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J. Calderon-Sanchez Universidad Polit´ecnicade Madrid Escuela T´ecnicaSuperior de Ingenieros Navales Programa de Doctorado en Ingenier´ıaNaval y Oce´anica Numerical studies of the sloshing phenomenon using the Smoothed Particle Hydrodynamics (SPH) method. Javier Calderon-Sanchez Supervisor: Daniel Duque Campayo January, 2020 `Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.' Marie Curie i ii Tribunal designado por la Comisión de Doctorado de la Universidad Politécnica de Madrid, en su reunión del día...............de.............................de 20..... Presidente: Vocal: Vocal: Vocal: Secretario: Suplente: Suplente: Realizado el acto de defensa y lectura de la Tesis el día..........de........................de 20 ... en la E.T.S.I. /Facultad.................................................... Calificación .................................................. EL PRESIDENTE LOS VOCALES EL SECRETARIO iv Declaration I hereby declare that the contents presented in this dissertation are original and, to the best of my knowledge, they contain no material published by another person, or substantial proportions of material that have been submitted for any degree or other purposes, except where specific reference is made to the work of others. I certify that the intellectual content of this thesis is the product of my own work and that all the assistance received in preparing this thesis and sources have been acknowledged. Javier Calderon-Sanchez January, 2020 v vi Abstract The purpose of the present thesis is to increase the applicability of Smoothed Particle Hydro- dynamics (SPH) method to sloshing problems relevant in engineering. The thesis is structured around three main topics: theoretical improvements on SPH, imple- mentation of tools and physical models within the open-source software AQUAgpusph, and studies on 3-D geometries and application cases. The theoretical aspects of the method which are considered crucial for sloshing flows are an- alyzed. Particular attention is paid to boundary conditions, and more specifically, to the approaches developed to deal with solid boundaries. A novel general formulation to compute the Shepard renormalization factor operator used within the boundary integrals methodology is developed. This allows for improved simulations of hydrostatic problems, reducing spurious motions induced at the free surface and improving accuracy near the boundary. Additionally, the conservation properties of the boundary integrals formulation are studied. Momentum conservation is assessed through a new methodology that links volume and surface integrals through generalized coordinates, and the energy balance in the boundary integrals framework is also presented. Verification of the novel formulations are assessed by means of a hydrostatic test and the motion of a body inside a fluid. These novel formulations have been added into the open-source code, AQUAgpusph. Moreover, a set of tools and physical models have been included in the set of capabilities available within the code: tools to improve particle initialization and free-surface tracking have been adopted and extended to a boundary integrals formulation. A set of physical models that have been identified as relevant improvements for sloshing flows have also been implemented. In particular, a turbulent Large Eddy Simulation (LES) model and phase change are incorporated into the code. Several benchmark test cases are performed in order to demonstrate the benefits of the novel im- plementations: a dam-break and a moving square inside a fluid have been extensively analyzed to compare new approaches versus standard formulations. Finally, theoretical additions and numerical implementations are tested and applied to three relevant engineering applications: a 3-D dam-break, an anti-roll tank of a seagoing ship and a vertical sloshing fuel aircraft tank. The 3-D dam-break shows how impact pressures computed vii at the wall with the novel boundary formulation are in accordance with state-of-the-art results obtained with SPH and with experimental data for the same problem, regardless of resolution. Simulations on the vertical motion of a tank filled with liquid have been carried out for different motion models, including a coupling with a Euler-Bernouilli beam model. Results demonstrate that SPH is a valid method for modeling damping forces due to fluid motion in liquid sloshing. This may open opportunities for using this effect to reduce turbulence-induced motions in aircraft wings. viii Resumen El prop´ositode esta tesis es incrementar el rango de aplicaci´ondel m´etodo de part´ıculas Smoothed Particle Hydrodynamics (SPH) a problemas de ingenier´ıaen los que el fen´omeno de sloshing es una parte determinante en su dise~no. La tesis est´aestructurada en torno a tres tem´aticas principales: mejoras en los aspectos te´oricos del m´etodo SPH, implementaci´onde herramientas y modelos f´ısicosen el software libre AQUAg- pusph, y