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In this paper, we examine the coupling between odor dynamics and vortex dynamics around undulating bodies, with a focus on bio-inspired propulsion mechanisms. Utilizing computational fluid dynamics (CFD) simulations with an in-house Immersed-Boundary Method (IBM) solver, we investigate how different waveform patterns, specifically carangiform and anguilliform, influence the dispersion of chemical cues in both water and air environments. Our findings reveal that vortex dynamics significantly impact the overall trajectory of odor spots, although the alignment between odor spots and coherent flow structures is not always precise. We also evaluate the relative contributions of diffusion and convection in odor transport, showing that convection dominates in water, driven by higher Schmidt numbers, while diffusion plays a more prominent role alongside convection in air. Additionally, the anguilliform waveform generally produces stronger and farther-reaching chemical cues compared to carangiform swimmers. The critical roles of Strouhal number and Reynolds number in determining the efficiency of odor dispersion are also explained, offering insights that could enhance the design of more efficient, adaptive, and intelligent autonomous underwater vehicles (AUVs) by integrating sensory and hydrodynamic principles inspired by fish locomotion.

This study introduces novel physics-based scaling laws to estimate the propulsive performance of synchronously pitching foils in various schooling configurations at Re=4000. These relations are derived from quasi-steady lift-based and added mass forces. Hydrodynamic interactions among the schooling foils are considered through vortex-induced velocities imposed on them, constituting the ground effect. Generalized scaling equations are formulated for cycle-averaged coefficients of thrust and power. These equations encompass both the pure-pitching and induced velocity terms, capturing their combined effects. The equations are compared to computational results obtained from two-foils systems, exhibiting foil arrangements over a wide range of parameter space, including Strouhal number (0.15 \leq St \leq 0.4), pitching amplitude (5 deg \leq \theta_0 \leq 14 deg), and phase difference (0 deg \leq \phi \leq 180 deg). The individual contributions of pure-pitching and induced velocity terms to propulsive performance elucidate that solely relying on the pure-pitching terms leads to inadequate estimation, emphasizing the significance of the induced velocity terms. Validity of the approach is further assessed by testing it with a three-foil configuration, which displays a collapse. This indicates that the scaling laws are not only applicable to two-foils systems but also extend their effectiveness to multi-foil arrangements.

The correspondence of secondary spanwise structures and pressure gradient is numerically evaluated for a foil, performing heaving and pitching motion, at a range of phase offsets (90$^\circ$ $\le \phi \le$ 270$^\circ$) and reduced frequency (0.32 $\le St_c \le$ 0.56). The Reynolds number is $Re =$ 8000. The wake is shown to be dominated by secondary hairpin-like structures that are formed due to an elliptic instability prompted by the paired primary and secondary leading edge vortex ($LEV$). The weaker secondary $LEV$ undergoes a core deformation, resulting in streamwise vorticity outflux across the span of the foil, and hence, the growth of hairpin-like structures. Evaluating pressure gradients on the surface of the foil reveals a unique fundamental measure to quantitatively characterize the growth of these coherent structures. Their dominant presence can be directly linked to the growth of the secondary $LEV$ formed due to the large-scale interactions under localized adverse pressure gradients. These promote a streamwise flow compression in neighboring regions of the primary $LEV$. This association also presents a vivid consistency across a range of kinematics. Therefore, this correspondence provides a novel procedure to investigate the mechanisms involved in the formation of secondary structures in the wake of an oscillating foil.

Three-dimensional wake of an oscillating foil with combined heaving and pitching motion is numerically evaluated at a range of chord-based Strouhal number (0.32 \le Stc \le 0.56) and phase offset (90 deg \le \phi \le 70 deg) at Re = 8000. The changes in \phi and Stc reflect a unique route of transition in mechanisms that govern the origin of spanwise instabilities and growth of secondary wake structures. At lower Stc, heave dominated kinematics demonstrates a strong secondary leading edge vortex (LEV ) as the source of growing spanwise instability on the primary LEV , followed by an outflux of streamwise vorticity filaments from the secondary LEV . With increasing heave domination, the origin of stronger spanwise instability is governed by a counter-rotating trailing edge vortex (TEV ) and LEV that leads to growth of streamwise secondary structures. A decreasing heave domination ultimately coincides with an absence of strong LEV undulations and secondary structures. The consistent transition routes are represented on a phase-space map, where a progression of spanwise instability and growth of secondary structures becomes evident within regimes of decreased heave domination. The increasing strength of circulation for the primary LEV , with increasing Stc, provides a crucial reasoning for this newly identified progression.

