Paulo Ferreira de Sousa

Thrust efficiency of harmonically oscillating flexible flat plates

We consider the efficiency of thrust-producing inextensible membranes with variable bending rigidities. The present study is a numerical investigation of the thrust generation and flow-field characteristics of a two-dimensional flapping flexible membrane, fixed at its leading edge. To study the time-dependent response of the membranes, a fluid/structure solver that couples a compact finite-difference immersed boundary method flow solver with a thin-membrane structural solver was developed. Using a body-fitted grid, external forcing to the structure is calculated from the boundary fluid dynamics. A systematic series of runs of the fluid/structure solver was performed in order to obtain a clear picture of the thrust-producing characteristics of membranes with bending rigidities ranging between EI = 5 × 10 −6 and EI = 2 × 10 −5 and structural mass coefficients between ρ s h = 0.01 and ρ s h = 0.04, for a Reynolds number of Re = 851.

Thrust performance of a flexible low-aspect-ratio pitching plate

We numerically investigate the hydrodynamic performance of an elastic plate of aspect ratio 0.54 and mass ratio 0.1 that pitches around its leading edge in a free stream at Reynolds number 640. It is found that for the rigid plate and the flexible plate with the first-mode deformation, the thrust coefficient nearly collapses onto the same curve when plotted against the Strouhal number that is defined using the tail excursion. Exceptions are found when the plate is overly flexible and higher deformation modes take place. On the other hand, the flexible plate has significantly higher power efficiency than the rigid plate at the same Strouhal number. Like the rigid plate, wake transition is observed for the flexible plate as the Strouhal number is varied. Specifically, at low Strouhal numbers (St 0.28), the wake turns into two trains of closed vortex rings with hairpin legs.

Dynamics of passive scalars and tracers advected by a two-dimensional tripolar vortex

The dynamics of passive scalars and tracers during the formation and subsequent persistence of a laminar tripolar vortex, obtained through an unstable monopolar vortex seeded with a k = 2 azimuthal perturbation, is investigated. Two-dimensional direct numerical simulations of passive scalars with Schmidt numbers Sc = 0.1, 1, 10 and 100 are performed. The scalar variance for the four cases is analysed, as well as the different dispersion patterns up to 10 times greater than the time for formation of the tripolar vortex. During the formation of the tripole, an accelerated scalar dissipation is observed. That dissipation is connected to the advection-dominated processes associated with the growth of the perturbation mode. During that process, the patterns of mixing of the different passive scalars are very much the same as for vorticity. This stage of accelerated dissipation is preceded and followed by stages of diffusion-dominated scalar dissipation. Passive Lagrangian tracers are used to explore the transport of fluid elements during the evolution, and to provide a detailed view of the tripolar vortex formation and behaviour for longer times. Chaotic mixing was studied by examining patterns of spatial variation of finite-time Lyapunov exponents. As the perturbation grows and the tripolar vortex is formed, two large regions of regular flow, divided by a region of chaotic flow, form for each satellite. When the tripole is fully formed, it is composed of three distinct regular regions, corresponding to the core of negative vorticity and the two satellites of positive vorticity. The comparison between the evolution for vorticity, concentration, randomly distributed particles and Lyapunov exponents shows that transport occurs mainly in the regions of chaotic flow that surround the tripolar vortex after its formation. For longer times, both the chaotic/regular flow interfaces and the vorticity gradients are responsible for the integrity of the tripolar system.