scholarly journals When a small thin two-dimensional body enters a viscous wall layer

2019 ◽  
Vol 31 (6) ◽  
pp. 1002-1028 ◽  
Author(s):  
R. A. PALMER ◽  
F. T. SMITH
Keyword(s):  
Fluid Layer ◽  
Body Movement ◽  
Wall Layer ◽  
Outer Edge ◽  
The Body ◽  
Thin Body ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Viscous Forces

If a body enters a viscous-inviscid fluid layer near a wall, then significant effects can be felt from the presence of incident vorticity, viscous forces and nonlinear forces. The focus here is on the response in the outer edge of such a wall layer. Nonlinear two-dimensional unsteady behaviour is examined through modelling, computation and analysis applied for a thin body travelling streamwise upstream or downstream or staying still relative to the wall. The wall layer with its balance between inviscid and viscous effects interacts freely with the body movement, causing relatively high magnitudes of pressure on top of the body and nonlinear responses in the gap between the body and the wall. The study finds explicit solutions for the motion of the body, separation of the flow arising near the wall and possible instabilities occurring over the length scale of any short body.

scholarly journals Hydromechanics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid

1971 ◽  
Vol 46 (2) ◽  
pp. 337-355 ◽  
Author(s):  
T. Yao-Tsu Wu
Keyword(s):  
Small Time ◽  
The Body ◽  
Optimum Shape ◽  
Large Reynolds Number ◽  
Inviscid Fluid ◽  
Flexible Plate ◽  
Two Dimensional ◽  
Fixed Power ◽  
Almost All ◽  
Maximum Thrust

The most effective movements of swimming aquatic animals of almost all sizes appear to have the form of a transverse wave progressing along the body from head to tail. The main features of this undulatory mode of propulsion are discussed for the case of large Reynolds number, based on the principle of energy conservation. The general problem of a two-dimensional flexible plate, swimming at arbitrary, unsteady forward speeds, is solved by applying the linearized in viscid flow theory. The large-time asymptotic behaviour of an initial-value harmonic motion shows the decay of the transient terms. For a flexible plate starting with a constant acceleration from at rest, the small-time solution is evaluated and the initial optimum shape is determined for the maximum thrust under conditions of fixed power and negligible body recoil.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

Shape Effects on Viscous Damping and Motion of Heaving Cylinders1

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Ronald W. Yeung ◽  
Yichen Jiang
Keyword(s):  
Fluid Motion ◽  
Vortex Method ◽  
The Body ◽  
Floating Body ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Fluid Viscosity ◽  
Viscous Damping ◽  
Viscous Effects ◽  
Shape Effects

Fluid viscosity is known to influence hydrodynamic forces on a floating body in motion, particularly when the motion amplitude is large and the body is of bluff shape. While traditionally these hydrodynamic force or force coefficients have been predicted by inviscid-fluid theory, much recent advances had taken place in the inclusion of viscous effects. Sophisticated Reynolds-Averaged Navier–Stokes (RANS) software are increasingly popular. However, they are often too elaborate for a systematic study of various parameters, geometry or frequency, where many runs with extensive data grid generation are needed. The Free-Surface Random-Vortex Method (FSRVM) developed at UC Berkeley in the early 2000 offers a middle-ground alternative, by which the viscous-fluid motion can be modeled by allowing vorticity generation be either turned on or turned off. The heavily validated FSRVM methodology is applied in this paper to examine how the draft-to-beam ratio and the shaping details of two-dimensional cylinders can alter the added inertia and viscous damping properties. A collection of four shapes is studied, varying from rectangles with sharp bilge corners to a reversed-curvature wedge shape. For these shapes, basic hydrodynamic properties are examined, with the effects of viscosity considered. With the use of these hydrodynamic coefficients, the motion response of the cylinders in waves is also investigated. The sources of viscous damping are clarified.

scholarly journals I. The flow of air and of an inviscid fluid around an elliptic cylinder and an aerofoil of infinite span, especially in the region of the forward stagnation point

1928 ◽  
Vol 227 (647-658) ◽  
pp. 1-19 ◽  
Keyword(s):  
Wind Tunnel ◽  
Flow Pattern ◽  
Stagnation Point ◽  
Elliptic Cylinder ◽  
Inviscid Flow ◽  
The Body ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Relationship

