Stability of slender inverted flags and rods in uniform steady flow

2016 ◽  
Vol 809 ◽  
pp. 873-894 ◽  
Author(s):  
John E. Sader ◽  
Cecilia Huertas-Cerdeira ◽  
Morteza Gharib
Keyword(s):  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Flow Direction ◽  
Flow Speed ◽  
Uniform Flow ◽  
Biological Phenomena ◽  
Cantilever Length ◽  
The Stability ◽  
Elastic Sheets ◽  
Clamped Edge

Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an ‘inverted flag’. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.

scholarly journals Entropy production and multiple equilibria: the case of the ice-albedo feedback

2011 ◽  
Vol 2 (1) ◽  
pp. 13-23 ◽  
Author(s):  
C. Herbert ◽  
D. Paillard ◽  
B. Dubrulle
Keyword(s):  
Entropy Production ◽  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Surface Heat ◽  
Earth System ◽  
Unstable Solution ◽  
Solar Constant ◽  
The Earth ◽  
Classical Dynamical System ◽  
The Stability

Abstract. Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive feedback which gives birth to multiple equilibria for some values of the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate unstable solution. In this study, we show an analogy between a classical dynamical system approach to this problem and a Maximum Entropy Production (MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the time evolution of a variable. It enables us in particular to resolve the question of the stability of the entropy production maxima. We also compare the surface heat flux obtained with MEP and with the bulk-aerodynamic formula.

Forces on Nets With Bending Stiffness: An Experimental Study on the Effects of Flow Speed and Angle of Attack

2012 ◽  
Author(s):  
L. C. Gansel ◽  
Ø. Jensen ◽  
E. Lien ◽  
P. C. Endresen
Keyword(s):  
Flow Direction ◽  
Angle Of Attack ◽  
Flow Speed ◽  
Bending Stiffness ◽  
Torque Sensor ◽  
Drag And Lift Coefficients ◽  
Flow Speeds ◽  
Drag And Lift ◽  
The Stability ◽  
Good Agreement

This study investigates the effects of changes in flow speed and angle of attack on drag and lift forces on nets with bending stiffness. Today most fish cage nets are made from nylon, but new cage materials are proposed in order to improve the stability of cages in currents and waves, to reduce biofouling, prevent escapes, and to secure fish from predator attacks. The use of some of these materials leads to nets with bending stiffness in at least one direction. However, not much is known about the performance of such nets in currents and waves. In this study three different nets with bending stiffness were tested together with nylon nets. Net panels were subjected to different flow speeds at different angles between flow direction and net plane, and the forces on the nets were measured with a multi-axis force/torque sensor system. Based on the experiments, drag and lift coefficients were determined for the different net materials and compared to existing theory [1,2]. The results are in reasonably good agreement with the existing theory for the nets with low solidity, however, for nets with higher solidity the results are significantly lower than the drag and lift coefficients provided by Aarsnes [1] and Løland [2].

scholarly journals Entropy production and multiple equilibria: the case of the ice-albedo feedback

2010 ◽  
Vol 1 (1) ◽  
pp. 325-355 ◽  
Author(s):  
C. Herbert ◽  
D. Paillard ◽  
B. Dubrulle
Keyword(s):  
Entropy Production ◽  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Surface Heat ◽  
Earth System ◽  
Unstable Solution ◽  
Solar Constant ◽  
The Earth ◽  
Classical Dynamical System ◽  
The Stability

Abstract. Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive feedback which gives birth to multiple equilibria for some values of the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate unstable solution. In this study, we show an analogy between a classical dynamical system approach to this problem and a Maximum Entropy Production (MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the time evolution of a variable. It enables us in particular to resolve the question of the stability of the entropy production maxima. We also compare the surface heat flux obtained with MEP and with the bulk-aerodynamic formula.

Forces on Nets With Bending Stiffness—An Experimental Study on the Effects of Flow Speed and Angle of Attack

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
L. C. Gansel ◽  
Ø. Jensen ◽  
E. Lien ◽  
P. C. Endresen
Keyword(s):  
Flow Direction ◽  
Angle Of Attack ◽  
Flow Speed ◽  
Bending Stiffness ◽  
Torque Sensor ◽  
Drag And Lift Coefficients ◽  
Flow Speeds ◽  
Drag And Lift ◽  
The Stability ◽  
Good Agreement

This study investigates the effects of changes in flow speed and angle of attack on drag and lift forces on nets with bending stiffness. Today most fish cage nets are made from nylon, but new cage materials are proposed in order to improve the stability of cages in currents and waves, to reduce biofouling, prevent escapes, and to secure fish from predator attacks. The use of some of these materials leads to nets with bending stiffness in at least one direction. However, not much is known about the performance of such nets in currents and waves. In this study, three different nets with bending stiffness were tested together with nylon nets. Net panels were subjected to different flow speeds at different angles between flow direction and net plane, and the forces on the nets were measured with a multi-axis force/torque sensor system. Based on the experiments, drag, and lift coefficients were determined for the different net materials and compared to existing theory with which they are in reasonably good agreement for the nets with low solidity. However, for nets with higher solidity the results are significantly lower than the drag and lift coefficients provided other authors. Also, the change of drag coefficient with changing flow speed and angle of attack was different for a monofilament and a multifilament net with similar solidity and aperture form and size. These differences may partly be due to differences in twine structures and net construction between the monofilament and multifilament net and between nets used by other authors and in the present study.

