AerE 344 Lecture Notes Lecture # 11: Particle image velocimetry Dr. Hui Hu Dr. Rye M Waldman Department of Aerospace Engineering Iowa State University Ames, Iowa 50011, U.S.A Sources/ Further reading: Raffel, Willert, Wereley, Kompenhans, Particle image velocimetry: A practical guide nd ed.
Particle-based Flow Diagnostic Techniques Seeded the flow with small particles (~ µm in size) Assumption: the particle tracers move with the same velocity as local flow velocity! Flow velocity V f = Particle velocity V p Measurement of particle velocity
Y (mm) Particle-based techniques: Particle Image Velocimetry (PIV) To seed fluid flows with small tracer particles (~µm), and assume the tracer particles moving with the same velocity as the low fluid flows. To measure the displacements (L) of the tracer particles between known time interval (t). The local velocity of fluid flow is calculated by U= L/t. L t= t 0 +t t=t 0 U L t 100 80 spanwise vorticity (1/s) -0.9-0.7-0.5-0.3-0.1 0.1 0.3 0.5 0.7 0.9 5.0 m/s 60 40 0 0 GA(W)-1 airfoil -0-40 shadow region -60 A. t=t 0 B. t=t 0 +10 s C. Derived Velocity field -50 0 50 100 150 X (mm)
PIV System Setup Particle tracers: track the fluid movement. Illumination system: illuminate the flow field in the interest region. Camera: capture the images of the particle tracers. Synchronizer: control the timing of the laser illumination and camera acquisition. Host computer: to store the particle images and conduct image processing. seed flow with tracer particles Illumination system (Laser and optics) camera Synchronizer Host computer
Tracer Particles for PIV Tracer particles should be neutrally buoyant and small enough to follow the flow perfectly. Tracer particles should be big enough to scatter the illumination lights efficiently. The scattering efficiency of trace particles also strongly depends on the ratio of the refractive index of the particles to that of the fluid. For example: the refractive index of water is considerably larger than that of air. The scattering of particles in air is at least one order of magnitude more efficient than particles of the same size in water. h Incident light Scattering light a. d=1μm b. d=10μm c. d=30μm
Tracer Particles for PIV 18 ); exp( (1 ) ( 18 ) ( p p s s p p p P s d t U t U g d U U U U g d U p p g 18 ) ( U P
Tracer Particles for PIV Tracers for PIV measurements in liquids (water): Polymer particles (d=10~100 m, density = 1.03 ~ 1.05 kg/cm 3 ) Silver-covered hollow glass beams (d =1 ~10 m, density = 1.03 ~ 1.05 kg/cm3) Fluorescent particle for micro flow (d=00~1000 nm, density = 1.03 ~ 1.05 kg/cm3). Quantum dots (d= ~ 10 nm) Tracers for PIV measurements in gaseous flows: Smoke Droplets, mist, vapor Condensations. Hollow silica particles (0.5 ~ μm in diameter and 0. g/cm3 in density for PIV measurements in combustion applications. Nanoparticles of combustion products
Illumination system The illumination system of PIV is always composed of light source and optics. Lasers: such as Argon-ion laser and Nd:YAG Laser, are widely used as light source in PIV systems due to their ability to emit monochromatic light with high energy density which can easily be bundled into thin light sheet for illuminating and recording the tracer particles without chromatic aberrations. Optics: always consist of a set of cylindrical lenses and mirrors to shape the light source into a planar sheet to illuminate the flow field. Laser beam Laser sheet laser optics
Double-pulsed Nd:Yag Laser for PIV
Optics for PIV
Cameras Types of cameras for PIV: Photographic film-based cameras (old) Charged-coupled device (CCD) cameras High speed Complementary metal-oxide semiconductor (CMOS) cameras Advantages of digital cameras: It is fully digitized Various digital techniques can be implemented for PIV image processing. Conventional auto- or cross- correlation techniques combined with special framing techniques can be used to measure higher velocities. Disadvantages of digital cameras: Low temporal resolution (defined by the video framing rate): Low spatial resolution:
Synchronizer Function of Synchronizer: To control the timing of the laser illumination and camera acquisition Frame straddling strategy for two-frame single exposure recordings To laser To camera 1st pulsed nd pulsed Synchronizer From computer Timing of pulsed laser t 1 st frame exposure 33.33ms (30Hz) Timing of CCD camera nd frame exposure time
Host computer To send timing control parameter to synchronizer. To store the particle images and conduct image processing. Image data from camera Host computer To synchronizer
