lecture #06 hotwire anemometry: fundamentals and

30
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved! Dr. Hui Hu Dr. Rye M Waldman Department of Aerospace Engineering Iowa State University Ames, Iowa 50011, U.S.A Lecture #06 Hotwire anemometry: Fundamentals and instrumentation AerE 344 Lecture Notes Sources/ Further reading: Tropea, Yarin, & Foss, “Springer Handbook of Experimental Fluid Mechanics,” Part B Ch 5.2 Jorgensen, “How to measure turbulence with hot-wire anemometers—a practicle guide,” Dantec Dynamics

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Page 1: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Dr. Hui Hu

Dr. Rye M Waldman

Department of Aerospace Engineering

Iowa State University

Ames, Iowa 50011, U.S.A

Lecture #06 Hotwire anemometry: Fundamentals

and instrumentation

AerE 344 Lecture Notes

Sources/ Further reading: Tropea, Yarin, & Foss, “Springer Handbook of Experimental Fluid Mechanics,” Part B Ch 5.2

Jorgensen, “How to measure turbulence with hot-wire anemometers—a practicle guide,” Dantec Dynamics

Page 2: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Technical Fundamentals -1

Thermal anemometers

• Measure the local flow velocity

through its relationship to the

convective cooling of

electrically heated metallic

sensors.

• Hot wire anemometers: for

clean air or other gas flows

• Hot film anemometers: for

liquid or some gas flows

© 2013 Dantec Dynamics

Page 3: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Hot wire sensor operation

The electric current (i) flowing through the wire generates heat (I2 Rw). In equilibrium, this must

be balanced by heat lost (primarily convective) to the surroundings.

Current, I

Flow, U

© 2013 Dantec Dynamics

Page 4: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Hot wire sensor operation

The electric current (i) flowing through the wire generates heat (Iw2 Rw). In equilibrium, this must

be balanced by heat lost (primarily convective) to the surroundings.

Current, Iw

Flow, U Rw – resistance of hot wire

Iw – current through hot wire

Tw – hot wire temperature

Ta – ambient temperature

~

Ra – wire resistance at ambient conditions

aw – overheat ratio

For unsteady flow: (m – mass, c – heat capacity)

Page 5: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Technical Fundamentals

Heat transfer characteristics:

• Convection (natural convection, forced convection, or mixed

convection depending on Richardson numbers)

• Conduction to the supporting prongs

• Radiation: <0.1%, is negligible.

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

),/,,,,Pr,(Re,

)(

dlaKnMGrNu

TTlk

qNu

T

w

T

TTa

Mcc

dKn

c

VM

dTTgGr

Ud

wT

vp

w

Re/

2

1

;)(

Pr;Re

2

3

Page 6: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Technical Fundamentals

44Re02.0,)2

11)(Re48.0

140Re44,)2

11)(Re56.024.0(

17.051.0

17.045.0

foraNu

foraNu

T

T

n

w

BVATT

E

)](1[ TTaRR wrrw

According to Collis and Willams (1959):

For a given sensor and fixed overheat ratio, the above equation establishes the relationship

between the voltage output, E, of the hot-wire operation circuit and the flow velocity

Following King’s Law (1915), m

T

n aBANu )2

11)(Re(

Wire temperature cannot be measured directly, but can be estimated from its relationship to the

wire resistance, Rw, directly measured by the operating bridge.

For metallic wires:

:thermal resistivity coefficient

:reference temepature

r

r

a

T

Page 7: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Technical Fundamentals

Flow Field

Current flow

through wire

The rate of which heat is

removed from the sensor is

directly related to the

velocity of the fluid

flowing over the sensor

The hot wire is electrically heated.

If velocity changes for a unsteady flow, convective

heat transfer changes, wire temperature will change

and eventually reach a new equilibrium.

V

Page 8: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Technical Fundamentals

• For a sensor placed in a unsteady flow, the unsteady energy equation will become:

),(2

www TVqRi

dt

dTmc

w

: the mass of the sensor

: specifich heat of the sensor

: convective heat flux q=q(V,T )

m

c

q

The above equation has three unknowns: i, Tw (or Rw) and V

To render this equation solvable, one must keep with the electric current, i, or the sensor

temperature (Tw) constant, which can be achieved with the use of suitable electric circuits.

The corresponding methods are known as:

(1). Constant-current anemometry

(2). Constant-temperature anemometry

Page 9: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

The unsteady energy

equation is highly-nonlinear.

Constant-current anemometry

sR

)()( opopw VVKEEdt

dE

:w TK a time constant, which is proportional to the overheat ratio, and a static sensitivity,

)()( opTwopww

w VVKTTdt

dT

ws RR

constRE

RREi

so

wso

/

)/(

wRiE

The voltage output will be

Since voltage, E, is proportional to, Rw , which, in turn, is linearly related to Tw, the linearized E-V

relationship will be:

:w is usually ~ 1ms for thin hot-wire and ~ 10 ms for slim cylindrical hot-film.

