Complex singularities near the intersection of a free surface and wall. Part 1. Vertical jets and rising bubbles

2018 ◽  
Vol 856 ◽  
pp. 323-350 ◽  
Author(s):  
Thomas G. J. Chandler ◽  
Philippe H. Trinh
Keyword(s):  
Free Surface ◽  
Scaling Law ◽  
The Body ◽  
Complex Singularities ◽  
Potential Flows ◽  
Rising Bubble ◽  
Coalescence Rate ◽  
State Potential ◽  
Gravity Driven ◽  
Vertical Jet

It is known that in steady-state potential flows, the separation of a gravity-driven free surface from a solid exhibits a number of peculiar characteristics. For example, it can be shown that the fluid must separate from the body so as to form one of three possible in-fluid angles: (i) $180^{\circ }$, (ii) $120^{\circ }$ or (iii) an angle such that the surface is locally perpendicular to the direction of gravity. These necessary separation conditions were notably remarked upon by Dagan & Tulin (J. Fluid Mech., vol. 51 (3), 1972, pp. 529–543) in the context of ship hydrodynamics, but they are of crucial importance in many potential-flow applications. It is not particularly well understood why there is such a drastic change in the local separation behaviours when the global flow is altered. The question that motivates this work is the following: outside of a formal balance-of-terms argument, why must cases (i)–(iii) occur and furthermore, what are the connections between them? In this work, we seek to explain the transitions between the three cases in terms of the singularity structure of the associated solutions once they are extended into the complex plane. A numerical scheme is presented for the analytic continuation of a vertical jet (or alternatively a rising bubble). It will be shown that the transition between the three cases can be predicted by observing the coalescence of singularities as the speed of the jet is modified. A scaling law is derived for the coalescence rate of singularities.

scholarly journals A numerical study of gravity-driven instability in strongly coupled dusty plasma. Part 1. Rayleigh–Taylor instability and buoyancy-driven instability

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Vikram S. Dharodi ◽  
Amita Das
Keyword(s):  
Dusty Plasma ◽  
Numerical Study ◽  
Fluid Model ◽  
Density Region ◽  
Strongly Coupled ◽  
Rising Bubble ◽  
Inhomogeneous Density ◽  
Gravity Driven ◽  
The Individual ◽  
Strongly Coupled Dusty Plasma

Rayleigh–Taylor (RT) and buoyancy-driven (BD) instabilities are driven by gravity in a fluid system with inhomogeneous density. The paper investigates these instabilities for a strongly coupled dusty plasma medium. This medium has been represented here in the framework of the generalized hydrodynamics (GHD) fluid model which treats it as a viscoelastic medium. The incompressible limit of the GHD model is considered here. The RT instability is explored both for gradual and sharp density gradients stratified against gravity. The BD instability is discussed by studying the evolution of a rising bubble (a localized low-density region) and a falling droplet (a localized high-density region) in the presence of gravity. Since both the rising bubble and falling droplet have symmetry in spatial distribution, we observe that a falling droplet process is equivalent to a rising bubble. We also find that both the gravity-driven instabilities get suppressed with increasing coupling strength of the medium. These observations have been illustrated analytically as well as by carrying out two-dimensional nonlinear simulations. Part 2 of this paper is planned to extend the present study of the individual evolution of a bubble and a droplet to their combined evolution in order to understand the interaction between them.

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

Influence of Free Surface Environment on the Shear Zone in Metal Cutting

1966 ◽  
Vol 181 (1) ◽  
pp. 687-705 ◽  
Author(s):  
P. L. Barlow
Keyword(s):  
Free Surface ◽  
Carbon Tetrachloride ◽  
Strain Hardening ◽  
Shear Zone ◽  
Chemical Reaction ◽  
Cutting Forces ◽  
Metal Cutting ◽  
The Body ◽  
Surface Barrier ◽  
Rehbinder Effect

It has previously been suggested that the reduction in cutting forces obtained by the presence of fluids such as CCl4 on the backface or free surface of the forming chip was due to diffusion of the fluid into the body of the chip in the region of the shear zone. In the present work, experiments with carbon tetrachloride tagged with carbon-14 and with carbon tetrachloride tagged with chlorine-36 were performed with the object of assessing the extent of diffusion of lubricants into the chip when present on the free surface only. The results obtained disprove former hypotheses and suggest that the reduced cutting force is due solely to chemical reaction at the surface of the chip. Confirmation of the sensitivity of the surface of the deforming shear zone to change in surface condition was obtained by removing metal from this region by an electropolishing technique during slow speed cutting. By varying the electropolishing conditions increased or decreased cutting forces could be obtained. It is proposed that the result both of chemical reaction at the surface and of surface removal is to reduce the strain-hardening rate of the metal undergoing shear by reducing the surface barrier to the flow of dislocations out of the metal. The association of the surface reaction of carbon tetrachloride with a change in the strain-hardening characteristics of the metal in the shear zone leads to a classification of the backface phenomenon as a Rehbinder effect and enables this effect to be more closely defined than was hitherto possible. Evidence is also presented which indicates that the backface effect does not contribute to the reduction in cutting forces during rakeface lubrication and is therefore unimportant in practice where flood lubrication of the cutting region invariably occurs.

