Slenderbody theory for viscous flow via dimensional reduction and. The accurate prediction of large amplitude ship mo tions in severe seas represents still a major chal lenge to naval architects. Application of slender body theory in ship hydrodynamics at high. The application of slender body theory enables the accurate inclusion of hydrodynamic effects, screening due to boundaries, and interactions between filaments. This means that forces in 1direction cannot be obtained by slender body theory.
Discussion if the 1axis is the longitudinal axis of the slender body, then the 3d added mass coe. To estimate these forces, lighthill developed the slenderbody theory, which assumes a potential flow and an asymptotically small aspect ratio. Applications of slender body theory in ship hydrodynamics. Applications of slenderbody theory in ship hydrodynamics. The mean forces and moment are computed using the farfield formulae, and the wave drift damping matrix is obtained by aranhas formula.
The derivation, reminiscent of slender body theory for filaments, assumes that the length of the ribbon is much larger than its width, which itself is much larger than its thickness. The theory is extended to the computation of the secondorder quantities. Computation of higherorder hydrodynamic forces on ships. Text or symbols not renderable in plain ascii are indicated by. Slender body theory has enjoyed great success in aerodynamics,and in recent years there has been considerable interest in applications in naval hydrodynamics. The motion of a slender toroidal ring in stokes flow is considered first. The basic idea of slender body theory is to approximate the e ect of the obstacle on the ow by a distribu tion of singularities, whose strength must be determined by imposing the required boundary conditions. Hydrodynamic, orientational diffusivities were obtained from an ensemble average of the fiberfiber interactions.
The idea of the slenderbody theory, under these assumptions, is to think of the body as a longitudinal stack of thin sections, each having an easilycomputed added mass. We made a comparison between the forces, bending moments, and shear moments calculated by resistiveforce theory and by the more accurate slender body theory for largeamplitude. The theory is developed for hulls of arbitrary crosssection, and a greens function method is outlined for solving the inner problem for hulls of arbitary section. Based on the present study, slender body theory is shown to be a useful. The body has a characteristic length scale l, and a boundary layer. A textbook that offers a unified treatment of the applications of hydrodynamics to marine problems.
The idea of the slenderbody theory, under these assumptions, is to think of the body. The added mass forces and moments derive from accelerations that fluid particles experience when they encounter. Higher order hydrodynamic interaction between two slender. Slenderbody theory for stokes flow and flagellar hydrodynamics. A linearized theory is developed for the oscillations of a slender body which is floating on the free surface of an ideal fluid, in the presence of incident plane progressive waves.
They use slender body theory for the symmetrical wing body combination in conjunction with super sonic thinwing theory for the wing alone to obtain results for wing body %. Principal applications are to stokes flow at very low reynolds numbers and in electrostatics theory for stokes flow. Review of hydroelasticity theories for global response of. The local flow around a cylinder that is moving along or perpendicular to its axis, and rotating, provides a first step in this theory. Introduction theresistiveforce theory developed for flagellar hydrodynamics in the pioneering work of grayand hancock1955 has been extensively used in subsequent studies of flagellar pro.
These two regions are then matched together to capture the total ow. We made a comparison between the forces, bending moments, and shear moments calculated by resistiveforce theory and by the more accurate slender body theory for largeamplitude, planar wave forms computed for a flagellar model. Anyway, the evidence of comparison with experiment seems to favour michell. Slender body theory approach to nonlinear ship motions. The general theory of long slender bodies described in this paper will be used. Application of slender body theory in ship hydrodynamics.
Newman, 1986 to admit distortions of the ships hull. In order to gain intuition, the paradigm expansioncontraction of a. The slender body theory utilizing the method of inner and outer expansions is applied to evaluate the yawing force and moment on a slender ship hull at highfroude number. Ship hulls are long and slender, and this is a logical feature to exploit in simplification of the governing equations. This technique relies on slender body having two regions of behaviour. Hydrodynamic surrogate models for bioinspired micro. Hydrodynamic interactions between nearby slender filaments. Vossers, some applications of the slender body theory in ship hydrodynamics. The hydrodynamic interaction problem between moored and passing ships was studied by krishnankutty 10 l l using the slender body theory with singularity distribution technique for the computation of forces in surge and. Slender body theory for stokes flow and flagellar hydrodynamics.