For flow with variable velocity or temperature, overheat ratio will vary as well.

Flow low speed flow, it may result in “burnout”, for high-speed flow, sensitivity is low

wREo

E Ec

R’c

Rc

C

Compensation

circuit

Voltage follower

sensor

When linearized in the vicinity of an operation point, namely at a particular flow speed, Vop, and

sensor temperature, Twop , it leads to the following first-order differential equation:

Page 10: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

• Electric current through the sensor is adjustable continuously through an

electric feedback system, and in response to the changes in convective cooling,

to make the temperature of the hot wire keep in constant.

• The unsteady energy equation becomes steady equation

• Dynamic response of the anemometer is the same as its static response with a

wide frequency range.

Constant-temperature anemometry (CTA) - 1

0)(),( 22 VqRiTVqRidt

dTmc www

w

Page 11: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Constant-temperature anemometry (CTA)-2

2R

dR wR

EB

R2

E

Rsw

sensor

Ew

Eoffset

Esw

-

+

Differential

amplifier

R1

Constant temperature circuit

are connected the input of a high-gain, low noise differential amplifier, whose output is fed

back to the top of the bridge.

• If R2/Rd= R1/Rw, then EB-Ew=0, the amplifier output will be zero.

• If Rd is increased to a value R’d, the resulting bridge imbalance will generate an input

imbalance to the amplifier.

• The amplifier will create some current through both legs of the bridge. The additional current

through the hot wire will create additional joule heating, which tend to increase its temperature

and thus its resistance, until the resistance increases sufficiently to balance the bridge once

more.

• Sensor, Rw, comprises one leg

of the Wheatstone bridge.

• An adjustable decade resistor

array, Rd, compress opposite leg

of the bridge.

• The bridge ratio R2/R1 is fixed,

and R2/R110~20 to make sure

to supply most of the available

power to the sensor

• The two midpoints of the bridge

Page 12: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Constant-temperature anemometry (CTA)-3

Temporal response determined by

electronics.

Sensor bandwidth is set using the

square-wave test:

• Expose probe to velocity

• Connect oscilloscope

• Apply square wave to bridge

• Adjust filter and gain for 15%

undershoot

• Determine ∆t for 3% regulation

• Determine bandwidth (-3 dB):

© 2013 Dantec Dynamics

2R

dR wR

EB

R2

E

Rsw

sensor

Ew

Eoffset

Esw

-

+

Differential

amplifier

R1

Constant temperature circuit

Page 13: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Various effects and error source

• Velocity orientation effects:

– Effective cooling velocity

Veff = V cos .

– In reality, flow velocity tangential to the

sensor would result in cooling.

– Veff = V (cos2 + k2 sin2 )1/2

– Typical values of k2 are 0.05 and 0.20.

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

Page 14: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Various effects and error source

• Prong interference effects:

– Interference of the prongs and the probe

body may produce additional complications

of the heat transfer characteristics.

– For example a stream in the binormal

direction will produce higher cooling than a

stream with the same velocity magnitude

but in the normal direction.

– In reality,Veff = (VN2+ K2 VT

2 + h2 VB2 )1/2

– VN , VT and VB are the normal tangential

and binormal velocity components.

– Typically, h2=1.1~1.2

– To minimize the effect, it usually use long

and thin prongs. Tapered prongs are also

recommended.

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

Page 15: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Various effects and error source

• Heat conduction effects:

– Previous analysis is based on 2-D assumption

with l/d = .

– In reality, the effect of end conduct may effect

the accuracy of the measurement results

– Cold length, lc = 0.5*d ((Kw2/K)(1+aR)/Nu) 1/2

– Kw is thermal conductivity of the sensor

– K is thermal conductivity of the fluid

– aR is overheat ratio

– Effect of the sensor length l/lc

– A recent study has demonstrated that end

conduction effects are expected to decrease

significantly as the Reynolds number

increasing

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

Page 16: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Various effects and error source

• Compressibility effects:

– The velocity and temperature fields around the

sensor become quite complicated when

M>0.6.

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

SSMFor

ST

S

SV

V

T

V

2.100

55.0

)(2

n

VBAE n

Modified King’s law for compressible flow:

Page 17: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Various effects and error source

• Temperature variation effects:

– Calibration at Temperature T1.

– Correlation is needed if real measurements

will be conducted at Temperature T2.

– When the flow temperature varies from

position to position or contain turbulent

fluctuations, corrections is much more

complicated.

– It requires simultaneous flow temperature

measurements.

