Particle Image Velocimetry Part - 3

Transcription

1 AerE 545X class notes #5 Particle Image Velocimetry Part - 3 Hui Hu Department of Aerospace Engineering, Iowa State University Ames, Iowa 50011, U.S.A

2 PIV System Setup Particle tracers: Illumination system: Camera: Synchronizer: Host computer: to track the fluid movement. to illuminate the flow field in the interest region. to capture the images of the particle tracers. the control the timing of the laser illumination and camera acquisition. to store the particle images and conduct image processing. seed flow with tracer particles Illumination system (Laser and optics) camera Synchronizer Host computer

3 Particle Tracking Velocimetry (PTV)- 1. Find position of the particles at each images. Find corresponding particle image pair in the different image frame 3. Find the displacements between the particle pairs. 4. Velocity of particle equates the displacement divided by the time interval between the frames. Search region for time step t=t 3 Search region for time step t=t 4 Search region for time step t=t Particle position of time step t=t 1 Four-frame frame-particle tracking algorithm PTV results

4 Correlation-based PIV methods t=t 0 t=t 0 +Δt Corresponding flow high particle-image density velocity field

5 Correlation-based PIV methods Searching window size (SB) SB SA SA Interrogation window SB q(x, P(x, SB t=t 0 t=t 0 +Δt Correlation coefficient function R ( p, q) = f )( g( x, f ) ( g( x,

6 Correlation coefficient distribution R(p,q) Peak location S1 S10 S19 S8 R ( p, q) = f )( g( f ) ( g(

7 FFT-based Cross Correlation and Direct Cross Correlation R ( p, q) = f )( g( f ) ( g( FFT-based Cross-correlation method aantage: Fast disaantage: additional error. Image 1 Image Direct calculation output Cross correlation data Direct cross-correlation correlation method aantage: accurate disaantage: time consuming

8 Sub-pixel interpolation for Digital PIV R ( p, q) = f )( g( f ) ( g( pixel Correlation coefficient R(x) Pixel With sub-pixel interpolation processing, the accuracy of the PIV measurement could be about 0.1 pixel

9 Overlapping rate for PIV image processing R ( p, q) = f )( g( f ) ( g( Interrogation window size, L Overlapping rate = D / S 50% overlapping is usually used for PIV image processing!! Distance between the centers of the two neighboring interrogation Copyright windows, by Dr. D Hui Iowa State University. All Rights Reserved!

10 Effect of interrogation window size Interrogation size usually determines the spatial resolution of the PIV measurements. Smaller interrogation window size will give better spatial resolution of the PIV measurement. However, too small mall interrogation window size would result in many bad vectors. However, too s Usually to have about 10 ~ 0 particles inside an interrogation window would give a good PIV result! R ( p, q) = f )( g( f ) ( g( Searching window size (SB) SA SA SB Interrogation window

11 Effect of search window size The size of the search window size would determine total time required for the cross correlation processing Smaller search window size could save the computational time, however, would result in error vectors for the particles with larger displacement. R ( p, q) = f )( g( f ) ( g( Searching window size (SB) SA SA SB Interrogation window

12 Effect of the Displacements of the Tracer Particles or the Time Delay between the Two Laser Pulses Too large displacement of the particles (i.e., longer time delay ) would result in bigger errors due to the relative movement of the particles inside the interrogation window. Too small displacement of the particles (i.e., smaller time delay ) would also result in bigger errors due to the relative small displacement related to the limited resolution of the digital camera. Too small displacement of the particles would also It usually to have particle displacement about 4~6 pixels if the interrogation size is chosen to be 3 pixels.

13 Effect of the out-of of-plan velocity for -D D PIV measurements case A F G H V M V X W M N 4,000 4,000 4,000 4,000 D M CR-U CR-V AVE-ERR ERR 7.1% 13.75% 41.30% 13.1% V M : average velocity (pixel/interval) V X : maximum Velocity (pixel/interval) W M : out of plane velocity (laser width/interval) N: tracer number D M : tracer average diameter (pixel) Aver-Err: average error of PIV results without sub-pixel interpolation. Out-of-plane velocity X Laser Sheet In-plane velocity Z Real velocity Laser sheet y x Camera z

14 Effect of the diameter of particle images CASE V M V X W M N D M CR-U CR-V AVE-ERR ERR , % , % , % V M : average velocity (pixel/interval) V X : maximum Velocity (pixel/interval) W M : out of plane velocity (laser width/interval) N: tracer particle number D M : tracer average diameter (pixel) Aver-Err: average error of PIV results without sub-pixel interpolation. Bigger particles maybe beneficial for PIV image processing Bigger particles would cause the problem for the unsteady flow tracking t!