An estimate of the Kelvin impulse of a transient cavity

1994 ◽  
Vol 261 ◽  
pp. 75-93 ◽  
Author(s):  
J. P. Best ◽  
J. R. Blake
Keyword(s):  
Velocity Potential ◽  
Fluid Velocity ◽  
The Body ◽  
Jet Formation ◽  
Rigid Boundary ◽  
Bodies Of Revolution ◽  
Cavity Collapse ◽  
Submerged Sphere ◽  
Body Shapes ◽  
Collapse Phase

The Lagally theorem is used to obtain an expression for the Bjerknes force acting on a bubble in terms of the singularities of the fluid velocity potential, defined within the bubble by analytic continuation. This expression is applied to transient cavity collapse in the neighbourhood of boundaries, allowing analytical estimates to be made of the Kelvin impulse of the cavity. The known result for collapse near a horizontal rigid boundary is recovered, and the Kelvin impulse of a cavity collapsing in the neighbourhood of a submerged and partially submerged sphere is estimated. A numerical method is developed to deal with more general body shapes and in particular, bodies of revolution. Noting that the direction of the impulse at the end of the collapse phase generally indicates the direction of the liquid jet that may form, the behaviour of transient cavities in these geometries is predicted. In these examples the concept of a zone of attraction is introduced. This is a region around the body, within which the Kelvin impulse at the time of collapse, and consequent jet formation, is expected to be directed towards the body. Outside this zone the converse is true.

scholarly journals Conserved quantities for axisymmetric cavities near boundaries

1990 ◽  
Vol 41 (2) ◽  
pp. 215-222
Author(s):  
R. Paull ◽  
J.R. Blake
Keyword(s):  
Perfect Fluid ◽  
Volume Change ◽  
Global Model ◽  
Bubble Collapse ◽  
Conserved Quantities ◽  
Jet Formation ◽  
Rigid Boundary ◽  
Cavity Collapse ◽  
Conservation Principles ◽  
Axisymmetric Cavities

In axisymmetric irrotational flows of a perfect fluid under gravity there are three basic conserved quantities; axial momentum, energy and a circulation based, radial moment of momentum. This paper adapts these conservation principles to describe cavity collapse adjacent to a rigid boundary in a semi-infinite perfect fluid. They afford a global model accounting for volume change, migration and jet formation; physically the most significant features of bubble collapse close to a rigid boundary.

The hydrodynamic forces on a submerged sphere moving in a circular path

1990 ◽  
Vol 428 (1874) ◽  
pp. 215-227 ◽  
Keyword(s):  
Green Function ◽  
Body Surface ◽  
Velocity Potential ◽  
Surface Condition ◽  
Hydrodynamic Forces ◽  
Constant Angular Velocity ◽  
The Body ◽  
Circular Path ◽  
Legendre Functions ◽  
Submerged Sphere

Analytical solutions for various hydrodynamic problems are briefly reviewed. The case of a submerged sphere moving in a circular path at constant angular velocity is then analysed based on the linearized velocity potential theory. The potential is expressed by means of a Green function and a distribution of sources over the body surface, written in terms of Legendre functions. The coefficients in the series of the Legendre functions are obtained by imposing the body surface condition. Figures are provided showing the hydrodynamic forces on the sphere.

Radiation and diffraction of water waves by a submerged sphere at forward speed

1988 ◽  
Vol 417 (1853) ◽  
pp. 433-461 ◽  
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Surface Condition ◽  
Wave Resistance ◽  
The Body ◽  
Legendre Functions ◽  
Forward Speed ◽  
Submerged Sphere ◽  
Exciting Forces ◽  
Similar Equation

A submerged sphere advancing in regular deep-water waves at constant forward speed is analysed by linearized potential theory. A distribution of sources over the surface of the sphere is expanded into a series of Legendre functions, by extension of the method used by Farell ( J . Ship Res . 17, 1 (1973)) in analysing the wave resistance on a submerged spheroid. The equations governing the velocity potential are satisfied by use of the appropriate Green function and by choosing the coefficients in the series of Legendre functions such that the body surface condition is satisfied. Numerical results are obtained for the wave resistance, hydrodynamic coefficients and exciting forces on the sphere. Some theoretical aspects of a body advancing in waves are also discussed. The far-field equation of Newman ( J . Ship Res . 5, 44 (1961)) for calculation of the damping coefficients is extended, and a similar equation for the exciting forces is derived.

Note on the swimming of an elongated body in a non-uniform flow

2013 ◽  
Vol 716 ◽  
pp. 616-637 ◽  
Author(s):  
Fabien Candelier ◽  
Mathieu Porez ◽  
Frederic Boyer
Keyword(s):  
Cross Sections ◽  
Potential Flow ◽  
Velocity Potential ◽  
Fluid Velocity ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Elliptical Cross ◽  
Fish Locomotion ◽  
Pitch Bending ◽  
Body Theory

AbstractThis paper presents an extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann’s boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Kármán vortex street.