Single-frame technique V L=V*t particle Streak line single-pulse Multiple-pulse Particle streak velocimetry
Multi-frame technique a. T=t 0 b. T=t 1 c. T=t a. T=t 3 L t= t 0 +t t=t 0 L U t
Example PIV raw data U Image: A B In-plane Δζ, Δz
Example PIV raw data U h Through-plane Trefftz plane In-plane
X/D Image Processing for PIV To extract velocity information from particle images. Image processing 5 t=t0 t=t0+4ms A typical PIV raw image pair - -1 0 1 3 Y/D 4.5 4 3.5 3.5 1.5 1 Velocity U/U in 1.100 1.050 1.000 0.950 0.900 0.850 0.800 0.750 0.700 0.650 0.600 0.550 0.500 0.450 0.400 0.350 0.300 0.50 0.00 0.150 0.100
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. t=t 0 t=t 0 +t Low particle-image density case
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-particle tracking algorithm PTV results
Correlation-based PIV methods t=t 0 +t Corresponding flow velocity field high particle-image density
Correlation-based PIV methods t=t 0 t=t 0 +t dv g y x g dv f y x f dv g y x g f y x f q p R ) ), ( ( ) ), ( ( ) ), ( )( ), ( (, Correlation coefficient function:
Cross Correlation Operation Signal A: Signal B: R u [ f ( x)* g( x u)] dx [ f ( x) ] dx* [ g( x u) ] dx
Correlation coefficient distribution R(p,q) Peak location 1 0.95 0.9 0.85 0.8 0.75 0.7 1 4 7 10 13 16 19 5 8 31S1 S10 S19 S8 R p, q ( f ( x, y) f )( g( x, y) g) dv ( f ( x, y) f ) dv ( g( x, y) g) dv
X/D Comparison between PIV and PTV Particle Tracking Velocimetry: Tracking individual particle Limited to low particle image density case Velocity vector at random points where tracer particles exist. Spatial resolution of PTV results is usually limited by the number of the tracer particles Correlation-based PIV: Tracking a group of particles Applicable to high particle image density case Spatial resolution of PIV results is usually limited by the size of the interrogation window size Velocity vector can be at regular grid points. PTV t=t 0 +t PIV 5 4.5 4 3.5 3.5 1.5 1 Velocity U/U in 1.100 1.050 1.000 0.950 0.900 0.850 0.800 0.750 0.700 0.650 0.600 0.550 0.500 0.450 0.400 0.350 0.300 0.50 0.00 0.150 0.100 - -1 0 1 3 Y/D
Y (mm) Estimation of differential quantities 0 15 10 5 10 15 0 5 30 35 X (mm)
Estimation of differential quantities
Estimation of Vorticity distribution z V x U y
Estimation of Vorticity distribution Stokes Theorem: V dl da z C da x y S
Y mm U out Y (mm) Vorticity distribution Examples 50 00 Spanwise Vorticity ( Z-direction ) -5.00-0.00-15.00-10.00-5.00 0.00 5.00 10.00 15.00 0.00 5.00 spanwise vorticity (1/s) 60-3. -.7 -. -1.7-1. -0.7-0. 0.3 0.8 1.3 1.8 10 m/s water free surface 40 150 100 Re =6,700 Uin = 0.33 m/s 0 0 50-0 GA(W)-1 airfoil 0 X mm -50-50 0 50 100 150 00 50 300-40 -60 shadow region -0 0 0 40 60 80 100 10 140 X (mm)
Ensemble-averaged quantities Mean velocity components in x, y directions: Turbulent velocity fluctuations: Turbulent Kinetic energy distribution: Reynolds stress distribution: N U u u N i i / ) ( ' 1 N i v i V v 1 ) ( ' N i u i N U 1 / N i v i N V 1 / ) ' ' ( 1 v u TKE N i i i N U v U u v u 1 ) )( ( ' '
Y (mm) Y (mm) Y (mm) Y (mm) Ensemble-averaged quantities 10 m/s 60 vort: -3.0 -.0-1.0 0.0 1.0.0 3.0 10 m/s 60 U m/s: -1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 40 40 0 0 0 GA(W)-1 airfoil 0 GA(W)-1 airfoil -0-0 -40 shadow region -40 shadow region -60-60 -0 0 0 40 60 80 100 10 140 X (mm) -0 0 0 40 60 80 100 10 140 X (mm) T.K.E 60 0.010 0.00 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 Normalized 60 Reynolds Stress -0.035-0.05-0.015-0.005 0.005 0.015 0.05 0.035 40 40 0 0 0 GA(W)-1 airfoil 0 GA(W)-1 airfoil -0-0 -40 shadow region -40 shadow region -60-60 -0 0 0 40 60 80 100 10 140 X (mm) -0 0 0 40 60 80 100 10 140 X (mm)
Pressure field estimation ) ( 1 ) ( 1 y v x v y p y v v x v u y u x u x p y u v x u u
Y (mm) Integral Force estimation t C. V. V dv C. S. ~ ( VV) da P da f C. S. C. V. dv F 10 m/s 60 U m/s: -1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 40 0 0 GA(W)-1 airfoil -0-40 shadow region -60-0 0 0 40 60 80 100 10 140 X (mm)
AerE344 Lab: Pressure Measurements in a de Laval Nozzle Tank with compressed air Test section Tap No. Distance downstream of throat (inches) Area (Sq. inches) 1-4.00 0.800-1.50 0.59 3-0.30 0.480 4-0.18 0.478 5 0.00 0.476 6 0.15 0.497 7 0.30 0.518 8 0.45 0.539 9 0.60 0.560 10 0.75 0.581 11 0.90 0.599 1 1.05 0.616 13 1.0 0.67 14 1.35 0.63 15 1.45 0.634
1 st, nd, and 3 rd critical conditions Underexpanded flow nd critical shock is at nozzle exit Flow close to 3 rd critical Over-expanded flow with shock between nozzle exit and throat Overexpanded flow 1 st critical shock is almost at the nozzle throat.