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Measurement of Flow Velocity
Václav Uruba CTU Prague, AS CR
Resolu2on • Time
– Mean value – Instantaneous values
• Independent • Time Resolved
• Space – 0D (point) – 1D (line) – 2D (plane) – 3D (volumetric)
• Velocity components – 1 – 2 – 3
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SPACE CORRELATION
TIME CORRELATION
Methods
• Pressure measurement (M or TR, 0D, 1-‐3c) • Thermal anemometry (TR, 0D, 1-‐3c) • Op2cal methods – LDA (TR, 0D, 1-‐3c) – PIV (I or TR, 2D or 3D, 2-‐3c)
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PRESSURE MEASUREMENT Velocity
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Pressure Probes
• Total pressure – Pitot
• Sta2c pressure
• Dynamic pressure – Prandtl (Pitot-‐sta2c) probe
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Incompressible Flow
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( )0 22 dynpp pU
ρ ρ−
= =
2
2Up constρ+ =
Bernoulli equa2on
air upto 50 (100) m/s
Subsonic Compressible Flow
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0,3 1M≤ ≤
120 11
2p Mp
γγγ −⎡ ⎤−⎛ ⎞= + ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
1
02 11
ppvp
γγγ
γ ρ
−⎡ ⎤⎛ ⎞⎢ ⎥= −⎜ ⎟⎢ ⎥− ⎝ ⎠⎢ ⎥⎣ ⎦
1
02 11
pvMa p
γγ
γ
−⎡ ⎤⎛ ⎞⎢ ⎥= −⎜ ⎟⎢ ⎥− ⎝ ⎠⎢ ⎥⎣ ⎦p
v
cc
γ =vMa
=
pa RTγ γρ
= =
isentropic
Supersonic Compressible Flow
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isentropic nonisentropic 1M >
Mul2hole probes -‐ direc2on
• Evaluated quan2ty – Total pressure – Sta2c pressure – 2-‐3 velocity comp.
• 3-‐6holes – A.a. 30-‐45°
• 7-‐12 holes sphere – A.a. upto 180°
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Mul2hole probes -‐ direc2on
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Omnidirec2onal Φ 9.5mm 12 holes
Φ 3mm 5 holes
Fast response
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Φ 6.3mm 5 holes Fast response
Φ 1.6mm 5 holes
THERMAL ANEMOMETRY
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Thermal Anemometry • Hot Wire or Film • Measures any fluid quan2ty depending on heat transfer (velocity, temperature, concentra2on, …)
• Measuring “point”:
• The only method for more then 10kHz (upto 200kHz)
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Velocity U
Current I
Sensor (thin wire)
Sensor dimensions:length ~1 mmdiameter ~5 micrometer
Wire supports (St.St. needles)
Constant Temperature Anemometry
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Frequency response
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Direc2onal sensi2vity
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U
U z
U x
U yx
y
zθ
α
Direc2onal ambiguity
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Sensor
• Wire
• Film
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Φ 1 -‐ 10μm
Nickel th. less 1μm
Probes – wires
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Probes -‐ films
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Calibra2on
• Velocity set using pressures
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Cooling law
Thermal anemometry
• Small measuring point • Good sensi2vity • High precision (depending
on calibra2on) • High frequency • Range of veloci2es (air:
0.1m/s – 5M) • Sensi2vity to other
quan22es (T, p, concentra2on)
• Intrusive method • Fragile probe • Problems in harsh
environment • Velocity orienta2on
ambiguity • Sensi2vity to other
quan22es (T, p, concentra2on)
• Calibra2on necessary
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OPTICAL METHODS Velocity
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Op2cal Methods
• Laser Doppler Anemometry (LDA, PDA) • Par2cle Image Velocimetry (PIV)
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Laser Doppler Anemometry
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LDA -‐ Fringe model • Focused laser beams intersect and form the measurement
volume • Plane wave fronts: beam waist in the plane of intersec2on • Interference in the plane of intersec2on • Pahern of bright and dark stripes/planes
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Flow with parHcles
d (known)
Velocity = distance/Hme
t (measured)
Signal
Time
Laser!Bragg!Cell! backscaPered light
measuring volume
Detector!
Processor!
LDA
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Measurement volume Length:
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Width: Height:
No. of fringes:
δλ
π θz
L
F
E D=
⎛⎝⎜
⎞⎠⎟
4
2sin
δ λ
π θx
L
F
E D=
⎛⎝⎜
⎞⎠⎟
4
2cos
NF
E DfL
=
⎛⎝⎜
⎞⎠⎟
82
tan θ
π
δz
δx
X!
Z!
δf
Fringe separaHon:
" λδθ
=⎛ ⎞⎜ ⎟⎝ ⎠
2sin2
f
4y
L
FE D
λδπ
=
LDA system
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Applica2on examples
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Par2cle Dynamics Analyzer
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LDA
• High precision • No calibra2on • Nonintrusive • Up to 3 components • Small measuring point • Velocity orienta2on
• Par2cles necessary • Unevent sampling • Expensive
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Par2cle Image Velocimetry
• Velocity vector fields -‐ space correla2on
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PIV
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Δt = 0.2 – 1000 μs f = 1 – 100 Hz TR: f = 500 – 2000 Hz
time
Velocity evalua2on
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PIV evalua2on
• Correla2on
• Par2cle tracking
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Image A
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Image B
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Image B
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Vector field
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Vectors + vor2city
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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.) • Micro PIV (<1mm) • Mega PIV, Large Scale PIV (LSPIV) (1-‐10m)
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Stereo PIV
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True displacement
Displacement seen from len
Displacement seen from right
Focal plane = Centre of light sheet
Len camera
Right camera
Volumetric PIV
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PIV
• Spa2al correla2on • No calibra2on • Nonintrusive • 2 to 3 components • Velocity orienta2on
• Par2cles necessary • Lower precission • Expensive
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Seeding par2cles
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Seeding: ability to follow flow
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ParHcle 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)
Par2cles Dynamics
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• Important parameters in par2cle mo2on – Par2cle shape – Par2cle size – Rela2ve density of par2cle and fluid – Concentra2on of par2cles in the fluid – Body forces
τ p =2mp
ρgCDAp!ug −!up
π6dp3ρ p
dUp
dt= 3πµdpV + π
6dp3ρ f
dU f
dt− π12dp3ρ f
dVdt
− 32dp2 πµρ f
dVdξt0
t
∫dξt −ξ
Acc. Drag Pressure Added mass History
!D
ParHcle trajectory
Fluid pathline
Repe22on rate
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