- Polydispersed bubbly flow model for ship hydrodynamics with application to Athena R/V Castro, Alejandro Miguel https://iro.uiowa.edu/discovery/delivery/01IOWA_INST:ResearchRepository/12730672190002771?l#13730783560002771 Castro, A. M. (2014). Polydispersed bubbly flow model for ship hydrodynamics with application to Athena R/V [University of Iowa]. https://doi.org/10.17077/etd.2p94jdnz https://iro.uiowa.edu Copyright 2011 Alejandro Miguel Castro Downloaded on 2021/09/27 18:24:16 -0500 - POLYDISPERSED BUBBLY FLOW MODEL FOR SHIP HYDRODYNAMICS WITH APPLICATION TO ATHENA R/V by Alejandro Miguel Castro An Abstract Of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Mechanical Engineering in the Graduate College of The University of Iowa December 2011 Thesis Supervisor: Associate Professor Pablo M. Carrica 1 ABSTRACT Bubbly flows around ships have been studied for years, mostly in relation with ship acoustic signatures. Bubbles are generated at the bow and shoulder breaking waves, at the hull/free surface contact line, the propeller and the highly turbulent stern flow. These bubbles are further transported downstream by the flow forming a two-phase mixture in the wake that can be kilometers long. The presence of bubbles in the wake of a ship significantly affects the acoustic response of the medium and can be detected by measuring acoustic attenuation and backscattering making a ship vulnerable to detection. Additionally, the bubbly wake shows at the surface as a characteristic signature of white water, and given the length of the bubbly wake, it makes a ship visible from satellites. Therefore, the bubbly wake can be used to detect and identify surface ships. Bubbly flows do not scale to model scale experiments, and experiments on full scale ships are scarce mostly due to difficult access areas and the high speeds involved. It is therefore of interest to simulate the bubbly flow around ships to provide information difficult, if not impossible, to obtain with experiments. This work presents the development of a code for the simulation of polydis- persed bubbly flows with a focus on ship hydrodynamics. The mathematical model implemented is based on a two-fluid formulation coupled with a Boltzmann-like transport equation describing the bubbly phase. The tool developed attempts to include most of the relevant physics of the problem to represent better the condi- tions of real scenarios. The resulting code allows the simulation of polydispersed bubbly flows in situations including free surface and air entrainment, high void fraction levels and moving control surfaces and propulsors. The code is two-way coupled, with a strong coupling between the two phases and between the bubble sizes. The complexity of the problems tackled in this research required the develop- 2 ment of novel numerical methods solving issues never identified before or simply neglected. These methods play an essential role in the accuracy, robustness and efficiency of the code and include: a two-phase projection method that not only couples pressure and velocity but also implicitly couples void fraction, a time split- ting marching scheme to solve separately coupling in space and in bubble sizes, and a stable numerical method to integrate the strong coupling introduced by collision forces. The implemented code is applied to the simulation of the bubbly flow around a full scale ship using the latest available models and computational techniques. A study is performed on the influence of several mechanisms on the predicted bubbly wake and comparisons with available experimental data are presented. The influence of breakup in the boundary layer is analyzed in detail as well. In addition, this work identifies several modeling and implementations issues and attempts to provide a path for future studies. To illustrate the flexibility and robustness of the code, a final demonstration case is presented that includes rotating propellers. The computation is performed at full scale, with the fully appended geometry of the vessel and includes incoming waves, oceanic background and rectified diffusion models. Many of these features are unique to this computation and make it the first of its kind. Abstract Approved: Thesis Supervisor Title and Department Date POLYDISPERSED BUBBLY FLOW MODEL FOR SHIP HYDRODYNAMICS WITH APPLICATION TO ATHENA R/V by Alejandro Miguel Castro A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Mechanical Engineering in the Graduate College of The University of Iowa December 2011 Thesis Supervisor: Associate Professor Pablo M. Carrica Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL PH.D. THESIS This is to certify that the Ph.D. thesis of Alejandro Miguel