AerE 344 Lecture Notes Lecture # 12: Illumination, imaging, and particle image velocimetry Dr. Hui Hu Department of Aerospace Engineering Iowa State University Ames, Iowa 50011, U.S.A Sources/ Further reading: Hecht, Optics 4 th ed. Raffel, Willert, Wereley, Kompenhans, Particle image velocimetry: A practical guide 2 nd ed.
Photon scattering: The nature of light as photons one finds experimentally that the frequency of the scattered wave is changed, which does not come out of a wave picture of light. However, when the light is viewed as a photon with energy proportional to the associated light wave, excellent agreement with experiment is found. The photoelectric effect: When light shines on a metal plate, electrons are ejected. These electrons are accelerated to a nearby plate by an external potential difference, and a photoelectric current is established, as below The photons hit an electron in the metal, giving up energy. If photon energy is sufficient to free the electron, it is accelerated towards the other side; hence, a flow of charges (current). The photoelectric current depends critically on the frequency of the light. This is a feature of the energy that the electrons gain when struck by the light. in the wave description, the energy of the light depends on the amplitude, and not on the frequency. however, in the photon description of light, the energy of the photon is proportional to the frequency of the associated wave, which provides a natural explanation of the frequency dependence of the photoelectric current. The explanation was first given by Einstein and won him the Nobel Prize. h Planck const 6.624 10 34 Js
Light Scattering Scattering Scattering is a general physical process whereby some forms of radiation, such as light, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which it passes. Elastic Scattering Excited electron or atoms emits a photo have exact the same frequency as the incident one. Inelastic scattering Excited electron or atoms emits a photo have a frequency different from the incident one.
Elastic scattering Rayleigh Scattering Light scattering from particles that are smaller than 1/15 of the incident light wavelength (d< /15). Efficiency of the scattering from a particle is expressed in terms of scattering cross section. 0 2 R T ( ) 29 2 T 6.6510 m Mie Scattering 0 is the charateristic wavelength of the atom. Light scattering from a particles with its size close on bigger than the incident light wavelength (d > ). Conservation of polarization direction Angle dependent Forward scattering Back scattering a. d=1μm b. d=10μm c. d=30μm
Inelastic Scattering Raman Scattering Inelastic scattering from molecules. Chance to occur is about 10-5 ~ 10-2 of times lower than the Rayleigh scattering Scattering cross section is several orders smaller than the Rayleigh scattering Stoke transition : the energy of the emitted photon is higher than the absorbed photo. Anti-stoke transition: the energy of the emitted photon is lower than the absorbed photo. Time between the absorption and emission: 10-14 s. Anti-stokes line will be stronger when the temperature is low.
Fluorescence and phosphorescence Rayleigh and Raman scattering occurs essentially instantaneously. Not allowing other energy conversion phenomena to occur. Fluorescence and phosphorescence Photoluminescence with time delay Fluorescence Emission when the excited from singlet state to ground, lifetime is about 10-10 ~ 10-5 s. Rhodamine B
Relative intensity Fluorescence and phosphorescence Phosphorescence Emission when the excited atom or molecule from triplet state to ground, lifetime is about 10-4 ~ 10-5 s. Spectraphotometer Output vs Wavelength 5000 Phosphorescence 4000 3000 T = 32.0 o C T= 25.4 o C T= 19.7 o C T= 14.5 o C T = 10.2 o C T= 3.40 o C 2000 1000 fluorescence 0 200 300 400 500 600 700 800 Wavelength (nm) MTV chemical: 1-BrNp M-CD ROH complex
Absorption Light is transmitted through a material, it will be absorbed by the molecules of the material Beer s law: I I 0 exp( L) is the absorption or attenuation coefficient Lc=1/ is called penetration depth. When L=L c, I/I 0 =1/e=37%, i.e., 63% energy was absorbed Metals have very small Lc=1/. Copper, Lc=0.6nm for 100 nm UV light Copper, Lc=6.0nm for 1000 nm infrared light. 2nm copper plate as a low pass filter. I 0 L
Light sources: Thermal source: Lamps: Continuous wave (CW) Flash lamps (Pulsed) Arc lamps Laser sources Continuous wave (CW) Pulsed laser Singe wavelength Point source: Plane source: Illumination
Thermal light source: Light source Emit electromagnetic radiation as a result of being heated to high-temperature Line sources: Continuum sources: Incandescent lamps: heated tungsten filament in a evacuated glass container. Electric discharge lamps: fluorescent lamps. Filled with mercury vapor at low pressure and utilize an electric discharge through it to produce light in ultraviolet (UV) range. Through fluorescent, it is convert to visible light. Flash lamps: tubes containing a noble gas such xenon, krypton or argon. For their operation, high voltage stored in a capacitor is discharged through the gas, producing a highly luminous corona discharge. Light pulse is about 1s to1 ms. Sparks: produced by the electric breakdown of a gas (helium, neo, argon or air) during an electric discharge between electrodes. The choice of different electrodes produces sparks of different shapes.
