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© 2010, TSI Incorporated Particle Image Velocimetry Fundamental Theory and Operation
© 2010, TSI Incorporated Outline I)Definition and Core Concepts of PIV II)Software Processing- Cross-Correlation III)Hardware Principles- Basic Operation
© 2010, TSI Incorporated Copyright© 2007 TSI Incorporated Particle Image Velocimetry 2-velocity component System 3-velocity component System 1.A particle-laden flow is illuminated by a thin sheet of light (2D) 2.Two images are taken with a short time between each capture 3.The two images are compared to determine particle displacement 4.Particle displacement is translated into an instantaneous velocity measurements Def n :Experimental means to determine the i nstantaneous flow field
© 2010, TSI Incorporated PIV Fundamentals PIV measures are taken very quickly (milliseconds in total) –At time t 1 Pulsed laser sheet illuminates a planar region of the flow Particles are imaged on the camera (Frame A) –At time t 1 + t A second image (Frame B) is taken of a second light sheet –Statistical (Cross-Correlation) methods are used to determine the particle displacement over the time t, and thus the local velocity
© 2010, TSI Incorporated FRAME A Copyright© 2007 TSI Incorporated
© 2010, TSI Incorporated FRAME B Copyright© 2007 TSI Incorporated
© 2010, TSI Incorporated Instantaneous Velocity Field Copyright© 2007 TSI Incorporated
© 2010, TSI Incorporated LDV PIV Measurement at one point over a period of time Provides time history of the flow and hence time averaged statistics at one point. Flow field mapped by traversing the measuring point Velocity obtained by measuring time to travel a known distance Measurement at many points at one instant of time Provides instantaneous vector fields. Time averaged statistics obtained by averaging several image fields Velocity obtained by measuring image displacement in a known time
© 2010, TSI Incorporated Cross Correlation All particles look alike, so it is hard to find the ‘same’ particle in both Frame A and B (PTV) Instead, PIV uses a statistical approach to find the most likely displacement of a group of particles Frame A is broken up into a grid of ‘interrogation regions’ The group of particles in the interrogation region creates a unique ‘fingerprint’ that we can look for in both frames (PIV)
© 2010, TSI Incorporated Cross Correlation The relative location of the interrogation region in Frame A is known A search area is defined in Frame B. Fame B Search Area (“Spot B”) Frame A Interrogation Region (“Spot A”)
© 2010, TSI Incorporated Cross Correlation Original Particle Positions in Frame A
© 2010, TSI Incorporated Cross Correlation Location of particles in Frame B
© 2010, TSI Incorporated Cross Correlation A ‘Spot Mask’ (above) created from Frame A, is scanned across the search area of Frame B to form a ‘correlation map’
© 2010, TSI Incorporated Cross Correlation The correlation map will have a peak relative to the location where the ‘fingerprint’ of the Spot Mask is identified in Frame B
© 2010, TSI Incorporated Cross Correlation The correlation values for different locations of the spot mask can be represented on a “correlation map” In the ideal case, there is a distinct, single, round peak in the correlation map
© 2010, TSI Incorporated Cross Correlation The X and Y displacements of the particles are determined by the offset of the interrogation regions YY XX
© 2010, TSI Incorporated Cross Correlation Since we know the time separation ( t) between the 2 laser pulses very accurately, we can measure the ‘group’ velocity as the displacement / t, and assign a single velocity vector
© 2010, TSI Incorporated A)B) Cross Correlation Frame A Spot Mask NOTE: Particles and Interrogation region are typically larger than represented here in this simplified example
© 2010, TSI Incorporated Cross Correlation Map Displacement (x,y) = (0,0) (1*1) (1*0) + (1*0) 1 1 A)B) Cross Correlation
© 2010, TSI Incorporated Cross Correlation Map Displacement (x,y) = (0,1) 1 (1*0) + (1*0) 0 A)B) Cross Correlation
© 2010, TSI Incorporated Cross Correlation Map Displacement (x,y) = (0,2) 1 2 (1*1) (1*0) + (1*0) 2 A)B) Cross Correlation
© 2010, TSI Incorporated Cross Correlation Map Displacement (x,y) = (1,2) 1 2 (1*0) + (1*0) 0 A)B) Cross Correlation
© 2010, TSI Incorporated Cross Correlation Map Displacement (x,y) = (2,2) 1 2 (1*1) + (1*1) 5 5 A)B) Cross Correlation
© 2010, TSI Incorporated Cross Correlation Map Displacement (x,y) = (2,2) Peak in the Correlation Map is at (+2,+2), indicating that the particles moved in this direction from Frame A) to Frame B). A)B) Cross Correlation
© 2010, TSI Incorporated Processing particledisplacement Interrogation region Crosscorrelation Vector field Frame A Frame B Spot A Spot B
© 2010, TSI Incorporated Cross Correlation The process is repeated for each interrogation region in Frame A, resulting in a 2- Dimensional velocity field for the imaged region
