1、Lyes KADEM,Ph.D;EngParticle Image Velocimetry for Fluid Dynamics Measurementskademencs.concordia.caLaboratory for Cardiovascular Fluid DynamicsMIE Concordia University2Presentation-A bit of history-What is PIV?-How to perform PIV measurements?-Which PIV system and for What?-How to post-process Data?
2、3A Little Bit fo History Origins:Flow visualizations 70s:Laser Speckle Velocimetry 80s:LSV,PTV,PIV,LASER development CCD cameras development Computers development First scientific paper on PIV(Adrian 1984 in Appl Opt)First commercial PIV systems 1988(TSI Inc.)Ludwig Prandtl operating his water chann
3、el in 19044What is PIV?Flow visualizationParticle tracking velocimetry(PTV)Particle image velocimetry(PIV)Particle soeckle velocimetry(PIV)5Very Basic Idea Behind Optical flow measurementsDisplacementTimeYou are HereVelocity6You are HereVery Basic Idea Behind Optical flow measurements7Very Basic Ide
4、a Behind Optical flow measurementsParticleBoundaryLaser sheetCCD Camera89Laser SheetUpper viewSide viewLaser Sheet thicknessLaser Sheet highThin laser sheetout of plane movement Thick laser sheetdecrease in S/N10Laser Sheet-Inter-pulse(t)timing may vary from less than 1 s to many ms depending upon t
5、he velocity of the flow.-A large amount of light(from 20 mJ to 400 mJ)must be available in a short time(5ns).-The repetition rate of a pulsed laser is typically 10-30Hz adequate only for velocities lightA part of the light is scattered at 90:Light scattering by a 10 m glass particle in water(from Ra
6、ffel 1998)510intensitylightLaserintensitylightcapturedCCDLight diffusion 1/r2:minimize the distance camera-laser sheetA large particle scatters more light than a small particle.Which particle size to choose?:the size dilemma!14The main Point:The particlesFor spherical particles,in a viscous flow at
7、low Reynolds number(Stokes flow)Velocity shift due to difference in densityadUpp182For gravitational velocity:a gWhich particle size to choose?:the size dilemma!15The main Point:The particlesStep response of a particleMeasures the tendency of a particle to attain velocity equilibrium with fluid182pp
8、sdA small particle follows better the flow than a large particle.Which particle size to choose?:the size dilemma!16The main Point:The particlesSmall particlesLarge particlesFollow the flowLight scatteringStep responseGoodBadGoodBadgoodBad Which particle size to choose?:the size dilemma!17The main Po
9、int:The particlesFor liquids-Polystyrene(10-100 m);aluminum(2-7 m);glass spheres(10-100 m).Usually particle diameter of 10-20 m is a good compromise.Which particle size to choose?:the size dilemma!18The main Point:The particlesWhich particle size to choose?:the size dilemma!For gas-Polystyrene(0.5-1
10、0 m);aluminum(2-7 m);magnesium(2-5 m);different oils(0.5-10 m).Usually particle diameter of 1-5 m is a good compromise.-Due to the great difference between the index of refraction of gas and particles:small particles in gas scatter enough light to be detected19The main Point:The particles-The probab
11、ility of finding a particle within the region of interest:1 Prob 0.Usually a concentration of 15-20 particles/mm3Higher particle concentrations are either not achievable or not desirable fluid dynamically(to avoid a two phase flow effect)Which particles concentration?20CCD CameraSingle frame/multi-e
12、xposureMulti-frame/multi-exposureThe spatial resolution of CCD arrays is at least two order of magnitude lower than photographic film.Ambiguity in the direction of the flow?Particle image acquisition21Pulse durationInter-pulse33.3 ms255 sCCD CameraParticle image acquisition22CCD Camera:Frame-stradel
13、ling techniquepixelframe storage areaTransfert time:-pixel to frame storage area:500 ns-frame storage area to PC:33 ms1000 x1000Particle image acquisition23CCD CameraWhat do you want from you camera?-Record sequential images in separate frames.-High spatial resolution.-Capture multiple frames at hig
