Hot-wire anemometry

Material prepared by Alessandro Talamelli, Antonio Segalini

& P. Henrik Alfredsson

•  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 hot wire 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 (thin wire)

Sensor dimensions:length ~1 mmdiameter ~5 micrometer

Wire supports (St.St. needles)

Hot wire and hot film probes

The sensors

Governing equation

•  Governing Equation: E = thermal energy stored in wire = heat capacity of wire W = power generated by Joule heating H = heat transferred to surroundings

•  At equilibrium:

SWTCE =

HWdtdE

!=

WC

WRIW 2=( )WWW TRR =

W = H

Governing equation

•  Heat transferred to surroundings

( convection to fluid + conduction to supports + radiation to surroundings)

Convection

Conduction f(Tw , lw , kw, Tsupports)" Radiation f(Tw

4 - Tf4)

H = !

!

!

( )aWC TTANuQ !""=#

( )µ

!"

UdMaGrfkdhNuf

==#

= Re,,Pr,Re,

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

Simplified static analysis

( )aWf

WW TTAdkNu

RIAhRIHW !"""

=#""=#= 22

Static heat transfer:

q = heat transfer/unit area = h(Tw-Ta) A = heat transfer area d = wire diameter kf = heat conductivity of fluid Nu = Nusselt number = hd/k

Forced convection regime (Re >>Gr1/3 )

Nu = A1 + B1 Ren = A2 + B2 Un “King’s law”

q

Temperature effects •  A and B depend on wire diameter and

flow temperature

•  Temperature correction or temperature control (better !)

a

a

TdT

AdA 886.0=

a

a

TdT

BdB 006.0=

Low Re effects

Wire material suitable for hot-wires

Nu vs Re, influence of Gr

Gr=gd3βΔT/ν2

To avoid buoyancy effects Re > Gr 1/3 In air at standard case: U > 0.07 m/s

21

02

120

21 )()( EEkEEkU n

eff −+−=Alfredsson and Johansson (???)

Directional response

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

Probe coordinate system

U

UzUx

Uyx

y

z!

"

Directional response

•  Finite wire (l/d~200) response includes yaw and pitch sensitivity:" U2

eff(a) = U2(cos2α + k2sin2 α ) θ = 0 ! !U2

eff (θ ) = U2(cos2θ +h2sin2θ ) α = 0 "where: k , h = yaw and pitch factors α , θ = angle between wire normal/wire-prong plane,

respectively, and velocity vector

•  General response in 3D flows:

U2eff = Ux

2 + k2Uy2 + h2Uz

2 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

Sensor directional response

•  Typical directional response for hot-wire probe

(From DISA 1971)

Directional response

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

(From Joergensen 1971)

Sensor types •  Miniature Wire Probes

Platinum-plated tungsten, 5 µm 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 conduction to the prongs - more uniform temperature distribution along wire - less probe interference to the flow field

Probe types

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 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)

Wire material suitable for hot-wires

Tungsten wire (W, also called Wolfram)

- high strength

- can be used at high temperatures

- need to be welded

- diameters down to 5µm available

Platinum (Pt) and Platinum/Rhodium (Pt/Rh) wires

- produced down to 0.6µm through Wollaston process

- can be soldered

• Boundary Layer types • Straight Type

• Wires (pure Pt/silver coated): o Stubbed = Partially Etched o Stubless = Fully Etched wires

Home made probes

Film Probe types

•  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)

Probe types

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

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

Constant current anemometer CCA •  Principle:

Current through sensor is kept constant

• Advantages: - Low noise

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

- low frequency response (a filter’s response is tuned to compensate the thermal lag of the sensor)

Constant Temperature Anemometer CTA

•  Principle: Sensor resistance is kept constant by servo amplifier

•  Advantages: - Easy to use - High frequency response - Accepted standard

•  Disadvantages: - More complex circuit - “high” noise

Constant Voltage Anemometer CVA

•  Principle: Voltage through sensor is kept constant

• Advantage - Large response - High frequency response - Stable - Cable independent

•  the thermal lag is partially compensated during measurements and is fully compensated when postprocessing the data

Output from CCA and CTA

Frequency response CCA

M=cwρwαRd2/kfNu

M is proportional to d3/2

Frequency response CTA

Frequency response determined from square wave test

Calibration

•  Dynamic •  Static

–  “in situ” (free stream, potential core,..) –  Ad hoc apparatus

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+(γ -1)/2Μ 2)γ /(γ- -1) a0 = (γ ΡΤ0 )0.5 a = ao/(1+(γ -1)/2Μ 2)0.5 U = Ma

Ad hoc apparatus

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 Dynamics’ 90H01/02)Calibrator)

4.0761.731

11.12 18.17U velocity

25.22 32.27 39.32

1.853

1.975

2.096

2.218

2.340

E1 (v)

E1 v.U

4.076-0.500

11.12 18.17U velocity

25.22 32.27 39.32

-0.300

-0.100

0.100

0.300

0.500

Error (%)

Error (%)

Calibration functions

Forced convection regime (Re >Gr1/3 )

Nu = A1 + B1 Ren = A2 + B2 Un “King’s law”

For CTA Rw is constant so Nu is proportional to I2

The voltage across the wire E is proportional to I E2 = (Tw-Ta)(A + B Un) (note the dependence on Ta) For CCA Rw decreases when U increases. I is constant which means that E decreases with U.

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

plitu

de (m

V rm

s)

1

103

102

102

103

104

105

106

10

10

Frequency (Hz)

-3 dB

Am

plitu

de (m

V rm

s)

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)

h 0.97 h

0.15 ht

fc

=1.3 τ

w

τw

1

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

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

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).

Hot wire response

|u|, |v|, |w| << U

X - hot wire response (1)

Sensor 1

Sensor 2

Determine the normal and tangential components on the wires of the velocity field.

Sensor 1

X - hot wire response (2)

Effective cooling velocity of sensor 1

Similar equation for sensor 2

Angle calibration of X-probe

Measurements in 3D Flows I

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

Probe 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+h12) ·cos235.264°= k1

2·U12+ U2

2+ h12·U3

2

U2cal2·(1+k2

2+h22)·cos235.264° = h2

2·U12+ k2

2·U22+ U3

2

U3cal2·(1+k3

2+h32)·cos235.264° = U1

2+ h32·U2

2+ k32·U3

2

A commercial system

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

Vorticity measurements

•  Need miniaturization •  New probes based on

hot-film technologies

Concentration measurements

•  A sonic nozzle fixes the flow ratio

•  Cooling depends only on the Prandtl number

•  Difficult to be repaired •  Need to be calibrated