Centrifugal instability of an oscillatory flow over periodic ripples

1990 ◽  
Vol 217 ◽  
pp. 1-32 ◽  
Author(s):  
Tetsu Hara ◽  
Chiang C. Mei
Keyword(s):  
Oscillatory Flow ◽  
Sandy Beach ◽  
Three Dimensional ◽  
Small Region ◽  
Oscillating Flow ◽  
Two Dimensional ◽  
Steady Streaming ◽  
Centrifugal Instability ◽  
Two Dimensional Flow ◽  
Finite Slope

An oscillating flow over a sandy beach can initiate and enhance the formation of bed ripples, with crests perpendicular to the direction of the ambient oscillation. Under certain circumstances, bridges may develop to span adjacent ripple crests, resulting in a brick pattern. It has been suggested that the onset of this transition is due to a three-dimensional centrifugal instability of an otherwise two-dimensional flow over periodic long-crested ripples. Here we analyse theoretically such an instability by assuming that the ripples are rigid and smooth. Two complementary cases are studied. We first consider a weak ambient oscillation over ripples of finite slope in Case (i). The three-dimensional disturbance is found to be localized in a small region either along the crests or along the troughs. In Case (ii) we analyse finite oscillations over ripples of mild slope. The region influenced by the instability is now comparable with a ripple wavelength and the unstable disturbance along adjacent ripples may interact with each other. Four types of harmonic and subharmonic instabilities are found. The associated steady streaming close to the ripple surface shows various tendencies of possible sand accumulations, some of which appear to be qualitatively relevant to the initiation of brick-patterned ripples.

Three-dimensional oscillatory flow over steep ripples

2000 ◽  
Vol 412 ◽  
pp. 355-378 ◽  
Author(s):  
P. SCANDURA ◽  
G. VITTORI ◽  
P. BLONDEAUX
Keyword(s):  
Oscillatory Flow ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Boundary Layer Separation ◽  
Vortex Structures ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Dimensional Flow ◽  
Continuity Equations ◽  
Two Dimensional Flow

The process which leads to the appearance of three-dimensional vortex structures in the oscillatory flow over two-dimensional ripples is investigated by means of direct numerical simulations of Navier–Stokes and continuity equations. The results by Hara & Mei (1990a), who considered ripples of small amplitude or weak fluid oscillations, are extended by considering ripples of larger amplitude and stronger flows respectively. Nonlinear effects, which were ignored in the analysis carried out by Hara & Mei (1990a), are found either to have a destabilizing effect or to delay the appearance of three-dimensional flow patterns, depending on the values of the parameters. An attempt to simulate the flow over actual ripples is made for moderate values of the Reynolds number. In this case the instability of the basic two-dimensional flow with respect to transverse perturbations makes the free shear layer generated by boundary layer separation become wavy as it leaves the ripple crest. Then the amplitude of the waviness increases and eventually complex three-dimensional vortex structures appear which are ejected in the irrotational region. Sometimes the formation of mushroom vortices is observed.

Three-dimensional streaming flow in confined geometries

2015 ◽  
Vol 777 ◽  
pp. 408-429 ◽  
Author(s):  
Bhargav Rallabandi ◽  
Alvaro Marin ◽  
Massimiliano Rossi ◽  
Christian J. Kähler ◽  
Sascha Hilgenfeldt
Keyword(s):  
Time Scales ◽  
Vortex Motion ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Hamiltonian Description ◽  
Steady Streaming ◽  
Dimensional Flow ◽  
Time Flow ◽  
Two Dimensional Flow ◽  
Streaming Flows

Steady streaming vortex flow from microbubbles has been developed into a versatile tool for microfluidic sample manipulation. For ease of manufacture and quantitative control, set-ups have focused on approximately two-dimensional flow geometries based on semi-cylindrical bubbles. The present work demonstrates how the necessary flow confinement perpendicular to the cylinder axis gives rise to non-trivial three-dimensional flow components. This is an important effect in applications such as sorting and micromixing. Using asymptotic theory and numerical integration of fluid trajectories, it is shown that the two-dimensional flow dynamics is modified in two ways: (i) the vortex motion is punctuated by bursts of strong axial displacement near the bubble, on time scales smaller than the vortex period; and (ii) the vortex trajectories drift over time scales much longer than the vortex period, forcing fluid particles onto three-dimensional paths of toroidal topology. Both effects are verified experimentally by quantitative comparison with astigmatism particle tracking velocimetry (APTV) measurements of streaming flows. It is further shown that the long-time flow patterns obey a Hamiltonian description that is applicable to general confined Stokes flows beyond microstreaming.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

