Hydro-dynamic Effects with Particular Consideration of Water Quality

and their Measurement Methods

Winfried Heller

Institut fr Strmungsmechanik Technische Universitt Dresden

_____________________________________ This work was approved by the Faculty of Engineering of Dresden University of Technology as habilitation thesis in order to grant the academic degree of a habilitated doctor (Doctor habilitatus): Habilitation thesis submitted: 18.04.2005 Day of the defense: 15.12.2005 Chairman: Prof. Dr.-Ing. habil. Prof. h.c. H.-J. Hardtke, Technische Universitt Dresden Reviewers: Prof. Dr.-Ing. habil. A. Dittmann, Technische Universitt Dresden Prof. Dr.-Ing. habil. N. A. Adams, Technische Universitt Mnchen Prof. Dr. rer.nat. habil W. Lauterborn, Universitt Gttingen

English translation of the original text by Gran Thomas, email: goeran_t@web.de Published (german) in: Strmungsmechanik, Band 2 Der Andere Verlag, Tnning, Lbeck and Marburg ISBN 3-89959-428-2

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Preface

Thanks to outstanding mathematicians and natural scientists of previous centuries such as Isaac Newton (1642 1727), Leonhard Euler (1701 1783), Claude Louis Marie Henry Navier (1785 1836), George Gabriel Stokes (1819 1903), Osborne Reynolds (1842 1912), John William Strutt Rayleih (1842 1919) and Ludwig Prandtl (1875 1953), the field of fluid mechanics has evolved into an independent branch of science with great significance for the basic education of engineers. However, the equations devised by these scientists for the calculation of fluid flows have one thing in common: They do not explicitly describe the hydrodynamic effects that result from a fluids quality. This founded the motivation for the present thesis because, during the last decades, this area was subject to intensive research, in which I also participated. This work is meant to be a contribution to summarizing the development of fluid mechanics with particular emphasis on water quality and hydro-dynamic effects. At this point, I would like to thank all those who greatly supported me during my work. I wish to express my particular gratitude to Dr. rer.nat. Andreas Keller of the Laboratory of Hydraulic Engineering at Munich University, whose exceptionally competent specialist support paved the way for this work. Moreover, for professionally discussing and reviewing this thesis, I would like to thank Prof. Dr. rer.nat. habil. Werner Lauterborn of Gttingen University, Prof. Dr.-Ing. habil. Nicolaus Adams of Munich Technical University and Prof. Dr.-Ing. habil. Achim Dittmann of Dresden Technical University. My deepest gratitude, however, goes to my wife Elke, who not only provided the necessary private backing throughout my professional career but also actively participated in it. Winfried Heller Possendorf, January 2006

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CONTENTS

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Contents

List of Symbols and Indices ................................................................................................ ix

1 Introduction ...................................................................................................................1

1.1 Historical Framework and Motivation .............................................................................................1

1.2 Physical Foundations for Fluids.........................................................................................................4

2 Diffusion and Bubble Growth ...................................................................................... 9

2.1 Basics of Solubility of Gases in Water ...............................................................................................9 2.1.1 Introductory Remarks....................................................................................................................9 2.1.2 Solubility ........................................................................................................................................10 2.1.3 Degree of Saturation.....................................................................................................................11

2.2 Nuclei ...................................................................................................................................................12 2.2.1 Introductory Remarks..................................................................................................................12 2.2.2 Bubble Nuclei.................................................................................................................................14 2.2.3 Pore Nuclei.....................................................................................................................................15 2.2.4 Quasi-static Nucleus Behavior.....................................................................................................17 2.2.5 Dynamic Nucleus Behavior..........................................................................................................18

2.3 Influence of Diffusion at Pressure Changes....................................................................................19 2.3.1 Introductory Remarks..................................................................................................................19 2.3.2 Differential Eqution for Bubble Growth by Kuz ......................................................................20 2.3.3 Diffusion Equation for Bubble Growth by Kmmel ................................................................23 2.3.4 Equation of the Total Gas Mass by Watanabe &Prosperetti..................................................25

2.4 Temporal Process of Gas Deposition...............................................................................................27 2.4.1 Introductory Remarks..................................................................................................................27 2.4.2 Determination of the Deposition Velocity by Schweitzer.........................................................27 2.4.3 Theoretical Expansion by Kuz ....................................................................................................28

3 Measurement Methods to Determine the Nucleus and Gas Content.......................31

3.1 Methods to Determine the Gas Content..........................................................................................31 3.1.1 Introductory Remarks..................................................................................................................31 3.1.2 Chemical Analytical Method ....................................................................................................31 3.1.3 Electro-Chemical Method ............................................................................................................32 3.1.4 Gadgets to Determine the Total Gas Content ...........................................................................33

3.1.4.1 Gadget by Van Slyke ..........................................................................................................33 3.1.4.2 Gadget by Numachi ............................................................................................................35 3.1.4.3 Gadget by Schneberger ....................................................................................................37 3.1.4.4 Gadget by Brand .................................................................................................................39 3.1.4.5 Gadget by Heller .................................................................................................................40

3.2 Methods fort the Determination of Nucleus Spectra.....................................................................41 3.2.1 Introductory Remarks..................................................................................................................41 3.2.2 Electrical Methods ........................................................................................................................41

3.2.2.1 Bubble Counter Resistance Measurement....................................................................41 3.2.2.2 Probe for Resistance Measurement to Determine Cavities in Fluids ...........................41

CONTENTS

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3.2.3 Acoustic Methods.......................................................................................................................... 42 3.2.3.1 Absorption of Ultrasonic Energy Measurement of Reverberation Decay................ 42 3.2.3.2 Counting of Bubbles Caused by Sound-Waves............................................................... 42

3.2.4 Optical Methods............................................................................................................................ 43 3.2.4.1 Photographic Direct......................................................................................................... 43 3.2.4.2 Photographic Indirect ..................................................................................................... 43 3.2.4.3 Holographic Reproduction ................................................................................................ 43 3.2.4.4 Transmitted Light Particle Counter for Fluids [TOPAS] ............................................. 45 3.2.4.5 Diffused Light Counting Method...................................................................................... 46 3.2.4.6 Center-Body-Method.......................................................................................................... 48 3.2.4.7 Phase Doppler Anemometer.............................................................................................. 49 3.2.