Su, Tsung-Chow

Vortex methods are grid-free; therefore, their use avoids a number of shortcomings of Eulerian, grid-based numerical methods for solving high Reynolds number flow problems. These include such problems as poor resolution and numerical diffusion. In vortex methods, the continuous vorticity field is discretized into a collection of Lagrangian elements, known as vortex elements. Vortex elements are free to move in the flow field which they create. The velocity field induced by these vortex elements is a solution to the Navier-Stokes equation, and in principle the method is suitable for high Reynolds number flows. In this dissertation, viscous vortex element methods are studied. Some modifications are developed. Discrete vortex element methods have been used to solve the Navier-Stokes equations in high Reynolds number flows. Globally satisfactory results have been obtained. However, computed pressure fields are often inaccurate due to the significant errors in the surface vorticity distribution. In addition, different ad hoc assumptions are often used in different proposed algorithms. In the present study, improvements are made to better represent the near-wall vorticity when obtaining numerical solutions for the Navier-Stokes equations. In particular, we split the boundary vortex sheet into two parts at each time step. One part remains a vortex sheet lying on the boundary of the solid body, and the other enters into the flow field as a free vortex element with a uniformly distributed vorticity. A set of kinematic relationships are used to determine the two appropriate portions of the split, and the position of the vortex element to be freed at the time of release. Another improvement is to include the nonlinear acceleration terms in the governing equations near the solid boundary when evaluating the surface pressure distribution. The aerodynamic force coefficients can then be obtained by summing up the pressure forces. By comparing the computed surface vorticities, surface pressures and aerodynamics force coefficients with existing numerical/experimental data in the cases of viscous flow around a circular cylinder, an aerofoil, and a bridge deck section, it is shown that the present approach is more accurate in modelling the flow features and force coefficients without making different ad hoc assumptions for different geometries. The computation is efficient. It can be useful in the study of the unsteady fluid flow phenomenon in practical engineering problems.

A mathematical model, which accounts for the essential effects of environmental loads and vehicle characteristics from a fluid dynamics point of view, is developed to forecast the position of a craft drifting on the sea surface. The study is intended to provide a better understanding of the dynamics of drift and thus to provide a reliable model of drift prediction for use in future search and rescue mission. In the mathematical formulation, three degrees of freedom (surge, sway and yaw) of a craft are analyzed, since they play the most significant role in the drift prediction problem. The governing equations of motions are derived from Newton's law of dynamics and the environmental loads considered are the forces and moments exerted by wind, current and waves. The forces are analyzed in terms of drag, lift, and inertial forces. The moments are obtained by summing the contribution from the above forces. For the computation of the wind loads, the wind gradient as well as craft geometry is accounted for. In the current loads, profile, friction and propeller drags are included. The wave forces are computed by the use of wave spectral density. The formulation includes the effects of craft rotation as well as craft translation. A computer algorithm for the mathematical model is implemented to obtain the numerical result in the time domain. The model is verified by comparing its result with field measurements. For this purpose, a field test was carried out. The agreement between the computed and field measured drift path was excellent. The real time prediction capability of the model was ascertained.