Hui Hu Department of Aerospace Engineering, Iowa State University Ames, Iowa 50011, U.S.A

Transcription

1 AerE 311L & AerE343L Lecture Notes Lecture # 14: Advanced Particle Image Velocimetry Technique Hui Hu Department of Aerospace Engineering, Iowa State University Ames, Iowa 511, U.S.A

2 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 (ΔL) of the tracer particles between known time interval (Δt). The local velocity of fluid flow is calculated by U= Δ L/Δt. ΔL t= t +Δt t=t ΔL U = Δ t 1 8 spanwise vorticity (1/s) m/s 6 4 Y (mm) GA(W)-1 airfoil - -4 shadow region -6 A. t=t B. t=t +1 μs C. Derived Velocity field (mm)

3 Effect of the out-of of-plane velocity for -D D PIV measurements case A F G H V M V W M N 4, 4, 4, 4, D M CR-U CR-V AVE-ERR ERR 7.1% 13.75% 41.3% 13.1% V M : average velocity (pixel/interval) V : 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 Laser Sheet In-plane velocity Z Real velocity Laser sheet y x Camera z

4 Stereoscopic PIV technique YPIEL YPIEL PIEL Displacement vectors in left camera PIEL Displacement vectors in right camera Laser Sheet Y Z Z α 1 α Camera 1 Camera m Y mm Wm/s

5 Stereoscopic PIV technique Laser Sheet Laser Sheet a. lens translation arrangement lens lens b. angle displacement arrangement Image recording plane Image recording plane Camera 1 Camera Camera 1 Camera Lens 1 Lens C. Angle displacement arrangement with sheimpflug condition Camera 1 Image recording plane 1 Camera Image recording plane

6 Stereoscopic PIV technique a. image of left camera b. rectangular grid in the object plane c. image of left camera The perspective effect of the angle displacement arrangement Laser Sheet Z α α 1 Copyright by Dr. Hui Hu Iowa 1 State University. Camera All Rights Reserved!

7 Mapping Function for Stereo PIV ( c) = F ( c) ( x i ) Δ Δ Δ Δ (1) 1 (1) () 1 () = F F F F (1) 1,1 (1),1 () 1,1 (),1 F F F F (1) 1, (1), () 1, (), F F F F (1) 1,3 (1),3 () 1,3 (),3 Δx Δx Δx 1 3 In-plane velocity Laser sheet y x Out-of-plane velocity Real velocity ( c) ( c) Fi Fi, j = c = 1,, i = 1, j = 1,,3 x j z ( c ) i Δ ( F) Δx Z Laser Sheet α α 1 Camera 1 Camera

8 Mapping Function for Stereo PIV ( c) ( c) = F ( xi ) F( x, y, z) = a + a1x + a y + a3z + a4x + a5xy + a6 y 3 + a13 y + a14x z + a15xyz + a16 y z + a17xz a y + a x z + a x yz + a xy z + a a7xz + a8 yz + a9z + a1x a18 yz + a19x + ax y + 3 y z + a x z + a xyz + a a x y + a z + a 3 11 a1x 3 y z 1 1 x xy 3 y Laser light sheet Location Z=-.5mm Location Z= Location Z=.5mm Z Laser Sheet Z α α 1 Camera 1 Camera a. image from the left camera b. image from the right camera

9 Flow Chart for Stereo PIV measurements Grid for left image recording camera Grid for Right image recording camera Calibration images from the left image recording camera L, Y L x,y,z In-situ calibration for general mapping function L (x,y,z), Y L (x,y,z) x,y,z In-situ calibration for General mapping function R (x,y,z), Y R (x,y,z) Calibration images from the right image recording camera R, Y R In-situ calibration to determine the mapping function Differential operation Derivatives of the mapping function d L (x,y,z)/ dx, d L (x,y,z)/ dy, d L (x,y,z)/ dz, dy L (x,y,z)/ dx, dy L (x,y,z)/ dy, dy L (x,y,z)/ dz, Differential operation Derivatives of the mapping function d R (x,y,z)/ dx, d R (x,y,z)/ dy, d R (x,y,z)/ dz, dy R (x,y,z)/ dx, dy R (x,y,z)/ dy, dy R (x,y,z)/ dz, Cross-Correlation Correlation operation by using HR-PIV method to calculate D L, D Y L PIV images of left camera Three-dimensional displacement vector ( D x, D y, D z) reconstruction by solving Equation (4-) with least square method Cross-Correlation Correlation operation by using HR- PIVmethod to calculate D R, D Y R PIV images of right camera To reconstruct the 3-3 component of the velocity vector using the mapping function Coordinate values of the point ( in the objective plane x,y ) Three-dimensional displacement vector ( D x, D y, D z) at the the point ( x,y)

10 Stereoscopic PIV system optics Host computer Laser sheet Double-pulsed Nd:YAG Laser 65mm Synchronizer Lobed nozzle 5 Measurement region 8mm by 8mm 65mm 5 high-resolution CCD cameras

11 Stereoscopic PIV technique a. PIV image from the left camera b. PIV image from the right camera YPIEL YPIEL PIEL Displacement vectors in left camera PIEL Displacement vectors in right camera