© 2010, TSI Incorporated Hardware Principles 2-component System 3-component System
© 2010, TSI Incorporated System Components Imaging Subsystem (Laser, Beam delivery system, light optics) –Illuminate a plane in the flow (seeded) using a pulsed laser –Pulse energy, duration, and repetition rate –Typically Nd:YAG laser operating at 532 nm Image Capture Subsystem (CCD Camera, Camera Interface, Synchronizer-Master control unit) –Master Timing devise triggers illumination and camera capturing –Camera captures particle images and records them Analysis and Display Subsystem –Calculates and displays a two dimensional vector field from the particle image fields –Capable of processing higher-order statistics of flow field
© 2010, TSI Incorporated Nd:YAG Laser 15 mJ mJ per pulse 4 ns - 20 ns pulse duration –Acts like strobe light freezes the particle images Wide range of T –to measure flow velocities from mm/s to supersonic speeds Hz Pulse Repetition Rate 532 nm Wavelength (Frequency Doubled) –Most visible wavelength
© 2010, TSI Incorporated Energy vs. Q-switch delay Q-Switch delay (microsec) Pulse energy - % of maximum % 80% 60% 40% 20% 0% HiMedLow
© 2010, TSI Incorporated Light sheet Optics “Fan” laser light to create 2D measurement plane Combination of cylindrical and spherical lenses –Cylindrical lens diverges (fans) light in one direction –Dictates measurement area –Spherical lens waists (thins) light sheet –Achieves “2D” sheet (very thin) Cylindrical lens Spherical lens waist Fan
© 2010, TSI Incorporated PIV Image Capture Synchronizer controls timing with high precision –Controls laser power and “que” timing –Initiates camera capture Camera captures 2 images “back to back” upon trigger –Frame A exposure Independent (user defined) –Frame B exposure Dependent (fixed) –Laser light intensity determines particle image brightness NOT exposure time Timing parameters chosen so that one laser pulse appears in frame A and another in frame B
© 2010, TSI Incorporated Synchronization Camera Exposures Camera Image Readout LaserPulses Pulse separation Image 1 ReadoutImage 2 Readout Image 2 Exposure Image 1 Exposure
© 2010, TSI Incorporated Synchronization-Example Timing Camera Exposures Camera Image Readout LaserPulses 500 us 2 ms 400 ns 400 us
© 2010, TSI Incorporated Synchronizer System External trigger -or- -or- Insight3G Software Lasercontrol Capture interface Computer
© 2010, TSI Incorporated PIV Rules of Thumb for great results The key to good measurements is good raw data The raw data of PIV measurements are particle images In the Ideal Case Seed particle images are 3 – 5 pixels in diameter 5 – 15 particles per interrogation region Maximum particle displacement approximately 25% of size of interrogation region It is not always possible to satisfy these in all measurements, but they are good experimental goals
© 2010, TSI Incorporated Experiment Considerations Important considerations: –What size field of view? –What desired spatial resolution? Are the above 2 realistic together? –Appropriate seeding –Optical access Camera 90 degrees with respect to laser sheet View is not distorted What does it look like when you view the measurement region from the perspective of the camera? 0.2 m Using 4MP (2k x 2k) Camera… …apply 32pxl x 32pxl interrogation region …apply 64pxl x 64pxl interrogation region Field of View
© 2010, TSI Incorporated Experimental Setup General Setup Laser illuminates plane of interest Camera 90 degrees to light sheet Good optical access (no distortions) Camera is focused on ‘waist’ of the light sheet Setup Tips Initial setup: steps should be performed in ‘free; continuous’ mode of the Insight 3G software –Use room light, no laser Final setup: the best practice is to focus camera on seed particles in the flow –This assures that the focus is optimized to the laser sheet
© 2010, TSI Incorporated When setting up the cameras to view laser light scattered from particles: –Start on a large f-number (small aperture) and low laser energy –Increase alternately until seed particles are well- illuminated with minimal pixel saturation WARNING: IF LARGE REGIONS OF SATURATED (PINK) PIXELS APPEAR, STOP CAPTURE IMMEDIATELY –Laser light can damage camera pixels –Reduce laser energy and/or increase f-number Experimental Setup
© 2010, TSI Incorporated Calibration What are we ‘calibrating’? –We need to show the software how to convert from pixel units to the physical units relevant to our flow space We are considering the simplest case in 2D PIV, where we view the light sheet at 90 degrees with good optical access Off-axis viewing and optical distortions are sometimes unavoidable, and appropriate corrections can be made –In these cases, we need to give the software more information to be able to convert pixels to mm over the entire image region –Addressed in future webinars
