This paper is related to the study of a nuclear propulsion reactor prototype for the French Navy. This prototype is built on ground and is to be dimensioned toward seismic loading. The dynamic analysis takes the coupled fluid structure analysis into account. The basic fluid models used by design engineers are inviscid incompressible or compressible. The fluid can be described in a bidimensional by slice or a three-dimensional approach. A numerical study is carried out on a generic problem for the linear FSI dynamic problem. The results of this study are presented and discussed. As a conclusion, the three-dimensional inviscid incompressible fluid appears to be the best compromise between the description of physical phenomena and the cost of modeling. The geometry of the reactor is such that large displacements of the structure in the fluid can occur. Therefore, the linearity hypothesis might not be longer valid. The case of large amplitude imposed oscillating motion of a cylinder in a confined fluid is numerically studied. A CFD code is used to investigate the fluid behavior solving the NAVIER-STOKES equations. The forces induced on the cylinder by the fluid are computed and compared to the linear solution. The limit of the linear model can then be exhibited.

The study of a interaction fluid-structure problem requires the calculation of fluid forces acting on moving boundaries. Since the first studies carried out by Stokes, a lot of work has been performed to derive various expressions of fluid forces, in particular for the case of simple geometry, such as infinite planes, spheres or circular cylinders. These bodies are subjected to elementary motions, namely harmonic motions or Dirac acceleration motions, (i.e. constant speed velocity motions). The present paper exposes a review of fluid forces exerted on accelerated rigid body in an incompressible viscous fluid initially at rest. The principal objective of this paper is to carry out a synthesis of the current literature and to develop a general analytical formulation of the fluid forces in order to deal with more general rigid body motions. The analytical formulation is exposed in the present paper for fluid forces acting on any moving body. This approach is limited to low displacements of the solid body, i.e. the non linear convective term of NS equation is not taken into account. The non-dimensional numbers is pointed out and detailed. The different solutions given in the literature are especially discussed with the influence of the viscosity compared to the irrotational model.

International audienceThis paper deals with fluid forces induced by an oscillating rigid circular cylinder in a fluid initially at rest. The amplitude of the imposed movement is assumed sufficiently small so that no wake is formed. The objective of the present paper is to review different theoretical methods to evaluate fluid forces. A wide variety of conditions is considered, from inviscid, compressible flows in infinite fluid domains, to viscous, incompressible and strongly confined ones. A special care is taken to underline the limits of the simplified models regarding real fluid effects, such as three-dimensional centrifugal instabilities. This review is related to a study whose ultimate aim is to predict dynamic fluid load during a typical shock encountered in the environment of a military ship

The present paper is related to the study of a generic linear coupled fluid/structure problem, in which an elastic beam is coupled with an inviscid fluid, with or without sloshing effects. A previous study [18] focussed on added mass effects; the present study is devoted to the coupling effects between fluid sloshing modes and structure with fluid added mass modes. The discretization of the coupled linear equations is performed with an axisymmetric fluid pressure formulated element, expanded in terms of a FOURIER series [14]. Various linear fluid model are taken into account (compressible, uncompressible, with or without sloshing) with the corresponding coupling matrix operator. The modal analysis is performed with a MATLAB program, using the non-symmetric LANCZOS algorithm [16]. The temporal analysis is performed with classical numerical techniques [10], in order to describe the dynamic response of the coupled problem subjected to a simple sine wave shock. The coupling effects are studied in various conditions represented by several non-dimensionnal numbers [12] such as the dynamic FROUDE number and the mass number, based on the geometrical and physical characteristics of the coupled problem. Comparisons are performed on the coupled problem with or without free surface modeling, with a model and temporal analysis. Coupling effects are exhibited and quantified; the numerical results obtained in the modal analysis here are in good agreement with other previous studies, carried out on different geometry [3,15]. The temporal analysis gives another point of view on the importance of the coupling effects and their importance at low dynamic FROUDE numbers. The present study gives and will be completed with a non-linear analysis (for both fluid and structure problems) of the coupled problem, using a finite element and finite volume explicit coupling procedure [19].

It is well known that a fluid may strongly influence the dynamic behaviour of a structure. Many different physical phenomena may take place, depending on the conditions: fluid flow, fluid at rest, small or high displacements of the structure. Inertial effects can take place, with lower vibration frequencies, dissipative effects also, with damping, instabilities due to the fluid flow (Fluid Induced Vibration). In this last case the structure is excited by the fluid. The paper deals with the vibration of tube bundles under a seismic excitation or an impact. In this case the structure moves under an external excitation, and the movement is influenced by the fluid. The main point in such system is that the geometry is complex, and could lead to very huge sizes for a numerical analysis. Important developments have been made in the last years to develop homogenization methods for the dynamic behaviour of tube bundles. The numerical size of the problem is reduced, and it is possible to make numerical simulations on large tube bundles with reasonable computer times. These methods consider that the fluid movement is governed by the Euler equations for the fluid. They are based on an analysis on an elementary cell, corresponding to one tube, and on an expression of the forces applied by the fluid to the structure. This force only depends on the fluid’s and tube’s acceleration. Only “inertial effects” will theoretically take place, with globally lower frequencies. A research program is under progress to take into account dissipative effects also, with a homogenization of the Navier-Stokes equations in the tube bundle. It is common, in numerical simulations, to add a damping for the structures by using a global Rayleigh damping. The paper deals with the physical meaning of this Rayleigh damping in the Euler homogenized equations. It can be demonstrated that this damping corresponds to a force applied by the fluid to the structure depending not only on the acceleration, but on the fluid and structure velocity also. This Rayleigh damping is a first step to take into account the dissipative effects for FSI in tube bundles.