Hydroelasticity of the Kirchhoff Rod: Buckling Phenomena

Galper, A.; Miloh, T.

doi:10.1006/jfls.2000.0309

Cited by 2 publications

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References 18 publications

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“…In the latter case, if fast simulations must be done, at present it seems that there is no other choice than to add empirical forces and moments to the models, which take into account viscous effect as is proposed for example by Taylor (1952) or, more recently, by Galper & Miloh (2000) or Lopes, Païdoussis & Semler (2002). Also, another improvement to the LAEBT could be to extend the results of Newman & Wu (1973), to account for the effect of the vorticity shed by the fins upstream of the caudal fin.…”

Section: Concluding Discussionmentioning

confidence: 96%

Three-dimensional extension of Lighthill's large-amplitude elongated-body theory of fish locomotion

2011

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The goal of this paper is to derive expressions for the pressure forces and moments acting on an elongated body swimming in a quiescent fluid. The body is modelled as an inextensible and unshearable (Kirchhoff) beam, whose cross-sections are elliptic, undergoing prescribed deformations, consisting of yaw and pitch bending. The surrounding fluid is assumed to be inviscid, and irrotational everywhere, except in a thin vortical wake. The Laplace equation and the corresponding Neumann boundary conditions are first written in terms of the body coordinates of a beam treating the body as a fixed surface. They are then simplified according to the slenderness of the body and its kinematics. Because the equations are linear, the velocity potential is sought as a sum of two terms which are linked respectively to the axial movements of the beam and to its lateral movements. The lateral component of the velocity potential is decomposed further into two sub-components, in order to exhibit explicitly the role of the two-dimensional potential flow produced by the lateral motion of the cross-section, and the role played by the curvature effects of the beam on the crosssectional flow. The pressure, which is given by Bernoulli's equation, is integrated along the body surface, and the expressions for the resultant and the moment are derived analytically. Thereafter, the validity of the force and moment obtained analytically is checked by comparisons with Navier-Stokes simulations (using Reynolds-averaged Navier-Stokes equations), and relatively good agreements are observed.

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