Passive dynamics of flexible body in the von Kármán vortex is complicated and has not yet been well understood. In this work we numerically studied the passive flapping motion of an inverted flexible foil pinned in the wake of a rigid circular cylinder by an robust fluid structure interaction framework. The non-dimensional parameters are Reynolds number and distance between the cylinder and pinned-point of the foil. Simulation results show that the flexible foil can extract energy from the vortex street and be induced to vibrate periodically. It is revealed that the foil's motion patterns can be divided into two categories: inverted flapping and forward flapping, which depended on the cylinder-foil distance. Both the cylinder and foil experiences a drag reduction, the foil can even obtain thrust in inverted flapping mode. Compared with a single one in the same uniform flow, the foil's flapping frequency here is smaller but its amplitude is greater. This work would help us to elucidate the energy-saving mechanism of fish swimming and inspire the promising applications in marine engineering
1) Streamwise vortices play an important role in sustaining wall turbulence by regenerating streaks through the lift-up effect.
2) In turbulent plane Couette flow at low Reynolds numbers, streamwise vortices that span the entire gap between plates have been observed.
3) The document proposes a two-step Galerkin projection method to derive a low-order model that can illustrate the dynamics and generation mechanism of these streamwise vortices, in a way that is analogous to what is observed in turbulent boundary layers.
Viscosity is a measure of the friction within a fluid that is shearing. It is defined as the ratio of the shear stress to the strain rate for a fluid undergoing laminar flow between two parallel plates. The viscosity determines the relationship between the shear stress and flow speed. It also determines equations like Poiseuille's equation, which relates viscosity, pressure change, and pipe radius to flow rate through a pipe. Stokes' law gives the drag force on a sphere moving through a fluid in laminar flow as proportional to viscosity and sphere velocity.
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
This document discusses sediment transport in channels. It summarizes that the cross-section and slope of a stable channel are controlled by discharge, sediment grain size/shape/density, and sediment load. It also classifies sediment as suspended load carried by the flow or bed load moving along the bed. Methods for calculating sediment discharge, suspended load distribution, bed load transport, and design of an irrigation channel carrying sediment load are presented.
This document discusses open channel flow and its various types. It defines open channel flow as flow with a free surface driven by gravity. It describes four main types of open channel flows:
1. Steady and unsteady flow
2. Uniform and non-uniform flow
3. Laminar and turbulent flow
4. Sub-critical, critical, and super-critical flow
It also discusses discharge equations for open channels including Chezy's formula, Manning's formula, and Bazin's formula. Finally, it covers specific energy, critical depth, and the hydraulic jump in open channel flow.
This document contains 31 questions regarding boundary layer concepts and fluid mechanics. It covers topics such as the range of Reynolds numbers for laminar and turbulent flow, Hagen-Poiseuille formula, velocity distribution formulas, boundary layer thickness definitions, and equations for major and minor head losses in pipes. The document also provides definitions for terms like boundary layer, laminar sublayer, displacement thickness, and momentum thickness.
Boundary layer concept for external flowManobalaa R
This document provides an overview of boundary layer concepts for external flow. It defines a boundary layer as the layer of fluid near a bounding surface where viscous effects are significant. It describes the assumptions of boundary layer theory, including that viscous effects are confined to the thin boundary layer. It also provides the governing equations for a 2D, laminar, steady boundary layer and discusses boundary layer thickness. Finally, it briefly summarizes literature on an experimental study of film cooling in a rotating turbine.
This laboratory experiment involves using Stokes' Law to determine the viscosity and density of unknown fluids. Students will time the fall of spheres through fluid columns, then use the measurements to calculate viscosity based on Stokes' Law. They will also consider how sphere and cylinder diameters affect calculations. The goals are to understand fluid mechanics concepts like viscosity and Reynolds number, and apply Stokes' Law to characterize unknown fluids.
1) Streamwise vortices play an important role in sustaining wall turbulence by regenerating streaks through the lift-up effect.
2) In turbulent plane Couette flow at low Reynolds numbers, streamwise vortices that span the entire gap between plates have been observed.
3) The document proposes a two-step Galerkin projection method to derive a low-order model that can illustrate the dynamics and generation mechanism of these streamwise vortices, in a way that is analogous to what is observed in turbulent boundary layers.
Viscosity is a measure of the friction within a fluid that is shearing. It is defined as the ratio of the shear stress to the strain rate for a fluid undergoing laminar flow between two parallel plates. The viscosity determines the relationship between the shear stress and flow speed. It also determines equations like Poiseuille's equation, which relates viscosity, pressure change, and pipe radius to flow rate through a pipe. Stokes' law gives the drag force on a sphere moving through a fluid in laminar flow as proportional to viscosity and sphere velocity.
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
This document discusses sediment transport in channels. It summarizes that the cross-section and slope of a stable channel are controlled by discharge, sediment grain size/shape/density, and sediment load. It also classifies sediment as suspended load carried by the flow or bed load moving along the bed. Methods for calculating sediment discharge, suspended load distribution, bed load transport, and design of an irrigation channel carrying sediment load are presented.
This document discusses open channel flow and its various types. It defines open channel flow as flow with a free surface driven by gravity. It describes four main types of open channel flows:
1. Steady and unsteady flow
2. Uniform and non-uniform flow
3. Laminar and turbulent flow
4. Sub-critical, critical, and super-critical flow
It also discusses discharge equations for open channels including Chezy's formula, Manning's formula, and Bazin's formula. Finally, it covers specific energy, critical depth, and the hydraulic jump in open channel flow.
This document contains 31 questions regarding boundary layer concepts and fluid mechanics. It covers topics such as the range of Reynolds numbers for laminar and turbulent flow, Hagen-Poiseuille formula, velocity distribution formulas, boundary layer thickness definitions, and equations for major and minor head losses in pipes. The document also provides definitions for terms like boundary layer, laminar sublayer, displacement thickness, and momentum thickness.
Boundary layer concept for external flowManobalaa R
This document provides an overview of boundary layer concepts for external flow. It defines a boundary layer as the layer of fluid near a bounding surface where viscous effects are significant. It describes the assumptions of boundary layer theory, including that viscous effects are confined to the thin boundary layer. It also provides the governing equations for a 2D, laminar, steady boundary layer and discusses boundary layer thickness. Finally, it briefly summarizes literature on an experimental study of film cooling in a rotating turbine.
