Mass transport under standing waves over a sloping beach

2012 ◽  
Vol 701 ◽  
pp. 460-472 ◽  
Author(s):  
Pietro Scandura ◽  
Enrico Foti ◽  
Carla Faraci
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Mass Transport ◽  
Cell Structure ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Sea Waves ◽  
Small Reynolds Numbers ◽  
Sloping Beach

AbstractThis paper deals with the mass transport induced by sea waves propagating over a sloping beach and fully reflected from a wall. It is shown that for moderate slopes the classical recirculation cell structure holds for small Reynolds numbers only. When the Reynolds number is large, the cells interact among themselves giving rise to the merging of the negative cells and the confinement of the positive ones near the bottom. Under such circumstances the fluid moves onshore near the bottom and offshore near the free surface. The seaward decrease of the vorticity produced at the bottom appears to be the reason for the merging phenomenon.

Numerical Simulation of Vortex Shedding From a Circular Cylinder in the Presence of a Free Surface

2003 ◽  
Author(s):  
S. Nagaya ◽  
R. E. Baddour
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Free Surface ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Cfd Simulations ◽  
Induced Drag

CFD simulations of crossflows around a 2-D circular cylinder and the resulting vortex shedding from the cylinder are conducted in the present study. The capability of the CFD solver for vortex shedding simulation from a circular cylinder is validated in terms of the induced drag and lifting forces and associated Strouhal numbers computations. The validations are done for uniform horizontal fluid flows at various Reynolds numbers in the range 103 to 5×105. Crossflows around the circular cylinder beneath a free surface are also simulated in order to investigate the characteristics of the interaction between vortex shedding and a free surface at Reynolds number 5×105. The influence of the presence of the free surface on the vortex shedding due to the cylinder is discussed.

Force on a Small Particle Attached to a Plane Wall in a Hiemenz Straining Flow

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
A. B. Maynard ◽  
J. S. Marshall
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Reynolds Numbers ◽  
Lower Surface ◽  
Ring Structure ◽  
Plane Wall ◽  
Small Reynolds Numbers ◽  
Particle Force ◽  
Volume Method ◽  
Excellent Accuracy

The force acting on a spherical particle fixed to a wall and immersed in an axisymmetric straining flow is examined for small Reynolds numbers. The steady, incompressible flow field is computed using an axisymmetric finite-volume method over conditions spanning five decades in the Reynolds number. The flow is characterized by the formation of a vortex ring structure in the wedge region formed between the particle lower surface and the plane wall. A power law expression for the dimensionless particle force is obtained as a function of the Reynolds number, which is found to hold with excellent accuracy for Reynolds numbers below about 0.1.

The slow motion of a sphere in a rotating, viscous fluid

1964 ◽  
Vol 20 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Viscous Fluid ◽  
Classical Problem ◽  
Slow Motion ◽  
Reynolds Numbers ◽  
Constant Angular Velocity ◽  
Axis Of Rotation ◽  
Small Reynolds Numbers ◽  
Analytical Result

The uniform, slow motion of a sphere in a viscous fluid is examined in the case where the undisturbed fluid rotates with constant angular velocity Ω and the axis of rotation is taken to coincide with the line of motion. The various modifications of the classical problem for small Reynolds numbers are discussed. The main analytical result is a correction to Stokes's drag formula, valid for small values of the Reynolds number and Taylor number and tending to the classical Oseen correction as the last parameter tends to zero. The rotation of a free sphere relative to the fluid at infinity is also deduced.

