3_cta1

8/13/2019 3_cta1

1/23

Fluid Flow Metrology Velocity Measurements

24

VELOCITY MEASUREMENTS

Pitot tube point measurement dynamic distortion of the signal

mean velocity

Hot-wire Anemometry (HWA): Constant Temperature

Anemometry (CTA) point measurement continuous signal

instantaneous velocity high frequency range

Pulsed-wire Anemometry measurement along the distance

average velocity discrete signal (t = const)

limited frequency range

Laser Doppler Anemometry (LDA) point measurement discrete signal (random time intervals t) high frequency range

Particle Image Velocimetry (PIV) planar measurement (2D or even 3D) triggered measurement discrete time domain (t = const) limited frequency range

8/13/2019 3_cta1

2/23


25

POINT MEASUREMENTS OF VELOCITY

The nature of turbulent flows:

random variation in time and space

3D (3-dimensionality)

fine scales

wide frequency range

Measuring technique should meet the following requirements:

Wide range of measured velocities

applicable to any flow situation (natural convection

transonic/supersonic flows)

High-frequency response to accurate follow the flow

instantaneous velocity

Small size of a probe (point measurement)

uniform distribution of velocity field

Independence of temperature, density and composition possibility to apply to nonisothermal flows,

mixtures of different species dependence enables to study temperature or

species concentration

Detection of velocity components and reverse flows

turbulence 3D motion

8/13/2019 3_cta1

3/23


26

High accuracy minimum uncertainty of instantaneous velocity

measurement signal form enabling easy and accurate data

processing accurate estimates of statistical

measures

Linearity of the transducer

nonlinearity may lead to distortions in inappropriate

signal processing careful data treatment or

application of the linearizer

Ease of output signals processing

output signals should have a useful form, easy to

deal with application of commercial software

Limited flow disturbance

perfect solution: nonintrusive sensor optical

techniques

Ease of use

alignment, calibration, adjustment, settings control

Reliability equipment should operate hundreds of hours free

of failures device characteristics should not change in time

Low cost (accessibility)

8/13/2019 3_cta1

4/23

Fluid Flow Metrology Hot-wire Anemometry

27

HOT-WIRE ANEMOMETRY

principle of operation

Hot-wire (thermal) anemometer measures fluid velocity by

sensing the changes in heat transfer from a small,

electrically heated sensor (fine wire) exposed to the fluid

motion

velocity change

heat flux transfer

wire

temperature

resistance of a wire material

typical wire parameters

diameter: d = 15m length: L = 0.53mm temperature: w = 100300

oC

materials: platinum, tungsten

8/13/2019 3_cta1

5/23


28

governing equation

)(]/[ 6mWqqdt

dqexEi

=

iq - thermal energy stored in a wire per unit length

Eq

- power generated by electrical current

exq

- heat flux transferred to the surroundings

)(/ 7LRIq w2

E =

[ ] )(....)( 8b1RR owo0w ++= where:

I - current

Rw, R0 - wire resistance in w, 0temperatures

0 - reference temperatureb0 - temperature coefficient of the electrical

resistivity of the wire material

possible ways of heat exchange between wire and a medium:

conduction small

)(),,( 9Lfq wsw =

radiation negligible

)()( 10fq 4f4wr

=

convection

)()( 11Nuq fwf =

8/13/2019 3_cta1

6/23

8/13/2019 3_cta1

7/23

8/13/2019 3_cta1

8/23


31

)19())(( **222 fwn

ww UBAERI +==

where:

A*, B* - constants (Kings law coefficients)

independent of velocity

n 0.5

)20(, fw UfE =

the voltage drop along the wire is a function ofvelocityand temperatureof the fluid

hot-wire anemometry can be applied for velocityand temperature measurements

8/13/2019 3_cta1

9/23

Fluid Flow Metrology Hot-wire anemometry

32

Modes of HWA operation

CCA (constant current anemometer)

- velocity measurements (history)

- temperature measurements

CTA (constant temperature anemometer)

velocity measurements

CVA (constant voltage anemometer)

practically not used

principle of operation

current through the probe (CCA) / voltage drop along

the wire (CVA) / sensor temperature (CTA) is kept

constant

the measurement is controlled by electrical circuitbased on a Wheatstone bridge with thefeedback

voltage drop across the bridgeEis measured instead ofvoltage drop along the wireEw

8/13/2019 3_cta1

10/23


33

constant current anemometer (CCA)

constI= while I 0 (1 3mA)

fw =

( ) )(UfE CCA

( ) )( fCCA fE =

CCA characteristic (voltage response to the variation of

ambient temperature)

)21(fofto sEE +=

st - sensitivity with respect to temperature

)22(constEE

sff

t =

=

=

8/13/2019 3_cta1

11/23


34

Putting

eEEff +=+=

leads to the following relation

)23()( 00 fftsEeE ++=+

which could be split into two parts concerning averageand fluctuating components, respectively

)24()( 00

=++=

t

fft

sesEE

constant temperature anemometer (CTA)

)()(

ff

wwfE

const

constR

=

=

( ) )(UfE CTA =

( ) )25(2 nCTA BUAE +=

A, B- constants and n 0.5

8/13/2019 3_cta1

12/23


35

Putting

eEEuUU +=+=

we have

[ ] )26(2/1uUBAeE ++=+

Splitting the above equation into constant and fluctuating

parts requires expanding right-hand side expression into

power series

[ ] )27(12/1

+++=+UuaUBAeE

where

)28(4

1UBA

UBa

+=

Neglecting the terms of higher orders leads to

[ ] )29(2/1UBAE +=

)30(4

usU

u

UBA

UBe u=

+=

where

su sensitivity with respect to velocity

)31(4 U

E

UBAU

UBsu

=

+=

8/13/2019 3_cta1

13/23


36

Nonlinear response of a constant temperature anemometer

nonlinearity

( )UEE

how to solve the problem ?

