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Abstract

Research on fish locomotion has made extensive progress towards a better understanding of how fish control their flexible body and fin for propulsion and maneuvering. Although the biologically flexible fish fins are believed to be one of the most important features to achieve optimal swimming performance, due to the limitations of the existing numerical modeling tool, studies on a deformable fin with a non-uniformly distributed stiffness are rare. In this work, we present a fully coupled fluid-structure interaction solver which can cope with the dynamic interplay between flexible aquatic animal and the ambient medium. In this tool, the fluid is resolved by solving Navier-Stokes equations based on the finite volume method with a multi-block grid system. The solid dynamics is solved by a nonlinear finite element method. A sophisticated improved IQN-ILS coupling algorithm is employed to stabilize solution and accelerate convergence. To demonstrate the capability of the developed Fluid-Structure-Interaction solver, we investigated the effect of five different stiffness distributions on the propulsive performance of a caudal peduncle-fin model. It is shown that with a non-uniformly distributed stiffness along the surface of the caudal fin, we are able to replicate similar real fish fin deformation. Consistent with the experimental observations, our numerical results also indicate that the fin with a cupping stiffness profile generates the largest thrust and efficiency whereas a heterocercal flexible fin yields the least propulsion performance but has the best maneuverability.

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... The communication between the fluid and structural solver is established via TCP/IP sockets, and the data mapping is achieved by the radial basis functions (RBF) based interpolation [30]. The details of the framework of the present FSI solver are described in [31]. ...
... The structural mesh comprises 123 quadratic wedge elements with standard shape functions [24]. Fig. 4. The computational domain layout (a) adopted from [31], and the generated medium mesh around the cantilever after the deformation when the tip displacement reaches the maximum (b The generated mesh after deformation when the tip displacement reaches its maximum is depicted in Fig. 4(b). The velocity and pressure contours around the square cylinder and the cantilever at this moment are shown in Fig. 6. ...
... Fig. 1. Flow chart of the implicit FSI coupling in a partitioned approach adopted from [31]. Table 1. ...
Article
In this paper, the propulsive performance of a caudal peduncle-fin swimmer mimicking a bio-inspired robotic fish model is numerically studied using a fully coupled FSI solver. The model consists of a rigid peduncle and a flexible fin which pitches in a uniform flow. The flexible fin is modelled as a thin plate assigned with non-uniformly distributed stiffness. A finite volume method based in-house Navier-Stokes solver is used to solve the fluid equations while the fin deformation is resolved using a finite element code. The effect of the fin flexibility on the propulsive performance is investigated. The numerical results indicate that compliance has a significant influence on performance. Under the parameters studied in this paper, the medium flexible fin exhibits remarkable efficiency improvement, as well as thrust augment, while the least flexible fin shows no obvious difference from the rigid one. However, for the most flexible fin, although the thrust production decreases sharply, the efficiency reaches the maximum value. It should be noted that by non-uniformly distributing the rigidity across the caudal fin, our model is able to replicate some fin deformation patterns observed in both the live fish and the experimental robotic fish.
... Therefore, for computation accuracy, the local Mach numbers in the whole computational domain are monitored during computation to ensure that they are always below the critical value. This compressible flow solver has been successfully applied to various incompressible flow simulations involving flexible deformation in our previous work (Liu et al 2016, Luo et al 2020a, Luo et al 2020b, Xiao and Liao 2010, Xiao et al 2012a. This numerical solver is validated in Luo et al (2020a) and Luo et al (2020b). ...
... This compressible flow solver has been successfully applied to various incompressible flow simulations involving flexible deformation in our previous work (Liu et al 2016, Luo et al 2020a, Luo et al 2020b, Xiao and Liao 2010, Xiao et al 2012a. This numerical solver is validated in Luo et al (2020a) and Luo et al (2020b). The quantitative validations include simulations of flow over a flexible plate attached behind a stationary square cylinder, the bending of a flexible plate in the uniform flow, the response of a flexible plate in forced heave motion (Luo et al 2020a), and flow over a NACA 0012 airfoil (Luo et al 2020b). ...
... This numerical solver is validated in Luo et al (2020a) and Luo et al (2020b). The quantitative validations include simulations of flow over a flexible plate attached behind a stationary square cylinder, the bending of a flexible plate in the uniform flow, the response of a flexible plate in forced heave motion (Luo et al 2020a), and flow over a NACA 0012 airfoil (Luo et al 2020b). Good agreements between the simulation results and the counterparts reported in the literature are obtained. ...
Article
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Inspired by a previous experimental study of fish swimming near a cylinder, we numerically investigate the swimming and station-holding behavior of a flexible plate ahead of a circular cylinder whose motion is controlled by a proportional-derivative (PD) controller. Specifically, the deformation of this two-dimensional plate is actuated by a periodically varying external force applied on the body surface, which mimics the fish muscle force to produce propulsive thrust. The actuation force amplitude is dynamically adjusted by a feedback controller to instruct the plate to swim the desired distance from an initial position to a target location and then hold the station there. Instead of directly using the instantaneous position signal, an average speed measured over one force actuation period is proposed with the inclusion of instantaneous position information to form the tracking error for the PD control. Our results show that the motion control of swimming and station holding has been achieved by this simple but effective feedback control without large overshoot when approaching the target at different flow conditions and actuation force formulas. Although the swimming distance remains the same, a plate whose initial position is closer to the cylinder requires less energy expenditure to swim to the target location and hold the station there. This is because the low-pressure zone near the trailing edge of the plate is reduced in size, which provides drag reduction, contributing to reduced swimming energy. A higher Reynolds number also leads to energy savings. Under the same control strategy, the swimming performance is more affected by the force-frequency while the phase shift of the actuation force has a less significant impact.
... L/s (L is the fish body length) (Gibb et al 1999). However, this dorsal-ventrally asymmetry is also frequently observed for bluegill sunfish during its braking manoeuvring, resulting in the loss of thrust and efficiency as compared with symmetric tail locomotion, e.g., the cupping tail movement (Esposito et al 2012, Flammang and Lauder 2009, Luo et al 2020b. Given the differences in morphology between these two fish species, i.e., scombrid and bluegill sunfish, what is the actual role of biologically asymmetric tail locomotion on the swimming behaviour for tuna-like swimmers remains unknown [see examples in (Feilich and Lauder 2015) and (Krishnadas et al 2018)]. ...
... Given the differences in morphology between these two fish species, i.e., scombrid and bluegill sunfish, what is the actual role of biologically asymmetric tail locomotion on the swimming behaviour for tuna-like swimmers remains unknown [see examples in (Feilich and Lauder 2015) and (Krishnadas et al 2018)]. Inspired by the above studies (Lucas et al 2015 andMariel-Luisa et al 2017), we systematically investigate the effects of non-uniform distributions of flexural stiffness on the kinematics and propulsion performance of a tuna-like swimmer (figure 1) using our recently developed fully coupled fluid-structure interaction (FSI) solver (Luo et al 2020b). Distinguish from previous studies, both the fish body and fin stiffness variation is considered. ...
... Additionally, with the non-uniform stiffness distribution in the spanwise direction of the caudal fin (figure 3), we aim to explore the possibility to passively control the fin deformation and replicate some features of tail kinematics observed from live fish (Gibb et al 1999), and understand the effect of these tail conformations on the hydrodynamic force production. Particularly, we are curious about the role of the aforementioned asymmetrical tail conformation during steady swimming of scombrid fish and the comparison with the experimental and numerical findings of bluegill sunfish (Esposito et al 2012 andLuo et al 2020b). ...