14、h speed.-High sensitivity.Particle image acquisition24Velocity determinationEach image is divided into a grid of small sections known as interrogation areas(8 to 64 pixels).The mean displacement(D)within each interrogation area is calculated and divided by the inter-pulse(t)Local mean velocity25Velo
15、city determinationHow to calculate de particles displacement:Auto-correlationAuto correlationCentral peakSatellite peaksD-The displacement D must be enough important to satellite peaks to be discernable from the central peak.-Directional ambiguity.26Velocity determinationt=0t=tCross correlationOutpu
16、t correlation planHow to calculate de particles displacement:Cross-correlation-No directional ambiguity.-Even very small displacements can be measured(dp).27Velocity determinationFFT based cross-correlationCross correlation fonction:2 N2 N2 operationsCross correlation using FFT:vuGvuFjiRFFTjigjifjiR
17、,).,(,),(*Number of operations:N2log2N In practical applications FFT is used for cross-correlation.28Velocity determinationFFT based cross-correlationLimitations of FFT based cross-correlationDirect cross correlation can be defined for a finite domain,whereas FFT based cross-correlation is well defi
18、ned for infinite domain.The two sub-samples have to be of square and equal size(N)and a power of 2(8 8;16 16;32 32;64 64).A loss in spatial resolution when N has to be selected larger than required.29Velocity determinationSummary of PIV measurement30Velocity determinationOptimization of the cross-co
19、rrelation-The displacement of the particles during inter-pulse duration must be less that of the interrogation area size:“the law”-To increase spatial resolution an interrogation cell overlap of 50%can be used.-Standard and deformed window shifting.-Using PTV and PIV.-Number of particle per interrog
20、ation area:10-15.31Velocity determinationOptimization of the cross-correlationSub-pixel interpolationStandard cross-correlation:1 pixelStandard cross-correlation and sub-pixel interpolation:0.1 pixelCorrelation peak32Other PIV techniques3D stereoscopic PIV4545TruedisplacementDisplacementseen from le
21、ftDisplacementseen from rightFocal plane=Centre oflight sheetLeftcameraRightcamera33Other PIV techniques3D stereoscopic PIV34Other PIV techniques3D stereoscopic PIV35Other PIV techniquesDual Plan PIV01210128ZZRlnRlnzDzOut of plane velocity36Other PIV techniquesEndoscopic PIV37Post-processing PIV dat
22、aSpurious vectors!-Low particles density -inhomogeneous particles seeding -Particles within a vortex -low S/N -3D movement of the particles Spurious vectorWhy the spurious vectors have to be eliminated?Induce errors in velocity derivatives.38How to eliminate spurious vectors?Post-processing PIV data
23、-Set a velocity threshold(ex.Max velocity 10m/s)-Median local filter-Mean local filter(may be biased by the surrounding spurious vectors)-Temporal median filter-Application of the continuity equation-Calculation of the circulation39Post-processing PIV dataFilling the holes of spurious vectors?-Mean
24、or median of the surrounding velocities.-A weighted average of the surrounding velocities.-An interpolation filtering(the spurious vectors are considered as high frequency signals).How to replace spurious vectors?40Post-processing PIV dataEstimation of differential quantitiesFinite difference method
25、:forward,backward,center,Richardson,Determination of the vorticity from the circulation(the 8 points circulation method)Turbulence micro scales(only with high speed PIV)Pressure field41Other PIV techniquesMicro PIVlaserpassemitPolychromatic PIV can be used for two phase flow.42Other PIV techniquesMi
26、cro PIVThe same old story:the particles-Particles size:from nanometers to several microns.-The particles should be large enough to dampen the effects of Brownian motion:Brownian motion results from the interaction between the particles.This prevents the particles to follow the flow.tDu21The relative error in the measured particle displacement is:
