Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in two dimensions

Ardakani, Hamid Alemi; Bridges, Thomas J.

doi:10.1016/j.euromechflu.2011.08.004

Cited by 11 publications

(8 citation statements)

References 50 publications

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“…A similar expanded formula can be developed for the Ω equation, with the Ω equation having only one non-zero component. When the velocity field u is restricted to be irrotational, the vessel equations agree with those in [9,10].…”

Section: Variationssupporting

confidence: 61%

“…The functions ( θ , q 1 , q 2 ) represent the orientation and translation of the body. These equations are derived in [9] and in §2 of [17]. Conservation of mass relative to the body frame is ux+vy=0,which also acts as an equation for the pressure.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Variational principles for the coupled motion have been given before, the first by Lukovsky (see [8] and references therein), for the fluid–vessel coupling, and more recently by Alemi Ardakani [9,10], which, in the latter case, includes coupling between the vessel and both interior and exterior fluid motion. However, in all these cases, the fluid motion is taken to be irrotational.…”

Section: Introductionmentioning

confidence: 99%

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A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

et al. 2019

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A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.

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Section: Variationssupporting

confidence: 61%

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

et al. 2019

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“…The configuration of the fluid in a rotating-translating vessel is shown in Figure 1. The fluid occupies the region 0 y η (x, t) with 0 x L. The two-dimensional Euler equations relative to a rotating-translating coordinate system (x, y) given by Alemi Ardakani and Bridges (2012) are…”

Section: A Variational Principle For the Interior Fluid Motionmentioning

confidence: 99%

A coupled variational principle for 2D interactions between water waves and a rigid body containing fluid

Ardakani

2017

J. Fluid Mech.

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New variational principles are given for the two-dimensional interactions between gravity-driven water waves and a rotating and translating rectangular vessel dynamically coupled to its interior potential flow with uniform vorticity. The complete set of equations of motion for the exterior water waves, the exact nonlinear hydrodynamic equations of motion for the vessel in the roll/pitch, sway/surge and heave directions, and also the full set of equations of motion for the interior fluid of the vessel, relative to the body coordinate system attached to the rotating–translating vessel, are derived from two Lagrangian functionals.

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“…Refs. [19], [20] generalized the sloshing equations in moving tanks for 2D and 3D motions for prescribed tank motions. Ref.…”

Section: Piezo Actuatorsmentioning

confidence: 99%

A port-Hamiltonian model of liquid sloshing in moving containers and application to a fluid-structure system

Cardoso-Ribeiro

Matignon

Pommier-Budinger

2017

Journal of Fluids and Structures

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Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in two dimensions

Cited by 11 publications

References 50 publications

A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

A coupled variational principle for 2D interactions between water waves and a rigid body containing fluid

A port-Hamiltonian model of liquid sloshing in moving containers and application to a fluid-structure system

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