DEVEL LOPME ENT OF F STERE EOSCO OPIC PA ARTICL LE IM MAGE VELOC CIMETR RY (PIV) SYSTEM BAC CHELOR THESIS T Submitted d to faculty of Bandung g Institute of o Technolog gy As partial fulfillment f o the requirements forr the degree of e of Bach helor of Engineering
By:
ANDREY GUN NAWAN 13602043
Advisor: Lavi R. Zuhal, Ph.D.
STUDY PRO OGRAM OF AERONAUT TICS AND AS STRONAUTICS FACULTY OF O MECHAN NICAL AND AEROSPACE A E ENGINEERING B BANDUNG IN NSTITUTE OF O TECHNOL LOGY 2008
For mum, pap, Retha and most of all Mother Marry and Her Beloved Son my Lord Jesus Christ
LEMBAR PENGESAHAN
TUGAS SARJANA dengan judul:
DEVELOPMENT OF STEREOSCOPIC PARTICLE IMAGE VELOCIMETRY (PIV) SYSTEM
Disusun oleh: Andrey Gunawan (13602043)
Telah diterima dan disetujui sebagai: Tugas Akhir Sarjana Strata Satu
Februari 2008 Pembimbing
Lavi R. Zuhal, Ph.D.
DEPARTEMEN PENDIDIKAN NASIONAL PROGRAM STUDI TEKNIK PENERBANGAN FAKULTAS TEKNIK MESIN DAN DIRGANTARA INSTITUT TEKNOLOGI BANDUNG
Jl. Ganesha 10 Bandung, 40132 Telp. (022) 2504529
TUGAS AKHIR SARJANA
Diberikan kepada
: Andrey Gunawan (13602043)
Dosen pembimbing
: Lavi R. Zuhal, Ph.D.
Jangka Waktu Penyelesaian
: 12 (dua belas) bulan
Judul Tugas Akhir
: Development of Stereoscopic Particle Image
Velocimetry (PIV) System Isi Tugas
: 1. Mengembangkan prosedur kalibrasi yang sesuai untuk sistem Stereoscopic PIV yang sedang dibangun. 2. Mendesain dan membuat sepasang dudukan kamera dan lensa (yang identik satu sama lain), khusus
untuk
mengakomodasi
konfigurasi
Scheimpflug. 3. Membuat software mapping (image dewarping) untuk meminimumkan, sekaligus memperbaiki ketidakseragaman dan distorsi perspektif yang terjadi pada gambar; yang disebabkan karena pengaplikasian konfigurasi Scheimpflug. 4. Mensimulasikan prosedur kalibrasi yang telah dikembangkan. 5. Membuat estimasi eror dari keseluruhan sistem
Stereoscopic PIV dengan menggunakan gambargambar partikel, hasil rekayasa komputer dari
Visualization
Society
of
Japan
(VSJ),
guna
menunjukkan bahwa keseluruhan sistem, baik
DEPARTEMEN PENDIDIKAN NASIONAL PROGRAM STUDI TEKNIK PENERBANGAN FAKULTAS TEKNIK MESIN DAN DIRGANTARA INSTITUT TEKNOLOGI BANDUNG
Jl. Ganesha 10 Bandung, 40132 Telp. (022) 2504529 hardware
dan
software,
dapat
digunakan
dengan baik.
Bandung, Februari 2008 Dosen Pembimbing
(Lavi R. Zuhal, Ph.D.)
Andrey Gunawan NIM : 13602043
DEVELOPMENT OF STEREOSCOPIC PARTICLE IMAGE VELOCIMETRY (PIV) SYSTEM Karya tulis ini adalah bukan hasil penerbitan sehingga peredarannya terbatas pada lingkungan akademik
Subjek judul: Particle Image Velocimetry, Stereoscopic
Dilarang menggandakan (sebagian atau seluruhnya) karya tulis ini tanpa seijin mahasiswa dan pembimbing yang bersangkutan.
