Viscous flow

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.

This research concerns with the determination of the base pressure related to the conical convergent nozzle flow when a sudden enlargement in cross-sectional area occurs. It is recognized at the outset that the problem belongs to the category of strong interaction where inviscid and viscous flows must be considered together before a solution can be established. The viscous flow analyses based on the integral formulations are guided more or less by the boundary layer concept. The inviscid flow field is established from the hodograph transformation, and the method of characteristics. Again the point of reattachment behaves as a saddle point singularity for the system of equations describing the viscous flow recompression process. After the point of reattachment is approached, an overall momentum balance is applied so that the base pressure and the location where recompression starts, may be determined. Experimental studies with specific conical angles and area ratios are also conducted in the laboratory. The results obtained from the theoretical analysis agreed well with the experimental data produced in the laboratory and the data available elsewhere. These evidences lead to the conclusion that the method developed in this investigation is effective in dealing with problems of this type.