scholarly journals On the added mass in a viscous incompressible fluid

2019 ◽  
Vol 488 (5) ◽  
pp. 493-497 ◽  
Author(s):  
G. Ya. Dynnikova
Keyword(s):  
Incompressible Fluid ◽  
Constant Velocity ◽  
Viscous Incompressible Fluid ◽  
Added Mass ◽  
The Body ◽  
Potential Flows ◽  
Acceleration Vector ◽  
Added Masses ◽  
History Of ◽  
Instantaneous Distribution

It is proved that at the same instantaneous distribution of the flow velocity of a viscous incompressible fluid, the forces acting on a body moving with acceleration differ from forces acting on the body moving with constant velocity by a vector, which is equal to the added masses tensor multiplied by the acceleration vector. The tensor of the added masses coincides with the tensor calculated for potential flows with the same geometry of the body and surrounding surfaces, and does not depend either on viscosity or on the distribution of vorticity in the flow space. While the force corresponding to the motion with constant velocity depends on the history of movement.

Forces, moments, and added masses for Rankine bodies

1956 ◽  
Vol 1 (3) ◽  
pp. 319-336 ◽  
Author(s):  
L. Landweber ◽  
C. S. Yih
Keyword(s):  
Unsteady Flow ◽  
Incompressible Fluid ◽  
Rotational Motion ◽  
Added Mass ◽  
Dynamical Theory ◽  
The Body ◽  
Added Masses

The dynamical theory of the motion of a body through an inviscid and incompressible fluid has yielded three relations: a first, due to Kirchhoff, which expresses the force and moment acting on the body in terms of added masses; a second, initiated by Taylor, which expresses added masses in terms of singularities within the bòdy; and a third, initiated by Lagally, which expresses the forces and moments in terms of these singularities. The present investigation is concerned with generalizations of the Taylor and Lagally theorems to include unsteady flow and arbitrary translational and rotational motion of the body, to present new and simple derivations of these theorems, and to compare the Kirchhoff and Lagally methods for obtaining forces and moments. In contrast with previous generalizations, the Taylor theorem is derived when other boundaries are present; for the added-mass coefficients due to rotation alone, for which no relations were known, it is shown that these relations do not exist in general, although approximate ones are found for elongated bodies. The derivation of the Lagally theorem leads to new terms, compact expressions for the force and moment, and the complete expressions of the forces and moments in terms of singularities for elongated bodies.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Selected topics in the history of the two-dimensional biharmonic problem

2003 ◽  
Vol 56 (1) ◽  
pp. 33-85 ◽  
Author(s):  
VV Meleshko
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Review Article ◽  
Creeping Flow ◽  
Two Dimensional ◽  
Historical Overview ◽  
Biharmonic Problem ◽  
Isotropic Plates ◽  
History Of ◽  
Analytical Approaches

This review article gives a historical overview of some topics related to the classical 2D biharmonic problem. This problem arises in many physical studies concerning bending of clamped thin elastic isotropic plates, equilibrium of an elastic body under conditions of plane strain or plane stress, or creeping flow of a viscous incompressible fluid. The object of this paper is both to elucidate some interesting points related to the history of the problem and to give an overview of some analytical approaches to its solution. This review article contains 758 references.

Numerical Simulation of the Added Mass and Drag of a Uniform and Accelerated Motion Projectile

2014 ◽  
Vol 685 ◽  
pp. 161-164
Author(s):  
Ning Kang ◽  
Bao Tai Yao ◽  
Wei Qi Zheng ◽  
Li Zhong Hu
Keyword(s):  
Numerical Simulation ◽  
Incompressible Fluid ◽  
Drag Coefficient ◽  
Viscous Incompressible Fluid ◽  
Added Mass ◽  
Dynamic Mesh ◽  
Uniform Motion ◽  
Accelerated Motion ◽  
Mesh Method ◽  
Launch Tube

The added mass, drag and drag coefficient of a uniform and accelerated motion projectile in viscous incompressible fluid were calculated by numerical simulation and dynamic mesh method. The effect of velocity and acceleration on the added mass, drag and drag coefficient of the projectile in a launch tube was investigated. The results show that the variation rules of added mass, drag and drag coefficient are basically the same when the projectile moves at different speeds. The added mass, drag and drag coefficient become smaller and drag becomes bigger with the increase of speed. The variation rules of the added mass, drag and drag coefficient are the same as uniform motion when the projectile moves at different accelerations. The added mass and drag coefficient become smaller and drag becomes bigger with the increase of acceleration. These reveal that the motion region, velocity and acceleration have some effect on the added mass, drag and drag coefficient.

Effects of Tilt of the Gravito-Inertial Acceleration Vector on the Angular Vestibuloocular Reflex During Centrifugation

1999 ◽  
Vol 81 (5) ◽  
pp. 2175-2190 ◽  
Author(s):  
Susan Wearne ◽  
Theodore Raphan ◽  
Bernard Cohen
Keyword(s):  
Time Constant ◽  
Constant Velocity ◽  
Linear Acceleration ◽  
The Body ◽  
Vestibuloocular Reflex ◽  
Time Constants ◽  
Cynomolgus Monkeys ◽  
Inertial Acceleration ◽  
Acceleration Vector ◽  
Eye Velocity