Alamat e-mail:
[email protected]
ACKNOWLEDGEMENTS At the moment, I would like to thank and praise Mother Marry and her Son, Jesus Christ for all of Their great gifts and affections through my entire life; thus, I was able to finish this long journey thesis. I devote this thesis to Thee, my Almighty God. Furthermore, I wish to express my deepest gratitude to my advisor Mr. Lavi R. Zuhal, Ph.D. for giving me the opportunity, not to mention the second chance to carry out this research and for the encouragements, trust, advices and guidance during and most of all, at the finishing point of this thesis. I would also like to thank my academic advisor, my examiner, my friend, Dr. Ir. Leonardo Gunawan for the hospitality, friendship, spirits, and priceless aids during my time as a student of Aeronautics and Astronautics. Finally yet importantly, I would also like to thank Dr. Tatacipta Dirgantara for his willingness on being my examiner. Next, I would like to thank all of my friends, especially the Kartipah’ers, for their big supports during my stay in Bandung. Thanks also go to Adrianus Indrat Aria for the countless support in dealing with PIV system and those unique hardware, as well as Arie Sukmajaya for the companion in doing the overnight experiments in the Lab. I enjoyed the cooperation with Radius Bayu Prasetyo a.k.a Jacky in our small but highly technology-ized environment. I also would like to thank Miss Devera Daisy Miranti Faridz for every single thing that she give to me in completing this thesis. Finally, I would like to express my warmest thanks to my family: my mum, my pap, and my little sister, for your loves to me. I will always give my best to you and may God bless you all the time.
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I also would like to apologize for all of the mistakes that I have ever made. I wish this thesis would be useful for those who want to carry on similar research in the future.
Bandung, February 2008
Andrey Gunawan
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ABSTRACT Nowadays, Particle Image Velocimetry (PIV) system has been developed and implemented extensively in many different areas in any institution throughout the world. The remarkable performance of capturing the image of instantaneous flow field and transforming it into a flow visualization has led many fluid mechanic scientists to understand the complex flow phenomena. Even so, this state of the art system still undergoes some limitations which only capable of recording the projection of 2-D flow displacements inside the plane of the luminous light sheet; though the out-of-plane (3-D) velocity component is neglected. However, these kinds of limitations have been solved by introducing a newer technique, the Stereoscopic Particle Image Velocimetry system. Generally, the Stereoscopic PIV only added some algorithm and hardware configurations to the previous PIV system in order to fulfill the task to measure and visualize the out-of-plane velocity components. Consequently, a fine calibration system has to be developed to guarantee the whole process to be carried out perfectly. The thesis discusses some fundamental principles of Stereoscopic PIV system, begins with different stereoscopic configurations that have been used, followed by the relative merits of reconstruction methods for recovering the 3-D displacement vectors. Next, a calibration code is developed to correct and minimize the perspective distortion caused by the stereo optical (camera and lens) configuration. In addition, to support the calibration need, to recover, as well as to reconstruct the out-of-plane velocity components, a new hardware configuration has been put in consideration, i.e. a pair of self-developed mounting devices developed to facilitate the Scheimpflug camera-lens configuration. Subsequently, the calibration procedure was noted and illustrated from top to bottom, in order to give a deep perception of how important the procedure is for the whole Stereoscopic PIV system. Finally, experiments followed by the error estimation are conducted to ensure that all systems (hardware and software) could be performed perfectly. By and large, Stereoscopic PIV is a sophisticated, yet a very complex experimental system. However, the greater advantages of its complexity have brought the fluid mechanics world, especially the PIV method itself, into a higher level.