The unsteady hydrodynamics of two in-phase pitching foils arranged in side-by-side (parallel) configurations is examined for a range of Strouhal number and separation distance. Three distinct vortex patterns are identified in the Strohual number-separation distance phase maps, which include separated wake, merged wake, and transitional-merged wake. Furthermore, a novel model is introduced based on fundamental flow variables including velocity, location, and circulation of dipole structures to quantitatively distinguish vortex patterns in the wake. The physical mechanism of wake merging process is also elucidated. When an oscillating foil experiences the jet deflection phenomenon, secondary structures shed from the primary street traverse in the other direction by making an angle with its parent vortex street. For parallel foils, secondary structures from the vortex street of the lower foil interact with the primary vortex street of the upper foil under certain kinematic conditions. This interaction triggers the wake merging process by influencing circulation of coherent structures in the upper part of the wake. It is unveiled that merging of the wakes leads to enhancements in propulsive efficiency by increasing thrust generation without a significant alteration in power requirements. These are attributed to the formation of a high-momentum jet by the merged vortex street, which possesses significantly larger circulation due to the amalgamation of the vortices, and major alterations in the evolution of leading edge vortices. Thus, flow physics that are thoroughly explored here are crucial in providing novel insights for future development of flow control techniques for efficient designs of bio-inspired underwater propulsors.

This study explored the aerodynamics of a new multi-stage co-axial vertical-axis wind turbine based on bio-inspiration from natural swimming habit of fish. The turbine was formed from a conventional straight-bladed vertical-axis turbine (VAWT) with a small inner rotor, also of three blades. The azimuthal and radial locations of the inner rotor were varied. Using numerical simulations, performance of the proposed new design was evaluated over a range of tip-speed ratios. The preliminary results identified a 600% increase in power output for multi-stage VAWTs at tip-speed rations TSR = 0 - 3, and a substantial drop in power coefficient at TSR > 3.0. The wake dynamics analyses revealed that the increase was due to interactions between the blades of one rotor and the other. This reduced the unsteady separation from the outer rotor which produced most of the power. A detailed parametric study was also completed, which showed the implications of geometric and kinematic details on the performance of the proposed multistage VAWT.

This study was inspired from the swimming habits of red nose tetra fish that prefer side-by-side configurations and exhibit changes to their synchronization mid-swimming. Using numerical simulations, alterations to the unsteady wake dynamics imposed by abrupt changes in the phase angle between two pitching side-by-side foils were examined at Reynolds number of 4;000 and Strouhal number of 0:50. Four hybrid modes were considered in thisstudy with two modes representing an abrupt phase change by pi during the 20th cycle. The other two modes represented a simplified case of burst-and-coast swimming, in which there was a brief (2 oscillation periods) suspension of oscillations before imposing a change in phase angle. In all cases, the foils initially performed out-of-phase pitching, and then they started their in-phase motion by either performing the upstroke or down-stroke first. This kinematic change resulted in the formation and growth of a secondary vortex street in between two primary streets, which enabled and maintained a split wake configuration. Furthermore, the phase switching altered the pressure levels on the top and bottom surfaces of both foils to almost similar levels, which attributed to a reduction in the side-force. The growth rate of the secondary vortex street remained consistent for all four hybrid modes.

The wavelength of undulatory kinematics of fish is an important parameter to determine their hydrodynamic performance. This study focuses on numerical examination of this feature by reconstructing the real physiological model and kinematics of steadily swimmning Jack Fish. We perform three-dimensional numerical simulations for flows over these models composed of the trunk, and dorsal, anal, and caudal fins. Moreover, we prescribe the carangiform-like motion for its undulation for a range of wavelengths. Undulation with larger wavelengths improves the hydrodynamic performance of the carangiform swimmer in terms of better thrust production by the caudal fin, lower drag production on the trunk, and reduced power consumption by the trunk. This coincides with the formation of stronger posterior body vortices and leading-edge vortices with more circulation on the caudal fin. The real kinematics of Jack Fish surpasses the performance of those with prescribed motion owing to the flexibility of the caudal fin., Comment: 11 pages, 9 figures

