Hotwire Probe Lecture

AAE 520 Experimental Aerodynamics

Purdue University - School of Aeronautics and Astronautics

Hot-Wire Anemometry

•Purpose:

to measure mean and fluctuating velocities in fluid flows

http://www.dantecmt.com/ www.tsi.com/



• 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.

Principles of operation

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

Current I

Sensor (th in w ire)

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

W ire supports (St.S t. needles)



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

dEdt W H



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,),

Re = U/

Conduction f(Tw , lw , kw, Tsupports)

Radiation f(Tw4 - Tf

4)

H



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

dE

dtO W H



Simplified static analysis II

Static heat transfer:

W = H I2Rw = hA(Tw -Ta) I2Rw = Nukf/dA(Tw -Ta)

h = film coefficient of heat transferA = heat transfer aread = wire diameterkf = heat conductivity of fluidNu = dimensionless heat transfer coefficient

Forced convection regime, i.e. Re >Gr1/3 (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.



Hot-wire static transfer function

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

2

3

4

5

5 10 15 20 25 30 35 40

U m/s

dU

/dE

/U v

olt

s^-1

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 Voltage derivative as fct. of velocity



Directional response I

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

Probe coordinate system

U

U z

U x

U yx

y

z



Directional response II

• Finite wire (l/d~200) response includes yaw and pitch sensitivity:

U2eff(a) = U2(cos2a + k2sin2a) = 0

U2eff() = U2(cos2+h2sin2) = 0

where:

k , h = yaw and pitch factors

, = 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



Directional response III

• Typical directional response for hot-wire probe

(From DISA 1971)



Directional response IV

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

(From Joergensen 1971)



Probe types I

• Miniature Wire ProbesPlatinum-plated tungsten, 5 m 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



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 << 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



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.”



Probe types IV

• X-probes for 2D flows2 sensors perpendicular to each other. Measures within ±45o.

• Split-fiber probes for 2D flows2 film sensors opposite each other on a quartz cylinder. Measures within ±90o.

• Tri-axial probes for 3D flows3 sensors in an orthogonal system. Measures within 70o cone.



Hints to select the right probe

• Use wire probes whenever possible

relatively inexpensive better frequency response can be repaired

• Use film probes for rough environments

more rugged worse frequency response cannot be repaired electrically insulated protected against mechanical and

chemical action



Modes of anemometer operation

Constant Current (CCA)

Constant Temperature (CTA)



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



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



Constant temperature anemometer CTA II

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



Modes of operation, CTA I

• Wire resistance can be written as:

Rw = Ro(1+

Rw = wire hot resistanceRo = wire resistance at To = temp.coeff. of resistanceTw = wire temperatureTo = reference temperature

• Define: “OVERHEAT RATIO” as:

a = (Rw-Ro)/Ro =

• Set “DECADE” overheat resistor as: RD = (1+a)Rw



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 commentsto CTA and to CCA:

- Response is non-linear: - CCA output decreases

- CTA output increases

- Sensitivity decreases with increasing U

1,6

1,8

2

2,2

2,4

5 10 15 20 25 30 35 40

U m/s

E v

olt

sCTA output as fct. of U



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)(A+BUn) + Cw(dTw/dt)

or expressing Tw in terms of Rw:

I2Rw = (Rw-Ra)(A+BUn) + Cw/

Cw = heat capacity of the wire = temperature coeff. of resistance of the wire



Dynamic response, CCA II

Hot-wire Probes:

The first-order differential equation is characterised by a single time constant :

= Cw/(n)

The normalised transfer function can be expressed as:

Hwire(f) = 1/(1+jf/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 = 1/2



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:

= (R/R0)2F2sCsks/(A+BUn)2

s = substrate densityCs = substrate heat capacityks = substrate heat conductivity

and the normalised transfer function becomes:

Hfilm(f) = 1/(1+(jf/fcp)0.5)



Dynamic response, CCA IV

• Dynamic characteristic may be described by the response to

- Step change in velocity or

- Sinusoidal velocity variation

Amplitude response and phase lag

Upper frequency lim it f = ½ Frequency

6 dB/octave

3 dB 30°

Ve locity

Resistance

Time

Time

U2

R1

U1

R2

0.63 (R1-R )

2



Dynamic response, CCA V

• The hot-wire response characteristic is specified by:

For a 5 µm wire probe in CCA mode~ 0.005s, typically.(Frequency response can be improved by compensation circuit)

(From P.E. Nielsen and C.G. Rasmussen, 1966)



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

CTA = CCA/(2aSRw)

where

a = overheat ratio S = amplifier gainRw = wire hot resistance

• Frequency limit:

fc defined as -3dB amplitude damping

(From Blackwelder 1981)



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)



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.



Velocity calibration (Static cal.) II

• Calibration in gases (example low turbulent free jet):

Velocity is determined from isentropic expansion:

Po/P = (1+(2)

a0 = (0 )0.5

a = ao/(1+(2)0.5

U = Ma



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



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)

4.0761.731

11.12 18.17

U velocity

25.22 32.27 39.32

1.853

1.975

2.096

2.218

2.340

E 1 (v)

E 1 v.U

4.076-0.500

11.12 18.17

U velocity

25.22 32.27 39.32

-0.300

-0.100

0.100

0.300

0.500

E rror (% )

E rror (% )



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 (<500 Hz)- Sound field simulation of turbulence (>500 Hz)- Vibrating the probe in a laminar flow (<1000Hz)

All methods are difficult and are restricted to low frequencies.



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.

103

102

102

103

104

105

106

10

101

Frequency (Hz)

-3 dB

Am

plit

ude

(m

V r

ms)

1

103

102

102

103

104

105

106

10

10

Frequency (Hz)

-3 dB

Am

plit

ude

(m

V r

ms)

1

Typical Wire probe response Typical Fiber probe response



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)

h0.97 h

0.15 ht

fc

=1.3

w

w

1

For a wire probe (1-order probe response):

Frequency limit (- 3dB damping): fc = 1/1.3



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).



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,

• 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.)



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



Problem SourcesProbe contamination II

• Drift due to particle contamination in air

5 m Wire, 70 m Fiber and 1.2 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 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!



Problem SourcesProbe contamination III

• Drift due to particle contamination in waterOutput 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 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)



Problem SourcesBubbles in Liquids II

• Effect of bubbling onportion of typicalcalibration curve

• Bubble size depends on- surface tension- overheat ratio- velocity

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

(From C.G.Rasmussen 1967)

155

e

175 195 cm/sec



Problem Sources (solved) Stability in Liquid Measurements

• Fiber probe operated stable in water

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

(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·cos

2

V = U1·sin1 - U2·sin

2

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·cos

2

V = U1·sin1 - U2·sin

2

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 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 angleM

eas.

- A

ct. v

el.,

m/s

Up-Uact

Vp-Vact

Wp-Wact

(Obtained with Dantec 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 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)

A nem om eter

E (1)E (t)-E off

G (E (t)-E off)

tt

t

E G

O ffse t A m p lifie r



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



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

Documents

Hotwire Probe Lecture