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ABSTRAK Pada masa sekarang ini, sistem Particle Image Velocimetry (PIV) telah banyak dikembangkan dan diimplementasikan di berbagai bidang, di hampir setiap institusi di seluruh dunia. Kemampuan yang luar biasa dari sistem tersebut untuk merekam gambar aliran dan mengubahnya secara langsung menjadi sebuah visualisasi aliran, telah
banyak
membantu
para ahli-ahli mekanika
fluida
dalam
memahami
fenomena-fenomena aliran kompleks. Walaupun demikian, sistem yang hampir mendekati sempurna ini masih memiliki beberapa keterbatasan, salah satunya adalah bahwa sistem ini hanya dapat merekam proyeksi 2-D dari perpindahan aliran di dalam sebuah bidang yang disinari oleh lembaran sinar laser, sedangkan komponen 3-D (out-of-plane) dari aliran tersebut dihiraukan begitu saja. Namun, keterbatasan ini telah dapat diatasi dengan diperkenalkannya sebuah sistem baru,
Stereosocopic Particle Image Velocimetry. Pada dasarnya, Stereocopic PIV ini hanyalah sebuah sistem PIV yang telah dilengkapi dengan beberapa algoritma perangkat lunak dan konfigurasi perangkat keras, guna memungkinkan sistem tersebut untuk dapat mengukur dan memvisualisaikan komponen kecepatan 3-D (out-of-plane) dari aliran fluida. Untuk itu, sebuah prosedur kalibrasi perlu dikembangkan untuk menjamin keseluruhan proses agar dapat berjalan dengan baik. Di dalam laporan tugas akhir ini dijelaskan beberapa prinsip dasar dari sistem Stereoscopic PIV, dimulai dari beberapa konfigurasi stereoscopic yang telah digunakan
sebelumnya,
diikuti
dengan
kualifikasi
dari
beberapa
metode
reconstruction yang berfungsi untuk mendapatkan vektor-vektor perpindahan 3-D. Selanjutnya, sebuah kode kalibrasi telah berhasil dikembangkan untuk memperbaiki dan meminimalisasi masalah perspektif yang disebabkan karena penggunaan konfigurasi stereo (dari kamera dan lensa). Untuk mendukung kebutuhan kalibrasi, sekaligus untuk mendapatkan dan merekonstruksi ulang komponen-komponen kecepatan 3-D tersebut, sebuah konfigurasi perangkat keras telah dikembangkan; untuk lebih tepatnya: sepasang dudukan kamera dan lensa telah didesain dan dibuat khusus, guna mengakomodasi konfigurasi Scheimpflug dari kamera dan lensa. Kemudian, semua prosedur kalibrasi disusun dan dipaparkan secara mendetail, dengan tujuan untuk memberikan persepsi secara mendalam tentang seberapa
penting
prosedur kalibrasi
tersebut
terhadap
keseluruhan sistem
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Stereoscopic PIV. Pada bagian akhir, beberapa eksperimen disertai dengan perhitungan galat dilakukan untuk memastikan keseluruhan sistem (perangkat keras/ lunak) dapat digunakan dengan sempurna. Secara keseluruhan, Stereoscopic PIV adalah sebuah sistem eksperimental mutakhir, nan kompleks. Walaupun demikian, kerumitan-kerumitan dari sistem tersebut telah berhasil membawa dunia mekanika fluida, terutama metode PIV itu sendiri, ke tingkat yang lebih tinggi.
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CONTENTS
ACKNOWLEDGEMENTS ............................................................................................. i ABSTRACT ............................................................................................................. iii ABSTRAK .............................................................................................................. iv CONTENTS ............................................................................................................. vi APPENDIX LIST ..................................................................................................... viii LIST OF TABLES ...................................................................................................... ix LIST OF FIGURES ..................................................................................................... x CHAPTER I
INTRODUCTION.................................................................................. 1
1.1
Background .............................................................................................. 1
1.2
Research Goal ........................................................................................... 4
1.3
Scope........................................................................................................ 5
1.4
Research Methodology .............................................................................. 5
1.5
Thesis Outline........................................................................................... 6
CHAPTER II STEREOSCOPIC PIV SYSTEM PRINCIPLES............................................... 9 2.1
Introduction .............................................................................................. 9
2.2
Stereoscopic Configurations.................................................................... 10
2.2.1
Translational System ........................................................................ 11
2.2.2
Rotational System ............................................................................ 14
2.2.3
Other Stereoscopic Configurations ................................................... 19
2.3
Reconstruction Methods.......................................................................... 19
2.3.1
Geometric reconstruction ................................................................. 20
2.3.2
Calibration-based reconstruction ..................................................... 20