© 2010, TSI Incorporated Calibration Procedure Assumption: Cameras focused on laser light sheet Calibration Steps 1.Capture and save image of “Ruler” in plane of laser light sheet 2.Create a calibration file with the saved image 3.Use the 2D-Calibration software tool to measure across a known distance in the calibration image
© 2010, TSI Incorporated Seed Density The true test of appropriate seed particle density is examining the Particle Images Considerations for Seeding Density: Field of View is known Desired Spatial Resolution known Interrogation Region Size Do I have enough particles in each interrogation region? 5-15 particles per region
© 2010, TSI Incorporated In addition to imaging the flow field, we must also determine the timing between Frame A and Frame B. This parameter is called Δt We must select a Δt so that the displacement follows our “rule of thumb” of 25% of our intended interrogation region Ensure consistency with experimental objectives –Field of view –Spatial resolution –Appropriate limits on particle displacement Maximum particle displacement should be approximately 25% of the interrogation region Optimizing t
© 2010, TSI Incorporated Optimizing t The first step in optimizing t is developing “an eye for it” Can you see the displacement? Although qualitative, this is a critical step in optimizing a PIV measurement If displacements appears random, reduce t If there is little / no displacement, increase t
© 2010, TSI Incorporated Optimizing t There are several ways to ‘measure’ the displacement for a more quantitative assessment –Zoom into individual particles –Perform ‘Point Processing’ and assess displacement of individual spots Remember, this process is iterative. Expect to alternate between experimental optimization and processing adjustments
© 2010, TSI Incorporated Optimizing t Timing Setup The Timing Setup Window in Insight 3G tt
© 2010, TSI Incorporated Basic PIV Processing Start with “general purpose” settings –Basic processing lets you know what the flow is doing and how well your images process –A good foundation for further optimization Iteratively optimize –This may include making experimental changes and acquiring new images
© 2010, TSI Incorporated PIV Rules of Thumb Review –Seed particle images are 3 – 5 pixels in diameter –5 – 15 particles per interrogation region –Maximum particle displacement approximately 25% of size of interrogation region –3-5 pixel particles allows for a Gaussian ‘fit’ to determine location to subpixel accuracy, but still allows for a high seeding density –Multiple particles per interrogation region strengthen the correlation –25% displacements keep most particles within the interrogation region, allowing the search to match with most of the spots
© 2010, TSI Incorporated Basic PIV Processing Insight3G’s default settings are a good starting point Classic PIV produces 1 vector field from 1 image 64x64 pixel size for both spot A and spot B works well for moderately- seeded flows with similar x and y velocity ranges Since we are using NyquistGrid, the starting spots are the final spots The Nyquist grid setting gives us 50% overlap between neighboring spots The FFT correlator is a good general- purpose choice. The Gaussian peak engine is normally the best choice for obtaining accurate velocities. This enforces our 25% rule of thumb
© 2010, TSI Incorporated Evaluating Processing The easiest way to evaluate your processing settings is to process a vector field. –Adjust the scale of the vectors for a clear view –Do the generated vectors appear physically reasonable? –Are there many “red” vectors that failed validation?
© 2010, TSI Incorporated Evaluating Processing Vector Statistics provide more useful information –Maximum U and V pixel displacements –Number and percentage good vectors
© 2010, TSI Incorporated Evaluating Processing This image is a good candidate for increasing the spatial resolution by decreasing interrogation region size –99.6% valid vectors –maximum particle displacements of >5 pixels –High seeding density suggests 5-15 particle rule of thumb possible for smaller interrogation region What to consider: –How much smaller? –Spot A? Spot B?
© 2010, TSI Incorporated Spot Dimensions The Spot A size is used to determine spatial resolution –Velocity of all particles in Spot A is averaged into a single vector The Spot B size and maximum dx, dy determine search area size –Larger sizes slow down processing, only help with large displacements Spot B Spot A
© 2010, TSI Incorporated Adjusting spot dimensions Dimensions of Spot A determines: –How many particles in the interrogation region (5-15) –Smallest resolvable flow features (spatial resolution) Maximum allowed displacement (dx, dy): –Maximum measurable particle displacements (dynamic range) in X and Y 25% spot width, height Adjusting these features can accommodate processing smaller interrogation regions.