Article
Full-text available
The work in this paper focuses on the examination of the effect of variable stiffness distributions on the kinematics and propulsion performance of a tuna-like swimmer. This is performed with the use of a recently developed fully coupled fluid-structure interaction solver. The two different scenarios considered in the present study are the stiffness varied along the fish body and the caudal fin, respectively. Our results show that it is feasible to replicate the similar kinematics and propulsive capability to that of the real fish via purely passive structural deformations. In addition, propulsion performance improvement is mainly dependent on the better orientation of the force near the posterior part of swimmers towards the thrust direction. Specifically, when a variable body stiffness scenario is considered, the bionic body stiffness profile results in better performance in most cases studied herein compared with a uniform stiffness commonly investigated in previous studies. Given the second scenario, where the stiffness is varied only in the spanwise direction of the tail, similar tail kinematics to that of the live scombrid fish only occurs in association with the heterocercal flexural rigidity profile. The resulting asymmetric tail conformation also yields performance improvement at intermediate stiffness in comparison to the cupping and uniform stiffness.
... Therefore, for computation accuracy, the local Mach numbers in the whole computational domain are monitored during computation to ensure that they are always below the critical value. This compressible flow solver has been successfully applied to various incompressible flow simulations in our previous work (Liu et al., 2016;Luo et al., 2020a;Luo et al., 2020b;Shi et al., 2019;Xiao and Liao, 2010;and Xiao et al., 2012). ...
... The details of this FSI solver and its validations are provided in the study by Luo et al. (2020b). The built-in k-ω model has been successfully applied to the simulation of turbulent flow with the Reynolds number up to O (10 6 ) and validated via comparisons with previous numerical and experimental data in Appendix A and the study by Sadeghi et al. (2003). ...
Article
An inflation-deflation propulsion system inspired by the jet propulsion mechanism of squids and other cephalopods is proposed. The two-dimensional squid-like swimmer has a flexible mantle body with a pressure chamber and a nozzle which serves as the inlet and outlet of water. The fluid-structure interaction simulation results indicate that larger mean thrust production and higher efficiency can be achieved in high Reynolds number scenarios compared with the cases in laminar flow. The improved performance at high Reynolds number is attributed to stronger jet-induced vortices and highly suppressed external body vortices which are associated with drag force. Optimal efficiency is reached when the jet vortices start to dominate the surrounding flow. The mechanism of symmetry-breaking instability under the turbulent flow condition is found to be different from that previously reported in laminar flow. Specifically, this instability in turbulent flow stems from irregular internal body vortices, which causes symmetry breaking in the wake. Higher Reynolds number or smaller nozzle size would accelerate the formation of this symmetry-breaking instability.
... Yang Luo, Qing Xiao, Guangyu Shi, et al. proposed the multi body dynamic algo rithm advanced code in 2019 [17] to carry out numerical simulation on the robot fish equipped with soft bionic fins. It is a fluid structure interaction (FSI) solver, which carrie out finite element calculation based on CalculiX software. ...
... Yang Luo, Qing Xiao, Guangyu Shi, et al. proposed the multi body dynamic algorithm advanced code in 2019 [17] to carry out numerical simulation on the robot fish equipped with soft bionic fins. It is a fluid structure interaction (FSI) solver, which carries out finite element calculation based on CalculiX software. ...
Article
Full-text available
Diver propulsion vehicles (hereinafter referred to as DPV) are a kind of small vehicle with underwater high-speed used by divers, who are able to grasp or ride on, and operate the volume switch to change the speed. Different from unmanned underwater vehicles (UUVs), the interference caused by diver’s posture changing is a unique problem. In this paper, a Diver–DPV multi-body coupling hydrodynamic model considering rigid body dynamics and fluid disturbance is established by analyzing the existing DPV related equipment. The numerical simulation of multi-body articulated motion is realized by using Star-CCM+ overlapping grid and DFBI 6-DOF body motion method. Five cases of DPVs underwater cruising in a straight-line when restraining diver movement is simulated, and five cases with free diver movement are simulated too. Finally, the influence of the diver’s posture changing on the cruising speed resistance is analyzed, and the motion equation including the disturbance is solved. The final conclusion is that, the disturbance is favorable at high speed, which can reduce the cruising resistance, and unfavorable at low speed, which increases the cruising resistance. The friction resistance Ff always accounts for the main part in all speed cases.
... Radial basis function-based (RBF) interpolation is used to map the exchanged data between the two solvers. The details of the coupling framework and its validations are given in [9]. ...
Conference Paper
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For a design of a bio-inspired fish like robot with caudal fin a Fluid Structure Interaction (FSI) analysis has been conducted to investigate the influence of material properties and undulation kinematic on the hydrodynamic performance and efficiency. This supports the design process with focus on practical prototype build up.
... This compressible flow solver has been successfully validated and applied to various incompressible flow simulations involving boundary motion in our previous work (Liu et al., 2016;Luo et al., 2020a;Shi et al., 2020;Xiao and Liao, 2010). The validations include simulations of flow over a flexible cantilever behind a square cylinder, the bending of a flexible plate in the uniform flow, the response of a flexible plate in forced heave motion (Luo et al., 2020b), and flow over a NACA 0012 airfoil (Luo et al., 2020c). ...
Article
Inspired by recent studies of a squid-like swimmer, we propose a three-dimensional jet propulsion system composed of an empty chamber enclosed within a deformable body with an opening. By prescribing the body deformation and jet velocity profile, we numerically investigate the jet flow field and propulsion performance under the influence of background flow during a single deflation procedure. Three jet velocity profiles, i.e., constant, cosine and half cosine, are considered. We find that the maximum circulation of the vortex ring is reduced at a higher background flow velocity. This is because stronger interaction between the jet flow and background flow makes it harder to feed the leading vortex ring. Regarding thrust production, our analysis based on conservation of momentum indicates that with the constant profile the peak thrust is dominated by the time derivative of the fluid momentum inside the body, while momentum flux related thrust accounts for the quasi-steady thrust. For the cosine profile, its peak is mainly sourced from momentum flux associated with the unsteady vortex ring formation. No prominent thrust peak exists with the half cosine profile whose thrust continuously increases during the jetting. For all the three jet velocity profiles, added-mass related thrust attributed to body deformation enhances the overall thrust generation non-negligibly. Under the present tethered mode, the background flow has negligible influence on the thrust attributed to momentum flux and momentum change of the fluid inside the body. However, it indeed affects the over pressure-related thrust but its effect is relatively small. The overall thrust declines due to the significantly increased drag force at large incoming flow speed despite the rise of added-mass related thrust. Unsteady thrust involving vortex ring formation becomes more important in the overall thrust generation with an increased background flow velocity, reflected by larger ratios of the unsteady impulse to jet thrust impulse.
... This provides insights into the structural design and material selection. Using a fully coupled FSI numerical solver consisting of a finite-volume-method-based fluid solver and finite-element-method based structural solver [28], a preliminary analysis was performed on the motion control of the simplified system [29]. The caudal fin was simplified as a 2D cross-section in rotation locomotion. ...
Article
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o reduce human risk and maintenance costs, Autonomous Underwater Vehicles (AUVs) are involved in subsea inspections and measurements for a wide range of marine industries such as offshore wind farms and other underwater infrastructure. Most of these inspections may require levels of manoeuvrability similar to what can be achieved by tethered vehicles, called Remotely Operated Vehicles (ROVs). To extend AUV intervention time and perform closer inspection in constrained spaces, AUVs need to be more efficient and flexible by being able to undulate around physical constraints. A biomimetic fish-like AUV known as RoboFish has been designed to mimic propulsion techniques observed in nature to provide high thrust efficiency and agility to navigate its way autonomously around complex underwater structures. Building upon advances in acoustic communications, computer vision, electronics and autonomy technologies, RoboFish aims to provide a solution to such critical inspections. This paper introduces the first RoboFish prototype that comprises cost-effective 3D printed modules joined together with innovative magnetic coupling joints and a modular software framework. Initial testing shows that the preliminary working prototype is functional in terms of water-tightness, propulsion, body control and communication using acoustics, with visual localisation and mapping capability.