We compare between leading and secondorder approximations, as well as approximate and exact separation distances. We made a comparison between the forces, bending moments, and shear moments calculated by resistiveforce theory and by the more accurate slenderbody theory for largeamplitude, planar wave forms computed for a flagellar model. Full text of application of slender body theory in ship hydrodynamics at highfroude number see other formats library technical report section naval postgraduate schocl monterey, california 93240 nps69gm77051 naval postgraduate 3c monterey, california ol application of slender body theory in ship hydrodynamics at highfroude number c. Topics discussed include bodies with nearconstant surface pressure, subsonic and supersonic aerodynamics, ship hydrodynamics, slender bodies in stokes. The singularity method for stokes flow is used to examine the flow past slender bodies possessing finite centerline curvature, in a viscous, incompressible fluid without any appreciable inertia effects. The waving motion in general propagates a wave distally down the body to generate a forward thrust tto balance out the hydrodynamic viscous. Slender body theory an overview sciencedirect topics. In this paper, we apply the slender body theory to study the effect of higher order hydrodynamic interactions between two slender bodies of revolution moving in close proximity, in an unbounded, inviscid, and incompressible fluid. In this case, however, most nontrivial hydrodynamic effects as well as the inertial force due to body mass are higher order by comparison to the hydrostatic restoring force.
Slender body theory sbt thegeneral sbtto be applied here has been summarized bywu1976, 1977 and developed in detail byjohnson 1977. Elastohydrodynamical instabilities of active filaments. The anziam journal on thin or slender bodies school of. Slenderbody theory calculations l of the effect on lift. A comparison between resistiveforce theory and slenderbody theory. However, experiments showed that the strip theory appears. Slender body theory has enjoyed great success in aerodynamics, and in recent years there has been considerable interest in applications in naval hydrodynamics.
Thesolution ofthe problem ofstokes flow resulting from the motion of a slenderbody is constructed using the singularity method. In this paper, we determine, asymptotically, the leadingorder hydrodynamic behavior of a slender ribbon in stokes flows. Newman, jn1970 applications of slenderbody theory in ship hydrodynamics, annual. In fluid dynamics and electrostatics, slenderbody theory is a methodology that can be used to take advantage of the slenderness of a body to obtain an approximation to a field surrounding it andor the net effect of the field on the body. Some applications of the slender body theory in ship. Slenderbody theory sbt is an asymptotic technique that can be used to obtain analytical. Vossers, some applications of the slender body theory. Pdf slender body theory for stokes flow past axisymmetric bodies. The theory of slow viscous flow around a slender body is generalized to the situation where the ambient fluid has a yield stress. A slenderbody theory for ship oscillations in waves. Greens theorem is used to represent the velocity potential and the firstorder slender body potential is developed from asymptotic approximation. We first study the stability of fixed and freely suspended spherefilament assemblies, calculate neutral stability curves separating stable oscillatory states from stable straight states. The applications of hydrodynamics to naval architecture and marine engineering expanded dramatically in the 1960s and 1970s.
The motion of long slender bodies in a viscous fluid part. Thus we are concerned with the motion of a fluid past a. The hydrodynamic interactions in dilute and semidilute suspensions have been studied using slender. This classic textbook, originally published in 1977, filled the need for a single volume on the applications of hydrodynamics to marine problems. Department of applied mathematics and theoretical physics. This page will automatically redirect to the new ads interface at that point. Applications of slenderbody theory in ship hydrodynamics applications of slenderbody theory in ship hydrodynamics newman, j n 19700101 00. The singularity method for stokes flow is used to examine the flow past slender bodies possessing finite centerline curvature, in a viscous. The strip theory is a slender body theory, so one should expect less accurate predictions for ships with low length to breadth ratios.
The effect of hydrodynamic interactions on the orientation. Then, according to slenderbody theory, the flow can be regarded as compounded of a the steady flow around the stretchedstraight body, which we shall ignore here and hence 2. Full text of application of slender body theory in ship. This paper investigates the accuracy of the resistiveforce theory gray and hancock method which is commonly used for hydrodynamic analysis of swimming flagella. Extension of lighthills slender body theory to moderate aspect ratios article pdf available in journal of fluids and structures 76. Dynamics and hydrodynamics of high speed craft june 29, 2010 barranquilla, colombia z cx vx z bx v jet y wlx z y z y approximation flow physics v n body, v nfluid, c pz 0. Addedmass and damping coefficients for oscillating bodies.
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