Measurement Techniques. Digital Particle Image Velocimetry

Transcription

1 Measurement Techniques Digital Particle Image Velocimetry Heat and Mass Transfer Laboratory (LTCM) Sepideh Khodaparast Marco Milan Navid Borhani 1

2 Content m Introduction m Particle Image Velocimetry features m System components for Particle Image Velocimetry m Principles of Particle Image Velocimetry m Practical test (TPA) description 2

3 Origins of Particle Image Velocimetry Ludwig Prandtl water tunnel (1904) Poohsticks (1928) Lausanne, 08/03/2010 3

4 Particle Image Velocimetry applications Fluid velocity measurement for fluid dynamic characterization: Air flowing around a car or an aircraft, water running through hydroelectric turbine, blood flow, etc. 4

5 Particle Image Velocimetry features Advantages: Non-intrusive technique: no modification of the flow property at the scale of interest Good resolution and accuracy: instantaneous velocity vector maps in a cross-section of the flow 2D-3D Velocity field reconstruction: 3D components may be obtained with the use of a stereoscopic arrangement Drawbacks: Setup Time: need to optimize a number of parameters Cost 5

6 System components for Particle Image Velocimetry Test section, seeding particles Laser sheet Camera 6

7 Principles of Particle Image Velocimetry Flow Direction Tube Wall Seeding particles Time: t Position: (x 1, y 1 ) Time: t + Δt Position: (x 2, y 2 ) Velocity vector at: x + x2 y1 +, 2 2 y x2 x = Δt y y Δ 1 2 1, 2 Δt t+ t 2 1 7

8 Cross-correlation function R ( s) = I ( x) I ( x + s) dx 1 2 I 1 and I 2 are sub-area (interrogation windows) of the total frame x is the interrogation location s is the shift between the images Two-dimensional discrete correlation function: R ( Δx Δy) = I ( x, y) I ( x + Δx, y + Δy), 1 2 x y R(Δx, Δx)= Correla-on Map 8

9 Particle Image Velocimetry protocol 1 - Divide the images into a regular grid of smaller regions: interrogation windows (IW) 2 - Each IW of the first image is correlated with the corresponding IW of the second image 3 - Find the location of the displacement peak and compute the velocity vector 4 - Reconstruct the flow velocity field 9

10 Particle selection Small enough to follow fluid motion Large enough to be visible Homogeneously distributed Tracer should not alter fluid / flow properties Optimal particle image diameter: D I =2.5 pixels Capturing fluid motion Stokes number: St v = particle _ response _ time time _ characteristic _ of _ flow τ V = τ F St v <<1: The particles and fluids will be in near equilibrium St v >>1: The particles will be unaffected by the fluid 10

11 Seeding particle density (number of particle per interrogation window) N CΔz = M 0 2 D I 2 I 0 C Δz 0 D I M 0 Particle concentration Light sheet tickness Interrogation window size Magnification N I = 5 N I = 10 N I = 15 More particles: better signal to noise ratio Unambiguous detection of peak from noise N I = 10 (10 particles per IW are sufficient to perform PIV) 11

12 Maximum in-plane particle displacement ΔX D I F I Particle displacement Interrogation window size In plane loss-of-correlation ΔX/D I = 0.00 F I = X,Y Displacements < quarter of the interrogation window size Choose the sampling interval and the optical magnification factor so that the maximum image displacement is less than a quarter of the interrogation window size 12

13 Maximum out-of-plane particle displacement ΔZ Δz 0 F o Particle displacement normal to the observed plane Light sheet thickness Out-of-plane loss-of-correlation ΔZ/ Δz 0 = 0.00 F o = Z Displacement < quarter of the light sheet thickness Define a suitable observation plane and choose a sampling interval so that the particle shift normal to the observed plane is less than a quarter of the light sheet thickness 13

14 Spatial gradient - Interrogation window size The PIV resolution is proportional to the IW size. It has to be defined to resolve local flow gradients Keeping constant the particle size and density, altering the IW size will change the number of particles used to calculate the local velocity in an interrogation window. The total number of vector for a given image pair depends directly on the IW size 14

15 Interrogation window overlap Overlap of the interrogation windows increase the number of particle that are used in calculating the flow field Better spatial resolution IW 1 IW 2 - Longer computational time 50% IW Overlap Interrogation window offset Offset increase the PIV accuracy for flow with a dominant direction. The IW is shifted between the first and the second image Better accuracy - Longer computational time IW 1 IW 1 IW Offset Image 1 Image 2 15

16 PIV Design rules Optimal particle image diameter Image density In-plane motion D I =2.5 pixels N I = 10 ΔX < 0.25 IW Size Out-of-plane motion Δz < 0.25 light sheet thickness The IW size and the sampling interval define the spatial and the temporal resolution 16

17 PIV system components: Test section Laser sheet Camera Practical test (TPA) description TP procedure: 1. Tune and calibrate the PIV system 2. Record images at 3 different locations 3. Process the images on the PC 4. Save and export the results TP objectives: PIV system tuning (Record nice images) 3: elbow 2: guiding vanes 1: Laminar flow Understand the principles of the PIV technique (ex: correlation function) and the influence of the measurement parameters (n of particles, size of the IW, overlap, etc.) 17

18 Enjoy the TPA!!! Lausanne, 08/03/