Doctoral Thesis
DOI
10.11606/T.3.2013.tde-22092014-110644
Document
Author
Full name
Flávia Milo dos Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Pesce, Celso Pupo (President)
Ragazzo, Clodoaldo Grotta
Simos, Alexandre Nicolaos
Sphaier, Sergio Hamilton
Title in Portuguese
Impacto hidrodinâmico vertical de corpos axissimétricos através de uma abordagem variacional.
Keywords in Portuguese
Abordagem GvKM
Impacto vertical de corpos axissimétricos
Método numérico variacional
Problema de impacto hidrodinâmico
Abstract in Portuguese
Title in English
Vertical hydrodynamic impact of axisymmetric bodies through a variational approach.
Keywords in English
Desingularized techniques
GvKM approach
Hydrodynamic impact problem
Variational numerical method
Vertical impact of axisymmetric bodies
Abstract in English
In terms of classical hydrodynamics, the hydrodynamic impact problem is characterized as a boundary problem with moving boundary which position must be determined simultaneously with the solution of the field equation. This feature brings difficulties to get analytical and numerical solutions. In this sense, the purpose of this work is to present a variational method technique specifically designed for the hydrodynamic impact problem of axisymmetric rigid bodies on the free surface. The solution of the nonlinear dynamic equation of the impacting motion depends on the determination of the added mass tensor and its derivative with respect to time at each integration time step. This is done through a variational method technique that leads to a second-order error approximation for the added mass if a first-order error approximation is sought for the velocity potential. This method is an example of desingularized numerical techniques, through which the velocity potential is approximated in a sub-space of finite dimension, formed by trial functions derived from elementary potential solutions, such as poles, dipoles, and vortex rings, which are placed inside the body. The potential problem of hydrodynamic impact, characterized by the dominance of inertial forces, is here formulated by assuming the liquid surface as equipotential, what allows the analogy with the infinity frequency limit in the usual free surface oscillating floating body problem. The method is applied to the vertical hydrodynamic impact of axisymmetric bodies within the so-called Generalized von Kármán Model (GvKM). In such approach, the exact body boundary condition is full-filled and the wet correction is not taken into account. Numerical results for the added mass coefficient for a family of spheroids are presented. Moreover, considerations are made on the effects of the free surface elevation for the specific case of an impacting sphere, through analytical approaches.