estudios en geometr´ıas 3-D y casos de aplicaci´on. Se han analizado los aspectos te´oricosdel m´etodo SPH que se consideran relevantes para el es- tudio del problema de sloshing. En concreto, se ha hecho ´enfasisen el estudio de las condiciones de contorno y, de forma m´asespec´ıfica, en las diferentes metodolog´ıas que se han desarrollado en las ´ultimasd´ecadas para afrontar este problema en paredes s´olidas. Se ha desarrollado una nueva formulaci´onpara calcular el factor de renormalizaci´onde Shepard, dentro de la metodolog´ıade integrales de contorno. De esta manera, se consigue mejorar la simulaci´ondel problema hidrost´atico,ya que se reducen los movimientos esp´ureosque aparecen en la superficie libre, as´ıcomo se consigue una mejora en la precisi´oncerca del contorno. Adem´as,se estudian las propiedades de conservaci´onde la metodolog´ıade integrales de con- torno. La conservaci´onde momento se consigue a trav´esde una metodolog´ıanovedosa que interrelaciona integrales de volumen y de superficie mediante coordinadas generalizadas. Por otro lado, se desarrolla la ecuaci´onde balance de energ´ıaen el contexto de las integrales de contorno. Todas estas formulaciones novedosas se han a~nadidoal c´odigolibre y abierto AQUAgpusph. Adem´as,se han incluido una serie de herramientas y modelos f´ısicosdentro de las capacidades del c´odigo: las herramientas implementadas se centran en la mejora de la disposici´oninicial de part´ıculasy la identificaci´onde part´ıculasde superficie libre, que se han adaptado desde otras metodolog´ıasa la metodolog´ıade integrales de contorno. Se han implementado as´ımismo una serie de modelos f´ısicosque se han considerado relevantes para el estudio de los problemas de sloshing. En concreto, se han incorporado un modelo de turbulencia LES, y un modelo de cambio de fase. Se han llevado a cabo una serie de casos de validaci´onpara demostrar las mejoras incluidas con las nuevas formulaciones: la rotura de una presa, y el movimiento de un objeto cuadrado ix dentro de un fluido se han analizado de forma extensiva, comparando los resultados obtenidos con las formulaciones est´andardel m´etodo. Finalmente, las mejoras te´oricasy las implementaciones num´ericasanteriormente descritas se han aplicado a tres aplicaciones relevantes para la ingenier´ıa: una rotura de presa en 3-D, el tanque de balance de un buque, y el movimiento vertical de un tanque de combustible de un avi´on. La rotura de presa 3-D muestra c´omolas presiones de impacto que se calculan en la pared con la nueva formulaci´onest´ande acuerdo con otros resultados obtenidos para el mismo problema, tanto experimentales como num´ericos,para un rango amplio de resoluciones. Se han realizado simulaciones del movimiento vertical del tanque de combustible para distintos modelos de movimiento, incluyendo un acoplamiento con una soluci´onbasada en el modelo de Euler-Bernouilli. Los resultados obtenidos demuestran que SPH es un m´etodo v´alidopara calcular el amortiguamiento a~nadidoque se debe al movimiento del fluido. De esta forma, se puede analizar este efecto de amortiguamiento para reducir los movimientos en las alas de avi´on debidos a cargas externas. x Acknowledgements It is difficult to reflect the unconditional support that I have received during the time I have been developing the present work from the people that I am mentioning in the following lines, but it would be unacceptable from my side to have, at least, a brief thought to each of them. Chiefly, I would like to express my gratitude to my supervisor, Daniel Duque, for the constant advise and continuous contact, and for the understanding during the trip the thesis has become. I want to thank deeply Antonio Souto-Iglesias for betting on me since the very beginning. I really appreciate all the discussions we had and how much I have learned from him I do not want to miss that this work would not have been possible without Jose Luis Cercos- Pita. His work building the fantastic software I have used in this thesis has been an invaluable contribution that I have just tried to maintain. I want also to express my gratitude to Jes´usG´omez Go~ni and the Physics FAIAN Department at UPM for the support given with the hardware and bureaucracy I had to deal with. I have been very fortunate, as I have been sharing the lab with a group of valuable and smart people. I would like to have a word for every person I have met at the CEHINAV: Luis, Ricardo, Richi, Leo, Paco, Nach, Elkin, Fabricio, H´ector,Adriana, Amadeo, Pablo and Jon. Among them, I want to have a special acknowledgment to Patricia Alcanda, who has been all along this time, and has always given me the different perspective that it is sometimes essential. I am really thankful to INSEAN, and especially, to Andrea, Salvo and Matteo, who welcomed me during my stay in Rome. I want also to extend my gratitude to all members in ETSIN Faculty and UPM for the oppor- tunity given and the resources invested on me.
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