This laboratory experiment involves using Stokes' Law to determine the viscosity and density of unknown fluids. Students will time the fall of spheres through fluid columns, then use the measurements to calculate viscosity based on Stokes' Law. They will also consider how sphere and cylinder diameters affect calculations. The goals are to understand fluid mechanics concepts like viscosity and Reynolds number, and apply Stokes' Law to characterize unknown fluids.
This document outlines introductory concepts in fluid dynamics, including:
- Streamlines represent the velocity field at a specific instant, while particle paths and streaklines show the velocity field over time.
- Equations relate the components of velocity to the tangential displacement along streamlines.
- Fluids are treated as continuous media and are often assumed to be incompressible and homogeneous.
- For incompressible flow, the mass flux across any stream tube section is constant. This leads to the continuity equation relating velocity and fluid density.
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance. Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the increment of vertical distance. Finally, the velocity became around 1.05 m/s.
This document describes an experiment to determine the viscosity of water using Poiseuille's Law. Students measure the flow rate and pressure difference across a glass tube for varying pump speeds. They then plot the results and calculate the viscosity. The Reynolds number is also considered to analyze if the flow is laminar or turbulent. Estimates of the critical velocity for transition between the two flow types are made based on the experimental setup.
1. The document discusses viscoelastic flow in porous media, including linear and non-linear models of viscoelasticity. 2. It describes continuum and pore-scale approaches to modeling viscoelastic flow, noting advantages and limitations of each. 3. Network modeling is presented as an example pore-scale approach, with the Tardy-Anderson algorithm provided as a specific technique for solving the network flow equations iteratively.
This document contains a question bank with answers for a fluid mechanics and machineries course. It includes 13 questions and answers about fluid properties, density, viscosity, surface tension, momentum equations, laminar flow, head losses, pumps, and cavitation. The questions are divided into 4 units covering fluid properties, flow through pipes, dimensional analysis, and pumps.
The document discusses boundary layer concepts introduced by Ludwig Prandtl in 1904. It describes that within the thin boundary layer adjacent to a solid surface, viscosity effects are significant, while outside the boundary layer viscosity effects are negligible and the fluid can be treated as inviscid. The boundary layer concept allows solving viscous flow problems by treating the flow as viscous in the boundary layer and inviscid elsewhere.
The document describes an experiment to determine the viscosity of water using capillary flow. It involves measuring the volume flow rate (Q) of water through capillary tubes at different pressure differences (p) and using Poiseuille's formula along with corrections to calculate viscosity. Temperature measurements are taken to account for water's changing viscosity with temperature. The corrections term is typically much smaller than the main term in Poiseuille's formula for typical flow rates.
When a body moves through a fluid, it experiences two forces: drag and lift. Drag acts parallel to the flow and slows the body down, while lift acts perpendicular to the flow. These forces depend on factors like the fluid's velocity and density, the body's size and shape, and its angle of attack relative to the flow. Streamlined shapes with small frontal areas experience less pressure drag than blunt bodies, which experience boundary layer separation and higher pressures on one side. The forces can be calculated using drag and lift coefficients, which vary based on the Reynolds number and other flow properties.
This document discusses flow measurement techniques. It begins by introducing different types of flow meters including mechanical, inferential, electrical, and other varieties. Key concepts are then explained such as units of flow, measurement principles, Reynolds number, discharge coefficient, and flow coefficient. Specific mechanical flow meters are covered in depth, including the theory and equations for fixed restriction variable head meters and orifice flow meters. Compressible gas flow is also analyzed using concepts such as rational expansion factor and moisture factor.
Convection involves fluid motion and heat conduction. It can be classified as internal, external, compressible, incompressible, laminar, turbulent, natural, or forced flow. Dimensionless numbers like Reynolds, Prandtl, and Nusselt are used to characterize convection problems. Solutions to the convection equations for a flat plate provide important results like boundary layer thicknesses and heat transfer coefficients.
Turbulent flows are characterized by chaotic, unpredictable changes in velocity. The document discusses turbulence, including defining turbulence, the transition from laminar to turbulent flow, Reynolds averaging to decompose variables into mean and fluctuating components, and the effects of turbulence on the Navier-Stokes equations. It also examines Reynolds stresses, time-averaged conservation equations for turbulent flow, and modeling approaches like Reynolds averaging to account for turbulent fluctuations and closure problems in the equations.
This document summarizes laminar flow of a fluid through a circular tube. It describes the assumptions of steady, laminar flow down a vertical tube with constant density and viscosity. It then presents the momentum balance equations for a cylindrical shell section of the tube. By applying the boundary conditions of no shear stress at the center axis and zero velocity at the tube wall, it arrives at equations for the velocity profile, maximum velocity, average velocity, and mass flow rate through the tube.
This document provides an overview of turbulent fluid flow, including:
1) Turbulent flow occurs when the Reynolds number is greater than 2000 and involves irregular, random movement of fluid particles in all directions.
2) The magnitude and intensity of turbulence can be calculated based on the root mean square of turbulent fluctuations and the average flow velocity.
3) The Moody diagram relates the friction factor to the Reynolds number and relative roughness of a pipe to characterize head losses in turbulent pipe flow.
This document provides an overview of turbulent fluid flow, including:
1) It defines laminar and turbulent flow and explains that turbulent flow occurs above a Reynolds number of 2000.
2) It describes methods for characterizing turbulence, including magnitude, intensity, and mixing length theory.
3) It discusses the universal law of the wall and how velocity is distributed in smooth and rough pipes. Friction factors depend on Reynolds number and relative roughness.
4) Experimental results from Nikuradse are presented showing relationships between friction factor and Reynolds number/relative roughness that can be used to model pressure losses in pipes.
This document discusses boundary layer theory and provides formulas to calculate boundary layer thickness, shear stress, and coefficient of drag based on Reynolds number for laminar boundary layer flows. It presents the velocity profile equation and uses it along with Newton's law of viscosity and the momentum integral equation to derive expressions for boundary layer thickness in terms of Reynolds number, shear stress in terms of Reynolds number, and coefficient of drag in terms of Reynolds number.