To understand the governing mechanisms of bio-inspired swimming has always been challenging due to intense interactions between the flexible bodies of natural aquatic species and water around them. In this paper, we employ advanced modal decomposition techniques; proper orthogonal decomposition and dynamic mode decomposition, to extract energetically strongest spatio-temporal orthonormal components of complex kinematics of a Crevalle Jack (Caranx hippos) fish. Then, we present a computational framework for handling fluid-structure interaction related problems in order to investigate their contributions towards the overall dynamics of highly nonlinear systems. We find that the undulating motion of this fish can be described by only two standing-wave like spatially orthonormal modes. Constructing the data set from our numerical simulations for flows over the membranous caudal fin of the Jack fish, our modal analyses reveal that only the first few modes receive energy from both the fluid and structure, but the contribution of fluid in the higher modes is minimal. For the viscous and transitional flow conditions considered here, both spatially and temporally orthonormal modes show strikingly similar coherent flow structures. Our investigations are expected to assist in developing data-driven reduced-dimensional mathematical models to examine the dynamics of bio-inspired swimming robots and develop new and effective control strategies to bring their performance closer to real fish species.

Natural swimmers usually perform undulations to propel themselves and perform a range of maneuvers. These include various biological species ranging from micro-sized organisms to large-sized fishes that undulate at typical kinematic patterns. In this paper, we consider anguilliform and carangiform swimming modes to perform numerical simulations using an immersed-boundary methods based computational solver at various Reynolds number regimes. We carry out thorough studies using wavelength and Strouhal frequency as the governing parameters for the hydrodynamic performance of undulating swimmers. Our analysis shows that the anguilliform kinematics achieves better hydrodynamic efficiency for viscous flow regime, whereas for flows with higher Reynolds number, the wavelength of the wavy motion dictates which kinematics will outperform the other. We find that the constructive interference between vortices produced at anterior parts of the bodies and co-rotating vortices present at the posterior parts plays an important role in reversing the direction of Benard-von Karman vortex street. Since most of the thrust producing conditions appear to cause wake deflection; a critical factor responsible for degrading the hydrodynamic efficiency of a swimmer, we discuss the underlying mechanics that would trigger this phenomenon. We demonstrate that the choice of kinematic and flow conditions may be restricted for the natural swimmers due to their morphological structures, but our findings provide a guideline on their selection for bio-inspired underwater vehicles., Comment: 26 pages

Getting inspired from swimming natural species, a lot of research is being carried out in the field of unmanned underwater vehicles. During the last two decades, more emphasis on the associated hydrodynamic mechanisms, structural dynamics, control techniques and, its motion and path planning has been prominently witnessed in the literature. Considering the importance of the involved acoustic mechanisms, we focus on the quantification of flow noise produced by an oscillating hydrofoil here employed as a kinematic model for fish or its relevant appendages. In our current study, we perform numerical simulations for flow over an oscillating hydrofoil for a wide range of flow and kinematic parameters. Using the Ffowcs-Williams and Hawkings (FW-H) method, we quantify the flow noise produced by a fish during its swimming for a range of kinematic and flow parameters including Reynolds number, reduced frequency, and Strouhal number. We find that the distributions of the sound pressure levels at the oscillating frequency and its first even harmonic due to the pressure fluctuations in the fluid domain are dipole-like patterns. The magnitudes of these sound pressure levels depend on the Reynolds number and Strouhal number, whereas the direction of their dipole-axes appears to be affected by the reduced frequency only. Moreover, We also correlate this emission of sound radiations with the hydrodynamic force coefficients.

For present study, setting Strouhal Number (St) as control parameter, numerical simulations for flow past oscillating NACA-0012 airfoil at 1,000 Reynolds Numbers (Re) are performed. Temporal profiles of unsteady forces; lift and thrust, and their spectral analysis clearly indicate the solution to be a period-1 attractor for low Strouhal numbers. This study reveals that aerodynamic forces produced by plunging airfoil are independent of initial kinematic conditions of airfoil that proves the existence of limit cycle. Frequencies present in the oscillating lift force are composed of fundamental (fs), even and odd harmonics (3fs) at higher Strouhal numbers. Using numerical simulations, shedding frequencies (f_s) were observed to be nearly equal to the excitation frequencies in all the cases. Unsteady lift force generated due to the plunging airfoil is modeled by modified van der Pol oscillator. Using method of multiple scales and spectral analysis of steady-state CFD solutions, frequencies and damping terms in the van der Pol oscillator model are estimated. We prove the applicability of this model to all planar motions of airfoil; plunging, pitching and flapping. An important aspect of currently-proposed model is capturing the time-averaged value of aerodynamic lift coefficient., Comment: 23 pages, 11 Figures, To be submitted to Applied Mathematics and Computation