Effects of tilt of the gravito-inertial acceleration vector on the angular vestibuloocular reflex during centrifugation. Interaction of the horizontal linear and angular vestibuloocular reflexes (lVOR and aVOR) was studied in rhesus and cynomolgus monkeys during centered rotation and off-center rotation at a constant velocity (centrifugation). During centered rotation, the eye velocity vector was aligned with the axis of rotation, which was coincident with the direction of gravity. Facing and back to motion centrifugation tilted the resultant of gravity and linear acceleration, gravito-inertial acceleration (GIA), inducing cross-coupled vertical components of eye velocity. These components were upward when facing motion and downward when back to motion and caused the axis of eye velocity to reorient from alignment with the body yaw axis toward the tilted GIA. A major finding was that horizontal time constants were asymmetric in each monkey, generally being longer when associated with downward than upward cross coupling. Because of these asymmetries, accurate estimates of the contribution of the horizontal lVOR could not be obtained by simply subtracting horizontal eye velocity profiles during facing and back to motion centrifugation. Instead, it was necessary to consider the effects of GIA tilts on velocity storage before attempting to estimate the horizontal lVOR. In each monkey, the horizontal time constant of optokinetic after-nystagmus (OKAN) was reduced as a function of increasing head tilt with respect to gravity. When variations in horizontal time constant as a function of GIA tilt were included in the aVOR model, the rising and falling phases of horizontal eye velocity during facing and back to motion centrifugation were closely predicted, and the estimated contribution of the compensatory lVOR was negligible. Beating fields of horizontal eye position were unaffected by the presence or magnitude of linear acceleration during centrifugation. These conclusions were evaluated in animals in which the low-frequency aVOR was abolished by canal plugging, isolating the contribution of the lVOR. Postoperatively, the animals had normal ocular counterrolling and horizontal eye velocity modulation during off-vertical axis rotation (OVAR), suggesting that the otoliths were intact. No measurable horizontal eye velocity was elicited by centrifugation with angular accelerations ≤40°/s2 and angular velocities ≤400°/s. We conclude that in rhesus and cynomolgus monkeys, differences between horizontal eye velocities recorded during facing and back to motion constant velocity centrifugation can be explained by orienting effects of the GIA tilt on the time constants of the horizontal aVOR and not by a superposed lVOR.

The Limiting Values of Added Masses of a Partially Submerged Cylinder of Arbitrary Shape

1988 ◽  
Vol 32 (01) ◽  
pp. 1-18
Author(s):  
G. A. Athanassoulis ◽  
P. D. Kaklis ◽  
C. G. Politis
Keyword(s):  
Arbitrary Shape ◽  
Integral Formula ◽  
Low Frequency ◽  
Added Mass ◽  
The Body ◽  
Geometrical Parameters ◽  
Body Contour ◽  
Added Masses ◽  
First Time ◽  
Limiting Values

Using Schwarz's integral formula, new series expressions are obtained for the low-and high-frequency limiting values of the added-mass tensor of partially submerged cylinders of arbitrary shape, including nonsmooth and non-symmetric ones. These series contain the Fourier coefficients of simple geometric quantities of the body contour, and their rate of convergence is controlled by geometrical parameters reflecting the smoothness of the double-body contour. Alternative expressions of a more usual form, in terms of the conformal mapping coefficients of the body contour, are also presented. The off-diagonal elements of the limiting added-mass tensors as well as the low-frequency added moment of inertia for nonsymmetric sections are apparently given for the first time. As an application, closed-form expressions for the limiting added-mass coefficients of an extended-Lewis family of ship sections are obtained. Numerical results are also presented for an extended-Lewis, a rectangular, and three ogival sections. The convergence of the frequency-dependent elements of the added-mass tensors towards their limiting values is also discussed in detail, and it is numerically illustrated for a heeled ship-like section.

Generalization of Taylor’s Added-Mass Formula for Two Bodies

1989 ◽  
Vol 33 (01) ◽  
pp. 1-9
Author(s):  
L. Landweber ◽  
A. T. Chwang
Keyword(s):  
Degrees Of Freedom ◽  
Added Mass ◽  
Simple Relation ◽  
The Body ◽  
Taylor Formula ◽  
Offshore Structure ◽  
Six Degrees Of Freedom ◽  
Moving Body ◽  
Added Masses ◽  
Two Bodies

A previous generalization of the Taylor formula, which expresses the added masses of a single body, moving with six degrees of freedom, in terms of the system of hydrodynamic singularities which generate the irrotational flow about the body, is further generalized for the case when another moving body is present. This work was stimulated by a study of the hydrodynamic interactions between an ice mass and a ground-based offshore structure. The results are applied to calculate the variation of the added masses as a rectangular cylinder approaches a circular one. A new simple relation between the added masses of a rectangle moving parallel to its longer or shorter side, and a more complete table of the added-mass coefficients for various thickness-length ratios than was previously available, is presented in the Appendix.

Locomotion of a Submerged Cosserat Beam

2009 ◽  
Author(s):  
Sigrid Leyendecker ◽  
Eva Kanso
Keyword(s):  
Incompressible Fluid ◽  
Potential Flow ◽  
Deformable Body ◽  
Mass Effect ◽  
Added Mass ◽  
The Body ◽  
Ambient Fluid ◽  
Torsional Loading ◽  
Neutrally Buoyant ◽  
Shape Deformations

We study the dynamics and locomotion of a neutrally-buoyant deformable body that can undergo finite shape deformations and is immersed in a perfect and incompressible fluid. We model the body as a constrained Cosserat beam, more precisely, a Kirchhoff beam, and we derive the equations governing its motion in potential flow where the ambient fluid is accounted for using the added mass effect. We show that the submerged beam can undergo net locomotion due to applied torsional loading on its centerline.

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