Interplay of chordwise stiffness and shape on performance of self-propelled flexible flapping plate
TL;DR: In this paper, the locomotion of a flapping flexible plate with different shapes and non-uniform chordwise stiffness distribution in a stationary fluid is studied numerically, and the normalized effective bending stiffness for three-dimensional plates with arbitrary stiffness distribution and shape parameters is proposed.
Abstract: The locomotion of a flapping flexible plate with different shapes and non-uniform chordwise stiffness distribution in a stationary fluid is studied numerically. The normalized effective bending stiffness K∗ for three-dimensional plates with arbitrary stiffness distribution and shape parameters is proposed, and the overall bending stiffness of non-uniform plates with different shapes is reasonably characterized. It is found that the propulsion performance in terms of cruising speed and efficiency of the self-propelled flapping plate mainly depends on the effective bending stiffness. Plates with moderate flexibility K∗ show better propulsion performance. Meanwhile, both a large area moment of the plate and a flexible anterior are favorable to significantly improve their propulsive performance. The evolution of vortical structures and the pressure distribution on the upper and lower surfaces of the plate are analyzed, and the inherent mechanism is revealed. These findings are of great significance to the optimal design of propulsion systems with different fins or wings.
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TL;DR: This survey of recent studies on highly simplified bio-inspired models that aim to reveal the flow physics associated with FSI plays a key role in the dynamics of such structures immersed in fluids.
Abstract: Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.
10 citations
TL;DR: In this article , the influence of serrated trailing edge on the aerodynamic and aero-acoustic performance of a flapping wing during hovering flight was investigated using a hybrid framework of an immersed boundary Navier-Stokes solver for the flow field and the Ffowcs Williams-Hawkings (FW-H) analogy for the sound field.
Abstract: The influences of serrated trailing edge on the aerodynamic and aeroacoustic performance of a flapping wing during hovering flight are investigated using a hybrid framework of an immersed boundary Navier–Stokes solver for the flow field and the Ffowcs Williams–Hawkings (FW–H) analogy for the sound field. A rigid rectangular wing with an aspect ratio of 2 undergoes pitching and stroke motions at a Reynolds number (Re) of 310 and a Mach number (M) of 0.012. Simulations are conducted by varying the dimensionless wavenumber k* from 2π to 10π and wave amplitude 2h* from 0.25 to 1.0. We find that at k*=8π and 2h*=1.5 (D4), the average sound power level is reduced by up to 6.8 dB within the Strouhal number (St) between 2.0 and 4.0 compared to that of a plain trailing edge while the lift coefficient is maintained. The directivity at St = 0.2, St = 0.4, St = 2.2, and St = 2.4 is discussed. It is found that the serrations of D4 do not affect the directivity for the first two frequencies and significantly reduce the magnitude of the directivity for the last two frequencies. The serrations of D4 considerably alter the flow field near the wing surface and reduced the surface pressure fluctuations near the wing tip, leading to the noise reduction. The lift coefficient of D4 is not significantly changed, because the reduction in the pressure-contributed lift is compensated by an increase in the shear stress-contributed lift. The serrations with higher 2h* and k* have larger shear stress-contributed lift.
8 citations
TL;DR: In this paper , a numerical study on the response of a two-dimensional bluff body wake subjected to harmonic forcing imposed by two rear pitching flaps is performed, where the wake is generated by a rectangle at a height-based Reynolds number $Re=100$, characterised by laminar vortex shedding.
Abstract: Abstract A numerical study on the response of a two-dimensional bluff body wake subjected to harmonic forcing imposed by two rear pitching flaps is performed. The wake is generated by a rectangle at a height-based Reynolds number $Re=100$, characterised by laminar vortex shedding. Two forcing strategies are examined corresponding to in-phase ‘snaking’ and out-of-phase ‘clapping.’ The effects of the bluff body aspect ratio ($AR=1,2,4$), flapping frequency, flapping amplitude, flap length and Reynolds number are investigated. For the snaking motion, a strong fundamental resonance of the root mean square (r.m.s.) drag is observed when the wake is forced near the vortex shedding frequency. For the clapping motion, a weak subharmonic resonance is observed when the forcing is applied near twice the vortex shedding frequency resulting in an increase of the lift r.m.s. whereas the drag r.m.s. remains unaffected. Both resonances intensify the vortex shedding and a concomitant mean drag increase is observed for the snaking motion. Forcing away from the resonant regimes, both motions result in considerable drag reduction through wake symmetrisation and propulsion mechanisms. The formation of two vortex dipoles per oscillation period due to the flapping motion, which weaken the natural vortex shedding, has been identified as the main symmetrisation mechanism. A single scaling parameter is proposed to collapse the mean drag reduction of the forced flow for both motions over a wide range of flapping frequencies, amplitudes and flap lengths. Finally, the assessment of the performance of the forcing strategies has revealed that clapping is more effective than snaking.
