Generalized two-dimensional Lagally theorem with free vortices and the method of fundamental solutions to the application of fluid-body interaction problems
Date Issued
2011
Date
2011
Author(s)
Wu, Chien-Ting
Abstract
A potential flow based numerical model which can be utilized to study the fully coupled fluid-structure interaction problems in two dimensions is developed in this work. The Lagally theorem is adopted in the current model to obtain the equation of motion for object. This theorem describes the unsteady hydrodynamic force on a body exhibiting arbitrary motion in an ideal fluid by the properties of the singularities employed to generate the flow. So far, only
sources and dipoles have been considered and the present work extends the theorem to include free vortices in a two-dimensional flow. The developed model is validated by reproducing the system dynamics or force evolution of
three existing problems reported in the literature: (1) a free cylinder interacting with a free vortex, (2) the moving Foppl problem, and (3) a cylinder in constant normal approach to a fixed identical cylinder. The present theorem
is then employed to study the problem when the cylinder in the moving F‥oppl system is forced to move at constant velocity normally towards an identical target cylinder that is fixed or free to move. The force developed on each cylinder is investigated with five different initially tail vortices configurations for each example. To extend the current model to further consider the problems involving irregular shaped objects, the method of fundamental solutions is applied to numerically solve the strength as well as the position of the internal image singularities employed to represent the flow. The new model is validated by re-examining the single vortex-object interaction. Then the inline approach of a vortex pair towards an ellipse is considered to demonstrate the capability of the proposed model.
Subjects
potential flows
fluid-body interaction
Lagally theorem
method of fundamental solutions
Type
thesis
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