Laser Laser: Light Amplification by Stimulated Emission of Radiation (LASER) Advantages of laser light over thermal light source: Coherent light (with all light wave front in phase) Collimated and concentrated (parallel light with small cross area) Monochromic (energy concentrated in a very narrow wavelength band) How a laser works: Radiation energy is produced by an activated medium( can be gas, crystal or semiconductor or liquid solution). The medium consists of particles (atom, ions or molecules). When a photo, having energy hv, approaching the particles, the photo may be absorbed cause an electron or atoms to be raised temporarily to high-energy level. When the excited electron or molecule to return ground level, spontaneous emission or stimulated emission would take place.
Laser Spontaneous emission: emit a photo with the same energy as that absorbed one, but in random direction. Stimulated emission: An electron or atom is already at a higher energy level could become excited by an incident photo, without absorb the photo, it will emission another photo with identical energy (frequency), phase, and direction as the incident photon. External power source is required to maintain the population of the atoms in higher energy level in order to make to stimulated emission taking place continuously. Optical cavity. Q-switch
Helium-neon (He-Ne) laser Active medium is helium neon atoms Continuous wave laser Power 0.3 ~15 mw =633nm (red) Commonly used Lasers Argon-ion (Ar-ion) laser Active medium is argon atoms maintained at the ion state. Continuous wave laser Power level: 100 mw ~10 W Have seven wavelengths =488n (blue) =514.5nm (green) LDV application LIF in liquid flows
Commonly used Lasers Nd-YAG laser Solid-state laser Active medium: neodymium (Nd+3) as active medium incorporated as an impurity into a crystal of Yattium- Aluminium-Garnet (YAG) as a host Flash lamp is used as external source pulsed laser: 10-400mJ/pulse or more Pulse duration: 100ps ~ 10ns Wavelenght of tube =1064nm (infrared) SHG: =532nm (green), THG: =355nm (UV), FHG: =266nm (deepuv) PIV, MTV, PLIF Repetition rate can be as high as 30 Hz.
Commonly used Lasers Copper Vapor laser Active medium: copper vapor Pulsed laser: 10mJ/pulse or more Pulse duration: 15 ~ 60ns =510.6nm (green), =578.2nm (yellow) Repetition rate can be as high as f=5,000~15,000 Hz. High-speed PIV, LIF and others Dye laser Active medium: complex multi-atomic organic molecules =200nm ~ 1500nm Excimer laser Gas laser KrF and Xecl High-energy UV wavelength Pulsed laser high repetition frequency
Light sensing and recording
Lenses Focal length: f f/#, F-number : defined as the ratio of focal distance of the lens and its clear aperture diameter. Depth of focus H = 2 f/# c Z/f
Photodetector Photo detector is a device to convert light to an electric current through photo electric effect. Quantum efficiency: Ne q N p Ne : Number of absorbed photons N : Number of emitted electrons p Noise: Shot noise: due to random fluctuation of the rate of photon collection and back ground illumination Thermal noise: caused by amplification of current inside the photo detector and by external amplifier. Dark current: the current produced by the photo detector even in the absence of a desirable light source. Two kinds of photo detectors: Photomultiplier tubes (PMT) photodiodes (PD) or photo electric cells
Photodetector photodiodes (PD) or photo electric cells P-n junctions of semiconductors, commonly silicon-silicon type. High quantum efficiency But not internal amplification
Interlaced Cameras The fastest response time of human being for images is about ~ 15Hz Video format: PAL (Phase Alternating Line ) format with frame rate of f=25hz (sometimes in 50Hz). Used by U.K., Germany, Spain, Portugal, Italy, China, India, most of Africa, and the Middle East NTSC format: established by National Television Standards Committee (NTSC) with frame rate of f=30hz. Used by U.S., Canada, Mexico, some parts of Central and South America, Japan, Taiwan, and Korea. Old field (1,3,5 639) Even field (2,4,6 640) 1 frame F=30Hz Odd field 16.6ms 16.6ms time Even field 480 pixels by 640 pixels Interlaced camera
Progressive scan camera All image systems produce a clear image of the background Jagged edges from motion with interlaced scan Motion blur caused by the lack of resolution in the 2CIF sample Only progressive scan makes it possible to identify the driver