CHAPTER III
IMAGE DEWARPING (CALIBRATION) PROCEDURE ............................ 26
3.1
Scheimpflug Configuration and Perspective Distortion............................. 26
3.2
The Dewarping Process ........................................................................... 28
3.2.1
Convolutional Filtering ..................................................................... 29
vi
Contents
3.2.2
Gaussian Interpolation ..................................................................... 31
3.2.3
Guessing the coordinates of new dewarped images .......................... 32
3.2.4
The twenty four mapping coefficients .............................................. 34
CHAPTER IV
THE CALIBRATION PROCEDURE ..................................................... 36
4.1
Introduction ............................................................................................ 36
4.2
Reconstruction Methods.......................................................................... 37
4.3
Hardware Configuration .......................................................................... 38
4.3.1
Calibration Grid ............................................................................... 39
4.3.2
Camera-Lens Mounting Devices ....................................................... 40
4.4
Systematic Detailed Calibration Procedure ............................................... 43
4.4.1
Hardware setup................................................................................ 43
4.4.2
Calibration Procedure....................................................................... 46
4.4.3
Image Dewarping Calibration ........................................................... 48
CHAPTER V EXPERIMENT RESULTS AND ERROR ANALYSIS .................................... 50 5.1
Introduction: Stereoscopic PIV Error Analysis ........................................... 50
5.2
Assumptions: Analytical Error Prediction ................................................. 51
5.3
First Test: Geometrical Configurations .................................................... 53
5.3.1
Off-axis angle (θ)............................................................................. 53
5.3.2
Zoom Performance ........................................................................... 58
5.4
Second Test: two 2-d calibration-based reconstruction method .............. 59
5.5
Out-of-plane to in-plane error ratio ....................................................... 62
5.6
Simulation Results .................................................................................. 65
CHAPTER VI
CONCLUSION AND FUTURE DEVELOPMENT .................................... 70
6.1
Conclusion.............................................................................................. 70
6.2
Future Development................................................................................ 72
REFERENCES .......................................................................................................... 73
vii
APPENDIX LIST
APPENDIX A TECHNICAL DRAWING OF CAMERA-LENS MOUNTING DEVICES (CLP) ... 75 APPENDIX B PARTICLE IMAGE SETS CAPTURED IN EXPERIMENTS ............................. 89
viii
LIST OF TABLES
Table IV.1
Reference values of high particle concentration (adapted from Okamoto 2000) ................................................................................ 44
Table V.1
Bias, RMS error, out-of-plane to in-plane error ratio resulted from the conventional and Willert’s (1997) procedures comparison ................. 60
Table V.2
Bias, RMS error, out-of-plane to in-plane error ratio resulted for each four variation of θ and α, with the comparison data .......................... 63
Table V.3
Reference
values
of
artificial
impinging
jet
flow
images
for
Stereoscopic PIV system (adapted from Okamoto 2000) .................... 66
ix
LIST OF FIGURES
Figure I.1
The wing tip vortex of an aircraft ........................................................ 2
Figure I.2
3-D velocity vectors of wing tip vortex using Stereoscopic PIV system (adapted from Zuhal 2001) ................................................................. 4
Figure II.1
Misinterpretation of in-plane displacements due to out-of-plane motion in conventional single camera PIV (adapted from Prasad 2000) 9
Figure II.2
Schematic of in-plane and out-of-plane displacement in stereo camera configuration (adapted from Prasad 2000) ........................................ 11
Figure II.3
Basic configuration for translational Stereoscopic PIV system (adapted from Prasad 2000) ............................................................................ 12
Figure II.4 Basic configuration for angular displacement Stereoscopic PIV systems (adapted from Prasad 2000).............................................................. 14 Figure II.5 Opposite stretching of a cartesian grid in the image plane when mapped onto the object planar (adapted from Prasad 2000) ............. 15 Figure II.6 The forward scatter arrangement with cameras on either side of the light sheet (adapted from Willert 1997) ............................................. 17 Figure II.7
The application of liquid prism in Stereoscopic PIV experiment (only one of two cameras is shown; adapted from Prasad and Jensen 1995) ... ........................................................................................................ 18