12 Stereoscopic PIV technique YPIEL YPIEL PIEL Displacement vectors in left camera PIEL Displacement vectors in right camera Y m/s Z Y mm Wm/s Copyright by Dr. Hui 1Iowa State University. All Rights Reserved! mm 3-3

13 Measurements Results Y Z Y mm Wm/s mm a. instantaneous velocity b. instantaneous velocity (-Y Y plane view) 1 m/s Wm/s c. ensemble m Z 3 c. ensemble-averaged velocity Y mm Y Wm/s mm m/s d. ensemble-avereged velocity(-y Y plane view)

14 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 (ΔL) of the tracer particles between known time interval (Δt). The local velocity of fluid flow is calculated by U= Δ L/Δt YPIEL YPIEL PIEL 5 1 PIEL A. t=t B. t=t +4ms Spanwise Vorticity ( Z-direction ) Displacement vectors in left camera Laser Sheet Displacement vectors in right camera Y 15 Re =6,7 water free surface Z Z 1 5 Uin =.33 m/s mm Uout C. Derived Velocity field α 1 α Camera 1 Camera Classic -D D PIV measurement Copyright by Dr. Hui Iowa State Stereoscopic University. All PIV Rights measurement Reserved! m Y mm Wm/s

15 Dual-plane Stereoscopic PIV System!? Why??? Vorticity vector is defined as the curl of the velocity vector : v u ϖ z = ; w v ϖ x = ; ϖ y x y y z u w = z x Simultaneous measurements of velocity vectors (three-components) at least at two spatially separated planes are need in order to get all three-components of vorticity vectors. z Measurement plane x y Classical PIV or SPIV systems can only provide measurement results in one single plane instantaneously z Measurement plane 1 Development of a Dual-plane Stereoscopic PIV system to achieve the stereoscopic PIV measurements at two parallel planes simultaneously. y x Measurement plane Dual-plane Stereoscopic PIV system can achieve stereoscopic PIV measurements at two parallel planes simultaneously

16 Dual-plane Stereoscopic PIV System!? How??? Key point for the simultaneous stereoscopic PIV measurements at two parallel planes is to achieve scattering light separation. color (wavelength) separation method. y y z x Measurement plane 1 Measurement plane The scattering light signals from two measurement planes will be mixed without special consideration z Color 1 x Color Color (wavelength) separation method polarization separation method. The polarization of Mie scattering light is conservative in air. y z x P- polarization(horizontal) S- polarization(vertical) polarization separation method

17 Optical Set-up for Dual-plane SPIV Illumination Mirror 15 Laser sheets Mirror 1 1a 8a 6a V V 7a V(s) V V (s) 9a SHG H(p) 5a V 1b 6b Cylindrical lens 14 Polarizer 13 H(p) Half wave plate 11 V 9b V V V(s) SHG V 8b 7b Laser tube 4 Laser tube 3 Laser tube Laser tube 1 Double-pulsed Nd:YAG laser set A Double-pulsed Nd:YAG laser set B 1 to 4 : laser tube 5,8,11: half wave plate 6,9, 1,15: mirror 7,13: polarizer 14: cylinder lens

18 Set-up for Dual-plane SPIV Image Recording Vertically polarized laser sheet (S-polarized lights) Schiemflug condition Lens plane Mirror 5 5 Horizontally polarized laser sheet (P-polarized lights) Mirror Image plane Camera 1 Camera Polarizing beam splitter cubes Camera 3 Camera 4 To laser system Synchronizer

19 Concept of Lobed Mixer/Nozzle Aero-engine: engine: enhance mixing between hot high- speed flow exhaust from core-engine engine with cold low-speed bypass flow civilian airplanes: reduce jet noise during take-off and landing thrust augmentation Military airplanes: reduce the length of the hot plume, therefore, reduce the infrared emission signals to improve its survivability from the attack of infrared guided missiles. Turbo-fan aero-engine Combustion: enhance mixing between the fuel with air in the combustion chamber improve combustion efficiency suppression pollutant formation Lobed mixer/nozzle NASA model

20 Vortex Structures Downstream a Lobed Mixer/Nozzle Two kinds of vortex structures are considered to play important roles for the mixing enhancement in a lobed mixing flow: Azimuthal (spanwise)) vortex structures due to the Kelvin-Helmholtz instability at the interface between two streams. Large-scale streamwise vortices generated by the special geometry of the lobed trailing edge The lobed nozzle used in the present study

21 Laser Induced Fluorescence (LIF) Flow Visualization (Axial Slices, Re=6,) Lobe peak slice Lobe trough slice Lobe trough slice Lobe peak slice

22 Laser Induced Fluorescence (LIF) Flow Visualization (Cross Sections, Re=3,) /D=.5 /D=.5 /D=.75 /D=1. Copyright by Dr. Hui /D=1.5 Iowa State University. All Rights Reserved! /D=.