... 22 When swimming, the special membrane-ray fin structure allows complex fin morphology that combines with the wave like bending of the fish body. 17,[23][24][25][26] The interrelations between the body and fin flexibility, tail beat frequency and amplitude have been studied, and findings show that body and fin flexibility affect the propulsive wavelength of the undulating swimming and the wave speed, thus the swimming speed and efficiency. [27][28][29][30][31][32] Swimming speed correlates positively with body flexibility and amplitude of the tailfin motion, but not with frequency. ...
Article
This paper addresses hydrodynamic performance of fins regarding their trailing edge convexity–concavity and flexibility distribution. The effects of trailing edge convexity–concavity on propulsive performance and vortex dynamics were investigated experimentally utilizing time-resolved particle image velocimetry and force sensors. It was found that the convex trailing edge shape always outperforms the concave shape. Wake contracting by the bent shape of the trailing edge vortex of a convex trapezoidal form resulted in higher thrust and efficiency. The results also showed that the rounded edges of fish fins did not provide additional hydrodynamic advantages. Furthermore, we found that a gradually flexible fin delivered better propulsive performance over a uniformly flexible fin. The hydrodynamic performance of the flexible fins depended on the strength and relative positions of the trailing edge vortexes shed by each fin, which were affected by the flexible deformations of the fins. In the lower Reynolds number operation (approaching, but below the first resonant mode), the fins with larger camber produced a stronger momentum footprint especially considering the far wake elements, while in the higher Reynolds number range due to resonant deformation the extent of trailing edge excursion became dominant in affecting the propulsive performance. The results showed that gradually flexible fins can improve the performance of future watercraft.
... The present flow solver has been extensively validated and applied to investigate the tidal turbine and biomimetic propulsion in previous publications (Shi et al., 2019;Xiao and Liao, 2010;Liu et al., 2016;Liu and Xiao, 2015;Luo et al., 2020). Here, it is further validated by evaluating the fluid dynamics of an oscillating hydrofoil at Re = 5 × 10 5 (Kinsey and Dumas, 2012). ...
Article
The propulsive performance of an undulating pectoral fin with various aspect ratios is numerically investigated with the consideration of the ground effect. The kinematics of the fin is prescribed as a sinusoidal wave and the flow field is calculated by solving the Unsteady Reynolds-Averaged Navier–Stokes equations. It is found that for higher aspect ratios, the mean thrust coefficient is linear with the square of the normalized relative velocity and the inverse square of the wavelength ratio whereas for lower aspect ratios, the relations with the velocity and wavelength become cubic and fourth power respectively. The Strouhal number is found to be a scaling parameter for longer wavelength cases. The ground effect reduces the thrust force in most cases examined in this paper while the propulsive efficiency remains relatively unchanged. Compared with the fin with longer wavelengths, the mean thrust created by the fin with a short wavelength is remarkably less influenced by the ground effect. It is believed that there is a switch from the lift-based mechanism to the added-mass mechanism as the wavelength decreases. The lift-based mechanism is the main thrust production mechanism at a longer wavelength whereas the fin with a short wavelength primarily utilizes the added-mass mechanism, i.e. is less sensitive to the change of the pressure distribution over the surface of the fin due to the ground effect.
... Applications and Software A non-exhaustive list of application fields includes mechanical and civil engineering (astronautics [57], manufacturing processes [64,67], aerodynamics [106,107,23,62,108,109,110], urban wind modeling [105], aeroacoustics [6,111], explosions [112,113]), marine engineering [22], bio engineering (heart valves [114], aortic blood flow [7], fish locomotion [115], muscle-tendon systems [10]), nuclear fission and fusion reactors [116,9,117], and geophysics [8,118,12]. Many users do not only use the official adapters (cf. ...
Preprint
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PreCICE is a free/open-source coupling library. It enables creating partitioned multi-physics simulations by gluing together separate software packages. This paper summarizes the development efforts in preCICE of the past five years. During this time span, we have turned the software from a working prototype -- sophisticated numerical coupling methods and scalability on ten thousands of compute cores -- to a sustainable and user-friendly software project with a steadily-growing community. Today, we know through forum discussions, conferences, workshops, and publications of more than 100 research groups using preCICE. We cover the fundamentals of the software alongside a performance and accuracy analysis of different data mapping methods. Afterwards, we describe ready-to-use integration with widely-used external simulation software packages, tests and continuous integration from unit to system level, and community building measures, drawing an overview of the current preCICE ecosystem.
... In recent research, studies on hydrodynamic complex phenomena and model close to live fish were reported by applying computational fluid dynamics: hydrodynamic interactions between fins, stability of a fish school and effect of fin flexibility (Liu et al., 2017;Li et al., 2019;Luo et al., 2020). On the contrary, based on the results obtained from biological experiments and numerical simulations, several bioinspired fish robots were developed. ...
Article
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For clarification of an ecological system or application to ship propulsion mechanisms, studies of fish swimming have been conducted. However, many parts remain unexplained due to complexity and diversity of the swimming mechanism. In this study, we focused on the shape change of the fish larvae’s fin fold and investigated effects of aspect ratio of fish larvae’s fin fold on its propulsion performance by numerical simulations. Flow around the fish model was simulated by the regularized lattice Boltzmann method. To describe curved boundary on a Cartesian grid, the virtual flux method was applied. 4-tired multi block method was employed, and calculation domain was divided into 4 blocks with different grid resolutions. In this simulation, aspect ratio was defined by the ratio of fin fold length to fin fold width at the tail end, and fish models with different aspect ratio of fin fold were applied under constant surface area condition. As a result, vortices were generated along the fish body, and edge vortices pairs rotating in the opposite direction were observed at the fin fold. The edge vortices contributed to generate thrust force by increasing the front-back pressure difference at the fin fold. Compared to lower aspect ratio models, higher aspect ratio models generated more edge vortices pairs during a cycle. Accordingly, at lower aspect ratio, thrust force became larger by the wider fin fold, but amplitude of swimming speed changes in a cycle also became larger. In contrast, higher aspect ratio models swam efficiently by stabilizing its swimming speed.
... Applications and Software A non-exhaustive list of application fields includes mechanical and civil engineering (astronautics [57], manufacturing processes [64,67], aerodynamics [106,107,23,62,108,109,110], urban wind modeling [105], aeroacoustics [6,111], explosions [112,113]), marine engineering [22], bio engineering (heart valves [114], aortic blood flow [7], fish locomotion [115], muscle-tendon systems [10]), nuclear fission and fusion reactors [116,9,117], and geophysics [8,118,12]. Many users do not only use the official adapters (cf. ...
Preprint
Full-text available
preCICE is a free/open-source coupling library. It enables creating partitioned multi-physics simulations by gluing together separate software packages. This paper summarizes the development efforts in preCICE of the past five years. During this time span, we have turned the software from a working prototype-sophisticated numerical coupling methods and scalability on ten thousands of compute cores-to a sustainable and user-friendly software project with a steadily-growing community. Today, we know through forum discussions, conferences, workshops, and publications of more than 100 research groups using preCICE. We cover the fundamentals of the software alongside a performance and accuracy analysis of different data mapping methods. Afterwards, we describe ready-to-use integration with widely-used external simulation software packages, tests and continuous integration from unit to system level, and community building measures, drawing an overview of the current preCICE ecosystem.