(1) A study of some of the characteristics of the two-dimensional flow around an aerofoil mounted in a wind tunnel has been made by L. W. Bryant and D. H. Williams. This work included measurements of velocity in the neighbourhood of the aerofoil, and showed that under certain conditions the theoretical law of Kutta and Joukowski can be applied in practice to an aerofoil. The flow pattern measured in the wind tunnel was also compared with that for an inviscid flow having an equal circulation. The purpose of the present paper is to examine, in detail, the relationship between the inviscid and the wind-tunnel flows at the nose of an elliptic cylinder and also of an aerofoil of infinite span. Throughout the paper the term circulation is used in the usual hydrodynamic sense, it being understood that for a wind-tunnel flow the contour is not taken too close to the boundary of the body. Attention has been focussed on the forward stagnation point, because it is a well-defined point on the surface where the pressure is a maximum.

The Influence of Viscous Effects on the Motion of a Body Floating in Waves

1993 ◽  
Vol 115 (1) ◽  
pp. 40-45 ◽  
Author(s):  
M. J. Downie ◽  
J. M. R. Graham ◽  
X. Zheng
Keyword(s):  
Three Dimensional ◽  
Vortex Method ◽  
Inviscid Flow ◽  
The Body ◽  
Viscous Effects ◽  
Local Flow ◽  
Discrete Vortex ◽  
Outer Flow ◽  
Viscous Forces ◽  
Singularity Distribution

This paper describes a method for calculating the forces experienced by a body floating in waves, including those due to vortex shedding from its surface. The method uses a purely theoretical approach, incorporating viscous forces, for calculating the motions of the body in the frequency domain. It involves the matching of an outer inviscid flow with the local flow in the regions of flow separation on the body, which must be well defined. The outer flow is computed by a three-dimensional singularity distribution technique and the inner flow by the discrete vortex method. The technique has been applied to the prediction of the motion response of barges floating in waves. The results compare favorably with experimental data.

scholarly journals Body-rock or lift-off in flow

2013 ◽  
Vol 735 ◽  
pp. 91-119 ◽  
Author(s):  
Frank T. Smith ◽  
Phillip L. Wilson
Keyword(s):  
Fluid Flow ◽  
Large Scale ◽  
Initial Conditions ◽  
Unsteady Motion ◽  
The Body ◽  
Thin Body ◽  
Relevant Parameter ◽  
Inviscid Fluid ◽  
Gravity Effects ◽  
Lift Off

AbstractConditions are investigated under which a body lying at rest or rocking on a solid horizontal surface can be removed from the surface by hydrodynamic forces or instead continues rocking. The investigation is motivated by recent observations on Martian dust movement as well as other small- and large-scale applications. The nonlinear theory of fluid–body interaction here has unsteady motion of an inviscid fluid interacting with a moving thin body. Various shapes of body are addressed together with a range of initial conditions. The relevant parameter space is found to be subtle as evolution and shape play substantial roles coupled with scaled mass and gravity effects. Lift-off of the body from the surface generally cannot occur without fluid flow but it can occur either immediately or within a finite time once the fluid flow starts up: parameters for this are found and comparisons are made with Martian observations.

The slumping of gravity currents

1980 ◽  
Vol 99 (4) ◽  
pp. 785-799 ◽  
Author(s):  
Herbert E. Huppert ◽  
John E. Simpson
Keyword(s):  
Buoyancy Force ◽  
Gravity Current ◽  
Inertial Force ◽  
Gravity Currents ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Homogeneous Fluid ◽  
Viscous Forces ◽  
Pass Through ◽  
Surrounding Fluid

Experimental results for the release of a fixed volume of one homogeneous fluid into another of slightly different density are presented. From these results and those obtained by previous experiments, it is argued that the resulting gravity current can pass through three states. There is first a slumping phase, during which the current is retarded by the counterflow in the fluid into which it is issuing. The current remains in this slumping phase until the depth ratio of current to intruded fluid is reduced to less than about 0.075. This may be followed by a (previously investigated) purely inertial phase, wherein the buoyancy force of the intruding fluid is balanced by the inertial force. Motion in the surrounding fluid plays a negligible role in this phase. There then follows a viscous phase, wherein the buoyancy force is balanced by viscous forces. It is argued and confirmed by experiment that the inertial phase is absent if viscous effects become important before the slumping phase has been completed. Relationships between spreading distance and time for each phase are obtained for all three phases for both two-dimensional and axisymmetric geometries. Some consequences of the retardation of the gravity current during the slumping phase are discussed.

