Jordanian – German Winter Academy

Amman, 4-11/ Feb. 2006

Hot-Wire AnemometryHWA

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Discussed Topics

•Definition.•Features.•Applications.•Operation and

Measurement principle.

•About probes.•Operation Modes.•Governing Equations.•Calibration.

•Deficiencies and Limitations.

•Measurements in 2 and 3 dimensions.

•Data acquisition.•Steps of a Good

HWA.•Ending and

Discussions.

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•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 to flow ).

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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 .

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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)

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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 ( I 2

Rw ). In equilibrium, this must be balanced by heat loss

(basically convection) to the surroundings.

•If the velocity changes, convective heat transfer

coefficient will change, so the wire’s 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)

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Principle of operation

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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 or

amplifier output voltage is, then an indication of flow velocity .

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Probes

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Probe Types

.1Hot film , which is used in regions where a hot wire

probe would quickly break such as in water flow

measurements.

2 .Hot wire , This is the type of 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

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Hot film sensor

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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 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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Modes of operation

•Constant Current anemometry (CCA)

•Constant Temperature anemometry (CTA)

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Constant current anemometer CCAPrinciple: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

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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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

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Governing equations II• Heat transferred to surroundings

( convection to fluidH = 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 )

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Simplified static analysis IFor 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

dE

dtO W H

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Simplified static analysis II•Static heat transfer: ••W = H I ² Rw = 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 · Re ⁿ= A2+ B2 · U ⁿ•I ² Rw ² = E² = (Tw -Ta)(A + B · U ⁿ) “King’s law”

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

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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 the heat transfer coefficient, which are merged into the

calibration constants A and B.

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Hot-wire static transfer function

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 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 knownflow velocity and then determine B from King’s law, were B = (E ^2 – A)/ U

ⁿ( 22/48

Calibration curve

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Problem sourcescontamination 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 -Recalibrate

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Problem SourcesProbe contamination II

•Drift due to particle contamination in air

5 m Wire, 70 m Fiber and 1.2 mm Steel Clad Probes

-20

-10

0

10

20

0 10 20 30 40 50

U (m/s)

(Um

-Uact)

/Uact*

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 for 40 hours

- Steel Clad probe exposed to outdoor conditions 3 months during winter conditions

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Problem SourcesProbe contamination III

•Drift due to particle contamination in water

Output voltage decreases with increasing dirt deposits

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) 26/48

Problem SourcesProbe 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

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Further 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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Bubbles in Liquids II•Effect of bubbling on:

portion of typicalcalibration curve ( noised signal )

•Bubble size depends on: -surface tension -overheating ratio -velocity

•Precautions: -Use low overheat -Let liquid stand before use

-Don’t allow liquid to mix with air

-Clean sensor

(From C.G.Rasmussen 1967)

155

e

175 195 cm/sec

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Stability in Liquid Measurements

•Fiber probe operated stable in water

-De-ionized water (reduces algae growth) -Filtration ( should be better than 2 m) -Keeping water temperature constant (within 0.1oC) (From Bruun 1996)

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Eddy shedding I

• Eddy shedding from cylindrical sensorsOccurs at Re ~50

* Select small sensor diameters/ Low-pass filter for signal

(Fro

m E

ckel

man

n 1

975)

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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.

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Temperature 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 overheating 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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Temperature Variations II

• Anemometer output depends on both velocity and temperature

When ambient temperature increases the velocity is found to be 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)

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Temperature Variations III

Film probe calibrated at different temperatures

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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:

U = U1·cos1 + U2·cos2

V = U1·sin1 - U2·sin2Ucal1

2·(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

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Measurements in 2D Flows II

• Directional calibration provides the 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

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Measurements in 3D Flows I

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

P robe stem

45°

55°

35°

3

1

z

x

35°

2

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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.

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

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* Measurements taken for previous situation

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.

-2

-1

0

1

2

3

4

5

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

Roll angle.

Velo

city

com

pone

nt, 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

Meas

. - Ac

t. vel.

, m/s

Up-Uact

Vp-Vact

Wp-Wact

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

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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 approximately 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.

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Measurement at Varying Temperature Temperature Correction II

• Temperature correction in liquids may require correction of power 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

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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 a number of samples

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Data acquisition II

• 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)

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

They have the following main characteristics:

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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

power spectra first, as basis for the choice

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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

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• Thank you for listening…

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