... Indeed, in fluid-structure interaction models, a "cupping" stiffness pattern for caudal fins (similar to the pattern seen in zebrafish; highest rigidity at the boundaries and lowest in the center) requires the least energy expenditures to generate the largest thrust. [43][44][45] Similar to the observed muscle-to-ray set pairings, PPRs and CPRs show distinct innervation. 35 Together, the different ontogeny of PPRs and CPRs under the control of three organizing centers may provide each ray set with distinct identities altering ray morphology as well as muscle and nerve targeting, collectively optimizing biomechanical properties for efficient thrust and maneuverability. ...
Article
Background: Caudal fin symmetry characterizes teleosts and likely contributes to their evolutionary success. However, the coordinated development and patterning of skeletal elements establishing external symmetry remains incompletely understood. We explore the spatiotemporal emergence of caudal skeletal elements in zebrafish to consider evolutionary and developmental origins of caudal fin symmetry. Results: Transgenic reporters and skeletal staining reveal that the hypural diastema-defining gap between hypurals 2 and 3 forms early and separates progenitors of two plates of connective tissue. Two sets of central principal rays (CPRs) synchronously, sequentially, and symmetrically emerge around the diastema. The two dorsal- and ventral-most rays (peripheral principal rays, PPRs) arise independently and earlier than adjacent CPRs. Muscle and tendon markers reveal that different muscles attach to CPR and PPR sets. Conclusions: We propose that caudal fin symmetry originates from a central organizer that establishes the hypural diastema and bi-directionally patterns surrounding tissue into two plates of connective tissue and two mirrored sets of CPRs. Further, two peripheral organizers unidirectionally specify PPRs, forming a symmetric "composite" fin derived from three fields. Distinct CPR and PPR ontogenies may represent developmental modules conferring ray identities, muscle connections, and biomechanical properties. Our model contextualizes mechanistic studies of teleost fin morphological variation. This article is protected by copyright. All rights reserved.
Article
Flow over a traveling wavy foil attached with a flexible plate has been numerically investigated using the lattice Boltzmann method combined with the immersed boundary method. The influence of the flexibility and length of the caudal fin on the locomotion of swimming fish through this simplified model, whereas the fish body is modeled by the undulating foil and the caudal fin by the plate passively flapping as a consequence of fluid-structure interaction. It is found that the plate flexibility denoted by the bending stiffness, as well as the length ratio of tail and body, plays an important role in improving thrust generation and propulsive efficiency. It is also revealed that there exists a parameter region of the plate length and stiffness, in which positive propeller efficiency can be achieved. The effect of the passively flapping flexible plate on the pressure field and the vortex production on the wake is further discussed. It is found that when the length ratio of caudal fin and body is greater than 0.2, a reverse von Kármán vortex street occurs when the bending stiffness is about greater than 1.0, and a great thrust is generated as a result of a large pressure difference occurring across the flexible plate. This work provides physical insight into the role of the caudal fin in fish swimming and may inspire the design of robotic fish.
Article
preCICE is a free/open-source coupling library. It enables creating partitioned multi-physics simulations by gluing together separate software packages. This paper summarizes the development efforts in preCICE of the past five years. During this time span, we have turned the software from a working prototype -- sophisticated numerical coupling methods and scalability on ten thousands of compute cores -- to a sustainable and user-friendly software project with a steadily-growing community. Today, we know through forum discussions, conferences, workshops, and publications of more than 100 research groups using preCICE. We cover the fundamentals of the software alongside a performance and accuracy analysis of different data mapping methods. Afterwards, we describe ready-to-use integration with widely-used external simulation software packages, tests, and continuous integration from unit to system level, and community building measures, drawing an overview of the current preCICE ecosystem.
Article
The effect of non-uniform chordwise stiffness distribution on the self-propulsive performance of three-dimensional flexible plates is studied numerically. Some typical stiffness distributions, including uniform, declining, and growing distribution, are considered. First, the normalized bending stiffness K̃ is derived, which can well represent the overall bending stiffness of the non-uniform plates. For different non-uniformly distributed plates with the same K̃, the maximum displacement difference between the trailing and leading edges of the plate during the flapping is almost identical. There exists a common optimal K̃ at which all the plates achieve their optimal performance, i.e., the highest cruising speed and efficiency. Second, we reveal what kind of non-uniform distribution could be the best at a specific K̃ in terms of the propulsive performance. The force analysis indicates that a larger bending deformation in the anterior part for the growing distribution leads to a larger thrust. Hence, the large local slope along the anterior flexible plate is preferred to enhance the propulsive performance. The results obtained in this study may shed some light on a better understanding of the hydrodynamic effect on the self-propulsion of the non-uniform stiffness wings or fins of animals.
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The technology of Autonomous Underwater Vehicles (AUVs) is developing in two main directions focusing on improving autonomy and improving construction, especially driving and power supply systems. The new Biomimetic Underwater Vehicles (BUVs) are equipped with the innovative, energy efficient driving system consisting of artificial fins. Because these driving systems are not well developed yet, there are great possibilities to optimize them, e.g. in the field of materials. The article provides an analysis of the propulsion force of the fin as a function of the characteristics of the material from which it is made. The parameters of different materials were used for the fin design and their comparison. The material used in our research was tested in a laboratory to determine the Young’s modulus. For simplicity, the same fin geometry (the length and the height) was used for each type of fin. The Euler–Bernoulli beam theory was applied for estimation of the fluid–structure interaction. This article presents the laboratory test stand and the results of the experiments. The laboratory water tunnel was equipped with specialized sensors for force measurements and fluid–structure interaction analysis. The fin deflection is mathematically described, and the relationship between fin flexibility and the generated driving force is discussed.
Article
This paper presents an efficient and versatile OpenFOAM (Open-source Field Operation And Manipulation)-based numerical solver for fully resolved simulations that can handle any rigid and deforming bodies moving in the fluid. The algorithm used for solving Fluid–Structure Interactions (FSI) involving the immersed structure with changeable shapes is based on the momentum redistribution method. The present approach excludes the need to solve elastic equations, obtain high-accuracy predictions of the flow field and provide a rigorous basis for implementing the Immersed Boundary Method (IBM). The OpenFOAM implementation of the algorithm is discussed along with the design methodology for developing bio-inspired underwater vehicles using the present solver. The computational results are validated with the experimental observations of the two-dimensional and three-dimensional anguilliform swimmer case studies. The study further extended to the three-dimensional hydrodynamics of a bioinspired, self-propelling manta bot. The motion of the body is specified a priori according to the reported experimental observations. The results quantify the vortex formation and shedding processes and enable the identification of the portions of the body responsible for the majority of thrust. The body accelerates from rest to an asymptotic mean forward velocity of 0.2 ms−1 in almost 5 s, consistent with experimental observations. It is observed that the developed computational model is capable of performing any motion simulation and manoeuvrability analysis, which are critical for the designers to develop novel unmanned underwater vehicles.
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Using fluid–structure interaction computational modelling, the hydrodynamic performance of bio-inspired elastic propulsors with tapered thickness that oscillate in an incompressible Newtonian fluid at Reynolds number $Re = 2000$ is investigated. The thickness tapering leads to an acoustic black hole effect at the trailing edge of the propulsor that slows down and attenuates flexural waves, thereby minimizing the flexural wave reflection and enhancing travelling wave propulsion. The simulations reveal that, by tuning the propulsor thickness profile modulating the acoustic black hole effect, the tapered propulsors can be designed to vastly outperform the uniformly thick propulsors in terms of the hydrodynamic efficiency and thrust, especially for the post-resonance frequencies. The enhanced hydrodynamic performance is directly linked to the ability of the tapered propulsors to generate travelling waves with a large amplitude displacement at the trailing edge. The results have implications for the development of highly efficient bio-mimetic robotic swimmers and, more generally, the better understanding of the undulatory aquatic locomotion.