23 Experimental Set-up Centrifugal compressor Cylindrical plenum chamber Test nozzle Convergent connection Flow condition : U jet = m/s D = 4 mm Re= 6, Two-dimension translationmechanism Jet supply system Mirror #1 S-polarized laser beam cylinder lens Mirror # P-polarized laser beam Half wave (λ/) plate Double-pulsed Nd:YAG Laser set A Double-pulsed Host computer Laser sheet with S-polarization direction Lobed nozzle Polarizer cube Laser sheet with P-polarization direction Measurement region 8mm by 8mm Polarizing beam splitter cubes Nd:YAG Laser set B Mirror #4 high-resolution CCD camera 4 65mm Synchronizer Mirror #3 high-resolution CCD camera mm high-resolution CCD camera high-resolution CCD camera 3 System setup

24 The Simultaneous Measurement Results of the Dual-plane Stereoscopic PIV System at Two Parallel Planes Y m/s A. Instantaneous velocity field at Z=1mm plane Z Y mm Wm/s mm Y m/s B. the simultaneous velocity field at Z=1mm plane Z Y mm Wm/s Copyright by Dr. Hui Iowa State University. All Rights Reserved! -3 - mm 1 3-3

25 Distributions of Three Components of Vorticity Vectors Vorticity distribution (-component) Vorticity distribution (Y-component) Vorticity distribution (Z-component) mm ϖ a. instantaneous vorticity x -4-4 mm ϖ b. instantaneous vorticity y -4-4 mm ϖ c. instantaneous streamwise vorticity z Vorticity distribution (in-plane) Vorticity distribution (Z-component) Vorticity distribution (in-plane) mm mm mm d. instantaneous azimuthal vorticity in plane x ϖ = ϖ + ϖ y e. ensemble-averaged streamwise ϖ f. ensemble-averaged azimuthal vorticity z vorticity ϖ in plane = ϖ x + ϖ y

26 Measurement Results of the Dual-plane Stereoscopic PIV System Y 4 Z 3 1. m/s Z=4mm plane mm Y mm Wm/s mm Vorticity distribution (in-plane) Y m/s Z=4mm plane mm Z Y mm Wm/s Copyright by Dr. Hui. Iowa State University. All Rights Reserved! mm Vorticity distribution (Z-component)

27 Reconstructed Three-dimensional Flow Field Lobed mixer a. three-dimensional velocity vectors b.iso-surface of velocity field

28 Evolution of Spanwise Kelvin-Helmholtz Vortex Structures 4 4 grow up 4 pinch-off Vorticity distribution (in-plane) Vorticity distribution (in-plane) Vorticity distribution (in-plane) mm a. Z=1mm cross plane (Z/D=.5) broken down mm b. Z=mm cross plane (Z/D=.5) dissipated mm c. Z=4mm cross plane (Z/D=1.) Vorticity distribution (in-plane) Vorticity distribution (in-plane) Vorticity distribution (in-plane) mm d. Z=6mm cross plane (Z/D=1.5) mm mm e. Z=8mm cross plane f. Z=1mm cross plane Copyright by Dr. (Z/D=.) Hui Iowa State University. All Rights Reserved! (Z/D=3.)

29 Evolution of Large-scale Streamwise Vortex Structures 4 4 grow up Streamwise Vortcitity Streamwise Vortcitity Streamwise Vortcitity mm 4 a. Z=1mm cross plane (Z/D=.5) mm b. Z=mm cross plane (Z/D=.5) dissipated mm 4 c. Z=4mm cross plane (Z/D=1.) Streamwise Vortcitity Streamwise Vortcitity Streamwise Vortcitity mm d. Z=6mm cross plane (Z/D=1.5) mm mm e. Z=8mm cross plane f. Z=1mm cross plane (Z/D=.) (Z/D=3.)

30 Comparison of Dual-plane Stereoscopic PIV and LDV results Lobed nozzle Laser sheet Measurement region 5 5 LDV probe 65mm 65mm CCD cameras Velocity (m/s) 15 1 V-SPIV W-SPIV W-LDV V-LDV time (s) One laser sheet on the other off Two laser sheets on simultaneously Point A (,,) Point B (,,4) Point A (,,) Point B (,,4) Stereoscopic PIV measurement Results Ensemble-averaged Deviation of the outof-plane out-of-plane velocity Velocity W(m/s) component STD(W) LDV measurement results Ensembleaveraged out-ofplane Velocity W (m/s) Deviation of the out-of-plane velocity component STD(W) W SPIV W LDV (1.7%) (1.7%) (1.3%) (.%)

31 Mass Conservation Equation Q = D U u ( + x v w + ) y z Z=4mm cross plane Error level in the mass conservation equation Error Level in the mass conservation equation mm mm Instantaneous distribution (averaged value Q=.35) (equivalent error velocity Δw/U =1.75%) ensemble-averaged distribution (averaged value Q=.13) (equivalent error velocity Δw/U =.65%)

32 3D-PTV Techniques System set-up measurement result of the flow over a riblet surface (Suzuki, Kasagi,, )

33 3-D D PTV (Willneff,, ETH Zurich. 3)

34 Holographic PIV (HPIV) technique Recording system A typical instantaneous HPIV result by J. Katz JHU reconstruction system

35 Defocusing digital particle image velocimetry (DDPIV) Defocusing concept M. Gharib California Institute of Technology