apply linearizer the instrument which makes the hot-

wire anemometer response linear

perform computer-aided measurement (CAM)

8/13/2019 3_cta1

14/23


37

Directional response of HWA

The output of a hot-wire anemometer, besides being a function

of the velocity magnitudeU, is also a function of the incoming

flow direction. However, if the flow direction is unknown, the

HWA output can be interpreted as a function of the velocity of

the hypothetical flow directed perpendicularly to the sensor.

effective velocity(responsible for cooling effect)

)32(),,( UfUeff =

hot-wire anemometer response remains of the same form

)33(2 neffUBAE +=

U

Uz

Ux

Uy

x

y

z

8/13/2019 3_cta1

15/23


38

YAW - the inclination of the velocity vector from the xz

plane (plane to the wire)

Champagnelaw:

)34()sin(cos 2122

1222

yxeff UkUkUU +=+=

PITCH - the inclination of the velocity vector from the xy

plane (plane created by prongs)

Gilmorelaw:

)35()sin(cos 2222

2222

zxeff UkUkUU +=+=

where:

Ux - normal

Uy - tangential

Uz - binormal

velocity vector components, and

k1, k2 - yaw and pitch factors, respectively

(From Joergensen 1971)

8/13/2019 3_cta1

16/23


39

k1= 0.1 0.3 (k10.2)

Ueff strongly decreases when increases because the wire is

cooled by fluid that has already flown along the hot cylinder

k2= 1.02 1.05 (k2> 1)

cooling effect is slightly intensified due to fluid acceleration of

the flow (cross-sectional area is reduced by the prongs -

continuity eq.)

Combining relation (34) and (35) gives single expression

proposed byJorgensen

)(36UkUkUU 2z22

y12

x2eff ++=

For the simplicity lets make the following assumptions:

the mean flow velocity vector lies inxyplane

)(370Uz =

the flow is characterised by low turbulence intensity

)(/,/,/ ''' 381UuUuUu zyx

8/13/2019 3_cta1

17/23


40

)(tgcoscos__

40

U

u

U

u1UUU

yxeff

++==

Putting (40) into (33) and splitting it into constant and

fluctuating parts we have

)(cos 41UBAE +=

)()tg( 42ususuuse yuyxuxyxu +=+=

Sensitivities:

)(cos

cos43

UBAU4

UBsu

+=

)(tg; 44ssss uuyuux ==

8/13/2019 3_cta1

18/23


41

Velocity correlation measurements

For turbulent flows there is a need to measure the stress tensor

jiuu (6 components)

Single-wire probe measurement

a) wire is located inxyplane

)45(00 ause x=

)45()tg( buuse yxI +=

)45()tg( cuuse yxII =

Squaring and averaging in time leads to

)46(/ 2020

2aseux =

( ) )46(tg2

ctg 220

2022

2

22 bc

s

eee

su IIIy

+=

)46()(ctg25.0

2

22

cs

eeuu IIIyx

=

b) wire is located inxzplane

zxzVIVIII uuandueee 2,,

8/13/2019 3_cta1

19/23


42

c) wire is located inyzplane

zyVIIIVIIVI uueee ,,

advantage relatively low cost:

single-wire probe

one-channel CTA

disadvantages:

non-simultaneous measurement high uncertainty

traversing problems

Double-wire probe (X-type probe)

Locating both the wires in z=const plane and assumingidentical sensitivities of the wires (guaranteed by the probeproducer) we have

)47()( auuse yxA +=

)47()( buuse yxB =

Squaring and averaging in time gives

8/13/2019 3_cta1

20/23


43

)48()(25.0

2

22

as

eeu BAx

+=

)48()(25.0

2

22

bs

eeu BAy

=

)48())((25.0

2c

s

eeeeuu BABAyx

+=

application of X-wire probe in turbulence studies:

common in 2D flows only one probes position required digital signal acquisition and data processing is

recommended

Triple-sensor probe

8/13/2019 3_cta1

21/23


Computer-aided measurement of a 3D non-isotherma

( ){}{},{},{

)()(

)(

5.02 ykxkk

iiiCTAi

foftoCCAUU

UBAE

sEE

+=

+=

8/13/2019 3_cta1

22/23


45

HWA signals acquisition and data processing

Analogue way

1D (2D) isothermal flows

statistical moments

correlation and spectral functions

analogue correlators,

band-pass filters

problems to overcome: nonlinearity of CTA characteristic temperature variations

long lasting experiment

nonsteady ambient conditions,

probe contamination

calibration checking

high uncertainty of experimental results

Digital way

1D 3D nonisothermal flows

signal conditioning: mean removal (offset or HPF) gain filtering (LPF, HPF)

AD conversion:

sampling frequency, number of samples selection simultaneous sampling for multi-wire probes

sample and hold system (S&H)

8/13/2019 3_cta1

23/23


specialised software required: data acquisition velocity components and/or temperature resolving data processing (statistical, correlation, spectral

analysis)

ease of use

DANTECs StreamLine System

compact, multi-channel hardware (up to 6 channels)

full PC control of all functions including fine tuning

dedicated software ensuring full experiment

documentation and data processing

automatic temperature correction

portable fully automatic calibration facility

traversing support extremely user-friendly

3_cta1

Documents