– SV is increasing with overheat ratio aT.

– At extremely low aT, a thermal anemometer is

totally insensitive to velocity variations, and

becomes a resistance thermometer. The

sensor is called cold wire.

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

Page 18: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Various effects and error source

• Composition effects:

– Composition of flow may affect the convective

heat transfer from a thermal anemometer in as

much as it affect the heat conductivity of

surrounding fluid.

– It requires simultaneous measurements of

fluid species concentration.

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

Page 19: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Various effects and error source

• Reverse flow and high-turbulence effects:

– thermal anemometer could not resolve velocity

orientation.

– Forward flow can not be identified from reversing

flow

– In highly turbulent flow (turbulent intensity >25%),

reverse flow will occurr statistically some time,

therefore, using thermal anemometer for the flow

velocity measurement may result quite large

measurement uncertainty.

– Pulsed Hot –wire concept

TTw

TV ,

wT

prongs

Hot wire

Fluid flow

Page 20: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Multi-sensor probes

• Cross-wire (X-wire) design:

V2

V1

V2

V1

V2

V1

V

Veff-A

Veff-B

)(2

2

)(2

2

21

21

VVV

VVV

Beff

Aeff

)(2

2

)(2

2

2

1

BeffAeff

BeffAeff

VVV

VVV

Page 21: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Multi-sensor probes

• Three sensor design

• Four sensor design

Use of these probes requires

extensive calibration

procedure!

Page 22: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Diameter of hot wires

• L = 0.8 ~ 1.5 mm

• D = ~ 5 m for conventional applications

• D = ~ 10 m for high-speed applications

• D = ~ 2 m for low speed applications

• Prongs: usually tapered to be d 1mm

Page 23: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Dr. Hui Hu

Department of Aerospace Engineering

Iowa State University

Ames, Iowa 50011, U.S.A

Lab #05: Determination of the Aerodynamic Performance of a Low

Speed Airfoil based on Pressure Distribution Measurements

Page 24: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Aerodynamic Performance of An Airfoil

X/C *100

Y/C

*10

0

-20 0 20 40 60 80 100 120

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12 14 16 18 20

CL=2

Experimental data

Angle of Attack (degrees)

Lift

Co

eff

icie

nt,

C

l

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 2 4 6 8 10 12 14 16 18 20

Experimental data

Angle of Attack (degrees)

Dra

g C

oe

ffic

ien

t,

Cd

X/C *100

Y/C

*10

0

-40 -20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

Airfoil stall

Airfoil stall

Before stall

After stall cV

DCd

2

2

1

cV

LCl

2

2

1

Page 25: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Determination of the Aerodynamic Performance of a Low Speed

Airfoil based on Pressure Distribution Measurements

Page 26: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Determination of the Aerodynamic Performance of a Low Speed

Airfoil based on Pressure Distribution Measurements

Page 27: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Determination of the Aerodynamic Performance of a Low Speed

Airfoil based on Pressure Distribution Measurements

NACA0012 airfoil with 49 pressure tabs

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7 8 9 10 11 12

X (inches)

Y (

inch

es)

1

5 10 21

25 30 40

4

7

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

upper surfacelower surface

x / c

Cp

-1.5

-1.0

-0.5

0

0.5

1.0

1.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

upper surfacelower surface

x / c

Cp

Before stall

After stall

2

2

1

V

PPC p

Page 28: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Determination of the Aerodynamic Performance of a Low Speed

Airfoil based on Pressure Distribution Measurements

What you will have available to you for this portion of the lab:

• A Pitot probe already mounted to the floor of the wind tunnel for acquiring dynamic

pressure throughout your tests.

• A Setra manometer to be used with the Pitot tube to measure the incoming flow

velocity.

• A thermometer and barometer for observing ambient lab conditions (for calculating

atmospheric density).

• A computer with a data acquisition system capable of measuring the voltage from

your manometer.

• The pressure sensor you calibrated last week

• A GA(W)-1 airfoil that can be mounted at any angle of attack up to 16.0 degrees.

• Two 16-channel Scanivalve DSA electronic pressure scanners.

Page 29: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

• Calculating airfoil lift coefficient and drag coefficient by numerically integrating the

surface pressure distribution around the airfoil:

Determination of the Aerodynamic Performance of a Low Speed

Airfoil based on Pressure Distribution Measurements

2

12

1

12/1

12/1

ppp

ppp

NN

iii

y ,

y ,

1N1

1i1

NNN

iiiii

yyxxx

yyxxx

iii xpN 2/1'

iii ypA 2/1'

cos'sin''

sin'cos''

AND

ANL

Page 30: Lecture #06 Hotwire anemometry: Fundamentals and

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Required Plots for the Lab Report