (for high sensitivity, signal to noise ratio and sensitivity, signal to noise ratio and frequency response)frequency response)

Wires of less than 5 µm diameter cannot be drawn Wires of less than 5 µm diameter cannot be drawn with reliable with reliable diametersdiameters

Modes of anemometer Modes of anemometer operationoperation

Constant Current (CCA) Constant Temperature (CTA)

Constant current Constant current anemometer CCAanemometer CCA

Principle:Current through sensor is kept constant Advantages:-High frequency response

Disadvantages:-Difficult to use-Output decreases with velocity-Risk of probe burnout

Constant Temperature Constant Temperature Anemometer CTAAnemometer CTA

Principle:Sensor resistance is kept constant by servo amplifierAdvantages:-Easy to use-High frequency response

-Low noise-Accepted standardDisadvantages:-More complex circuit

Governing equation IGoverning equation I

Governing Equation:

E = thermal energy stored in wire

E = CwTs Cw = heat capacity of wireW = power generated by Joule

heating W = I² Rw

recall Rw = Rw(Tw)H = heat transferred to

surroundings

Governing equation II• Heat transferred to surroundings

( convection to fluidH = sum off + conduction to supports

+ radiation to surroundings)Convectio 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 )

Simplified static analysis I

For equilibrium conditions the heat storage is zero:

and the Joule heating W equals the convective heat transfer H

AssumptionsRadiation losses smallConduction to wire supports smallTw uniform over length of sensorVelocity impinges normally on wire, and is uniform over its entire length, and also small compared to sonic speed.Fluid temperature and density constant

dE

dtO W H

Simplified static analysis Simplified static analysis IIII

Static heat transfer :

W=H I²Rw = hA(Tw -Ta) I²Rw = Nu kf/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 >Gr^(1/3 ) (0.02 in air) and Re<140

Nu = A1 + B1 · Reⁿ= A2+ B2 · Uⁿ I²Rw² = E² = (Tw -Ta)(A + B · Uⁿ) “King’s law”

The voltage drop is used as a measure of velocity.

Heat transfer from ProbeHeat transfer from Probe

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

where Aw is the wire surface area and h the where Aw is the wire surface area and h the heat transfer coefficient, which are merged into heat transfer coefficient, which are merged into the calibration constants A and B.the calibration constants A and B.

Hot-wire static transfer Hot-wire static transfer functionfunction

Velocity sensitivity (King’s law coeff. A = 1.51, B = 0.811, n = 0.43)

1,6

1,8

2

2,2

2,4

5 10 15 20 25 30 35 40

U m/s

E v

olt

s

Output voltage as fct. of velocity

HOT WIRE HOT WIRE CALIBRATIONCALIBRATION

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

where where E E is the voltage across the wire, is the voltage across the wire, u u is the velocity of the is the velocity of the flow normal to the wire and flow normal to the wire and A, B,A, B,

and and n n are constants. You may assume are constants. You may assume n n =0.5, this is common =0.5, this is common for hot-wire probes. for hot-wire probes. A A can becan be

found by measuring the voltage on the hot wire with no flow, found by measuring the voltage on the hot wire with no flow, i.e. for i.e. for u u = 0, = 0, A A = = EE2. Make sure2. Make sure

there is no flow, any small draft is significant. The HWLAB there is no flow, any small draft is significant. The HWLAB software operating in calibrationsoftware operating in calibration

mode will give you a voltage.) Once you know mode will give you a voltage.) Once you know AA, you can , you can measure the wire voltage for a knownmeasure the wire voltage for a known

flow velocity and then determine flow velocity and then determine B B from King’s law, i.e. from King’s law, i.e. BB=2=2EE2-2-AA7 7 uu0.45 .0.45 .