Numerical and asymptotic methods for certain viscous free-surface flows

1992 ◽  
Vol 340 (1656) ◽  
pp. 1-45 ◽  
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Lubrication Approximation ◽  
Navier Stokes Equations ◽  
Flow Rates

This paper concerns the two-dimensional motion of a viscous liquid down a perturbed inclined plane under the influence of gravity, and the main goal is the prediction of the surface height as the fluid flows over the perturbations. The specific perturbations chosen for the present study were two humps stretching laterally across an otherwise uniform plane, with the flow being confined in the lateral direction by the walls of a channel. Theoretical predictions of the flow have been obtained by finite-element approximations to the Navier-Stokes equations and also by a variety of lubrication approximations. The predictions from the various models are compared with experimental measurements of the free-surface profiles. The principal aim of this study is the establishment and assessment of certain numerical and asymptotic models for the description of a class of free-surface flows, exemplified by the particular case of flow over a perturbed inclined plane. The laboratory experiments were made over a range of flow rates such that the Reynolds number, based on the volume flux per unit width and the kinematical viscosity of the fluid, ranged between 0.369 and 36.6. It was found that, at the smaller Reynolds numbers, a standard lubrication approximation provided a very good representation of the experimental measurements but, as the flow rate was increased, the standard model did not capture several important features of the flow. On the other hand, a lubrication approximation allowing for surface tension and inertial effects expanded the range of applicability of the basic theory by almost an order of magnitude, up to Reynolds numbers approaching 10. At larger flow rates, numerical solutions to the full equations of motion provided a description of the experimental results to within about 4% , up to a Reynolds number of 25, beyond which we were unable to obtain numerical solutions. It is not known why numerical solutions were not possible at larger flow rates, but it is possible that there is a bifurcation of the Navier-Stokes equations to a branch of unsteady motions near a Reynolds number of 25.

scholarly journals Plunging jets from orifices of different geometry

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Giorgio Moscato ◽  
Giovanni Paolo Romano
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Air Bubbles ◽  
Natural Processes ◽  
Water Jets ◽  
Starting Point ◽  
Air Water Interface ◽  
Plunging Jets ◽  
Small Reynolds Numbers ◽  
Jet Characteristics

Plunging jets are used in many industrial and civil applications, as for example in sewage and water treatment plants, in order to enhance aeration and mass transfer of volatile gases. They are also observed in natural processes as rivers self-purification, waterfalls and weirs. Many investigations dealt with the plunging jets in different configurations, but the dependence on Reynolds number and jet geometry were still not sufficiently addressed. For example, Mishra et al. (2020) studied an oblique submerged water impinging jet at different nozzle-to-plate distances and impingement angles, but only at a rather small Reynolds numbers (2600). On the other hand, different jet geometries have been extensively considered, but not for the plunging jet configuration (Mi, 2000; Hashiehbaf &Romano, 2013). In this work, plunging water jets issuing in air from orifices of different shape are considered. The aim of the work is to detail and compare jet behaviors in terms of velocity fields generated after impacting the air-water interface, as a function of Reynolds number and orifice geometry. However, air bubbles entrainment is mainly avoided in order to study the jet characteristics in a simpler case and use it as a reference starting point for future works.

Sea waves and mass transport on a sloping beach

2002 ◽  
Vol 458 (2025) ◽  
pp. 2053-2082 ◽  
Author(s):  
Paolo Blondeaux ◽  
Maurizio Brocchini ◽  
Giovanna Vittori
Keyword(s):  
Mass Transport ◽  
Sea Waves ◽  
Sloping Beach

The flow of fluids from nozzles at small Reynolds numbers

1980 ◽  
Vol 370 (1740) ◽  
pp. 61-72 ◽  
Keyword(s):  
Free Surface ◽  
Newtonian Fluid ◽  
Reynolds Numbers ◽  
Continuous Functions ◽  
Free Surface Flows ◽  
Die Swell ◽  
Alternative Version ◽  
Small Reynolds Numbers ◽  
Set Up ◽  
Well Posed

The aim of this paper is to provide a basis for determining the solution of certain free-surface flows when a fluid is extruded from a nozzle. We have chosen here to consider the problem in a form different from that usually adopted for the so-called ‘die-swell problem’, the modified version being considerably easier to set up experimentally and also being well posed mathematically. It is not clear that this latter aspect is true of the conventional die-swell problem, where the fluid is assumed to separate from the die at a sharp lip. Indeed, we have been unable to justify such an assumption; so we prefer to allow the point of attachment of the free surface with the nozzle boundary to remain one of the unknowns to be determined by the solution. An outline is given of a mathematical procedure by which, we claim, problems of this kind can be approached. By considering an alternative version of the problem on a bounded domain, it can be shown that such a problem has a solution within a class of continuous functions. Some experiments are described showing how the free surface does not necessarily separate from the nozzle at a sharp edge, and also illustrating some of the differences between the flow of a Newtonian fluid and that of a non-Newtonian fluid.