The aerodynamic theory of sails. I. Two-dimensional sails

1961 ◽  
Vol 261 (1306) ◽  
pp. 402-422 ◽  
Keyword(s):  
Lift Coefficient ◽  
Linear Equations ◽  
Three Dimensional ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Two Dimensional Flow ◽  
Linearized Theory ◽  
High Degree ◽  
Additional Equation

This paper deals with the preliminaries essential for any theoretical investigation of three-dimensional sails—namely, with the two-dimensional flow of inviscid incompressible fluid past an infinitely-long flexible inelastic membrane. If the distance between the luff and the leach of the two-dimensional sail is c , and if the length of the material of the sail between luff and leach is ( c + l ), then the problem is to determine the flow when the angle of incidence α between the chord of the sail and the wind, and the ratio l / c are both prescribed; especially, we need to know the shape of, the loading on, and the tension in, the sail. The aerodynamic theory follows the lines of the conventional linearized theory of rigid aerofoils; but in the case of a sail, there is an additional equation to be satisfied which ex­presses the static equilibrium of each element of the sail. The resulting fundamental integral equation—the sail equation—is consequently quite different from those of aerofoil theory, and it is not susceptible to established methods of solution. The most striking result is the theoretical possibility of more than one shape of sail for given values of α and l / c ; but there appears to be no difficulty in choosing the shape which occurs in reality. The simplest result for these realistic shapes is that the lift coefficient of a sail exceeds that of a rigid flat plate (for which l / c = 0) by an amount approximately equal to 0.636 ( l / c ) ½ . It seems very doubtful whether analytical solutions of the sail equation will be found, but a method is developed in this paper which comes to the next best thing; namely, an explicit expression, as a matrix quotient, which gives numerical values to a high degree of accuracy at so many chord-wise points. The method should have wide application to other types of linear equations.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

The Effect of a Wall Boundary Layer on Local Mass Transfer From a Cylinder in Crossflow

1984 ◽  
Vol 106 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. J. Goldstein ◽  
J. Karni
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Tunnel Wall ◽  
Wall Boundary Layer ◽  
Naphthalene Sublimation Technique ◽  
Displacement Thickness ◽  
Two Dimensional Flow

A naphthalene sublimation technique is used to determine the circumferential and longitudinal variations of mass transfer from a smooth circular cylinder in a crossflow of air. The effect of the three-dimensional secondary flows near the wall-attached ends of a cylinder is discussed. For a cylinder Reynolds number of 19000, local enhancement of the mass transfer over values in the center of the tunnel are observed up to a distance of 3.5 cylinder diameters from the tunnel wall. In a narrow span extending from the tunnel wall to about 0.066 cylinder diameters above it (about 0.75 of the mainstream boundary layer displacement thickness), increases of 90 to 700 percent over the two-dimensional flow mass transfer are measured on the front portion of the cylinder. Farther from the wall, local increases of up to 38 percent over the two-dimensional values are measured. In this region, increases of mass transfer in the rear portion of the cylinder, downstream of separation, are, in general, larger and cover a greater span than the increases in the front portion of the cylinder.

Theoretical Aspects of Thrust Vector Control by Secondary Gas Injection in Rocket Nozzles

1968 ◽  
Vol 72 (686) ◽  
pp. 171-177 ◽  
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist ◽  
Chee K. Lee
Keyword(s):  
Vector Control ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Side Force ◽  
Thrust Vector Control ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Thrust Vector ◽  
Secondary Injection

This work deals with theoretical aspects of thrust vector control in rocket nozzles by the injection of secondary gas into the supersonic region of the nozzle. The work is concerned mainly with two-dimensional flow, though some aspects of three-dimensional flow in axisymmetric nozzles are considered. The subject matter is divided into three parts. In Part I, the side force produced when a physical wedge is placed into the exit of a two-dimensional nozzle is considered. In Parts 2 and 3, the physical wedge is replaced by a wedge-shaped “dead water” region produced by the separation of the boundary layer upstream of a secondary injection port. The modifications which then have to be made to the theoretical relationships, given in Part 1, are enumerated. Theoretical relationships for side force, thrust augmentation and magnification parameter for two- and three-dimensional flow are given for secondary injection normal to the main nozzle axis. In addition, the advantages to be gained by secondary injection in an upstream direction are clearly illustrated. The theoretical results are compared with experimental work and a comparison is made with the theories of other workers.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

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