The Dynamical Behaviour of a Flexible Cable in a Uniform Flow Field

1971 ◽  
Vol 22 (2) ◽  
pp. 183-195 ◽  
Author(s):  
R. R. Huffman ◽  
Joseph Genin
Keyword(s):  
Mathematical Model ◽  
Shock Waves ◽  
Flow Field ◽  
Flow Speed ◽  
Dynamical Behaviour ◽  
Uniform Flow ◽  
Aerodynamic Forces ◽  
Cable Length ◽  
Flow Speeds ◽  
The Stability

SummaryA non-linear mathematical model for the study of the dynamics of an extensible cable subjected to aerodynamic forces generated by a uniform flow field is formulated. Solutions are found considering large displacement caused by suddenly applied loads (i.e., gusts, shock waves, turbulence) for a range of flow speeds and cable lengths. Transition from overdamped to oscillatory motion is observed when flow speed and cable length are increased and decreased respectively. The stability of the system is discussed.

Energy Production Characteristics of a Spring-Mounted Cantilevered-Free Flexible Plate in a Uniform Flow

2012 ◽  
Author(s):  
Richard M. Howell ◽  
Anthony D. Lucey
Keyword(s):  
Energy Harvesting ◽  
Flow Direction ◽  
Leading Edge ◽  
Flow Speed ◽  
Uniform Flow ◽  
Present System ◽  
Beam Model ◽  
Flexible Plate ◽  
Mean Flow ◽  
Energy Harvesting System

We study a new fundamental system that comprises a cantilevered thin flexible plate exactly aligned with the direction of a uniform flow in which the upstream end of the flexible plate is not fixed. Instead, it is attached to a spring-damper system that allows the entire system to oscillate perpendicularly to the flow direction as a result of the mounting’s dynamic interaction with the flow-induced oscillations of the flexible plate. This models an energy-harvesting system whereby the rate of energy extraction by the damper represents power generation from the kinetic-energy flux of the mean flow transferred via fluttering motions of the flexible plate to the motion of the mounting system. The two-dimensional modelling presented is an extension of the methods in [1,2] that mixed numerical simulation with eigenvalue analysis to study a fixed cantilevered flexible plate. The present system also includes a rigid inlet surface upstream of and fixed to the spring-mounted cantilever. Ideal flow is assumed wherein the rotationality of the boundary-layers is modelled by vortex elements on the solid-fluid interface and the imposition of the Kutta condition at the plate’s trailing edge. The Euler-Bernoulli beam model is used for the structural dynamics. Results presented first show how the replacement of the fixed leading edge with an interactively oscillating mounting modify the well-known linear-stability characteristics of a fluttering plate. The overall effect is that the critical flow speed for flutter onset is reduced and this is desirable for the present energy-harvesting application. This entails some subtle but important changes to the destabilisation mechanisms. The power generating potential of the fluid-structure interaction system is then illustrated. The present model of the dynamics of the plate-support interaction has been simplified so as to demonstrate proof-of-concept; thus, a discussion of the way forward to a more complete model is presented to close the paper.

Snap-through oscillations of tandem elastic sheets in uniform flow

2021 ◽  
Vol 103 ◽  
pp. 103283
Author(s):  
Junsoo Kim ◽  
Hyeonseong Kim ◽  
Daegyoum Kim
Keyword(s):  
Uniform Flow ◽  
Elastic Sheets

Fluid Control with Hydrophobic Pillars in Paper-Based Microfluidics

2021 ◽  
Author(s):  
Jingji Liu ◽  
Boyang Zhang ◽  
Yajun Zhang ◽  
Yiqiang Fan
Keyword(s):  
Propagation Velocity ◽  
Control Method ◽  
Flow Direction ◽  
Flow Speed ◽  
Hydrophobic Barrier ◽  
Pillar Arrays ◽  
Paper Based Microfluidics ◽  
Fluid Control ◽  
Medical Analysis ◽  
Fluid Manipulation

Abstract Paper-based microfluidics has been widely used in chemical and medical analysis applications. In the conventional paper-based microfluidic approach, fluid is propagating inside the porous structure, and the flow direction of the fluid propagation is usually controlled with the pre-defined hydrophobic barrier (e.g. wax). However, the fluid propagation velocity inside the paper-based microfluidic devices largely depends on the material properties of paper and fluid, the relative control method is rarely reported. In this study, a fluid propagation velocity control method is proposed for paper-based microfluidics: hydrophobic pillar arrays with different configurations were deposited in the microchannels in paper-based microfluidics for flow speed control, result indicates the deposited hydrophobic pillar arrays can effectively slow down the fluid propagation at different levels and can be used to passively control the fluid propagation inside microchannels for paper-based microfluidics. For the demonstration of the proposed fluid control methods, a paper-based microfluidic device for nitrite test in water was also fabricated. The proposed fluid control method for paper-based microfluidics may have significant importance for applications that involve sequenced reactions and more actuate fluid manipulation.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

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