Article
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The caudal fins of adult zebrafish are supported by multiple bony rays that are laterally interconnected by soft interray tissue. Little is known about the fin's mechanical properties that influence the bending in response to hydrodynamic forces during swimming. Here, we developed an experimental setup to measure the elastic properties of caudal fins in-vivo by applying micro-Newton forces to obtain bending stiffness and a tensional modulus. We detected overall bending moments of 1.5 - 4x10-9 Nm2 along the proximal-distal axis of the appendage showing a non-monotonous pattern that is not due to the geometry of the fin itself. Surgical disruption of the interray tissues along the proximal-distal axis revealed no significant changes to the overall bending stiffness, which we confirm by determining a tensional modulus of the interray tissue. Thus, the biophysical values suggest that the flexibility of the fin during its hydrodynamic performance predominantly relies on the mechanical properties of the rays.
Conference Paper
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To deal with the increasing complexity of today’s multiphysics applications, the reuse of existing simulation software often becomes a necessity. Coupling to open-source simulation codes, in particular, is a time-efficient way to tackle new applications. The open-source coupling library preCICE enables such coupling in a minimally-invasive way. In this contribution, we give an overview on ready-to-use preCICE adapters for standard open-source solvers, namely CalculiX, Code Aster, OpenFOAM, and SU2.
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This paper presents the implementation of a fluid-structure interaction solver intended to be used for the analysis of flexible flapping airfoils. The governing equations associated to elastic solids with large deformations but small strains, and to incompressible fluids are presented. The solver is implemented in the OpenFOAM software. The fluid-structure coupling is handled by an iterative partitioned algorithm where each field (the solid and the fluid) are treated separately. The spatial discretization is achieved with the segregated finite-volume method for both fields. The fluid module implements the Navier-Stokes equations using a SIMPLE algorithm whereas the solid module implements the St. Venant Kirchhoff constitutive law in a Lagrangian formulation where nonlinear and component-coupled terms are treated iteratively in a fixed point manner. Typical test simulations are carried out and results are found to be in good agreement with literature. Finally, preliminary results of flexible flapping wings are presented, showing that the solver seems well suited for this kind of application.
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In order to study the role of the passive deformation in the aerodynamics of insect wings, we computationally model the three-dimensional fluid–structure interaction of an elastic rectangular wing at a low aspect ratio during hovering flight. The code couples a viscous incompressible flow solver based on the immersed-boundary method and a nonlinear finite-element solver for thin-walled structures. During a flapping stroke, the wing surface is dominated by non-uniform chordwise deformations. The effects of the wing stiffness, mass ratio, phase angle of active pitching, and Reynolds number are investigated. The results show that both the phase and the rate of passive pitching due to the wing flexibility can significantly modify the aerodynamics of the wing. The dynamic pitching depends not only on the specified kinematics at the wing root and the stiffness of the wing, but also greatly on the mass ratio, which represents the relative importance of the wing inertia and aerodynamic forces in the wing deformation. We use the ratio between the flapping frequency, , and natural frequency of the wing, , as the non-dimensional stiffness. In general, when , the deformation significantly enhances the lift and also improves the lift efficiency despite a disadvantageous camber. In particular, when the inertial pitching torque is assisted by an aerodynamic torque of comparable magnitude, the lift efficiency can be markedly improved.
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A non-sinusoidal trajectory profile is proposed for the oscillating hydrofoil in the energy generators instead of conventional sinusoidal plunging/pitching motions to seek better energy extraction performance. The novel profile is achieved by combining a specially designed trapezoidal-like pitching motion with a sinusoidal plunging motion and investigated numerically on its output energy coefficient and total output efficiency. Through an adjustable parameter β, the pitching profile can be altered from a sinusoidal (β = 1.0) to a square wave (β → ∞). In this work, a series of β ranging from 1.0 to 4.0 are investigated to examine the effect of combined motion trajectory on the energy extraction performance. The study encompasses the Strouhal numbers (St) from 0.05 to 0.5, nominal effective angle of attacks α0 of 10° and 20° and plunging amplitude h0/c of 0.5 and 1.0. Numerical results show that, for different β pitching motions, a larger α0 always results in a higher extraction power Cop and total efficiency ηT. Compared with the sinusoidal motion (β = 1), significant increment of Cop and ηT can be observed for β > 1 over a certain range of St. The investigation also shows that there exists an optimal pitching profile which may increase the output power coefficient and total output efficiency as high as 63% and 50%, respectively, over a wide range of St. Detailed examination on the computed results reveal that, the energy extraction performance is determined by the relative ratio of the positive and negative contributions from the different combination of lift force, momentum and corresponding plunging velocity and pitching angular velocity, all of which are considerably affected by β.
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The hydrodynamics of a highly deformable fish pectoral fin used by a bluegill sunfish (Lepomis macrochirus) during steady forward swimming are examined in detail. Low-dimensional models of the fin gait based on proper orthogonal decomposition (POD) are developed, and these are subjected to analysis using an incompressible Navier– Stokes flow solver. The approach adopted here is primarily motivated by the quest to develop insights into the fin function and associated hydrodynamics, which are specifically useful for the design of a biomimetic, pectoral fin propulsor. The POD analysis shows that the complex kinematics of the pectoral fin can be described by a few (<5) POD modes and that the first three POD modes are highly distinct. The significance of these modes for thrust production is examined by synthesizing a sequence of fin gaits from these modes and simulating the flow associated with these gaits. We also conduct a scale study of the pectoral fin in order to understand the effect of the two key non-dimensional parameters, Reynolds number and Strouhal number, on the propulsive performance. The implications of the POD analysis and performance scaling on the design of a robotic pectoral fin are discussed.
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Numerical simulations are used to investigate the effect of aspect ratio on the wake topology and hydrodynamic performance of thin ellipsoidal flapping foils. The study is motivated by the quest to understand the hydrodynamics of fish pectoral fins. The simulations employ an immersed boundary method that allows us to simulate flows with complex moving boundaries on fixed Cartesian grids. A detailed analysis of the vortex topology shows that the wake of low-aspect-ratio flapping foils is dominated by two sets of interconnected vortex loops that evolve into distinct vortex rings as they convect downstream. The flow downstream of these flapping foils is characterized by two oblique jets and the implications of this characteristic on the hydrodynamic performance are examined. Simulations are also used to examine the thrust and propulsive efficiency of these foils over a range of Strouhal and Reynolds numbers as well as pitch-bias angles.
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Numerical simulations have been used to analyze the effect that vortices, shed from one flapping foil, have on the thrust of another flapping foil placed directly downstream. The simulations attempt to model the dorsal–tail fin interaction observed in a swimming bluegill sunfish. The simulations have been carried out using a Cartesian grid method that allows us to simulate flows with complex moving boundaries on stationary Cartesian grids. The simulations indicate that vortex shedding from the upstream (dorsal) fin is indeed capable of increasing the thrust of the downstream (tail) fin significantly. Vortex structures shed by the upstream dorsal fin increase the effective angle-of-attack of the flow seen by the tail fin and initiate the formation of a strong leading edge stall vortex on the downstream fin. This stall vortex convects down the surface of the tail and the low pressure associated with this vortex increases the thrust on the downstream tail fin. However, this thrust augmentation is found to be quite sensitive to the phase relationship between the two flapping fins. The numerical simulations allows us to examine in detail, the underlying physical mechanism for this thrust augmentation.
