Siddharth Gupta

The present study aims to provide an understanding of the influence of an afterbody on the flow-induced vibration (FIV) of cylinders. This is achieved through experimental and numerical investigations into the FIV response of a reverse-D-cross-section cylinder of aspect ratio $AR=5$ . By carefully monitoring the point of flow separation to show it always occurs at the sharp top and bottom edges and never further upstream, it is demonstrated that vortex-induced vibration (VIV) can occur without an afterbody. However, for other aspect ratios, an afterbody does play a crucial role in determining the type of fluid forces responsible for sustaining VIV from low to moderate Reynolds numbers in the range $100$ – $4700$ . For a cylinder without an afterbody, it is found that the viscous force originating from the presence of strong compact vortices forming close to the leeward side of the cylinder is responsible for sustaining strong transverse vibration. In contrast, for a cylinder with an afterbody, the dominant force component depends on the size of the afterbody. In cylinders with a small afterbody, such as a reverse-D semi-circular cylinder, the viscous force dominates, while in cylinders with a larger afterbody such as a circular cylinder, the pressure force dominates.

In the present two-dimensional numerical study, we investigate the roles of geometrical parameters of a hydrofoil (shape/curvature of the leading and trailing edges and thickness) and kinematic parameters (phase difference between heave and pitch ($\varphi$)) on the propulsive performance of different-shaped hydrofoils oscillating at maximum angles of attack up to ${\alpha }_{max}={30}^{\circ }$. The study was carried out at a fixed non-dimensional maximum heave to chord ratio $h_{\circ }/C=0.75$, Strouhal number $St=0.25$, and Reynolds number $Re=5000$. Our findings reveal that hydrofoil performance and stability improve with leading and trailing edge curvatures but decline as thickness increases. By analyzing the near-wake structure, we establish that even minimal flow separation increases power consumption while moderate flow separation enhances thrust. Over the range of different-shaped hydrofoils at different ${\alpha }_{max}$ and $\varphi$, maximum propulsion efficiency occurs for those parameters for which there is a small degree of flow separation but with no roll-up of a separating vortex. In comparison, maximum thrust generation occurs when there is a moderately strong flow separation but without induction of a significant amount of fluid around the trailing edge. These insights offer valuable knowledge for understanding fish propulsion efficiency and have applications in designing autonomous underwater vehicles (AUVs) and micro-air vehicles (MAVs).

Flow transitions are an important fluid-dynamic phenomena for many reasons, including the direct effect on the aerodynamic forces acting on the body. In the present study, two-dimensional (2-D) and three-dimensional (3-D) wake transitions of a NACA0012 airfoil are studied for angles of attack in the range $0^\circ \leq \alpha \leq 20^\circ$ and Reynolds numbers $500 \leq {\textit {Re}} \leq 5000$ . The study uses water-channel experiments and 2-D and 3-D numerical simulations based on the nodal spectral-element method, level-set function-based immersed-interface method and Floquet stability analysis. The different wake states are categorised based on the time-instantaneous wake structure, non-dimensional frequency and aerodynamic force coefficients. The wake states and transition boundaries are summarised in a wake regime map. The critical angle of attack and Reynolds number for the supercritical Hopf bifurcation (i.e. steady to periodic wake transition) varies as $\alpha _1 {\sim} {\textit {Re}}^{-0.65}$ , while the critical angle of attack for the onset of three dimensionality varies as $\alpha _{3D} {\sim} {\textit {Re}}^{-0.5}$ . Over the entire Reynolds number range, the transition to 3-D flow occurs through a mode C (subharmonic) transition. Beyond this initial transition, further instabilities of the 2-D periodic base flow arise and are investigated. For instance, at $ {\textit {Re}}=2000$ and $\alpha _{3D,2}=11.0^\circ$ , mode C coexists together with modes related to modes A and QP seen in a stationary circular cylinder wake. In contrast, at $ {\textit {Re}}=5000$ and $\alpha _{3D,2}=8.0^\circ$ , the dominant mode C coexists with mode QP. Three-dimensional simulations well beyond critical angles indicate that 2-D vortex-street transitions are approximately maintained in the fully saturated 3-D wakes in a spanwise-averaged sense.

A comprehensive two-dimensional numerical investigation has been undertaken to calculate the energetic cost of propulsion and the various flow transitions of a fish-like body undulation mechanism based on a National Advisory Committee for Aeronautics 0012 hydrofoil. This covers a wide range of Strouhal $(0\le St\le 1.4)$ and Reynolds $(500\le Re\le 5000)$ numbers from simulations based on a level-set function immersed-interface method. It is found that the time-averaged thrust coefficient displays a quadratic relationship with increasing St, and increases significantly with Re. Additionally, the time-averaged input power coefficient exhibits a cubic dependence with increasing St but is independent of Re. Both St dependences agree with those previously observed experimentally and numerically for an oscillating foil; however, for similar ranges of governing parameters, comparisons suggest that the body undulation mechanism possesses a higher propulsive efficiency. The $St\propto R{e}^{-0.19}$ scaling for the drag-to-thrust transition is consistent with that found for a wide variety of fish and birds in nature. Interestingly, for cases with an undulation wave-speed below the free-stream speed, the time-averaged drag coefficient is found to be higher than that of a stationary hydrofoil at the same Re. Furthermore, the time-averaged input power coefficient is negative, indicating the potential for the undulation mechanism to extract energy from the free-stream. Eight different wake patterns/transitions are documented for the parameter space; these have been assembled into a wake-regime parameter-space map. The present findings should aid in predicting and understanding different hydrodynamic forces and wake patterns for undulating kinematics.

The present study examines the energy efficiency of self-propelled hydrofoils for various modes and kinematics of swimming adopted by various body-caudal fin fish. In particular, this work considers the intermittent burst-and-coast (B&C) and continuous swimming modes, and examines the effect of the undulating and/or pitching swimming kinematics, adopted by the undulating body of anguilliform fish and pitching caudal fin of carangiform and thunniform fish. Notably, B&C swimming is adopted in nature mostly by the latter class but rarely by the former. This fact forms the basis of our study on the hydrodynamics and propulsion performance for both classes of fish-inspired swimming using a NACA0012 hydrofoil model. This analysis explores a large parameter space covering undulation wavelength, $0.8\le {\lambda }^{*}<\infty$ , Reynolds number, $50\le R{e}_f\le 1500$ , and duty cycle (DC), $0.1\le DC\le 1$ , with the DC representing the fraction of time in B&C swimming. The fluid–structure dynamics-based vortex-shedding-process is investigated, where B&C swimming results in either an asymmetric reverse von Karman (RVK) or forward von Karman vortex street, rather than a symmetric RVK vortex street observed during continuous swimming. It is demonstrated that the B&C swimming results in an energy saving, although there is a concomitant increase in the travel time. Moreover, our results show that B&C swimming is effective for carangiform and thunniform tail-like kinematics but not for anguilliform body-like kinematics of the hydrofoil. Thus, the predictions are consistent with the observed swimming behavior adopted by a fish in nature and provide input into the efficient design of unmanned underwater vehicles.