This pdf includes about the submerged bodies and the forces acting on the submerged bodies. Different terminologies are discussed. Definitions of different bodies in the fluid are discussed as well.
It is small pdf with great knowledge, hope it will be helpful to the students.
The document discusses fluid mechanics concepts including:
1) Boundary layers form as fluid flows past objects due to viscosity and velocity gradients within the boundary layer.
2) Drag and lift are forces exerted on objects by fluid flow and depend on factors like boundary layer thickness, pressure distribution, and object shape.
3) The Reynolds number compares inertia and viscous forces and indicates laminar or turbulent flow.
This document discusses turbulent fluid flow. It defines turbulence as an irregular flow with random variations in time and space that can be expressed statistically. Turbulence occurs above a critical Reynolds number when the kinetic energy of the flow is enough to sustain random fluctuations against viscous damping. Characteristics of turbulent flow include fluctuating velocities and pressures, and more uniform velocity distributions compared to laminar flow. Turbulence can be generated by solid walls or shear between layers, and can be categorized as homogeneous, isotropic, or anisotropic. Transition from laminar to turbulent flow is also discussed.
1) The document discusses different definitions of boundary layer thickness, including nominal thickness, displacement thickness, momentum thickness, and energy thickness. Equations are provided for calculating each type of thickness.
2) Key assumptions of boundary layer theory are that the boundary layer is thin compared to the body and flow is two-dimensional and steady. The Prandtl boundary layer equations are derived using control volume analysis and assumptions of constant density and viscosity.
3) The Prandtl boundary layer equation equates forces within the boundary layer, including pressure and shear stress, to the net rate of momentum change and forms the basis for boundary layer analysis.
Este documento resume los tipos de relaciones en Access, incluyendo relaciones uno a uno, uno a varios, y varios a varios. Explica que las relaciones permiten el uso simultáneo de datos de múltiples tablas evitando duplicidad y mejorando el rendimiento. Detalla que las relaciones requieren de un campo en común y una clave principal para vincular tablas, y provee ejemplos de cada tipo de relación.
Three security feature technologies are described for protecting documents: ICS®, ICI®, and M-ICI®. ICS® embeds hidden images in banknote screens and is for banknotes. ICI® and M-ICI® embed hidden images or text in high security products and can be used with offset or intaglio printing. Digital watermarking features IDP and Digital-IDP allow personalized hidden data and stronger encryption for certificates and documents.
This document outlines introductory concepts in fluid dynamics, including:
- Streamlines represent the velocity field at a specific instant, while particle paths and streaklines show the velocity field over time.
- Equations relate the components of velocity to the tangential displacement along streamlines.
- Fluids are treated as continuous media and are often assumed to be incompressible and homogeneous.
- For incompressible flow, the mass flux across any stream tube section is constant. This leads to the continuity equation relating velocity and fluid density.
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance. Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the increment of vertical distance. Finally, the velocity became around 1.05 m/s.
This document describes an experiment to determine the viscosity of water using Poiseuille's Law. Students measure the flow rate and pressure difference across a glass tube for varying pump speeds. They then plot the results and calculate the viscosity. The Reynolds number is also considered to analyze if the flow is laminar or turbulent. Estimates of the critical velocity for transition between the two flow types are made based on the experimental setup.
1. The document discusses viscoelastic flow in porous media, including linear and non-linear models of viscoelasticity. 2. It describes continuum and pore-scale approaches to modeling viscoelastic flow, noting advantages and limitations of each. 3. Network modeling is presented as an example pore-scale approach, with the Tardy-Anderson algorithm provided as a specific technique for solving the network flow equations iteratively.
This document contains a question bank with answers for a fluid mechanics and machineries course. It includes 13 questions and answers about fluid properties, density, viscosity, surface tension, momentum equations, laminar flow, head losses, pumps, and cavitation. The questions are divided into 4 units covering fluid properties, flow through pipes, dimensional analysis, and pumps.
The document discusses boundary layer concepts introduced by Ludwig Prandtl in 1904. It describes that within the thin boundary layer adjacent to a solid surface, viscosity effects are significant, while outside the boundary layer viscosity effects are negligible and the fluid can be treated as inviscid. The boundary layer concept allows solving viscous flow problems by treating the flow as viscous in the boundary layer and inviscid elsewhere.
The document describes an experiment to determine the viscosity of water using capillary flow. It involves measuring the volume flow rate (Q) of water through capillary tubes at different pressure differences (p) and using Poiseuille's formula along with corrections to calculate viscosity. Temperature measurements are taken to account for water's changing viscosity with temperature. The corrections term is typically much smaller than the main term in Poiseuille's formula for typical flow rates.
When a body moves through a fluid, it experiences two forces: drag and lift. Drag acts parallel to the flow and slows the body down, while lift acts perpendicular to the flow. These forces depend on factors like the fluid's velocity and density, the body's size and shape, and its angle of attack relative to the flow. Streamlined shapes with small frontal areas experience less pressure drag than blunt bodies, which experience boundary layer separation and higher pressures on one side. The forces can be calculated using drag and lift coefficients, which vary based on the Reynolds number and other flow properties.
This document discusses flow measurement techniques. It begins by introducing different types of flow meters including mechanical, inferential, electrical, and other varieties. Key concepts are then explained such as units of flow, measurement principles, Reynolds number, discharge coefficient, and flow coefficient. Specific mechanical flow meters are covered in depth, including the theory and equations for fixed restriction variable head meters and orifice flow meters. Compressible gas flow is also analyzed using concepts such as rational expansion factor and moisture factor.
Convection involves fluid motion and heat conduction. It can be classified as internal, external, compressible, incompressible, laminar, turbulent, natural, or forced flow. Dimensionless numbers like Reynolds, Prandtl, and Nusselt are used to characterize convection problems. Solutions to the convection equations for a flat plate provide important results like boundary layer thicknesses and heat transfer coefficients.
Turbulent flows are characterized by chaotic, unpredictable changes in velocity. The document discusses turbulence, including defining turbulence, the transition from laminar to turbulent flow, Reynolds averaging to decompose variables into mean and fluctuating components, and the effects of turbulence on the Navier-Stokes equations. It also examines Reynolds stresses, time-averaged conservation equations for turbulent flow, and modeling approaches like Reynolds averaging to account for turbulent fluctuations and closure problems in the equations.