Calibration curveCalibration curve

Problem sourcesProblem sourcescontamination Icontamination I

Most common sources:Most common sources:

- - dust particlesdust particles- - dirtdirt- - oil vapoursoil vapours- - chemicalschemicals

Effects: Probe Effects: Probe

- - Change flowChange flow sensitivity of sensitivity of sensor sensor (DC drift of (DC drift of calibration curve)calibration curve)- - Reduce frequency responseReduce frequency response

Cure:Cure:

- - Clean the sensorClean the sensor- - RecalibrateRecalibrate

Problem SourcesProblem SourcesProbe contamination IIProbe contamination II

Drift due to particle Drift due to particle contamination in aircontamination in air5 5 m Wire, 70 m Wire, 70 m Fiber and m Fiber and 1.2 mm SteelClad Probes1.2 mm SteelClad Probes

-20

-10

0

10

20

0 10 20 30 40 50

U (m/s)

(Um

-Uac

t)/U

act*

100%

w ire

fiber

steel-clad

Poly. (steel-clad)Poly. (f iber)

(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

Problem SourcesProblem SourcesProbe contamination IIIProbe contamination III

Drift due to particle contamination in waterDrift due to particle contamination in water

Output voltage decreases with increasing dirt depositOutput voltage decreases with increasing dirt deposit

0,1

1

10

0,001 0,01 0,1 1

Dirt thicknes versus sensor diameter, e/D

% v

olt

age

red

uct

ion

theory

fiber

w edge

(From Morrow and Kline 1971)

Problem SourcesProblem SourcesProbe contamination IVProbe contamination IV

- - slight effect of dirt on heat transferslight effect of dirt on heat transfer- heat transfer may even increase!- heat transfer may even increase!- effect Low Velocity- effect Low Velocity

of increased surface vs. insulating effectof increased surface vs. insulating effect

High VelocityHigh Velocity- more contact with particles- more contact with particles- bigger problem in laminar flow- bigger problem in laminar flow- turbulent flow has “cleaning effect”- turbulent flow has “cleaning effect”

Influence of dirt INCREASES as wire diameter Influence of dirt INCREASES as wire diameter DECREASESDECREASES

Deposition of chemicals INCREASES as wire Deposition of chemicals INCREASES as wire temperature INCREASES temperature INCREASES

* FILTER THE FLOW, CLEAN SENSOR AND * FILTER THE FLOW, CLEAN SENSOR AND RECALIBRATE! RECALIBRATE!

Problem SourcesProblem SourcesBubbles in Liquids IBubbles in Liquids I

Drift due to bubbles in waterDrift due to bubbles in water

In liquids, dissolved gases form bubbles on sensor, resulting in:In liquids, dissolved gases form bubbles on sensor, resulting in:- reduced heat transfer- reduced heat transfer- downward calibration drift- downward calibration drift

(From C.G.Rasmussen 1967)

Problem SourcesProblem SourcesBubbles in Liquids IIBubbles in Liquids II

Effect of bubbling onEffect of bubbling onportion of typicalportion of typicalcalibration curvecalibration curve

Bubble size depends onBubble size depends on- - surface tensionsurface tension- - overheat ratiooverheat ratio- - velocityvelocity

PrecautionsPrecautions- - Use low overheat!Use low overheat!- - Let liquid stand before use! Let liquid stand before use! - - Don’t allow liquid to cascade in Don’t allow liquid to cascade in air! air! - - Clean sensor!Clean sensor!

(From C.G.Rasmussen 1967)

155

e

175 195 cm/sec

Problem Sources Problem Sources (solved)(solved)

Stability in Liquid MeasurementsStability in Liquid Measurements

Fiber probe operated stable in waterFiber probe operated stable in water

- - De-ionised water (reduces algae growth)De-ionised water (reduces algae growth)- Filtration (better than 2 - Filtration (better than 2 m)m)- Keeping water temperature constant (within 0.1- Keeping water temperature constant (within 0.1ooC) C)

(From Bruun 1996)

Problem sourcesEddy shedding I

• Eddy shedding from cylindrical sensorsOccurs at Re ~50

Select small sensor diameters/ Low pass filter the signal

(Fro

m E

ckel

man

n 1

975)

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.

