Particle Image Velocimetry Chapter 1: Introduction
Introduction Particle Image Velocimetry R. J. Adrian, J. Westerweel (2011) Introduction Praticles Imaging Pixelization Particle Image Velocimetry Systems Digital Image Processing Low Image Density High Image Density Postprocessing Practical Guidelines
PIV 의기초 일반적인평면 PIV system 은 Double-pulsed laser Light-sheet-forming optics Particle seeding Monoscopic (single-lens) camera Image digitization hardware Computer for data storage and analysis 으로구성됨
Illumination 일반적으로 Double pulsed illumination 방식의 laser 가조명으로활용 solid-state Nd:YAG laser 에 frequency-doubling crystal 을이용해 532nm 파장의레이저가주로사용됨 요구되는 laser 출력은추적입자의산란특성과관련이있음
Camera and Imaging Single-Particle Imaging y x X x M 0 Y y Field of View z Camera Lens Z Video Array M Z / z 0 0 0 1 1 1 Z z f 0 0 (Gauss Lens Law) X Y
Camera and Imaging 속도벡터의계산 Laser pulse 조명의시간간격인 Δt 동안추적입자가이동한거리를계측해속도를구함 Pulse 간격은입자의이동이일차함수로표현될수있을정도로짧아야함 X P (t) ΔX P ( v, v ) px py ( xp, y p ) ( X p, Yp ) t M t 0 X P (t+δt)=x P +ΔX P
Camera and Imaging Exposure 시간동안들어온광량의총합 단위면적당들어온빛에너지의양 (, ) p I X t dt p 노출의평균은 laser power에대한영향보다 length scale에큰영향을받음 p ~ J D d 0 4 a q p z Z y z 2 2 n 0 0 0 0
Particles Particle 의크기를결정하는요인 유체의가속을따를수있을만큼작아야함 빛을산란하여이미지를밝힐수있을만큼커야함 기체의경우수μm, 액체의경우수십μm의지름을이용함 u[ xp( t), t] vp( t) vp b p b 는중력과부력의차, τ p 는 particle time constant p ( ) d 18 2 p f p f f
Particles Particle time constant Particle이유체의가속을따르는정도는 particle time constant에반비례 p ( ) d 18 2 p f p 밀도차가작을때추종성이증가 f f 굴절성의액체유동에서는빛의산란정도가감소하기때문에굴절률이큰산화알루미늄이나이산화티타늄, 속이빈구를이용하지만지름이 5~30 μm정도는되어야좋은이미지를얻을수있음
Particles Mixing 입자의분포정도에차이가없는 Uniform mixing 이중요 Turbulent mixing 을사용할수있지만난류의와동에서는원심력으로인해입자가밖으로밀려나는현상이발견 Particle time constant 를줄이면해결
Image Digitization 계측되는빛의양을전압신호로바꾸어저장 8bit, 12bit 등의정보로기록됨 (256, 4096 gray scales) 카메라의노출시간은 light pulse 의지속시간에의해결정되는데이는 shutter speed 에비해 light pulse 의지속시간이매우짧기때문
Displacement Interrogation Low density PIV (PTV) 개별입자를구별하여변위를파악 Particle 의중심은 gray level 의중심을찾아계산 입자밀도, laser sheet 두께가줄어들거나 magnification factor 가크면더큰입자변위를식별할수있음 M C z X 1/2 0( 0) p
Displacement Interrogation High density PIV Frame 1에서기록된밝기 I 1 I 2 의일치정도를판단 R( s ) I ( X ) I ( X s ) dx W1 1 2
Validating the Interrogation Error vector 의유형 Correlation noise peak 이 signal peak 보다강한경우 Surface 의반사로인한경우
Validating the Interrogation 주위 vector 와비교하여 error 벡터를판별 Frame 상의모든벡터의평균을구해 root mean square 분포를검사하여 error vector 를없앰 이웃한벡터의중간값이나평균값을이용하여벡터를검사 제거한 error 벡터는 correlation 함수에서찾은두번째, 세번째의 peak 값을이용하여다시채워넣거나이웃벡터들을이용해보간함 90% 이상의벡터가통과할수있는 filtering 방법을신뢰할만한수준으로삼음
Accuracy, Resolution, and Performance of PIV Root mean square velocity error Dynamic velocity range u DVR t M t x X u 0 max u 0 p,max cd Dynamic spatial range lx LX / M 0 DSR xp,max xp,max 높은 Reynolds 수의난류유동에서는 DVR*DSR값이높은 PIV시스템을사용 LX DVR* DSR cd M x
Stereographic PIV Z 방향 out of plane 성분유동으로인한오차가서로다른위치의두카메라에서다르게기록되는점을이용 Object Δx r Lens ΔX L ΔX R Image
Three-Dimensional Velocity in Swept-beam PIV Volumes 평면 PIV 시스템의축방향연장 공간에대한속도장이계측가능하지만동시간의속도장을계측한것은아님
Three-Dimensional Velocity in Volumes Photogrammetric PTV 여러카메라를이용하여입자의 3 차원위치를결정 높은조리개값을통해공간내부에서초점이모두맞아야함 부족한광량을보상하기위해큰추적입자를사용 (30~100 μm )
Three-Dimensional Velocity in Tomographic PIV Volumes 여러카메라를이용하여 3 차원의입자공간분포를확인 3 차원공간에대한 correlation 을수행 결과물의속도벡터개수가매우많음