Self-propelled anguilliform swimming: simultaneous solution of the two-dimensional navier-stokes equations and Newton's laws of motion

1998 ◽  
Vol 201 (23) ◽  
pp. 3143-3166 ◽  
Author(s):  
J. Carling ◽  
T. L. Williams ◽  
G. Bowtell
Keyword(s):  
Swimming Speed ◽  
Stokes Equations ◽  
Finite Difference Methods ◽  
Lateral Force ◽  
Travelling Wave ◽  
The Body ◽  
Two Dimensional ◽  
Centre Of Mass ◽  
Surrounding Water ◽  
Viscous Forces

Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; it follows a path determined by the forces acting upon it,as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature's body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creature's body and in the growth and dissolution of the vortex structures has been illustrated.

Dynamics and Stability of a Flexible Cylinder in a Narrow Coaxial Cylindrical Duct Subjected to Annular Flow

1990 ◽  
Vol 57 (1) ◽  
pp. 232-240 ◽  
Author(s):  
M. P. Paidoussis ◽  
D. Mateescu ◽  
W.-G. Sim
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Flexible Cylinder ◽  
Viscous Forces ◽  
Annular Gap ◽  
Narrow Annuli ◽  
Cylindrical Duct

This paper considers analytically the dynamics of a flexible cylinder in a narrow coaxial cylindrical duct, subjected to annular flow. In the present analysis, in contrast to existing theory, the viscous forces are not derived by an adaptation of Taylor’s unconfined-flow relationships, but by a systematic, albeit approximate, solution of the Navier-Stokes equations, which accounts for the unsteady viscous effects much more fully than heretofore; it is found that, for very narrow annuli, the contribution of these unsteady viscous forces to the overall unsteady forces on the cylinder can be much larger than that of the steady skin friction and pressure-drop effects alone. The present analysis also differs from existing theory in that the in-viscid forces are not derived via the slender-body approximation, and hence the analysis is also applicable to bodies of relatively small length-to-radius ratio. The dynamics and stability of typical systems with fixed ends is investigated, concentrating mainly on viscous effects and comparing the results with those of previous work. It is found that, as the annular gap becomes narrower, the system loses stability by divergence at smaller flow velocities, provided the gap size is such that inviscid fluid effects are dominant. For very narrow annuli, however, where viscous forces predominate, this trend is reversed, and further narrowing of the annular gap has a stabilizing effect on the system; furthermore, in some cases the system loses stability by flutter rather than divergence.

A 2.5D TRACTION BOUNDARY ELEMENT METHOD FORMULATION APPLIED TO THE STUDY OF WAVE PROPAGATION IN A FLUID LAYER HOSTING A THIN RIGID BODY

2008 ◽  
Vol 16 (02) ◽  
pp. 177-198 ◽  
Author(s):  
J. ANTÓNIO ◽  
A. TADEU ◽  
P. AMADO MENDES
Keyword(s):  
Wave Propagation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Fluid Layer ◽  
Thin Body ◽  
Two Dimensional ◽  
Line Load ◽  
Fluid Medium ◽  
Element Method

This paper models three-dimensional wave propagation around two-dimensional rigid acoustic screens, with minimal thickness (approaching zero), and placed in a fluid layer. Rigid or free boundaries are prescribed for the flat fluid surfaces. The problem is computed using the Traction Boundary Element Method (TBEM), which is appropriate for modeling thin-body inclusions, overcoming the difficulty posed by the conventional direct Boundary Element Method (BEM). The problem is solved as a summation of two-dimensional problems for different wave numbers along the direction for which the geometry does not vary. The source in each problem is a spatially sinusoidal harmonic line load. The influence of the horizontal boundaries of the fluid medium on the final wave field is computed analytically using appropriate 2.5D Green's functions for each model developed. Thus, only the boundary of the rigid acoustic screen needs to be discretized by boundary elements. The computations are performed in the frequency domain and are subsequently inverse Fourier transformed to obtain time domain results. Complex frequencies are used to avoid aliasing phenomena in the time domain results.

Sign in / Sign up

Export Citation Format

Share Document