3 citations
TL;DR: In this article , a customized experimental platform is built, which eases the adjustment of the non-uniform stiffness ratio, the stiffness of the flexible part, the flapping frequency, and flapping amplitude.
Abstract: Live fish in nature exhibit various stiffness characteristics. The anguilliform swimmer, like eels, has a relatively flexible body, while the thunniform swimmer, like the swordfishes, has a much stiffer body. Correspondingly, in the design of biomimetic robotic fish, how to balance the non-uniform stiffness to achieve better propulsion performance is an essential question needed to be answered. In this paper, we conduct an experimental study on this question. First, a customized experimental platform is built, which eases the adjustment of the non-uniform stiffness ratio, the stiffness of the flexible part, the flapping frequency, and the flapping amplitude. Second, extensive experiments are carried out, finding that to maximize the propulsion performance of the biomimetic robotic fish, the non-uniform stiffness ratio is required to adapt to different locomotor parameters. Specifically, the non-uniform stiffness ratio needs to be reduced when the robotic fish works at low frequency, and it needs to be increased when the robotic fish works at high frequency. Finally, detailed discussions are given to further analyze the experimental results. Overall, this study can shed light on the design of a non-uniform biomimetic robotic fish, which helps to increase its propulsion performance.
2 citations
TL;DR: In this paper , the effects of the morph position and amplitude on the flow dynamics and propulsion of a morphing-heaving foil are investigated, and it is found that the foil is highly efficient in generating propulsive forces at high morph amplitudes and low morph positions.
Abstract: Locomotion of aquatic animals involves flapping of their body to generate lift and thrust. Through evolution, they have mastered their ability to move through complex environments in an energy-efficient manner. A crucial component of this movement is the ability to actively bend their bodies to generate maximum thrust. This motion is widely termed as morphing. A simplification of this motion is implemented for a foil in this study to realize a thrust-generating bio-inspired device. The propulsive performance of the heaving foil undergoing a prescribed trailing-edge morphing is numerically studied by a stabilized finite element moving mesh formulation. The effects of the morph position and amplitude on the flow dynamics and propulsion of the foil are investigated in the present work. The position of trailing-edge morphing varies from the leading edge to half of the foil's chord, whereas the morph amplitude varies from [Formula: see text] to [Formula: see text] at the trailing edge. The instantaneous thrust is analyzed with vorticity plots and surface pressure diagrams. Within the parametric space, it is found that the foil is highly efficient in generating propulsive forces at high morph amplitudes and low morph positions. The interplay between the thrust-generating leading-edge vortex (LEV) and the drag-inducing trailing-edge vortex (TEV), which governs the thrust cycle of a morphing–heaving foil, is elucidated. It is observed that the LEV-induced thrust is higher at low morph positions, while the TEV-induced drag is dominant at high morph amplitudes. An ideal balance of these opposing effects of LEV and TEV occurs at the lowest morph position and intermediate morph amplitudes, emphasizing the optimal flexibility for the maximum propulsive performance of the foil.
1 citations
References
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TL;DR: An overview of the lattice Boltzmann method, a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities, is presented.
Abstract: We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.
6,565 citations
TL;DR: In this article, the authors propose a definition of vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor, which captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers.
Abstract: Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.
5,837 citations
TL;DR: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics.
Abstract: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics. The IB formulation of such problems, derived here from the principle of least action, involves both Eulerian and Lagrangian variables, linked by the Dirac delta function. Spatial discretization of the IB equations is based on a fixed Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for the Lagrangian variables. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function. Eulerian/Lagrangian identities govern the transfer of data from one mesh to the other. Temporal discretization is by a second-order Runge–Kutta method. Current and future research directions are pointed out, and applications of the IB method are briefly discussed. Introduction The immersed boundary (IB) method was introduced to study flow patterns around heart valves and has evolved into a generally useful method for problems of fluid–structure interaction. The IB method is both a mathematical formulation and a numerical scheme. The mathematical formulation employs a mixture of Eulerian and Lagrangian variables. These are related by interaction equations in which the Dirac delta function plays a prominent role. In the numerical scheme motivated by the IB formulation, the Eulerian variables are defined on a fixed Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely through the fixed Cartesian mesh without being constrained to adapt to it in any way at all.
4,164 citations
TL;DR: The term immersed boundary (IB) method is used to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries.
Abstract: The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the
3,184 citations
TL;DR: It is shown that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation, and a representation of the forcing term is proposed that derived the Navier-Stokes equation through the Chapman-Enskog expansion.
Abstract: We show that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation. A representation of the forcing term is then proposed. With the representation, the Navier-Stokes equation is derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Several other existing force treatments are also examined.
1,829 citations