SIMULATION OF AN AXISYMMETRIC RISING BUBBLE BY A MULTIPLE RELAXATION TIME LATTICE BOLTZMANN METHOD

2009 ◽  
Vol 23 (24) ◽  
pp. 4907-4932 ◽  
Author(s):  
ABBAS FAKHARI ◽  
MOHAMMAD HASSAN RAHIMIAN
Keyword(s):  
Free Surface ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rise Velocity ◽  
Rising Bubble ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Multiple Relaxation Time ◽  
Bubble Rising ◽  
Boltzmann Method

In this paper, the lattice Boltzmann method is employed to simulate buoyancy-driven motion of a single bubble. First, an axisymmetric bubble motion under buoyancy force in an enclosed duct is investigated for some range of Eötvös number and a wide range of Archimedes and Morton numbers. Numerical results are compared with experimental data and theoretical predictions, and satisfactory agreement is shown. It is seen that increase of Eötvös or Archimedes number increases the rate of deformation of the bubble. At a high enough Archimedes value and low Morton numbers breakup of the bubble is observed. Then, a bubble rising and finally bursting at a free surface is simulated. It is seen that at higher Archimedes numbers the rise velocity of the bubble is greater and the center of the free interface rises further. On the other hand, at high Eötvös values the bubble deforms more and becomes more stretched in the radial direction, which in turn results in lower rise velocity and, hence, lower elevations for the center of the free surface.

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

scholarly journals Bilge Keel Induced Roll Damping of an FPSO With Sponsons

2016 ◽  
Author(s):  
Babak Ommani ◽  
Nuno Fonseca ◽  
Trygve Kristiansen ◽  
Christopher Hutchison ◽  
Hanne Bakksjø
Keyword(s):  
Free Surface ◽  
Two Dimensions ◽  
The Body ◽  
Proximity Effects ◽  
Roll Damping ◽  
Damping Coefficients ◽  
Free Decay ◽  
Strip Theory ◽  
Decay Tests ◽  
Bilge Keel

The bilge keel induced roll damping of an FPSO with sponsons is investigated numerically and experimentally. The influence of the bilge keel size, on the roll damping is studied. Free decay tests of a three-dimensional ship model, for three different bilge keel sizes are used to determine roll damping coefficients. The dependency of the quadratic roll damping coefficient to the bilge keel height and the vertical location of the rotation center is studied using CFD. A Navier-Stokes solver based on the Finite Volume Method is adopted for solving the laminar flow of incompressible water around a section of the FPSO undergoing forced roll oscillations in two-dimensions. The free-surface condition is linearized by neglecting the nonlinear free-surface terms and the influence of viscous stresses in the free surface zone, while the body-boundary condition is exact. An averaged center of rotation is estimated by comparing the results of the numerical calculations and the free decay tests. The obtained two-dimensional damping coefficients are extrapolated to 3D by use of strip theory argumentations and compared with the experimental results. It is shown that this simplified approach can be used for evaluating the bilge keel induced roll damping with efficiency, considering unconventional ship shapes and free-surface proximity effects.

scholarly journals Microvilli on the External Surfaces of Gastropod Tentacles and Body-Walls

1963 ◽  
Vol s3-104 (68) ◽  
pp. 495-504
Author(s):  
NANCY J. LANE
Keyword(s):  
Free Surface ◽  
Surface Area ◽  
Body Surface ◽  
Body Wall ◽  
Free Cell ◽  
The Body ◽  
Outer Cell ◽  
Lamellar Bodies ◽  
Cell Surfaces ◽  
Histochemical Tests

In Helix aspersa the ‘cuticle’ on the free surface of the external epithelial cells of the optic tentacles has been shown to consist of a layer of microvilli. Microvilli are also present in the same species on the free cell borders of the body-wall, and in the slug Arion hortensis, on the outer cell surfaces of the external epithelium. In all three cases the microvilli are arranged in a hexagonal pattern. There are indications that branching may possibly occur. The microvilli have granular cores with cross- and longitudinal-striations and there are fibrillar connexions between their tips. On the tentacular and body surfaces of H. aspersa, the microvilli increase the surface area 15 and 12 times, respectively. On A. hortensis the increase in surface area is only 4 times. In H. aspersa, beneath the microvilli on the tips of the optic tentacles there is a layer, about 3 to 4 µ deep, composed of vertical, horizontal, and tangential fibres. Some of these fibres are attached to lamellar bodies, which may have a lipid content. Granules are also found among the fibres. Further, a greater depth of cuticle is found to be present on the tips of the inferior tentacles of H. aspersa than on their sides; this seems to indicate that a fibrillar layer, similar to that on the optic tentacles, may lie beneath the cuticle of microvilli on the tips of the inferior tentacles. A thicker cuticle is also found on the tips of the optic tentacles in other stylommatophoran pulmonates. It has not been found possible to ascertain whether the fibrillar layer is intracellular or extracellular, although the evidence points to the latter. Histochemical tests indicate that mucopolysaccharide is present on the surface of the cuticle. Electron micrographs show a granular precipitate caught on and between the fibrillae connecting the tips of the microvilli. It is suggested that the function of the microvilli is to hold the mucous secretions on the body-surface, which would give protection to the animals.

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

1978 ◽  
Vol 22 (04) ◽  
pp. 203-211
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Stream ◽  
The Body ◽  
Two Dimensional ◽  
Third Order ◽  
Submerged Body ◽  
The Mean ◽  
The Waves

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

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