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In this paper, we present a numerical model capable of solving the fluid-structure interaction problems involved in the dynamics of skeleton-reinforced fish fins. In this model, the fluid dynamics is simulated by solving the Navier-Stokes equations using a finite-volume method based on an overset, multi-block structured grid system. The bony rays embedded in the fin are modeled as nonlinear Euler-Bernoulli beams. To demonstrate the capability of this model, we numerically investigate the effect of various ray stiffness distributions on the deformation and propulsion performance of a three-dimensional caudal fin. Our numerical results show that with specific ray stiffness distributions, certain caudal fin deformation patterns observed in real fish (e.g., the cupping deformation) can be reproduced through passive structural deformations. Among the four different stiffness distributions (uniform, cupping, W-shape and heterocercal) considered here, we find that the cupping distribution requires the least power expenditure. The uniform distribution, on the other hand, performs the best in terms of thrust generation and efficiency. The uniform stiffness distribution, per se, also leads to 'cupping' deformation patterns with relatively smaller phase differences between various rays. The present model paves the way for future work on dynamics of skeleton-reinforced membranes.
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Experimental investigations on biomimetic mechanical fins have been carried out by researchers to study and mimic the behaviour of fish. Flexible fins are proven to be better than rigid fins in terms of thrust force generation and efficiency when the degree of flexibility is chosen appropriately. It is observed that fishes can modulate their fin stiffness by muscle coactivation. Also, fins of different variety of fishes are developed with different stiffnesses through natural evolution to cope up with different living conditions. Inspired by the natural design of fish fins with varying flexural stiffness along the chord, in this work, a search-based numerical optimization study is conducted to investigate on the optimal flexural stiffness distribution yielding maximum thrust force. For this, a dynamic model of a flexible fin is developed through multi-body dynamics approach by considering the flexible fin as multiple rigid segments connected with torsion springs. Blade element method is utilized to compute the hydrodynamic forces acting on the fin segments. Based on the design optimizations several flat plate fins of trapezoidal geometry are developed with varied distribution of stiffness. Experiments are conducted with the fabricated fins to validate the optimization results for maximized propulsion performance.
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In this paper, a versatile Multi-Body Dynamic (MBD) algorithm is developed to integrate an incompressible fluid flow with a bio-inspired multibody dynamic system. Of particular interest to the biomimetic application, the algorithm is developed via four properly selected benchmark verifications. The present tool has shown its powerful capability for solving a variety of biomechanics fish swimming problems, including self-propelled multiple degrees of freedom with a rigid undulatory body, multiple deformable fins and an integrated system with both undulatory fish body and flexible fins. The established tool has paved the way for future investigation on more complex bio-inspired robots and live fish, for either propulsion or manoeuvring purposes.
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Using a fluid-structure interaction model, we study the effect of ray stiffness distribution on the deformation and performance of a caudal fin. By prescribing a simple swaying motion, our results show that through passive structural deformation alone it is possible to reproduce some complicated fin movements (e.g. the cup and "W''-shape deformations) observed in real fish. Moreover, it has been numerically shown that compared with the fin with uniform ray stiffness, at the same (average) ray stiffness the fins with nonuniform stiffness distribution may achieve further performance enhancement, e.g. increase in propulsion efficiency and decrease in lateral force generation. This is attributed to spanwise deformations caused by phase differences between different rays.
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The versatility of fish to adapt to different swimming requirements is attributed to their complex muscular system. Fish modulate their fin stiffness and shape for maximized performance. In this paper, optimal chordwise stiffness profiles that maximize the propulsive performance have been predicted using theoretical studies. An experimental setup has been fabricated to measure the stiffness profiles of real fish caudal fins. Chordwise varying stiffness robotic fins fabricated using carbon fiber reinforced composites (CFRC) have been tested in the water tunnel to evaluate their performance over constant stiffness fins. It is observed that the varying stiffness fins produce larger thrusts and efficiencies compared to constant stiffness fins for all the operating conditions considered in this work. A comparison of the digital image correlation (DIC) measured deformations of the fins showed that the better performance of varying stiffness fins is due to their larger curvatures and trailing edge amplitudes. These theoretical and experimental studies provide a greater understanding of the role of stiffness in fish fins for locomotion.
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This paper presents a numerical investigation of the effects of chordwise flexibility on flapping wings at low Reynolds number. The numerical simulations are performed with a partitioned fluid–structure interaction algorithm using artificial compressibility stabilization. The choice of the structural dimensionless parameters is based on scaling arguments and is compared against parameters used by other authors. The different regimes, namely inertia-driven and pressure-driven wing deformations, are presented along with their effects on the topology of the flow and on the performance of a heaving and pitching flapping wing in propulsion regime. It is found that pressure-driven deformations can significantly increase the thrust efficiency if a suitable amount of flexibility is used. Significant thrust increases are also observed in zero pitching amplitude cases. The effects of the second and third deformation modes on the performances of pressure-driven deformation cases are discussed. On the other hand, inertia-driven deformations generally deteriorate aerodynamic performances of flapping wings unless the behavior of the wing deformation is modified by the presence of sustainable superharmonics in a way that produces slight improvements. It is also shown that wing flexibility can act as an efficient passive pitching mechanism that allows fair thrust and better efficiency to be achieved when compared to a rigid pitching–heaving wing.
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In the emerging field of multi-physics simulations, we often face the challenge to establish new connections between physical fields, to add additional aspects to existing models, or to exchange a solver for one of the involved physical fields. If in such cases a fast prototyping of a coupled simulation environment is required, a partitioned setup using existing codes for each physical field is the optimal choice. As accurate models require also accurate numerics, multi-physics simulations typically use very high grid resolutions and, accordingly, are run on massively parallel computers. Here, we face the challenge to combine flexibility with parallel scalability and hardware efficiency. In this paper, we present the coupling tool preCICE which offers the complete coupling functionality required for a fast development of a multi-physics environment using existing, possibly black-box solvers. We hereby restrict ourselves to bidirectional surface coupling which is too expensive to be done via file communication, but in contrast to volume coupling still a candidate for distributed memory parallelism between the involved solvers. The paper gives an overview of the numerical functionalities implemented in preCICE as well as the user interfaces, i.e., the application programming interface and configuration options. Our numerical examples and the list of different open-source and commercial codes that have already been used with preCICE in coupled simulations show the high flexibility, the correctness, and the high performance and parallel scalability of coupled simulations with preCICE as the coupling unit.
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Recent advances in understanding fish locomotion with robotic devices have included the use of biomimetic flapping based and fin undulatory locomotion based robots, treating two locomotions separately from each other. However, in most fish species, patterns of active movements of fins occur in concert with the body undulatory deformation during swimming. In this paper, we describe a biomimetic robotic caudal fin programmed with individually actuated fin rays to mimic the fin motion of the Bluegill Sunfish (Lepomis macrochirus) and coupled with heave and pitch oscillatory motions adding to the robot to mimic the peduncle motion which is derived from the undulatory fish body. Multiple-axis force and digital particle image velocimetry (DPIV) experiments from both the vertical and horizontal planes behind the robotic model were conducted under different motion programs and flow speeds. We found that both mean thrust and lift could be altered by changing the phase difference (φ) from 0° to 360° between the robotic caudal peduncle and the fin ray motion (spanning from 3 mN to 124 mN). Notably, DPIV results demonstrated that the caudal fin generated multiple wake flow patterns in both the vertical and horizontal planes by varying φ. Vortex jet angle and thrust impulse also varied significantly both in these two planes. In addition, the vortex shedding position along the spanwise tail direction could be shifted around the mid-sagittal position between the upper and lower lobes by changing the phase difference. We hypothesize that the fish caudal fin may serve as a flexible vectoring propeller during swimming and may be critical for the high maneuverability of fish.
