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Inspired by the natural motion of insects, fish, and other animals, flapping airfoils have gained significant importance due to their applications in fields such as ship propulsion, micro aerial vehicles, and autonomous underwater vehicles. Over the past two decades, extensive research has focused on understanding the dynamics of these airfoils, their thrust production capabilities, and methods to enhance this thrust in unsteady flows. This study investigates how the presence of a cylinder oscillating due to incoming flow affects the thrust performance of the flapping airfoil. The results indicate that the flapping airfoil generates increased thrust when placed in the wake of the oscillating cylinder compared to a scenario without the cylinder's wake. A direct relationship has been found between the strouhal number ($St$) of the flapping airfoil and its pitching amplitude, which significantly influences the airfoil's performance. This analysis highlights the potential for optimizing flapping airfoil efficiency through strategic selection of flapping parameters and the placement of an oscillating cylinder.

Proper orthogonal decomposition (POD) is often employed in developing reduced-order models (ROM) in fluid flows for design, control, and optimization. Contrary to the usual practice where velocity field is the focus, we apply the POD analysis on the pressure field data obtained from numerical simulations of the flow past stationary and oscillating cylinders. Since pressure mainly contributes to the hydrodynamic forces acting on the structure, we compute the pressure POD modes on the cylinder surface oscillating in lock-in and lock-out regions. These modes are then dissected into sine and cosine magnitudes to estimate their contribution in the development of pressure lift and drag decomposition coefficients, respectively. The key finding of this study is that more POD modes are required to capture the flow physics in nonsynchronous regimes as compared to synchronization case. Engineering application of this study is the development of reduced-order models for effective control techniques., Comment: 7 figures

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.

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

This paper puts forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model. These models, which are considered state-of-the-art in large eddy simulation, together with the mixing length and the Smagorinsky closure models, are tested in the numerical simulation of a 3D turbulent flow around a circular cylinder at Re = 1,000. Two criteria are used in judging the performance of the proper orthogonal decomposition reduced-order models: the kinetic energy spectrum and the time evolution of the POD coefficients. All the numerical results are benchmarked against a direct numerical simulation. Based on these numerical results, we conclude that the dynamic subgrid-scale and the variational multiscale models perform best., Comment: 28 pages, 6 figures