This document summarizes laminar flow of a fluid through a circular tube. It describes the assumptions of steady, laminar flow down a vertical tube with constant density and viscosity. It then presents the momentum balance equations for a cylindrical shell section of the tube. By applying the boundary conditions of no shear stress at the center axis and zero velocity at the tube wall, it arrives at equations for the velocity profile, maximum velocity, average velocity, and mass flow rate through the tube.
This document provides an overview of turbulent fluid flow, including:
1) Turbulent flow occurs when the Reynolds number is greater than 2000 and involves irregular, random movement of fluid particles in all directions.
2) The magnitude and intensity of turbulence can be calculated based on the root mean square of turbulent fluctuations and the average flow velocity.
3) The Moody diagram relates the friction factor to the Reynolds number and relative roughness of a pipe to characterize head losses in turbulent pipe flow.
This document provides an overview of turbulent fluid flow, including:
1) It defines laminar and turbulent flow and explains that turbulent flow occurs above a Reynolds number of 2000.
2) It describes methods for characterizing turbulence, including magnitude, intensity, and mixing length theory.
3) It discusses the universal law of the wall and how velocity is distributed in smooth and rough pipes. Friction factors depend on Reynolds number and relative roughness.
4) Experimental results from Nikuradse are presented showing relationships between friction factor and Reynolds number/relative roughness that can be used to model pressure losses in pipes.
This document discusses boundary layer theory and provides formulas to calculate boundary layer thickness, shear stress, and coefficient of drag based on Reynolds number for laminar boundary layer flows. It presents the velocity profile equation and uses it along with Newton's law of viscosity and the momentum integral equation to derive expressions for boundary layer thickness in terms of Reynolds number, shear stress in terms of Reynolds number, and coefficient of drag in terms of Reynolds number.
This pdf includes about the submerged bodies and the forces acting on the submerged bodies. Different terminologies are discussed. Definitions of different bodies in the fluid are discussed as well.
It is small pdf with great knowledge, hope it will be helpful to the students.
The document discusses fluid mechanics concepts including:
1) Boundary layers form as fluid flows past objects due to viscosity and velocity gradients within the boundary layer.
2) Drag and lift are forces exerted on objects by fluid flow and depend on factors like boundary layer thickness, pressure distribution, and object shape.
3) The Reynolds number compares inertia and viscous forces and indicates laminar or turbulent flow.
This document discusses turbulent fluid flow. It defines turbulence as an irregular flow with random variations in time and space that can be expressed statistically. Turbulence occurs above a critical Reynolds number when the kinetic energy of the flow is enough to sustain random fluctuations against viscous damping. Characteristics of turbulent flow include fluctuating velocities and pressures, and more uniform velocity distributions compared to laminar flow. Turbulence can be generated by solid walls or shear between layers, and can be categorized as homogeneous, isotropic, or anisotropic. Transition from laminar to turbulent flow is also discussed.
1) The document discusses different definitions of boundary layer thickness, including nominal thickness, displacement thickness, momentum thickness, and energy thickness. Equations are provided for calculating each type of thickness.
2) Key assumptions of boundary layer theory are that the boundary layer is thin compared to the body and flow is two-dimensional and steady. The Prandtl boundary layer equations are derived using control volume analysis and assumptions of constant density and viscosity.
3) The Prandtl boundary layer equation equates forces within the boundary layer, including pressure and shear stress, to the net rate of momentum change and forms the basis for boundary layer analysis.
Este documento resume los tipos de relaciones en Access, incluyendo relaciones uno a uno, uno a varios, y varios a varios. Explica que las relaciones permiten el uso simultáneo de datos de múltiples tablas evitando duplicidad y mejorando el rendimiento. Detalla que las relaciones requieren de un campo en común y una clave principal para vincular tablas, y provee ejemplos de cada tipo de relación.
Three security feature technologies are described for protecting documents: ICS®, ICI®, and M-ICI®. ICS® embeds hidden images in banknote screens and is for banknotes. ICI® and M-ICI® embed hidden images or text in high security products and can be used with offset or intaglio printing. Digital watermarking features IDP and Digital-IDP allow personalized hidden data and stronger encryption for certificates and documents.
El documento describe cómo realizar búsquedas simples y avanzadas en la base de datos CINAHL, estableciendo filtros para reducir los resultados. Se muestra que una búsqueda simple arrojó 70 resultados mientras que una búsqueda con descriptores produjo 199 resultados. También se explica cómo crear una alerta por correo electrónico para futuras actualizaciones sobre la búsqueda.
Analysis and Design of Information Systems Financial Reports with Object Orie...ijceronline
Micro, Small and Medium Enterprises (SMEs) are a group effort proved resistant to a wide range of economic crisis shocks. But in the operation of their business financial management is still not transparent and are also still mixed between business finance and personal finance. So that needs to be done with good financial management. In this research, analysis and information system design financial reports as a basis for the development of the system. Software development life cycle (SDLC) using the model of the object oriented approach. With object-oriented approach, the tools used by the notation Unified Modelling Language (UML). In object-oriented approach all systems applications are Viewed as a collection of objects that allow organisasi interloking and end users to Easily understand logical entities. Object-oriented approach Provides the benefits of the reuse of codes and saves the time for developing quality product.
Fight for Better Legislation - Chris Hartgerink - OpenCon 2016Right to Research
The document discusses text and data mining (TDM) legislation and advocacy efforts. It mentions the OpenCon 2015 and 2016 conferences, advocating for better TDM laws. TDM blocks were widely discussed, including blocks by Elsevier and bugs found in databases during TDM work. The European Union's strategy and proposals around TDM and disciplinary procedures for TDM work were also covered. Advocates are encouraged to share their stories and challenge publishers like Elsevier.