Figure III.1 The Scheimpflug arrangement for Stereoscopic PIV ........................... 26 Figure III.2 The 5mm2 black-line spacing calibration grid ................................... 27 Figure III.3 Trapezoidal image grabbed by stereo camera using Scheimpflug arrangement ..................................................................................... 28 Figure III.4 The comparison images (black and white cross likes image) ............. 30 Figure III.5 The general process of convolutional filtering ................................... 30 Figure III.6 The result: intersection nodes of the grid image ............................... 31 Figure III.7 The rule for picking the reference grid (four reference nodes) ........... 33 Figure III.8 The final result of the guessing process ............................................ 34
x
List of Figures
Figure IV.1 Whole steps involved in 2-d calibration-based reconstruction method (adapted from Prasad 2000).............................................................. 38 Figure IV.2 Artificial particle image and calibration grid (right), which are placed on the traverse stage ............................................................................. 39 Figure IV.3 Self-developed
camera-lens
mounting
device
to
accommodate
Scheimpflug configuration ................................................................ 40 Figure IV.4 The CLP are used to connect the camera Pulnix TM-1040 and the 2880 mm Cosina macro lens ................................................................ 41 Figure IV.5 The camera can be rotated by an angle of α (to the right/left) with respect to the lens plane, to accommodate the Scheimpflug criterion 42 Figure IV.6 The gap between the camera and the lens are sealed by black tape (left); the future development of the shutter, inspired by view camera in era 40’s (right) .............................................................................. 42 Figure IV.7 The finished camera and lens mounting on the CLP .......................... 43 Figure IV.8 Artificial high concentration particle image ....................................... 45 Figure IV.9 The locking devices for the CLPs: the θ angle set-up (left), the locking bolt for the θ angle set-up (upper-middle), the α angle set-up with the locking device (right) ........................................................................ 46 Figure IV.10 The overlapping image results for: θ = 45⁰/ α =5⁰ (upper left); θ = 45⁰/ α =2.5⁰ (lower left), θ = 30⁰/ α =5⁰ (upper right); and θ = 30⁰/ α =2.5⁰ (lower right) ............................................................................ 47 Figure IV.11 The traverse stage can be shifted for x, y, and z-direction (with accuracy of 0,01mm in each axis) ..................................................... 48 Figure IV.12 The resulting overlapped image from image dewarping algorithm for Scheimpflug configuration of θ = 30⁰/ α =2.5⁰ ................................ 49 Figure V.1
Variation of out-of-plane to in-plane error ratios with off-axis position (y = 0, z = 0) for angular displacement system (adapted from Lawson and Wu 1997) ....................................................................... 52
Figure V.2
Grabbed calibration grid images for: θ = 45⁰| α =5⁰ (upper left); θ = 45⁰| α =2.5⁰ (lower left), θ = 30⁰| α =5⁰ (upper right); and θ = 30⁰| α =2.5⁰ (lower right) ............................................................................ 54
Figure V.3
Non-uniformity in magnification across the object plane in the Scheimpflug system (adapted from Prasad 2000) .............................. 55
xi
List of Figures
Figure V.4
The resulting of non-uniformity in magnification across the object plane in the current Stereoscopic PIV system for θ = 45⁰ and 30⁰, with variation of α = 5⁰ and 2.5⁰ .............................................................. 56
Figure V.5
Non-uniformity in magnification towards y-axis for a given θ = 45⁰, α = 5⁰ ................................................................................................. 59
Figure V.6
Bias and RMS errors for all four procedures (data plotted from Table V.1) .................................................................................................. 62
Figure V.7
Bias and RMS Error for all four Scheimpflug configurations (data plotted from Table V.2)..................................................................... 63
Figure V.8 Variation of the resulted out-of-plane to in-plane error ratios for four variation of θ and α, with the comparison data for θ = 45⁰ and θ = 30 ⁰ adapted from Lawson and Wu 1997 ................................................ 64 Figure V.9
The whole Stereoscopic PIV procedure completed with the artificial particle image pairs and calibration grid images(both for left and right cameras) provided by VSJ, the resulting velocity vector fields, the resulting overlapped calibration grid images from image dewarping process, and finally, three-dimensional velocity vectors (from different views, i.e. 0⁰, 60⁰, 75⁰, and 90⁰) ....................................................... 69
Figure VI.1 Pictured above from left to right are the Canon TS-E 24mm f/3.5 L Tilt-Shift Lens (set to maximum tilt), Canon TS-E 45mm f/2.8 Tilt-Shift Lens and Canon TS-E 90mm f/2.8 Tilt-Shift Lens (set to maximum tilt). All three lenses are shown with their included lens hoods. ................ 72
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