A Homogenization Method for the Modal Analysis of a Nuclear Reactor With Fluid-Structure Interaction

The present paper exposes a homogenization method developed in order to perform the modal analysis of a nuclear reactor with fluid-structure interaction effects. The homogenization approach is used in order to take into account the presence of internal structures within the pressure vessel. A homogenization method is proposed in order to perform a numerical calculation of the frequencies and modal masses for the eigenmodes of the coupled fluid-structure problem. The technique allows the use of a simplified fluid-structure model that takes into account the presence of internal structures: the theory bases are first recalled, leading to a new formulation of the fluid-structure coupled problem. The finite element discretization of the coupled formulation leads to the modification of the classical fluid-structure interaction operators. The consistency of the formulation is established from a theoretical point of view by evaluating the total mass of the coupled system with the fluid and structure mass operator, and the modified added mass operator. The method is tested and validated on a 2D case (two concentric cylinders with periodical rigid inclusions within the annular space) and applied on the industrial case. A complete modal analysis (calculation of frequencies and modal masses) is performed on a simplified geometry of a nuclear reactor with and without internal structures. Numerical results are then compared and discussed, and the influence of the internal structures on the fluid-structure coupled phenomenon is highlighted.

Coupling of Lattice Boltzmann and Finite Element Methods for Fluid-Structure Interaction Application

In order to analyze the Fluid-Structure Interaction (FSI) between a flow and a flexible structure, an algorithm was presented to couple the Lattice Boltzmann Method (LBM) and the Finite Element Method (FEM). The LBM was applied to the fluid dynamics while the FEM was applied to the structural dynamics. The two solution techniques were solved in a staggered manner, i.e. one solver after another. Continuity of the velocity and traction was applied at the interface boundaries between the fluid and structural domains. Furthermore, so as to make the fluid-structure interface boundary more flexible in terms of the computational modeling perspective, a technique was also developed for the LBM so that the interface boundary might not coincide with the fluid lattice mesh. Some example problems were presented to demonstrate the developed techniques.

Fluid Forces on a Circular Cylinder Moving Transversely in Cylindrical Confinement: Extension of the Fritz Model to Larger Amplitude Motions

This paper is related to the fluid forces prediction on a rapidly moving circular cylinder in cylindrical confinement. The Fritz model, which mainly assumes infinitesimal motions of the inner cylinder in an inviscid fluid, is one of the simplest model available in the scientific literature and is often used by design engineers in the nuclear industry. In this paper, simple non-linear expressions of fluid forces are derived for the case of finite amplitude motions of the inner cylinder. Assuming a potential flow, advection term and geometrical deformations can be taken into account. The problem, formulated as a boundary-perturbation problem, is solved thanks to a regular expansion. The range of validity of the approximate analytical solution thus obtained is theoretically discussed. The results are also confronted to numerical simulations, which allows to emphasize some limits and advantages of the analytical approach.

A Study on the Hydrodynamic Load in a Water Pool When Discharged Air Forms a Bubble Cloud

This paper presents a numerical and qualitative study on the expected hydrodynamic load-reducing effect of bubbly media near a volumetrically oscillating bubble. In this study, the bubble or bubble cloud is assumed to be spherically symmetric, and its motion is analyzed as a one-dimensional compressible two-phase flow in the radial direction in spherical coordinates. We adopted the CCUP (CIP-Combined Unified Procedure) method, which is a unified analysis method for both compressible and incompressible fluids proposed by Yabe et al. (1991) in order to treat interaction among gas, liquid, and two-phase media, and to avoid large numerical dissipation at density discontinuities. To verify the analysis program we developed, we analyzed free oscillations of a bubble with a unity void fraction and of a bubble cloud with an initial void fraction of 0.5, and found that the natural frequency from numerical results are well reproduced with an error of 0.9% for the bubble and 5% for the bubble cloud as compared to those obtained on a theoretical basis. Using this method, we analyzed the free oscillation of a bubble cloud in which a bubble with a unity void fraction is covered by a bubbly media layer with an initial void fraction of 0.5. Numerical results show that the amplitude of pressure oscillation inside the bubble is about halved, and that a higher mode of oscillation appears when a bubbly media layer covers the bubble. The measured results from a blowdown test we previously reported also shows a similar higher mode of oscillation. The amplitude of pressure oscillation in the water region was apparently reduced when a thick bubbly media layer covers the bubble. Thus, if the bubbly media is ejected from sparger holes prior to the ejection of a high-pressure bubble, the bubbly media might reduce the hydrodynamic load induced in a water pool made by volumetric oscillation of the bubble.