El documento analiza las características del español hablado en los medios de comunicación como la radio, televisión y escritos. Señala que en la radio y televisión hay pocas opciones de corregir errores del idioma en transmisiones en vivo, mientras que los escritos permiten correcciones previas. Además, destaca la influencia masiva de la radio y televisión en el uso correcto del español y cómo los manuales escritos guían su desarrollo adecuado. Finalmente, discute el auge de expansión del españ
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6 Week PHP Training In Ambala ! BATRA COMPUTER CENTREjatin batra
The document provides information about Batra Computer Centre, including its contact details, website and email. It then discusses PHP as a scripting language especially suited for web development. PHP is described as open source, cross-platform, user friendly and designed to work well with the web. The document also mentions SQL, databases, web development and the tools and technologies taught at the computer centre like HTML, CSS, JavaScript, PHP and SQL.
La semiótica en la arquitectura estudia el significado y razón de los elementos, formas y colores de un edificio. El lenguaje que elige un arquitecto al diseñar una estructura le da carácter y significado. Cada detalle, ya sea la escalera, columna o acabado, crea sentimientos en los espectadores. Es importante que todo el proyecto use un mismo lenguaje para crear unión. El significado y lenguaje de una obra son importantes porque transmiten el mensaje artístico del arquitecto y llevan la
Theoretical Behaviourof Soil Stability Using Geo Grids.ijceronline
The subgrade of any pavement plays an important role in load bearing and support of traffic in the form of foundation. The present scenario describes that use of geogrid is used to stabilize a soft soil of highway subgrade so that a firm working platform could be provided for pavement construction.It is found that geo-grids placed at 3/5 the distance from the base shows higher CBR value than when placed at 2/5 and 4/5 distances from the base.The first objective of the study is to be the evaluation of the soil properties like particle size, liquid limit, plastic limit, plasticity index to identify as a soft soil. Second objective of the study is to, improve the bearing capacity of soft soil by using flyash, lime, lime/flyash as a admixture and geogrids as a reinforcement. California Baring Ratio (CBR) and Unconfined Compression (UCC) tests were conducted in the laboratory on the soil
Este documento trata sobre conceptos básicos de variables, funciones y límites. Explica que una variable puede asignar valores ilimitados durante un proceso, mientras que una constante mantiene un valor fijo. También define funciones como la relación entre una variable dependiente cuyo valor está determinado por una variable independiente, y explica la notación de funciones f(x). Por último, introduce los conceptos de límite de una variable y función, así como infinito y infinitésimo.
Para crear una cuenta de correo electrónico en Hotmail, primero debes conectarte a www.hotmail.com e ir a la opción de registrarse. Luego, llena un formato con tu nombre de usuario deseado, correo electrónico alternativo o pregunta de seguridad, y datos personales. Finalmente, acepta los términos para establecer tu nueva cuenta de correo electrónico.
This risk assessment form is for a filming project taking place at The Netherhall School and Sixth Form Centre in Cambridge, England. It identifies three main activities: laying cables, knocking down a film set, and using lighting. For each activity, potential hazards are outlined along with control measures to reduce the risk level. The cable laying poses a trip hazard but tape will be used to secure the wire. The film set could fall on people if run into, so no running will be allowed. The lighting could overheat or fall, so people will be warned not to touch it. With these controls, all activities are deemed to have a low or medium risk level.
Oportunidades de inversion y asociaciones publico privadas en uruguay cndpuntanews
El documento describe las oportunidades de inversión y asociaciones público-privadas (PPP) en Uruguay. Resalta que Uruguay tiene una economía fuerte y estable, seguridad jurídica, y fortaleza institucional que lo hacen apropiado para PPP. También presenta la estrategia de desarrollo e inversión de Uruguay, y propone un nuevo marco normativo para proyectos de infraestructura a través de PPP, incluyendo la creación de una unidad especializada para gestionar estos proyectos.
El documento trata sobre varios temas relacionados con la informática como lenguajes informáticos, corriente eléctrica, corriente continua y alterna, personas que aportaron a la informática como Leonardo da Vinci, John Napier, Blaise Pascal, Gottfried Leibniz y Joseph Marie Jacquard, periféricos de entrada y salida y sistemas operativos. Explica conceptos clave de cada tema de manera concisa.
Este documento describe un programa para mejorar la calidad de vida de familias en situación de pobreza extrema a través de tres componentes: 1) acompañamiento familiar y comunitario, 2) acceso preferente a programas y servicios sociales del estado, y 3) fortalecimiento institucional de entidades vinculadas al estado. El objetivo general es mejorar la calidad de vida de estas familias mediante atención personalizada y reconocimiento de sus potenciales para salir de la pobreza.
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Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
1. ISSN (e): 2250 – 3005 || Volume, 06 || Issue, 11|| November – 2016 ||
International Journal of Computational Engineering Research (IJCER)
www.ijceronline.com Open Access Journal Page 34
Passively Flapping Dynamics of a Flexible Foil Immersed in the
Wake of a Cylinder
Dibo Dong1
, Weishan Chen, Zhenxiu Hou, Zhenbo Han
1
State Key Laboratory of Robotics and System Harbin Institute of Technology Harbin, Heilongjiang Province,
China.
I. INTRODUCTION
The interaction between a rigid structure and a flexible body is a common phenomenon, like fishes swimming
behind a ship or staying in the wake of a stationary structure. Fishes may take advantage of the interaction to
save energy and lift efficiency. Two rigid bodies arranged in tandem, the downstream one enjoys a drag
reduction [1]. Recently, the interaction between flexible bodies has been widely studied by simulations and
experiments [2, 3]. For two tandem flexible bodies, the downstream will suffer a drag increase, which is
opposite to the situation of two tandem rigid bodies. The interaction of coupled rigid and flexible bodies may be
much different. Interaction between a upstream flexible filament and a downstream rigid cylinder is investigated
in [4]. Reference [5] studied the effect of a thin wire placed in the wake of a rigid cylinder. In this paper, we
places a flexible foil at the downstream of a rigid cylinder to study the interaction between rigid and flexible
bodies in a viscous flow numerically. An immersed boundary-lattice Boltzmann method is adopted to carry out
the simulations.
II. COMPUTATIONAL MODEL
A schematic diagram of the cylinder-foil system is shown in Fig. 1. A thin foil with length L is placed in
downstream of a rigid circular cylinder with diameter d. The foil is considered as a two-dimensional thin beam
with a simply supported boundary condition at the leading-edge. Both the center of the cylinder and the leading-
edge of the foil are fixed at the center line of the fluid domain, the trailing-edge of the foil is free. The minimum
distance between the cylinder and the leading-edge of the foil is the cylinder-foil distance Ds. Here we introduce
a non-dimensionalize cylinder-foil distance ratio defined as D = Ds/d. The incoming flow is parallel to the X-
axis with a velocity of U∞.