Incompressible potential flow past ‘not-so-slender’ bodies of revolution at an angle of attack

1975 ◽  
Vol 70 (4) ◽  
pp. 651-661 ◽  
Author(s):  
P. Sivakrishna Prasad ◽  
N. R. Subramanian
Keyword(s):  
Velocity Potential ◽  
Angle Of Attack ◽  
The Body ◽  
Virtual Mass ◽  
Bodies Of Revolution ◽  
Exact Theory ◽  
Pressure Distributions ◽  
Ellipsoid Of Revolution ◽  
Slender Bodies ◽  
Good Agreement

Using the method of matched asymptotic expansions, an expansion of the velocity potential for steady incompressible flow has been obtained to order ε4for slender bodies of revolution at an angle of attack by representing the potential due to the body as a superposition of potentials of sources and doublets distributed along a segment of the axis inside the body excluding an interval near each end of the body. Also, expansions of the coefficients of longitudinal virtual mass and lateral virtual mass have been found. The pressure distributions over an ellipsoid of revolution of thickness ratio ε = 0·3 at zero angle of attack and at an angle of attack of 3° obtained by the present method are compared with results obtained from the exact theory and that of Van Dyke. The virtual-mass coefficients are also compared with those obtained from the exact theory and are found to be in good agreement up to ε = 0·3.

A body without a head

2020 ◽  
Author(s):  
Ali Chavoshian ◽  
Sophia Park
Keyword(s):  
Liberation Theology ◽  
The Body ◽  
Women's Spirituality ◽  
Passive Condition ◽  
Sexual Identities ◽  
Logical Square ◽  
The Social ◽  
Feminine Sexuality ◽  
Body Shapes ◽  
Body Theory

Along with the recent development of various theories of the body, Lacan’s body theory aligns with postmodern thinkers such as Michael Foucault and Maurice Merlot-Ponti, who consider body social not biological. Lacan emphasizes the body of the Real, the passive condition of the body in terms of formation, identity, and understanding. Then, this condition of body shapes further in the condition of bodies of women and laborers under patriarchy and capitalism, respectively. Lacan’s ‘not all’ position, which comes from the logical square, allows women to question patriarchy’s system and alternatives of sexual identities. Lacan’s approach to feminine sexuality can be applied to women’s spirituality, emphasizing multiple narratives of body and sexual identities, including gender roles. In the social discernment and analysis in the liberation theology, we can employ the capitalist discourse, which provides a tool to understand how people are manipulated by late capitalist society, not knowing it. Lacan’s theory of ‘a body without a head’ reflects the current condition of the human body, which manifests lack, yet including some possibilities for transforming society.

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

1950 ◽  
Vol 1 (4) ◽  
pp. 305-318
Author(s):  
G. N. Ward
Keyword(s):  
Supersonic Flow ◽  
Velocity Potential ◽  
Operational Calculus ◽  
The Body ◽  
Body Of Revolution ◽  
Internal Flows ◽  
Flow Past ◽  
External Forces ◽  
Internal Pressures ◽  
Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

scholarly journals DESIGNING A TEMPORARY COLD PROTECTIVE GEAR CONSTRUCTED BY FOLDING NEWSPRINT PAPER CONSIDERING HEAT-RETAINING PROPERTY AND RIGIDITY

2021 ◽  
Vol 1 ◽  
pp. 1123-1132
Author(s):  
Tatsuya Oda ◽  
Shigeru Wesugi
Keyword(s):  
Natural Disaster ◽  
Cold Season ◽  
Apex Angle ◽  
The Body ◽  
Experimental Results ◽  
Protective Gear ◽  
Significant Difference ◽  
Body Shapes

AbstractDuring the cold season, the cold protective products are often short during evacuation life after a natural disaster. If evacuees can make and wear simple cold protective gears by using materials obtainable on site, it will reduce the burden on the evacuees in emergent situation. Therefore, we investigated the structure constructed by folding newsprint paper, which can improve the heat retention effect and be applied to various body shapes. Focusing on the glide reflection structure repeating a smaller chamber, the basic size was determined by experiments with reference to the accordion shape, and the experimental results indicated that the heat retention effect was significantly greater than that of a mere air layer and those of ordinary fabrics. Next, it was found that the apex angle of structure had no significant difference in the heat retention effect. Then, the dimensions of the structure were determined to maintain the air layer under the pressure of the clothes by simulation of structural analyses. Finally, we made a temporary cold protective gear that can practically cover the trunk of the body and found that the heat retention effect was significantly higher than that of unprocessed newsprint and that of accordion shape.

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