Measurement of Flow Velocity

Measurement of Flow Velocity

Václav Uruba CTU Prague, AS CR

Resolution

• Time

– Mean value

– Instantaneous values

• Independent

• Time Resolved

• Space

– 0D (point) – 1D (line) – 2D (plane)

– 3D (volumetric)

• Velocity components

SPACE CORRELATION TIME CORRELATION

Methods

• Pressure measurement (M or TR, 0D, 1-3c)

• Thermal anemometry (TR, 0D, 1-3c)

• Optical methods

– LDA (TR, 0D, 1-3c)

– PIV (I or TR, 2D or 3D, 2-3c)

PRESSURE MEASUREMENT

Velocity

Pressure Probes

• Total pressure – Pitot

• Static pressure

• Dynamic pressure – Prandtl (Pitot-static) probe

Incompressible Flow

Bernoulli equation

air upto 50 (100) m/s

 0  2

2 p p p_dyn

U  

  

2

2

p U const

 

Subsonic Compressible Flow

isentropic

0,3  M 1

2 1

0 1

1 2

p M

p



 ^

    

     

1

2 0

1 1

p v p

p



 

 

  

 

 

     

1

2 0

1 1 p M v

a p







   

 

      

p v

c

  c v

M  a a  p RT

  

Supersonic Compressible Flow

isentropic nonisentropic

1 M 

Multihole probes - direction

• Evaluated quantity

– Total pressure – Static pressure

– 2-3 velocity comp.

• 3-6holes

– A.a. 30-45°

• 7-12 holes sphere

– A.a. upto 180°

Multihole probes - direction

 3mm 5 holes

Fast response

 6.3mm 5 holes

Fast response

 1.6mm 5 holes

THERMAL ANEMOMETRY

Thermal Anemometry

• Hot Wire or Film

• Measures any fluid quantity depending on heat transfer (velocity, temperature, concentration, …)

• Measuring “point”:

• The only method for more then 10kHz (upto 200kHz)

V e l o c i t y U

C u r r e n t I

S e n s o r ( t h i n w i r e )

S e n s o r d i m e n s i o n s : l e n g t h ~ 1 m m

d i a m e t e r ~ 5 m i c r o m e t e r

W i r e s u p p o r t s ( S t . S t . n e e d l e s )

Constant Temperature Anemometry

Frequency response

Directional sensitivity

U

U z U x

U y x

y

 z



Directional ambiguity

Sensor

• Wire

• Film

 1 - 10m

Nickel th. less 1m

Probes – wires

Probes - films

Calibration

• Velocity set using pressures

Cooling law

Thermal anemometry

• Small measuring point

• Good sensitivity

• High precision (depending on calibration)

• High frequency

• Range of velocities (air:

0.1m/s – 5M)

•

• Intrusive method

• Fragile probe

• Problems in harsh environment

• Velocity orientation ambiguity

• Sensitivity to other

OPTICAL METHODS

Velocity

Optical Methods

• Laser Doppler Anemometry (LDA, PDA)

• Particle Image Velocimetry (PIV)

Laser Doppler Anemometry

LDA - Fringe model

• Focused laser beams intersect and form the measurement volume

• Plane wave fronts: beam waist in the plane of intersection

• Interference in the plane of intersection

• Pattern of bright and dark stripes/planes

Flow with particles

d (known)

Velocity = distance/time

t (measured) Signal

Time

Laser Bragg

Cell backscattered light

measuring volume

Detector Processor

LDA

Measurement volume

Length:



Width: Height:

No. of fringes:

_z

Z

Fringe separation:

 

f  



 

 2

2 sin

 

 

z

L

F E D

 

 



4

sin 2

 



y

L

F

 4E D

 

 

x

L

F E D

 

 



4 cos 2

LDA system

Application examples

Particle Dynamics Analyzer

LDA

• High precision

• No calibration

• Nonintrusive

• Up to 3 components

• Small measuring point

• Velocity orientation

• Particles necessary

• Unevent sampling

• Expensive

Particle Image Velocimetry

• Velocity vector fields - space correlation

PIV

t = 0.2 – 1000 s f = 1 – 100 Hz

TR: f = 500 – 2000 Hz

Velocity evaluation

PIV evaluation

• Correlation

• Particle tracking

Image A

Image B

Image B

Vector field

Vectors + vorticity

PIV variants

• Classical PIV

– Plane

– 2 velocity components – Low frequency

• Time Resolved PIV (high frequency)

• Stereo PIV (3 comp.)

• Tomographic PIV, 3D PIV (volume, 3 comp.)

Stereo PIV

Truedisplacement Displacement

seen from lef Displacement

seen from right Focal plane =

Centre of light sheet

Lef

camera Right

camera

Volumetric PIV

PIV

• Spatial correlation

• No calibration

• Nonintrusive

• 2 to 3 components

• Velocity orientation

• Particles necessary

• Lower precission

• Expensive

Seeding particles

Seeding: ability to follow flow

Particle Fluid Diameter (m)

f = 1 kHz f = 10 kHz

Silicone oil atmospheric air 2.6 0.8

TiO₂ atmospheric air 1.3 0.4

TiO₂ oxygen plasma 3.2 0.8

(2800 K)

MgO methane-air flame 2.6 0.8

(1800 K)

Particles Dynamics

• Important parameters in particle motion

– Particle shape – Particle size

– Relative density of particle and fluid – Concentration of particles in the fluid – Body forces

Acc. Drag Pressure Added mass

Particle trajectory

Fluid pathline





 

 

 



 

 





 ^{d V d dU}_dt ^{d dV}_dt ^d  ^dV_{d t}^d

dt

d dU ^t

f t p

f p f

f p p

p p

p 0

2 3

3 3

2 3 12

3 6 6

D

Repetition rate