The problem on a rigid body and a flexible foil immersed in a viscous flow is solved by the IB-LBM [6]. The
fluid is discretized by a regular Cartesian lattice, the foil is discretized by a group of Lagrangian coordinate
markers. The viscous fluid is govern by the incompressible Navier–Stokes and continuity equations:
21
p
t R e
f
v
v v v ,
(1)
0 v .
(2)
ABSTRACT
Passive dynamics of flexible body in the von Kármán vortex is complicated and has not yet been well
understood. In this work we numerically studied the passive flapping motion of an inverted flexible
foil pinned in the wake of a rigid circular cylinder by an robust fluid structure interaction
framework. The non-dimensional parameters are Reynolds number and distance between the
cylinder and pinned-point of the foil. Simulation results show that the flexible foil can extract energy
from the vortex street and be induced to vibrate periodically. It is revealed that the foil's motion
patterns can be divided into two categories: inverted flapping and forward flapping, which
depended on the cylinder-foil distance. Both the cylinder and foil experiences a drag reduction, the
foil can even obtain thrust in inverted flapping mode. Compared with a single one in the same
uniform flow, the foil's flapping frequency here is smaller but its amplitude is greater. This work
would help us to elucidate the energy-saving mechanism of fish swimming and inspire the promising
applications in marine engineering.
Keywords: flow control, elastic plate; passively flapping, fluid-structure interaction.
2. Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
www.ijceronline.com Open Access Journal Page 35
p is the pressure of the fluid, ρ is the fluid density, v =(v, u) is the fluid velocity as a function of time /t L U
.
Re is the Reynolds number defined as /R e U d
, μ is the fluid dynamic viscosity. The added momentum
force f represents the force exerted by the structure on the fluid. The dynamics of the foil is governed by the
equation:
2 4
2 4
0l
d d d d
T K
ds dsdt ds
X X X
F .
(3)
ρl is the linear density of the foil, ,X YX represents the position of the foil markers. s represents the
Lagrangian coordinate along the foil. 2
/cT T U L
is the tension. Tc (s, t) is the tension within the foil which
determined by the markers
LDd
U∞
X
Y
Leading-edge
Trailing-edge
Fig. 1 Schematic diagram of the cylinder-foil system.
position X. K is the bending stiffness defined as 2 3
/ ( )K E I U L
, EI is the bending rigidity of the foil. F is the
hydrodynamic force exerts on the fluid by the foil which defined on the foil markers. The foil is considered to be
inextensible, which provided by:
1
d d
ds ds
X X
.
(4)
The boundary condition for the foil is:
2
0
2
, 0
d
ds
X
X X
(5)
for the leading-edge,
2
2
0, 0
d
T
ds
X
(6)
for the trailing-edge. The momentum force f = (fx, fy) can be calculated by:
1
,
( ), ( ) ( ) ( )
t d s
t
s t s d s
f x
X y y X y x XU v
(7)
Γ is boundary of the foil markers, Ω denotes the domain of the fluid. x denotes the coordinate of the Cartesian
lattice of the fluid. U represents the velocity of the foil marker at X. v represents the fluid velocity field. δ is a
mollifier [7] to perform the convolution which defined as:
2
2
1
5 3 3(1 ) 1 0 .5 1 .5
6
1
( ) 1 3 1 0 .5
3
0 o h terw ise
d d d
d d d
.
(8)
Where d represents the distance between the Lagrangian coordinate s and the lattice coordinate x . As
shown in Fig. 2, by placing the tension points between each foil markers, equation (3) and (4) can be discretised
into a staggered fashion:
3. Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
www.ijceronline.com Open Access Journal Page 36
1 1
1 1
2
1 1
( )2
1
S S S S
n n n n
n n n
s s
l
n n
s s
D T D K D
t
D D
X X FX X X
X X
(9)
t is the increment of time. Ds denotes the standard second-order center finite difference for s. The lattice
Boltzmann equation (LBE) [8] is used to solve the fluid instead of the Navier–Stokes equations because of its
efficiency. The LBE with the BGK approach is:
Xi-1
Ti Ti+1
Xi Xi+1
Fig. 2 Discretisation grid of the plate in a staggered form. Blue circles represents tension points, between
tension points are coordinate markers.
, , , ,
eq
i i i i i
t
f t t t f t f t f t t
x e x x x F
(10)
Where τ is a relaxation time which related to the dynamic viscosity as 1 / 2 / 3 . ,i
f tx denotes the
distribution function with respect to the fluid particles at position x and time t, ei is the discrete particles velocity
which is shown in Fig. 3. The subscript i is the directions of the fluid particles, in this model, ei is defined as:
0 1 1 0 0 1 1 1 0
0, 1, ... , 8
0 0 0 1 1 1 1 1 0
i i
e
(11)
,
eq
f tx is the equilibrium function which can be obtained by:
2
2
2 4 2
, 1
2 2
ieq i
i
s s s
f t
c c c
ee
x
vv v
(12)
cs is the sound velocity and ωi is the weighting coefficients. The discretised force Fi relates to the f is defined as
follows:
2 4
1
1
2
i i
i i i
s s
c c
e e
F e f
v v
(13)
the macroscopic quantities of density ρ and v can are obtained by:
i
i
f
(14)
2
i i
i
t
f
e fv
(15)
The dimensionless mass ratio of the foil is defined as: / ( )l
M L , the dimensionless drag coefficient for the
foil and cylinder is: 2
2 /d d
C F U L
and 2
2 /d d
C F U d
. The dimensionless lift coefficient is defined
as 2
2 /l l
C F U L
and 2
2 /l l
C F U d
. Fd and Fl are the hydrodynamic force along the X-axis and Y-axis
respectively.
e2 f2
e0 f0
e5
f5
e7
f7 e4 f4
e6
f6
e8
f8
e3
f3
e1
f1
Fig. 3 The distribution function and the discrete particles velocity.
4. Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
www.ijceronline.com Open Access Journal Page 37
The flapping amplitude Af is defined as the displacement along the Y-axis of the trailing-edge, and A = AT / L is
the dimensionless flapping amplitude. The flapping frequency of the foil and the vortex shedding frequency of
the cylinder are represented by f.
The X-axis length for the fluid domain is 80d and the Y-axis length is 40d. The center of the cylinder is placed
20d away from the inlet of the fluid domain. The position of the foil is decided by the distance ratio D. The foil
is parallel to the X-axis at the beginning of the simulation. The foil markers and the Cartesian lattice is in
uniform distribution. Both the distance between two neighboring markers and the lattice spacing is set to 0.01.
The diameter d and the foil length L is set to d = L, so the size for the fluid domain is 2000 × 1500. Unless other
stated, the Reynolds number is Re = 100 , the mass ratio of the foil is M = 0.3 and the bending stiffness is K =
10-4
. In such parameters, the flexible foil can flap in a stable motion periodically as the simulation results
showed. All the results analyzed below are obtained by these stable periods.
III. RESULT AND DISCUSSION
Two categories of the foil's motion patterns are founded by changing the cylinder-foil distance: inverted
flapping and forward flapping, as shown in Fig. 4. When the cylinder-foil distance is small enough, the foil will
flap towards the opposite direction of the incoming flow. The free end of the foil will move upstream and go
across the pinned-point, then gets into a stable flapping motion with the free end pointing to the upstream
cylinder. There is a backflow zone behind the cylinder, as shown in Fig. 5, the flow speed of this area is contrary
to the streamwise [9], and the pressure is low. The foil in the backflow zone will experiences a force along the
negative direction of the X-axis, and finally the foil will turn around and flap towards the upstream direction.
With the increasing of the cylinder-foil distance, the foil's motion patterns will turn to the forward flapping
mode, which the trailing-edge points to the downstream. The crucial cylinder-foil distance of the mode shift is
decided by the length of the backflow zone. Fig. 4 plots the flapping pattern of the inverted flapping mode at D
= 2.1 and the forward flapping mode at D = 3.5. The flapping amplitude and the Y-velocity of the trailing-edge
in the inverted flapping mode is obviously smaller than that of the forward flapping mode. From Fig.5 (e) we
can see the flapping trajectory of the trailing-edge at D = 2.1 is not fully symmetrical about the centre line of the
fluid. We can find the reason in Fig. 6 which plots the stream lines for the two different flapping mode. For D =
2.1, the backflow zone deviates to one side of the cylinder, which has a attraction for the foil and lead to the
unsymmetrical of the flapping motion of the foil. The backflow zone at D = 2.1 is much bigger than that at D =
3.5, we can infer that the exists of the foil may has a influence on the shape of the backflow zone.
The average drag coefficient and the amplitude of lift coefficient and the flapping frequency of the foil are
shown in Fig. 7. All the figures are divided into two parts: part I and part II corresponding to the inverted
flapping mode and forward
(a) (b)
-1.6 -1.2 -0.8 -0.4 0.0 0.0 0.4 0.8 1.2 1.6
0.8
0.4
0.0
-0.8
-0.4
0.8
0.4
0.0
-0.8
-0.4
Y-coordinateofthe
trailing-edge(L)
X-coordinate of the
trailing-edge (L)
X-coordinate of the
trailing-edge (L)
(c) (d)
5. Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
www.ijceronline.com Open Access Journal Page 38
0.8
0.4
0.0
-0.8
-0.4
-0.8 -0.4 0.0 0.4 0.8
0.8
0.4
0.0
-0.8
-0.4
-0.8 -0.4 0.0 0.4 0.8
Y-velocityofthe
trailing-edge(V)
Y-coordinate of the
trailing-edge (L)
Y-coordinate of the
trailing-edge (L)
(e) (f)
Fig. 4 The flapping patterns of the foil, the flapping trajectory and the phase plot of the of the trailing-edge of
the foil at Re = 100, origin of coordinates for flapping trajectory and phase plot is set at the leading-edge and
trailing-edge respectively, with (a), (c), (e) D = 2.1 and (b), (d), (f) D = 3.5.
Fig. 5 The backflow zone
(a)
(b)
Fig. 6 Stream lines for (a) D = 2.1 and (b) D= 3.5
Dragcoefficient(Cd)
I III II
1.4
1.3
1.2
0.8
0.4
0.0
-0.4
1 4 8 12 16 1 4 8 12 16
(a) Cylinder-foil distance ratio (D) (b) Cylinder-foil distance ratio (D)
Liftcoefficient(Cl)
I II I II
1.2
0.8
0.4
0.0
1.2
0.8
0.4
0.0
1 4 8 12 16 1 4 8 12 16
(c) Cylinder-foil distance ratio (D) (d) Cylinder-foil distance ratio (D)
6. Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
www.ijceronline.com Open Access Journal Page 39
I II I IIFrequency(f) 0.20
0.15
0.10
0.4
0.3
0.2
0.1
1 4 8 12 16 1 4 8 12 16
(e) Cylinder-foil distance ratio (D) (f) Cylinder-foil distance ratio (D)
Fig. 7 The average drag coefficient Cd, the amplitude of lift coefficient Cl, the flapping frequency of the foil and
the vortex shedding frequency of the cylinder versus the cylinder-foil distance ratio with (a), (c), (e) for the
cylinder and (b), (d), (f) for the foil.
flapping mode respectively. The range D ≤ 2.2 corresponds to the inverted flapping mode (part I), drag on the
foil is negative, drag on the cylinder is much smaller than that of the single cylinder, both of foil and cylinder
experiences a significant drag reduction. The tendency of the amplitude of lift and vortex shedding frequency
for the cylinder is similar with that of drag. The range D ≥ 2.3 corresponds to the forward flapping mode (part
II). Average drag and the amplitude of lift of the cylinder is much larger than that of the inverted flapping mode.