Mystery of flying rods
Electronic shutter modes Rolling shutter: The sensor is exposed line by line. Each of the pixels integrate light for the specified exposure time; however, not all pixels are exposing at the same time. The start time for each pixel s exposure is a function of sensor position. This mode is typical of large formate sensors, such as digital SLR cameras. Global shutter: Each pixel integrates light for the specified exposure time simultaneously. This method is preferred for capturing highly dynamic events. This mode is typical of high-speed CMOS cameras which can operate at frame rates beyond 1 million frames per second. Point Grey Cameras Rolling shutter Point Grey Cameras Gobal shutter
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 20 0 GA(W)-1 airfoil -20-40 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 ) ( 2 2 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 ) ( 2 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=200~1000 nm, density = 1.03 ~ 1.05 kg/cm3). Quantum dots (d= 2 ~ 10 nm) Tracers for PIV measurements in gaseous flows: Smoke Droplets, mist, vapor Condensations. Hollow silica particles (0.5 ~ 2 μm in diameter and 0.2 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 2nd pulsed Synchronizer From computer Timing of pulsed laser t 1 st frame exposure 33.33ms (30Hz) Timing of CCD camera 2nd 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 2 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 -2-1 0 1 2 3 Y/D 4.5 4 3.5 3 2.5 2 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 0.250 0.200 0.150 0.100
Particle Tracking Velocimetry (PTV) 1. Find position of the particles at each images 2. 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)-2 1. Find position of the particles at each images 2. 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 2 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 2 2 ) ), ( ( ) ), ( ( ) ), ( )( ), ( (, Correlation coefficient function:
Cross Correlation Operation Signal A: Signal B: R u [ f ( x)* g( x u)] dx [ f ( x) 2 ] dx* [ g( x u) 2 ] 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 22 25 28 31S1 S10 S19 S28 R p, q ( f ( x, y) f )( g( x, y) g) dv ( f ( x, y) f ) 2 dv ( g( x, y) g) 2 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 2.5 2 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 0.250 0.200 0.150 0.100-2 -1 0 1 2 3 Y/D
Y (mm) Estimation of differential quantities 20 15 10 5 10 15 20 25 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 C S z x y da
Y mm U out Y (mm) Vorticity distribution Examples 250 200 Spanwise Vorticity ( Z-direction ) -25.00-20.00-15.00-10.00-5.00 0.00 5.00 10.00 15.00 20.00 25.00 spanwise vorticity (1/s) 60-3.2-2.7-2.2-1.7-1.2-0.7-0.2 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 20 0 50-20 GA(W)-1 airfoil 0 X mm -50-50 0 50 100 150 200 250 300-40 -60 shadow region -20 0 20 40 60 80 100 120 140 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 2 N i v i V v 1 2 ) ( ' N i u i N U 1 / N i v i N V 1 / ) ' ' ( 2 1 2 2 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: -3.0-2.0-1.0 0.0 1.0 2.0 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 20 20 0 GA(W)-1 airfoil 0 GA(W)-1 airfoil -20-20 -40 shadow region -40 shadow region -60-60 -20 0 20 40 60 80 100 120 140 X (mm) -20 0 20 40 60 80 100 120 140 X (mm) T.K.E 60 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 Normalized 60 Reynolds Stress -0.035-0.025-0.015-0.005 0.005 0.015 0.025 0.035 40 40 20 20 0 GA(W)-1 airfoil 0 GA(W)-1 airfoil -20-20 -40 shadow region -40 shadow region -60-60 -20 0 20 40 60 80 100 120 140 X (mm) -20 0 20 40 60 80 100 120 140 X (mm)
Pressure field estimation ) ( 1 ) ( 1 2 2 2 2 2 2 2 2 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. ~ ( V V ) 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 20 0 GA(W)-1 airfoil -20-40 shadow region -60-20 0 20 40 60 80 100 120 140 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 2-1.50 0.529 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 12 1.05 0.616 13 1.20 0.627 14 1.35 0.632 15 1.45 0.634
1 st, 2 nd, and 3 rd critical conditions Underexpanded flow 2 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.