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We use three dimensional computer simulations to investigate the free swimming of plunging elastic plates with aspect ratios ranging from 0.5 to 5 in a viscous fluid with Reynolds number 250. We show that maximum velocity occurs near the first natural frequency regardless of aspect ratio, whereas the maximum swimming economy occurs away from the first natural frequency and is associated with a specific swimmer bending pattern. Moreover, we show that the low aspect ratio swimmers, those with wider spans, are not only the fastest but also the most economical. The faster speeds are associated with a decrease in effective drag for low aspect ratio plunging swimmers. We find that the recently proposed vortex-induced drag model adequately explains the drag reduction by suggesting that the smaller relative size of side vortices in low aspect ratio swimmers creates less drag per unit width.
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A code is developed for the computation of three-dimensional aeroelastic problems such as wing flutter. The unsteady Navier-Stokes flow solver is based on a flnite-volume approach with centered flux discretization and artificial diffusion. For the structural displacements a modal approach is applied. The temporal discretization is implicit for both the flow equations and the structural equations. An explicit dual-time method is used to integrate the coupled governing equations. A multigrid method is applied to advance the flow solution, and the computation is performed in parallel with a multiblock approach. A supercritical 2-D wing and the AGARD 445.6 wing serve as test cases for flutter investigations. Results for inviscid flow are compared with results obtained by solving the Navier-Stokes equations with the Baldwin-Lomax and k-ω turbulence models, respectively. Inclusion of viscous effects is critical for the 2-D wing. LCO of the 2-D wing is predicted, but with larger amplitude compared to experimental measurements. Predicted flutter boundary for the AGARD wing agrees well with experimental data in subsonic and transonic range but deviates significantly from experimental data in the supersonic range. Inclusion of viscous effects only slightly improves the result for this case. © 2003 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc.
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Research on fish locomotion has expanded greatly in recent years as new approaches have been brought to bear on a classical field of study. Detailed analyses of patterns of body and fin motion and the effects of these movements on water flow patterns have helped scientists understand the causes and effects of hydrodynamic patterns produced by swimming fish. Recent developments include the study of the center-of-mass motion of swimming fish and the use of volumetric imaging systems that allow three-dimensional instantaneous snapshots of wake flow patterns. The large numbers of swimming fish in the oceans and the vorticity present in fin and body wakes support the hypothesis that fish contribute significantly to the mixing of ocean waters. New developments in fish robotics have enhanced understanding of the physical principles underlying aquatic propulsion and allowed intriguing biological features, such as the structure of shark skin, to be studied in detail. Expected final online publication date for the Annual Review of Marine Science Volume 7 is January 03, 2015. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
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The deformability of insect wings is associated with the embedded skeleton (venation). In this paper, the aerodynamic performance of wings with nonuniform flexibility is computationally investigated. By using a two-dimensional rendition, the underlying veins are modeled as springs, and the membrane is modeled as a flexible plate. The focus is on the effects of the detailed distribution of vein flexibility upon the performance of such a wing in the generation of lift force. Specifically, we are interested in finding the importance of leading edge strengthening. Towards this end, the aerodynamic performances of three wings, a rigid wing, a flexible wing with identical veins, and a flexible wing with strengthened leading edge, are studied and compared against each other. It is shown that the flexible wing with leading edge strengthening is capable of producing significantly higher lift force without consuming more energy. This is found to be related to the stabilizing and cambering effects at the leading edge, which enhances the leading edge vortices. In addition, in contrast to the other two wings, which show sensitivity to kinematic parameters, the wing with strengthened leading edge perform well over a wide range of parameters.
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Previous research on the flexible structure of flapping wings has shown an improved propulsion performance in comparison to rigid wings. However, not much is known about this function in terms of power efficiency modification for flapping wing energy devices. In order to study the role of the flexible wing deformation in the hydrodynamics of flapping wing energy devices, we computationally model the two-dimensional flexible single and twin flapping wings in operation under the energy extraction conditions with a large Reynolds number of 10(6). The flexible motion for the present study is predetermined based on a priori structural result which is different from a passive flexibility solution. Four different models are investigated with additional potential local distortions near the leading and trailing edges. Our simulation results show that the flexible structure of a wing is beneficial to enhance power efficiency by increasing the peaks of lift force over a flapping cycle, and tuning the phase shift between force and velocity to a favourable trend. Moreover, the impact of wing flexibility on efficiency is more profound at a low nominal effective angle of attack (AoA). At a typical flapping frequency f * = 0.15 and nominal effective AoA of 10°, a flexible integrated wing generates 7.68% higher efficiency than a rigid wing. An even higher increase, around six times that of a rigid wing, is achievable if the nominal effective AoA is reduced to zero degrees at feathering condition. This is very attractive for a semi-actuated flapping energy system, where energy input is needed to activate the pitching motion. The results from our dual-wing study found that a parallel twin-wing device can produce more power compared to a single wing due to the strong flow interaction between the two wings.
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Water tunnel experiments on chordwise-flexible airfoils heaving with constant amplitude have been carried out for Reynolds numbers of 9,000 to 27,000. A degree of flexibility was found to increase both thrust coefficient and propulsive efficiency. Measurements of the flow field revealed stronger trailing-edge vortices corresponding to higher thrust coefficients, and weaker leading-edge vortices corresponding to higher efficiencies. By analogy with a rigid airfoil in coupled heave and pitch, thrust coefficient and propulsive efficiency were found to be functions of the Strouhal number and pitch phase angle. Propulsive efficiency peaks at a pitch phase angle of 95-100 deg (consistent with experimental and computational simulations of rigid airfoils in coupled heave and pitch), and a Strouhal number of 0.29, which lies in the middle of the range observed in nature. Thrust peaks at pitch phase angles in the region of 110-120 deg, but at higher Strouhal numbers. The results suggest the effect of chordwise flexibility is beneficial for purely heaving airfoils at low Reynolds numbers.
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Effects of effective angle of attack (AOA) profile on an oscillating foil thrust performance are studied using a computational method. The foil is subject to a combined pitching/plunging motion with effective AOA satisfying a harmonic cosine function. To achieve this, either the pitching or plunging motion is modified from the conventional harmonic sinusoids. Investigations are performed over a series of Strouhal numbers (St), three maximum effective angles of attack and three different phase angles between pitching and plunging. It is shown that the degradation of thrust force and efficiency with sinusoidal pitching/plunging oscillation, at higher St, is effectively alleviated or removed when the AOA is imposed as a cosine profile. The improvement is more significant for the phase angle being different from 90°. A better performance is obtained with the imposed modification on pitching motion. The stronger reversed Von Karman vortex wake associated with leading-edge vortex development is observed with the modified motions, which is believed to induce the improved thrust performance.
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Fin ray structure in ray-finned fishes (Actinopterygii) largely defines fin function. Fin rays convert the muscle activity at the base of the fin to shape changes throughout the external fin web. Despite their critical functional significance, very little is known about the relationship between form and function in this key vertebrate structure. In this study we demonstrate that morphological specializations of the pectoral fin rays of the benthic longhorn sculpin (Myoxocephalus octodecimspinosus) have specific functional consequences both within and among individual rays. The fin rays of longhorn sculpin have an elongate unjointed region with a cylindrical shape in cross-section proximally, and are jointed with a crescent-shaped cross-section distally. Variation in the relative length of the proximal versus distal regions affects the location of maximum curvature as well as the mean curvature along the length of individual rays. We experimentally manipulated fin rays to mimic the differential muscle activity that generates curvature of fin rays in living animals. We found that the shape of the fin rays in cross-section affects their curvature. Among fin rays, the most ventral fin rays with relatively longer proximal unjointed regions have a more distal location of maximum curvature. These ventral rays also have higher mean curvature, likely because of a combination of features including the cross-sectional shape, area and diameter of the distal segments as well as their relative size and number, which were not examined in detail here. Because these rays are used routinely for substrate contact, this higher curvature could contribute to increased flexibility for substrate contact behaviors such as clinging or gripping the substrate. These morphological and functional differences among fin rays are correlated with the functional regionalization of the fin. Specifically, the ventral fin rays that are used during substrate contact are more stiff proximally and more highly curved distally than the pectoral rays in the dorsal region, which are longer and used during slow swimming. This study highlights the importance of examining morphological and functional variation both within and among complex structures such as fin rays.