Flow separation from a stationary meniscus

2009 ◽  
Vol 633 ◽  
pp. 137-145 ◽  
Author(s):  
J. SÉBILLEAU ◽  
L. LIMAT ◽  
J. EGGERS
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Critical Reynolds Number ◽  
Cylindrical Tube ◽  
Reynolds Numbers ◽  
Flow Lines ◽  
Low Reynolds Numbers ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Meniscus Region

We consider the steady flow near a free surface at intermediate to high Reynolds numbers, both experimentally and theoretically. In our experiment, an axisymmetric capillary meniscus is suspended from a cylindrical tube, held slightly above a horizontal water surface. A flow of dyed water is released through the tube into the reservoir, and flow lines are thus recorded. At low Reynolds numbers, flow lines follow the free surface, and injected water spreads horizontally inside the container. Increasing the Reynolds number, the injected fluid penetrates to a certain distance into the bath, but ultimately follows the free surface. Above a critical Reynolds number of approximately 60, the flow separates from the free surface in the meniscus region and a jet projects vertically into the bath. We find no indication that the flow reattaches at higher Reynolds numbers, nor are our findings sensitive to surface contamination. We show theoretically and confirm experimentally that the separating streamline forms a right angle with the free surface.

A general theory for the motion of a body through a fluid at low Reynolds number

1990 ◽  
Vol 430 (1878) ◽  
pp. 89-104 ◽  
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Problem ◽  
Low Reynolds Number ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Linear Velocity ◽  
Special Cases ◽  
Small Reynolds Numbers ◽  
Low Reynolds

The motion of a body through a viscous fluid at low Reynolds number is considered. The motion is steady relative to axes moving with a linear velocity, U a , and rotating with an angular velocity, Ω a . The fluid motion depends on two (small) Reynolds numbers, R proportional to the linear velocity and T proportional to the angular velocity. The correction to the first approximation (Stokes flow) is a complicated function of R and T ; it is O ( R ) for T ½ ≪ R and O ( T ½ )for T ½ ≫ R . General formulae are derived for the force and couple acting on a body of arbitrary shape. From them all the terms O ( R + T ) or larger can be calculated once the Stokes problem has been solved completely. Some special cases are considered in detail.

Numerical Simulation of Two-Dimensional Drops Suspended in Simple Shear Flow at Nonzero Reynolds Numbers

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
S. Mortazavi ◽  
Y. Afshar ◽  
H. Abbaspour
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Normal Stress ◽  
Reynolds Numbers ◽  
Normal Stress Difference ◽  
Two Dimensions ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Areal Fraction ◽  
Small Reynolds Numbers

The motion of deformable drops suspended in a linear shear flow at nonzero Reynolds numbers is studied by numerical simulations in two dimensions. It is found that a deformable drop migrates toward the center of the channel in agreement with experimental findings at small Reynolds numbers. However, at relatively high Reynolds numbers (Re=80) and small deformation, the drop migrates to an equilibrium position off the centerline. Suspension of drops at a moderate areal fraction (φ=0.44) is studied by simulations of 36 drops. The flow is studied as a function of the Reynolds number and a shear thinning behavior is observed. The results for the normal stress difference show oscillations around a mean value at small Reynolds numbers, and it increases as the Reynolds number is raised. Simulations of drops at high areal fraction (φ=0.66) show that if the Capillary number is kept constant, the effective viscosity does not change in the range of considered Reynolds numbers (0.8–80). The normal stress difference is also a weak function of the Reynolds number. It is also found that similar to flows of granular materials, suspension of drops at finite Reynolds numbers shows the same trend for the density and fluctuation energy distribution across the channel.

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