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Full-Volume, Three-Dimensional, Transient Measurements of Bubbly Flows Using Particle Tracking Velocimetry and Shadow Image Velocimetry Coupled with Pattern Recognition Techniques Final Report - 2001

Hassan, Y.

Texas A&M

Table of Contents

Report
615kb		 Final Report July 15, 2000 to July 14, 2001
Phase III
Refereed Journal Publications
Figures

Transient Three-Dimensional Experimental Investigation of the Shape and Dynamics of an Air Bubble in Stagnant Water in a Small Diameter Pipe with Particle Tracking Velocimetry - A Dissertation by Javier Ortiz Villafuerte

Table of Contents

Section 1
1212kb		 Abstract iii
Dedication v
Acknowledgements vi
Table of Contents vii
List of Figures ix
List of Tables xiii

I

 Introduction 1
  1.1 Bubbly flow studies 2
1.2 Single bubble dynamics 3
1.3 Bubble shape analysis and three-dimensional reconstruction 5
1.4 Three-dimensional particle image velocimetry and tracking algorithms 7
1.5 Objectives 9

II

 Experimental Setup and Camera Calibration 11
  2.1 Experimental setup 11
2.2 Camera Calibration 14
  2.2.1 The pinhole camera model and the direct linear transformation method 15
2.2.2 Calibration data 17
2.2.3 Computation of transformation coefficients 19
2.2.4 Calibration error 21
Section 2
732kb

III

 Hybrid Particle Tracking Velocimetry and Three-Dimensional Velocity Field Reconstruction 24
  3.1 Pulsed-light velocimetry 24
3.2 Particle image velocimetry 25
3.3 Hybrid particle tracking technique 26
3.4 Matching of velocity vectors from stereo images 28
3.5 Determination of three-dimensional position of the tracer particles 32

IV

 Bubble Shape Identification and Reconstruction 34
  4.1 Bubble detection in a bubbly flow 35
4.2 The shadow particle image velocimetry flow visualization technique 36
4.3 Two-dimensional bubble shape reconstruction 37
Section 3
513kb		   4.3.1 The dynamic generalized Hough transform algorithm 41
4.3.2 Accuracy of the reconstruction 42

4.4

 Three-dimensional bubble shape reconstruction 45

V

 Flow Around a Rising Bubble and Within Its Wake 49
 

5.1

 Uncertainty analysis of PIV measurements and error propagation 49
  5.1.1 The Stokes number 50
5.1.2 Accuracy of two-dimensional localization of particle centroid 50
5.1.3 Uncertainty of three-dimensional particle position and instantaneous velocity 51
5.1.4 Error propagation 51
5.2 Theoretical background 53
Section 4
549kb		 5.3 Nodalization and conditional sampling 57
5.4 Mean flow field description 62
Section 5
651kb		 5.5 Turbulent flow field description 72
5.6 Transient analysis of the kinetic energy 77

VI

 Shape, Trajectory and Forces Acting on a Bubble Rising in a Small Diameter Pipe 86
 

6.1

 Theoretical background 86
  6.1.1 Bubble shape 87
6.1.2 The equation of motion 88
Section 6
805kb		 6.1.3 Nature of the forces acting on the bubble 89

6.2

 Accuracy of measurements 92

6.3

 Experimental results and discussion 94
  6.3.1 Bubble shape and velocity analysis 94
6.3.2 Drag and lift forces acting on the bubble 100
Section 7
649kb

VII

 Conclusions 112
References 118
Vita 126