Article
In fluid-structure interaction simulations the meshes at the fluid-structure interface usually do not match, because of the different mesh requirements for the flow and structure. The exchange of data over the discrete interface becomes then far from trivial. In this paper we investigate the difference in accuracy and efficiency between a conservative and a consistent coupling approach. This is done for an analytical test prob-lem as well as a quasi-1D FSI problem, for different coupling methods found in literature. It is found that when the coupling method is based on a weak formulation of the coupling conditions the conservative approach is the best choice. For other coupling methods the consistent approach provides the best accuracy and efficiency, because the conservative approach results in unphysical oscillations in the pressure received by the structure and is therefore not consistent.
Article
A numerical model of a ray-reinforced fin is developed to investigate the relation between its structural characteristics and its force generation capacity during flapping motion. In this two-dimensional rendition, the underlying rays are modelled as springs, and the membrane is modelled as a flexible but inextensible plate. The fin kinematics is characterized by its oscillation frequency and the phase difference between different rays (which generates a pitching motion). An immersed boundary method (IBM) is applied to solve the fluid–structure interaction problem. The focus of the current paper is on the effects of ray flexibility, especially the detailed distribution of ray stiffness, upon the capacity of thrust generation. The correlation between thrust generation and features of the surrounding flow (especially the leading edge separation) is also examined. Comparisons are made between a fin with rigid rays, a fin with identical flexible rays, and a fin with flexible rays and strengthened leading edge. It is shown that with flexible rays, the thrust production can be significantly increased, especially in cases when the phase difference between different rays is not optimized. By strengthening the leading edge, a higher propulsion efficiency is observed. This is mostly attributed to the reduction of the effective angle of attack at the leading edge, accompanied by mitigation of leading edge separation and dramatic changes in characteristics of the wake. In addition, the flexibility of the rays causes reorientation of the fluid force so that it tilts more towards the swimming direction and the thrust is thus increased.
Article
A fixed-point fluid–structure interaction (FSI) solver with dynamic relaxation is revisited. New developments and insights gained in recent years motivated us to present an FSI solver with simplicity and robustness in a wide range of applications. Particular emphasis is placed on the calculation of the relaxation parameter by both Aitken’s D2{\Delta^{2}} method and the method of steepest descent. These methods have shown to be crucial ingredients for efficient FSI simulations.
Article
Over the past 20 years, experimental analyses of the biomechanics of locomotion in fishes have generated a number of key findings that are relevant to the construction of biomimetic fish robots. In this paper, we present 16 results from recent experimental research on the mechanics, kinematics, fluid dynamics, and control of fish locomotion that summarize recent work on fish biomechanics. The findings and principles that have emerged from biomechanical studies of fish locomotion provide important insights into the functional design of fishes and suggest specific design features relevant to construction of robotic fish-inspired vehicles that underlie the high locomotor performance exhibited by fishes.
Article
This paper presents a fully coupled three-dimensional solver for the analysis of time-dependent fluid–structure interaction. A partitioned time marching algorithm is employed for the solution of the time-dependent coupled discretised problem, enabling the use of highly developed, robust and well-tested solvers for each field. Conservative transfer of information at the fluid–structure interface is combined with an effective block-Gauss–Seidel iterative scheme to enable implicit coupling of the interacting fields at each time increment. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit dual time stepping technique with explicit multi-stage Runga–Kutta time stepping in pseudo-time and an ALE formulation for moving boundaries. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a Newton–Raphson second-order optimisation method. Test cases are presented to benchmark the algorithm and to demonstrate the potential applications of this method.
Article
The aim of this work is to provide a mathematical contribution to explain the numerical instabilities encountered under certain combinations of physical parameters in the simulation of fluid–structure interaction (FSI) when using loosely coupled time advancing schemes. It is also shown how the same combinations of parameters lead, in the case of strongly coupled schemes, to problems that demand a greater computational effort to be solved, requiring for example a high number of subiterations. The application that we have in mind is FSI simulation for blood flow in large human arteries, but the discussion applies as well to several FSI problems in which an incompressible fluid interacts with a thin elastic structure. To carry out the mathematical analysis, we consider a simplified model representing the interaction between a potential fluid and a linear elastic thin tube. Despite its simplicity, this model reproduces propagation phenomena and takes into account the added-mass effect of the fluid on the structure, which is known to be source of numerical difficulties. This allows to draw conclusions that apply to more realistic problems, as well.
Article
Fluid–structure interaction (FSI) can be simulated in a monolithic way by solving the flow and structural equations simultaneously and in a partitioned way with separate solvers for the flow equations and the structural equations. A partitioned quasi-Newton technique which solves the coupled problem through nonlinear equations corresponding to the interface position is presented and its performance is compared with a monolithic Newton algorithm. Various structural configurations with an incompressible fluid are solved, and the ratio of the time for the partitioned simulation, when convergence is reached, to the time for the monolithic simulation is found to be between 1/2 and 4. However, in this comparison of the partitioned and monolithic simulations, the flow and structural equations have been solved with a direct sparse solver in full Newton–Raphson iterations, only relatively small problems have been solved and this ratio would likely change if large industrial problems were considered or if other solution strategies were used.
Article
Numerical simulation of fluid–structure interaction is often attempted in the context of partitioned methods, where already existing solvers for fluid or structure alone are used jointly. Mostly this is done by exchanging information from time step to time step in an alternating fashion. These weak coupling methods are explicit and hence suffer from possible instabilities. Therefore often strong coupling––where equilibrium is satisfied jointly between fluid and structure in each time step––is desired; the simplest computational procedure is similar to the time stepping an alternating iteration. We show why also this approach may experience difficulties, and how they may be circumvented with block-Newton methods, still in the partitioned framework, by only using the solvers of the subproblems fluid and structure.
Article
Within this paper the so-called artificial added mass effect is investigated which is responsible for devastating instabilities within sequentially staggered Fluid–structure Interaction (FSI) simulations where incompressible fluids are considered.A discrete representation of the added mass operator MA is given and ‘instability conditions’ are evaluated for different temporal discretisation schemes. It is proven that for every sequentially staggered scheme and given spatial discretisation of a problem, a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable. The analysis is quite general and does not depend upon the particular spatial discretisation schemes used. However here special attention is given to stabilised finite elements employed on the fluid partition. Numerical investigations further highlight the results.
Article
Oscillating foils produce thrust through the development of a jet-like average flow. It is found that such jets are convectively unstable with a narrow range of frequencies of maximum amplification, resulting in the formation of a staggered array of vortices with direction opposite to that of the classical Karman street. A stable co-existence of the jet profile and the large-scale patterns is ensured only at the frequency of maximum amplification, hence at this frequency optimal efficiency is obtained, i.e., maximum thrust per unit input energy. The nondimensional frequency of maximum amplification (Strouhal number) is in the range of 0·25 to 0·35. Experiments confirms this results, while the analysis of a large number of data from observations on fish and cetaceans confirm that optimal fish propulsion is achieved within this range of Strouhal number.