The cylinder still experiences a drag reduction but the amplitude of lift exceeds the single cylinder. With the
increasing of the cylinder-foil distance, all this three parameters of the cylinder approach to that of the single
cylinder, at D ≥ 8.0, they are almost equal to those of the single cylinder. Drag and lift on the foil increases
sharply when the foil's motion patterns shift too. At the range 2.3 ≤ D ≤ 4.0, there is still a obvious drag
reduction on the foil, when D ≥ 5.0, the drag reduction vanishes. The amplitude of lift coefficient of the foil
goes a opposite tendency with that of the drag coefficient. At 2.3 ≤ D ≤ 8.0, the amplitude of lift is larger than
the single foil case. The vortex shedding frequency of the cylinder decreases because of the exists of the foil,
especially when the cylinder and foil are close to each other. The downstream foil can be treat as a barrier and a
wake splitter which inhibits the flow, from Fig. 6 we can see the stream lines around the foil are distorted. This
hinders the vortex shedding and also enlarges the size of the backflow zone. This will lead to a drag reduction of
the upstream cylinder. More closer the foil to the cylinder, more significant the influence is, which conforms to
the results shown in Fig. 7.
Flapping frequency of the foil is much smaller than that of the single foil, and always equal to the vortex
shedding frequency even the distance ratio increase to D = 15.0. The flapping amplitude of the trailing-edge of
the foil shown in Fig. 8 is much larger than the single foil case in the forward flapping mode. We can infer that
the vortexes shedding by the cylinder has a strong influence on the flapping motion of the downstream foil. As
shown in Fig. 7 and 8, When D ≥ 8.0, the influence of the foil on the cylinder is almost gone, but even at D =
15.0, the cylinder still changes the motion of the foil.
1 4 8 12 16
1.8
1.2
0.6
0.0
Amplitude(L)
I II
Fig. 8 The flapping amplitude of the trailing-edge of the foil versus the cylinder-foil distance ratio.
For a more detailed analysis, the time history of Y-position of trailing-edge, drag coefficient Cd of the foil and
lift coefficient Cl of the foil at D = 2.1 and D = 3.5 are shown in Fig. 9. At time point A and C, drag on the foil
reaches its maximum, the trailing-edge Y-position is near zero, at time point B, drag reaches its minimum, the
Y-position is near its peak. But the situation for time point D, E and F is just opposite. Maximum drag
corresponds to the peak of Y-displacement of the trailing-edge and minimum drag corresponds to the zero point
of Y-displacement. Lift at point D to F shows that the peak of lift happens when the Y-displacement of trailing-
edge is near zero. But due to the unsymmetrical of the flapping motion at D = 2.1, the lift at point A and C are
not exactly zero. The different corresponding relationship in the two motion patterns shows that the cylinder
influent the downstream foil in two different ways. Fig. 10 shows the vorticity contours at time point A, B, D
and E.
We can see from the vorticity contours at time point A and B, between foil and cylinder is small that the foil is
in the area the cylinder vortexes doesn't start to shed. The foil is in between of the positive and negative
vorticity, the vorticity around the foil is opposite with the vorticity generated by the cylinder because of the
inverted flapping of the foil. The contact of two kinds of opposite vortexes will decrease the vorticity around the
7. Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
www.ijceronline.com Open Access Journal Page 40
foil and inhibits the flapping motion. The vorticity contours at time point D and E shows that the downstream
foil encounters the vortexes shedding by the cylinder. The positive vorticity at one side of the foil merges with
the upstream positive vortex, and the negative vorticity at the other side of the foil decreases, this makes the
positive vorticity around the foil is much larger than the negative vorticity, and it’s the same situation when the
foil contours the upstream negative vortex, which lead to the increase of the flapping amplitude of the foil. This
interaction also induce the foil to vibrate with the same frequency the cylinder sheds the vortex.
1.0
0.5
0.0
-1.0
-0.5
300 305 310 315 320
1.0
0.5
0.0
-1.0
-0.5
300 305 310 315 320
Trailing-edgeY-position(L)
B
CA
D
E
F
(a) Time(L / U∞ ) (b) Time(L / U∞ )
0.3
0.1
-0.1
-0.5
-0.3
300 305 310 315 320
0.8
0.6
0.4
0.0
0.2
300 305 310 315 320
Dragcoefficient(Cd)
B
CA
FD
E
(c) Time(L / U∞ ) (d) Time(L / U∞ )
0.6
0.3
0.0
-0.6
-0.3
300 305 310 315 320
0.6
0.3
0.0
-0.6
-0.3
300 305 310 315 320
Liftcoefficient(Cl)
B
C
A D F
E
(e) Time(L / U∞ ) (f) Time(L / U∞ )
Fig. 9 Time history of Y-position of trailing-edge, drag coefficient Cd of the foil and lift coefficient Cl of the foil
with (a), (c), (e) at D = 2.1 and (b), (d), (f) at D = 3.5. Point A to E corresponding to the two peaks of Cd and
minimum value of Cd within a cycle.
Fig. 10 Vorticity contours at time point (a) A, (b) B ,(c) D and (d) E
8. Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cylinder
www.ijceronline.com Open Access Journal Page 41
IV. CONCLUSION
The passive dynamics of flexible foil in the downstream of a rigid cylinder has been studied by the immersed
boundary-lattice Boltzmann method. Simulation results show that the cylinder has a strong influence on the
downstream foil. By varying the cylinder-foil distance, the foil's motion patterns can be divided into two
categories: inverted flapping mode and forward flapping mode. In the inverted flapping mode, the foil will
invert and flap towards the upstream cylinder because of the attraction of the backflow zone. In the forward
flapping mode, the amplitude of the foil is greater but the frequency is smaller compared with a single one in the
same uniform flow. Both the cylinder and foil experiences a drag reduction. Compared with a single one in the
same uniform flow, the foil's flapping frequency here is smaller but its amplitude is greater. The flexible foil can
extract energy from the vortex street and be induced to vibrate periodically. Exists of the foil also change the
dynamics of the cylinder. The foil can be treated as a barrier and a wake splitter which inhibits the vortex
shedding and enlarges the size of the backflow zone when the cylinder-foil distance is small. This also leads to a
drag reduction of the upstream cylinder. The interactions between the rigid cylinder and the flexible foil would
help us to understand the energy-saving mechanism of fish swimming behind a structure and inspire the
promising applications in marine engineering.
ACKNOWLEDGMENT
We would like to acknowledge sincerely the grant from National Natural Science Foundation of China (No.
50905040) and the Fundamental Research Funds for the Central Universities.
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