© 2010, TSI Incorporated Adjusting Spot Dimensions Reprocessed with 32x32 Now we are starting to get more invalid vectors. Why? Let’s look closer: –Uneven seeding leaves some spots empty
© 2010, TSI Incorporated Adjusting Spot Dimensions Point Processing lets us evaluate the outcome of processing at a given spot. Here we see how low seeding density affects the correlation map –Multiple peaks –Lumpy Background
© 2010, TSI Incorporated Point Processing Point Processing shows us other information as well –Peak Ratio –Processing Algorithms –Input and as-processed spots –Location of the correlation peak within the map Near the center is best –Dx, Dy
© 2010, TSI Incorporated Adjusting Spot Dimensions For some flows, square spots may not be optimal –For example, a boundary layer Large displacements, low gradients in X (need large spot size) Small displacements, sharp gradients in Y (need small spot size) Can use rectangular spots to optimize both dimensions –Rectangular spot A averages velocities over a rectangular region –Rectangular spot B combined with larger allowed displacements looks for a correlation over a larger area
© 2010, TSI Incorporated Adjusting spot dimensions This flow is sufficiently seeded for 32x32 (or even 24x24) interrogation, but we still get many invalid vectors. –Dx is too large for 32x32 spot A and spot B size Try different spotA and spotB sizes Here we could also offset the search region in spot B –Requires knowledge of the flow field –Only works in flows with a dominant flow direction
© 2010, TSI Incorporated Adjusting spot dimensions 32x32 Spot A 64x32 Spot B 0.49 Maximum dx 64x24 Spot A 64x24 Spot B 0.25 Maximum dx
© 2010, TSI Incorporated Single-Pass drawbacks With a fixed spot size and single pass, smaller interrogation regions give higher spatial resolution but reduced dynamic range There are workarounds –We can relax the 25% rule of thumb and use a larger spot B if the image quality is high –We can use rectangular interrogation regions if the flow geometry permits –We can offset spot B There is a better option – Multi-pass processing –Can optimize for both spatial resolution and dynamic range –Improves SNR for better quality vector fields –Operates like a dynamic spot offset
© 2010, TSI Incorporated Multi-Pass PIV Processing Using the RecursiveNyquist- Grid Multi-pass PIV processing lets us increase our spatial resolution
© 2010, TSI Incorporated Multi-pass PIV Processing Process PIV image multiple times in sequence –Successive passes use the initial results as a starting guess The search area in Spot B is “offset” relative to Spot A – centered on the displacement “guess” Spot A and Spot B will contain only the “fingerprint” Higher SNR, more and better vectors –25% rule of thumb only applies to first pass Spot B Spot A
© 2010, TSI Incorporated Vector Post Processing Vector Validation –Basic PIV processing checks only SNR to validate vectors –Need a way to “weed out” invalid vectors In final data In between passes Vector Conditioning –Interpolation to replace discarded vectors –Smoothing –Especially important for intermediate passes in multi-pass techniques Avoids using a bad vector as a guess for additional processing
© 2010, TSI Incorporated Vector Validation Global Validation –Check velocity against specified range or number of standard deviations from the mean –Good when you know what range of velocities to expect
© 2010, TSI Incorporated Vector Validation Local Validation –More flexible, compares a vector with its neighbors –Discriminates based on difference between the vector and the median or mean displacement (in pixels), or dimensionless “Universal” median –Decrease neighborhood size for flows with high gradients –Option to replace discarded vectors with local median or secondary correlation peak
© 2010, TSI Incorporated Vector Conditioning Apply After discarding invalid vectors Replace discarded vectors with the local median or mean velocity Optionally apply a low-pass filter to the vector field for smoothing –Keep in mind that smoothing changes all vectors – modifying your data
© 2010, TSI Incorporated Deformation Grid Processing Means to sharpen peak of correlation map Accounts for high rotation or velocity gradients within interrogation regions Anticipates displacement of particles, and deforms Spot B to account for such gradients Surrounding velocities used to determine deformation (Overlaid Spot Masks) Deformed Spot B Spot A “Traditional” Spot B
© 2010, TSI Incorporated Deformation Grid Processing Stronger correlation peak and better accuracy with high gradients Higher computational cost
© 2010, TSI Incorporated Thank you! Questions?
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