Problem SourcesTemperature Variations I

• Fluctuating fluid temperatureHeat 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 overheat ratio- changes in fluid properties are small

Liquid measurements effected more, because of:- lower overheats- stronger effects of T change on fluid properties

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.

Hot-wire calibrations at diff. temperatures

1,51,61,71,81,92,02,12,22,32,4

5 10 15 20 25 30 35 40

T=20

T=25

T=30

T=35

T=40

Relative velocity error for 1C temp. increase

-2,7

-2,5

-2,3

-2,1

-1,9

-1,7

-1,5

0 10 20 30 40

Tdiff=10 C

(Fro

m J

oer

gen

sen

an

d M

oro

t199

8)

Problem Sources Temperature Variations III

Film probe calibrated at different temperatures

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.

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:

U = U1·cos1 + U2·cos2

V = U1·sin1 - U2·sin2

Ucal12·(1+k1

2)·(cos(90 - 1))

2 = k1

2U1

2 + U22

Ucal22·(1+k2

2)·(cos(90 - 2))

2 = U1

2 + k22U2

2

U = U1·cos1 + U2·cos2

V = U1·sin1 - U2·sin2

Ucal12·(1+k1

2)·(cos(90 - 1))

2 = k1

2U1

2 + U22

Ucal22·(1+k2

2)·(cos(90 - 2))

2 = U1

2 + k22U2

2

Measurements in 2D Flows II

• Directional calibration provides yaw coefficients k1 and k2

(Obtained with Dantec Dynamics’ 55P51 X-probe and 55H01/H02 Calibrator)

-40.00

34.68

29.14

23.59

18.04

12.49

6.945-24.00 -8.000 8.000

Angle (deg)

Uc1,Uc2 vs. Angle

Uc1,Uc2

24.00 40.00 -40.00

3.000

0.600

0.200

-0.200

-0.600

-1.000-24.00 -8.000 8.000

Angle (deg)

K1,K2 vs. Angle

K1,K2

24.00 40.00

Measurements in 3D Flows I

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

P robe stem

45°

55°

35°

3

1

z

x

35°

2

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.

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

U1cal2·(1+k1

2+h1

2) ·cos

235.264= k1

2·U1

2+ U2

2+ h1

2·U3

2

U2cal2·(1+k2

2+h2

2)·cos

235.264 = h2

2·U1

2+ k2

2·U2

2+ U3

2

U3cal2·(1+k3

2+h3

2)·cos

235.264 = U1

2+ h3

2·U2

2+ k3

2·U3

2

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.

-2

-1

0

1

2

3

4

5

0 30 60 90 120 150 180 210 240 270 300 330 360

Roll angle.

Vel

oci

ty c

om

po

nen

t, m

/s

Umeas

Vmeas

Wmeas

Res,meas

Uact

Vact

Wact

Res,act -0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0 60 120 180 240 300 360

Roll angle

Mea

s. -

Act

. vel

., m

/s

Up-Uact

Vp-Vact

Wp-Wact

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

Measurement at Varying TemperatureTemperature Correction I

Ecorr = ((Tw- Tref)/(Tw- Tacq))0.5(1±m)

Eacq.

• 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.

Ecorr = ((Tw- Tref)/(Tw- Tacq))0.5

Eacq.

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

Acorr = (((Tw-To)/(Tw-Tacq))(1±m)

·(kf0/kf1)·(Prf0/Prf1)0.2

·A0

Bcorr = ((Tw-To)/(Tw-Tacq))(1±m)

·(kf0/kf1)·(Prf0/Prf1)

0.33·(f1/

f0)n·(f0/

f1)

n·B0

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

Data acquisition II

• 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)

A/D boards convert analogue signals into digital information (numbers)

They have following main characteristics:

Data acquisition IIISample 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

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

End of PresentationEnd of Presentation

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