In this paper, variable confinement parameters were successfully developed for compressible vorticity confinement. Three variable confinement parameters, that have velocity dimension, were defined, based on three artificial dissipation schemes. The resulting confinement parameters are functions of the spectral radii of the Jacobian matrices and the Jacobian matrices themselves.Therefore, the confinement parameter implicitly contains the grid size and other local fluid properties. Preliminary results for moving vortices showed that the new confinement parameters allow the capture of vortical layers that, effectively, do not decay in time, like Hu et al.'s confinement. Calculations of the supersonic base flow and supersonic shear layer showed good agreement with experimental and analytical data, especially for the variable CUSP confinement parameter. When variable confinement parameters are used, the tuning constant is equal to, or larger than, the equivalent value of the constant confinement (Hu et al.). This means that the tuning constant varies in a range smaller than that of the Hu et al. constant confinement, especially for the CUSP confinement parameter.

The apparent mass effect is enhanced significantly when the motion of a body changes quickly, such as a flapping wing or an impulsively started plate. Previous method for calculating the apparent mass of a given body needs to adopt the assumption of ideal flow and know the potential of velocity field arising in the fluid due to the motion of the body. However, the assumption of ideal flow is contrary to real fluid field and it is hard to obtain the potential of velocity field in most cases. In this paper, a new method based on the vorticity moment theorem for calculating the apparent mass of the body of revolution in the axial direction due to axial acceleration is developed. This method has no assumption of ideal flow and establishes the relationship between the apparent mass and the vorticity loops adjacent to the surface of the body. Using this method, the value of the apparent mass can be easily figured out and the physical mechanism of the apparent mass can be revealed from the view of the vorticity loop. The comparisons between different bodies have shown the influences of the fineness ratio (the ratio of the length to the maximum diameter) and the trailing edge type on the apparent mass.

A numerical study of particle motion in a cubic lid driven cavity is presented. As a computational tool, a boundary element based flow solver with a Lagrangian particle tracking algorithm is derived.Flow simulations were performed using an in-house boundary element based 3D viscous flow solver.The Lagrangian particle tracking algorithm is capable of simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient and added mass. The derived algorithm is used to simulate particle behaviour in a cellular flow field and in a lid driven cavity flow. Simulations of particle movement in a cellular flow field were used to validate the algorithm. The main goal of the paper was to numerically simulate the flow behaviour of spheres of different densities and different diameters, as experimentally observed in work of Tsorng et al.The study of slightly buoyant and non-buoyant particles in a lid driven cavity was aimed at discovering cases when particles leave the primary vortex and enter into secondary vortices, a phenomenon described in the work of Tsorng et al. A parametric study of this phenomenon was preformed.The presented computational results show excellent agreement with experiments, confirming the accuracy of the developed computational method.

The present study aims to describe flow structures and cavitation phenomenon in the submerged waterjet. A non-intrusive experimental work was performed. The waterjet was produced through a nozzle characterized by a short straight segment adjacent to the nozzle outlet. Waterjet pressures were varied from 5 to 22 MPa. The time-resolved particle image velocimetry (TR-PIV) was used to measure velocity distributions. The proper orthogonal decomposition (POD) method was employed to extract flow structures from the flow-measurement results. Cavitation was created through increasing the waterjet pressure. A comparison of cavitation patterns at different waterjet pressures was implemented. Similarity of the distribution of average velocity is revealed as the waterjet pressure varies. The POD results indicate that two high-vorticity bands close to the nozzle, symmetrically distributed with respect to the nozzle axis, dominate the waterjet stream. Further downstream, small-scale flow structures are sparsely distributed and assume a low percentage of the total energy. Initial cavitation is featured by small-scale cavities which are formed near the high-vorticity zone. As the waterjet pressure increases, the volume fraction of cavitation increases and morphological features of cavitation change significantly as waterjet develops. At a later stage, stable cavity clouds are evidenced. A high relevance between vorticity distribution and cavitation cloud pattern is demonstrated.

In this paper, vorticity confinement parameters are successfully developed for compressible flows. The first new confinement parameter is proportional to spectral radii of the flux Jacobian matrix. Therefore, the confinement parameter implicitly contains the local conditions of the flow field. This new method is named as lambda vorticity confinement method. In order to gain confidence in the applicability of vorticity confinement, it would be ideal to completely eliminate constant coefficients from confinement parameters. Because these constant coefficients should be determined for every problem by trial and error and it takes a long time. In the next part of this paper, a suitable relation is introduced for the vorticity confinement parameter that doesn't need any constant coefficient. This new method is named as adaptive vorticity confinement method. Then the capability of these new methods is compared with the other vorticity confinement methods for solving shock-vortex interaction and three dimensional moving vortex problems.

The vorticity dynamics of a Lamb-like dipole colliding with flat boundaries are investigated for high Reynolds number flows by implementation of the lattice Boltzmann method (LBM). The standard LBM based on the single-relaxation-time collision model suffers from numerical instabilities at high Reynolds numbers. Herein, a regularized collision model is employed for the LBM to preserve the stability and accuracy of the numerical solutions at such flow conditions. The computations are performed for the normal collision of the dipole with the no-slip boundary for several Reynolds numbers in the range of 4 5 Re 10 10  . The results obtained based on the regularized lattice Boltzmann (RLB) method for the statistical flow characteristics like the vorticity field and enstrophy quantity of the dipole-wall collision problem are investigated. The present study demonstrates that the shear-layer instabilities near the wall are responsible for rolling-up of the boundary layer before it is detached from the surface for high Reynolds numbers. This detachment mechanism leads to a viscous rebound and formation of small scale vortices. The shear-layer vortices formed dramatically influence the flow evolution after the collision and result strong enhancement of the total enstrophy of the flow field. By comparing the present results with those of provided by other numerical solutions, it is also concluded that the RLB scheme implemented is robust and sufficiently accurate numerical technique in comparison with the flow solvers based on the Navier-Stokes equations for predicting the statistical features of separated fluid flows even at high Reynolds numbers.