Deformation of a vortex ring caused by its impingement on a sphere

Abstract

The deformation of a vortex ring caused by its impingement on a sphere was numerically investigated using a proposed vortex-in-cell method. The method was validated by simulation of the collision of a vortex ring with a rigid planar surface and proved to be most satisfactory in the analysis of the dynamics of a vortex structure. In a coaxial collision, the behavior of the vortex structure is similar to that in the case of a planar surface. A secondary vortex ring is formed owing to the separation of the boundary layers on the sphere, caused by the effect of the primary vortex ring. The interaction between the secondary and primary vortex rings plays an important role in the dynamics of the vortex structure when the secondary vortex ring is completely formed. In a noncoaxial collision, the structure of the secondary vortex is moderately different from that in the coaxial collision. Moreover, the vortex structure in the coaxial collision is two-dimensional, in which the vorticity field is dominated by two transverse components, whereas that in the noncoaxial collision is three-dimensional. The total kinetic energy in both the cases decreases gradually during the entire period of evolution, whereas the enstrophy reduces in the early stage, then increases considerably, before a gradual reduction in the final stage. The enstrophy reaches a peak when the secondary vortex ring is completely formed, at which stage the effects of vortex stretching and vorticity production at the solid boundary are higher than that of vortex diffusion.

A large-eddy simulation study on vortex-ring collisions upon round cylinders

“…In contrast, vortex-ring collisions upon round solid boundaries such as spheres, convex/concave walls or round cylinders have received significantly less attention as the above vortex-ring collision configurations. Nguyen et al (2019) conducted both experiments and simulations on vortex-ring collisions upon a round sphere, where the sphere diameter was 3 times the orifice size. The effects of lateral offset between the vortex-ring and sphere were investigated as well and results showed that coaxial collisions are relatively two-dimensional, while non-coaxial collisions led to nonuniform circulation of the primary vortex-ring and more three-dimensional resulting flow structures and behaviour.…”

Collisions of vortex rings with hemispheres

“…Similar to Allen et al (2007), only a secondary vortex ring was observed to form. In the more recent study by Nguyen et al (2019) where the diameter of the sphere is much larger, at three times the vortex ring orifice, formations of secondary and tertiary vortex rings after the primary vortex ring collides with the sphere coaxially can be observed. However, experimental and numerical flow visualizations were presented only up to a non-dimensionalized time t * = 0.917, and subsequent interactions between the three different vortex rings were lacking.…”

“…Other than convex cylindrical surfaces, there are other curved geometries that are of interest, but one that is of particular interest here involves hemispheric surfaces. Several past works studied coaxial vortex ring collisions with full spheres and shed much light on how the formations of vortex ring structures differ from those associated with planar geometries due to inherent differences between the pressure gradients and boundary layers of planar and spherical surfaces, as well as how non-coaxial collisions will affect the vortex dynamics (Allen, Jouanne & Shashikanth 2007; Ferreira de Sousa 2012; Nguyen, Takamure & Uchiyama 2019). In the study by Allen et al.…”

“…Other than convex cylindrical surfaces, there are other curved geometries that are of interest, but one that is of particular interest here involves hemispheric surfaces. 980 A17-2 Several past works studied coaxial vortex ring collisions with full spheres and shed much light on how the formations of vortex ring structures differ from those associated with planar geometries due to inherent differences between the pressure gradients and boundary layers of planar and spherical surfaces, as well as how non-coaxial collisions will affect the vortex dynamics (Allen, Jouanne & Shashikanth 2007;Ferreira de Sousa 2012;Nguyen, Takamure & Uchiyama 2019). In the study by Allen et al (2007), a single and freely suspended sphere with a diameter close to that of the vortex ring orifice was studied, and the results show good agreement between the behaviour of the sphere's kinematics and that of the moment of vorticity during the vortex ring collision.…”

Archive of Mechanical Engineering

“…Cottet and Koumoutsakos [13] combined it with a viscous model to simulate two-and three-dimensional incompressible viscous flows. A VIC method was developed to simulate the flow around two tandem cylinders, the flow around four cylinders of various shapes, and the vortex−wall interaction by Nguyen et al [14][15][16]. It was proven that the method could capture the vortex shedding, the interaction between the vortex wakes, the fluid forces exerted on the cylinders, and the vortex formation and deformation due to the wall effects.…”