Castro has been approved by the Examining Committee for the thesis requirement for the Doctor of Philosophy degree in Mechanical Engineering at the December 2011 graduation. Thesis Committee: Pablo M. Carrica, Thesis Supervisor Christoph Beckermann Mark Hyman Frederick Stern H.S. Udaykumar To my parents and sister ii ACKNOWLEDGEMENTS First and foremost, I owe my deepest gratitude to my thesis supervisor Pablo M. Carrica, whose constant support helped me along my journey. Pablo, thank you for your guidance, encouragement, critique (lots of it) and, most of all, your friendship. Thank you for your constant and virtually endless willingness to teach and stimulate my imagination. I feel immensely fortunate for having had you as my thesis supervisor and I am deeply grateful for the lessons you have taught me not only on a professional level, but also on a personal level. I am also very grateful to Marcela Politano, Pablo’s wife, who would come downstairs to my cubicle to provide me with warm and calming words in times of deadlines when I was about to loose it. I also had the chance to professionally interact with Marcela and I can say that those interactions were very beneficial and influential for my education. I would like to specially thank Dr. Mark Hyman, the first user of our code, for his suggestions, comments, useful discussions and for providing the geometry for Athena’s propeller. Dr. Hyman traveled from Pasadena, CA to Iowa City not only for my final PhD defense but also for my comprehensive examination. I know how busy his schedule is and therefore I am very grateful for this. I am grateful to my thesis committee members, who took time out of their busy schedule to review my thesis and provided helpful suggestions and advice. This work was sponsored by the US Office of Naval Research grant N00014-08- 1-1084, under the administration of Dr. Patrick Purtell whose support is greatly appreciated. iii TABLE OF CONTENTS LIST OF TABLES . vii LIST OF FIGURES . viii CHAPTER 1 INTRODUCTION . 1 1.1 Background . 1 1.2 Bubbly Flow Around Ships . 2 1.3 Computational Ship Hydrodynamics . 4 1.4 Models and Numerical Methods for Two-Phase Flows . 4 1.5 Contribution of this Thesis . 11 2 MATHEMATICAL DESCRIPTION OF POLYDISPERSED FLOWS . 16 2.1 The Boltzmann Equation . 19 2.2 Multigroup Approach . 23 2.3 Intergroup Transfer Discretization . 26 2.3.1 Breakup . 28 2.3.2 Coalescence . 36 2.3.3 Dissolution . 41 2.3.4 Full System of Equations . 45 2.4 Derived Quantities . 46 2.4.1 Integral Quantities . 46 2.4.2 Size Distributions . 48 2.4.3 Intergroup Transfer Budget . 49 2.4.4 Intergroup Transfer Frequencies . 52 3 POLYDISPERSED BUBBLY FLOW MODEL . 54 3.1 Two Fluid Model . 55 3.1.1 Dispersed Phase . 56 3.1.2 Jump Conditions . 58 3.1.3 Continuous Phase . 59 3.1.4 Interfacial Forces . 61 3.1.5 Bubble Radius . 73 3.2 Coalescence Modeling . 75 3.2.1 Model of Prince and Blanch . 77 3.2.2 Model of Lehr et al. 81 3.3 Breakup Modeling . 81 3.3.1 Turbulence Induced Breakup . 82 iv 3.3.2 Viscous Shear Breakup . 89 3.4 Dissolution . 92 3.5 Modeling Considerations for Sea Water . 94 3.6 Turbulence Modeling . 97 3.7 Free Surface Tracking: Single Phase Level Set . 99 3.8 Entrainment Modeling . 100 3.9 Oceanic Background . 104 3.10 Bubble Growth by Rectified Diffusion . 106 3.10.1 Discrete Form . 109 3.10.2 Limitations and Known Problems of the Model . 112 3.11 Dimensionless Equations . 113 4 NUMERICAL METHODS AND IMPLEMENTATION . 118 4.1 CFDShip-Iowa V4.5 . 119 4.2 Time Splitting . 120 4.2.1 The Problem . 120 4.2.2 The Proposed Solution . 123 4.2.3 Guaranteeing Mass Conservation . 127 4.2.4 Solving the Intergroup Transfer System . 128 4.2.5 Full Dispersed Phase Solver . 129 4.3 Global Coupling Strategy . 129 4.4 Pressure-Velocity Coupling . 132 4.4.1 Scheme I . 133 4.4.2 Scheme II . 135 4.4.3 Example Case: Self-Propelled Athena with Heading Waves . 139 4.5 Dispersed Phase Momentum Equation . 141 4.6 Number Density Transport . 143 4.6.1 Near Wall Integration . 144 4.7 Air Entrainment Source Integration . 148 4.8 Treatment of Forces with Number Density Gradients . 152 4.8.1 1D Test Case . 155 4.8.2 Implementation in CFDShip-Iowa V4.5 . 158 5 POLYDISPERSED MODEL VALIDATION . 161 5.1 Study Case . 162 5.2 Convergence Study . 165 5.3 Dependence with the Initial Conditions . 168 5.4 Comparison with Previous Works . 169 5.5 Prince and Blanch Coalescence Kernel . 171 5.6 Luo and Svendsen Breakup Kernel . 175 5.7 Salt Water . 179 v 6 ATHENA R/V ................................183 6.1 Summary of Experiments . 184 6.2 Geometry and Grids . 186 6.3 Conditions Used in the Simulations . 189 6.4 Breakup in Athena’s Boundary Layer . 190 6.4.1 Frictional Resistance and Wall Shear Stress .