A two phase consistent particle method for wave impact problems with entrapped air pockets

A TWO-PHASE CONSISTENT PARTICLE METHOD FOR WAVE IMPACT PROBLEMS WITH ENTRAPPED AIR POCKETS LUO MIN NATIONAL UNIVERSITY OF SINGAPORE 2015 A TWO-PHASE CONSISTENT PARTICLE METHOD FOR WAVE IMPACT PROBLEMS WITH ENTRAPPED AIR POCKETS LUO MIN (B.ENG, HARBIN INSTITUTE OF TECHNOLOGY, CHINA) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2015 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety I have duly acknowledged all the sources of information which have been used in the thesis This thesis has also not been submitted for any degree in any university previously Ph.D Candidate: Luo Min Signature: Date: Acknowledgement I am happy to take this opportunity to express my gratitude to my advisor, Professor Koh Chan Ghee for his invaluable guidance, support and encouragement throughout my study at NUS His critical attitude and rigorous scholarship in research has a great influence on me And I think this influence will accompany me in the study and work of the rest of my life Great thanks are also expressed to my co-supervisor Professor Bai Wei I am really appreciative of his kindness to arrange a meeting with me whenever I need a discussion on my research From these heuristic discussions, I have learned how to analyze a new problem and then think a way out to solve it Professor Lin Pengzhi in Sichuan University and Professor Shao Songdong in the University of Sheffield are acknowledged for the useful discussions and valuable comments from them In addition, the instructive comments and suggestions from Professors Khoo Boo Cheong and Vivien Chua in NUS are also appreciated Heartfelt gratitude is sent to Dr Gao Mimi, who guided me to learn the in-home developed numerical algorithm and laboratory experiments Without her patience and help, I could not have finished my Ph.D study in the tight time frame I would like to thank the staff in the Structural and Concrete Laboratory, especially Mr Koh Yian Kheng, Mr Ang Beng Oon and Mr Ow Weng Moon Without their help and assistance, I could not have finished my experimental study successfully I also would like to thank my friends: Dr Zhang Zhen, Dr Zhang Jian, Dr Zhang Mingqiang, Dr Zhang Yi, Dr Gao Ruiping, Ms Han Qinger, Ms Zhang Shanli, Ms I Zhang Hong, Mr Sun Gang, Mr Gao Qingfei, Mr Wang Yu, Dr Yu Chao and Mr Zhang Xiaodong, and all the other friends who have helped me It was the discussions with them that inspired my study and research And it was the recreational time spent with them that made my Ph.D journey relaxed and colorful Last but not least, I wish to express my love to my family: my parents, grandparent, younger sister and my girlfriend Thanks for their understanding, encouragement and love Without their supports, the completion of my thesis would not have been possible II Summary In many circumstances, violent fluid motions such as wave impacts on coastal/offshore structures generate air entrapment The entrapped air may affect the amplitude and duration of impact pressure because of the air cushion effect Numerical treatment of this problem remains a challenge because of its complexity, and most of the research findings were obtained from experiments In this context, the main objective of this thesis is to develop a new numerical method that can simulate violent wave impact processes with entrapped air pocket so as to achieve further insight into wave-impact processes and better prediction of impact pressures Most of the numerical methods developed for fluid dynamics problems can be classified into the mesh-based and meshless methods Among these methods, a Lagrangian meshless method (also called particle method) is adopted in this study because it is, in principle, capable of modelling large deformation, tracking fluid interface and avoiding the numerical diffusion induced by the discretization of the convection term of the Navier-Stokes Equations Among existing particle methods, the recently developed Consistent Particle Method (CPM) that computes the spatial derivatives in a way consistent with Taylor series expansion and eliminates the use of kernel function is selected because of its promising features to generate smooth fluid pressure without the use of artificial parameters such as the artificial viscosity The main challenges in modeling wave impact with entrapped air pocket include (a) approximations of gradient and Laplacian operators involving large density difference (three orders of magnitude for water-air flows) and (b) integrated modelling of incompressible water and compressible air To resolve the first issue, a new scheme is III proposed by dealing with the pressure gradient normalized by density Based on the generalized finite difference scheme, this approach uses all the neighbor particles (including those of another fluid) in the influence domain of a reference particle to compute the spatial derivatives with abrupt density discontinuity In addition, an adaptive particle selection scheme is proposed to overcome the problem of ill-conditioned coefficient matrix of pressure Poisson equation when particles are sparse and nonuniformly spaced These two improvements lead to the incompressible two-phase CPM (I-2P-CPM) for incompressible two-phase flows characterized by high density ratio To address the second challenge, a compressible solver is developed in the framework of thermodynamics In this way sound speed is not explicitly involved and thus the compressible solver avoids the problem as encountered by some other numerical methods in the determination of numerical or artificial sound speed In addition, this compressible solver can be easily integrated with the I-2P-CPM because they both use the same predictor-corrector scheme to solve the governing equation of primitive form This leads to the two-phase CPM (2P-CPM) that is applicable to incompressiblecompressible two-phase flows with abrupt density discontinuity The developed algorithms are validated by numerical examples in comparison with published results in the literature and the present experimental studies To demonstrate the performance of 2P-CPM, a new experiment is designed and conducted particularly for obtaining an air pocket and measuring its shape and pressure change under wave impact In all the cases considered, the numerical results agree well with the experimental results, including air pressure oscillation due to air cushion effect The results show that modelling of compressible air is crucial in wave impact scenarios with entrapped air pocket IV References Cooker, M.J and Peregrine, D.H (1995) Pressure-impulse theory for liquid impact problems, Journal of Fluid Mechanics, 297: 193-214 Cuomo, G., Allsop, W and Takahashi, S (2010) Scaling wave impact pressures on vertical walls, Coastal Engineering, 57(6): 604-609 Dalrymple, R.A and Rogers, B.D (2006) Numerical modeling of water 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by W  pdV (A-5) Substituting Equations (A-4) and (A-5) into the First Law of Thermodynamics, which can be represented as  Q  dU  W , gives 193 Appendix TdS  dU  pdV , (A-6) where U is the internal energy of the system This equation is frequently called the Gibbs equation and can be written for a unit mass as follows Tds  du  pdv , (A-7) where v is called the specific volume The ideal gas law as shown in Equation (3-4) also can be written in the form as pv  RT (A-8) where the ideal gas constant R  c p  cv , and c p and cv are respectively the specific heats at constant pressure and volume The ratio of specific heats is defined as   c p cv The change of internal energy of an ideal gas is du  cv dT (A-9) Further assuming an adiabatic process, since  Q  , we have Tds  (A-10) Substituting Equations (A-8) to (A-10) into Equation (A-7) gives  dv dp   v p (A-11) Integrating by part of Equation (A-11) and substituting v=1  leads to p   constant , which is the polytropic gas law for isentropic processes 194 (A-12) ... such as wave impacts on coastal/offshore structures generate air entrapment The entrapped air may affect the amplitude and duration of impact pressure because of the air cushion effect Numerical... such as breakwater, oil platform, tension leg platforms and ships can lead to serious structural damage and instability As a result, the loads generated by wave impacts are among the most important... develop a new numerical method that can simulate violent wave impact processes with entrapped air pocket so as to achieve further insight into wave- impact processes and better prediction of impact