Nonlinear Finite Element Analysis of Moving Coil Loudspeaker Suspension

The surround and the spider of the loudspeaker suspension are modelled in ANSYS to carry out finite element analysis. The displacement dependent nonlinearities arising from the suspension are studied and the material and geometric effects leading to the nonlinearities are parameterised. The ANSYS models are simulated to be excited by a sinusoidal load and the results are evaluated by comparison with the results obtained by a physical model. The paper illustrates how practical models can be analysed using cost effective finite element models and also the extension of the models to experiment on various parameters, like changing the geometry for optimisation, by computer simulation.

A Qualified Method for Fluid-Structure Interaction in Piping Design

In piping design hydraulic load cases and the resulting dynamic structural loads are induced and generated by strongly time dependent pressure surges and subsequent oscillations. Therefore, with liquid filled piping, the implementation of fluid-structure interaction by coupling the fluiddynamic and the structural dynamic codes gives a substantial contribution to more realistic loading results. Considering this effect, usually a load reduction due to energy losses and the phase and frequency shift from fluid to structure and vice versa is achieved. In cases of fluid structure resonance the results are more reliable and can help to develop an optimized support concept. To realize the coupled calculation of both codes they are bundled by a special user environment, where the coupling points are specified and marked. We describe the input of fluid forces at those points and the treatment of the liquid masses inside the piping, as well as the method of back-coupling the resulting structural displacements into the fluid calculation. The method was validated against measurements of load cases in power plant piping systems and experimental results for various boundary conditions. The most realistic results were obtained by combining the coupling with the application of dynamic friction in the fluid code.

An Evaluation of Fuel Rod Fretting Wear in Spacer Grid With Conformal Shape

Turbulent flow-induced vibration in nuclear fuel may cause fretting wear of fuel rod at grid support locations. An advanced nuclear fuel for Korean PWR standard nuclear power plants (KSNPs), has been developed to get higher performance comparing to the current fuel considering the safety and economy. One of the significant features of the advanced fuel is the conformal shape in mid grid springs and dimples, which are developed to diminish the fretting wear failure. Long-term hydraulic tests have been performed to evaluate the fretting wear of the fuel rod with the conformal springs and dimples. Wear volume is a measure to predict the fretting wear performance. The shapes of a lot of scars are non-uniform such as wedge shapes, and axially non-symmetric shapes, etc., depending on the contact angle between fuel rod and springs/dimples. In addition, conformal springs and dimples make wear scars wide and thin comparing to conventional ones with convex shape. It is found that wear volumes of these kinds of non-uniform wear scars are over-predicted when the traditionally used wear depth-dependent volume calculation method is employed. In order to predict wear volume more accurately, therefore, the measuring system with high accuracy has been used and verified by the known wear volumes of standard specimens. The wear volumes of the various wear scars have been generated by the measuring system and used for predicting the fretting wear-induced failure time. Based on new evaluation method, it is considered that the fretting wear-induced fuel failure duration with this conformal grid has increased up to 8 times compared to the traditionally used wear depth-dependent volume calculation method.

Variational Analysis of Sloshing in Spherical Industrial Vessels Under Earthquake Loading

A variational formulation is developed for calculating liquid sloshing effects on the dynamic response of spherical containers under external dynamic excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the configuration of the containers, the associated spatial functions are non-orthogonal, and the problem is not separable and results in a system of coupled non-homogeneous ordinary linear differential equations, which is solved numerically. The solution can be obtained through either direct integration or modal analysis. Sloshing frequencies and masses are calculated rigorously for arbitrary liquid height, and convergence of the solution is thoroughly examined. Particular emphasis is given on the cases of half-full spheres, where explicit expressions for the coefficients of the governing equations are derived. Furthermore, the behavior of nearly-full and nearly-empty vessels is briefly discussed.

Fluid-Dynamic Loading on a Tilted Rectangular Cylinder Near a Solid Wall

We investigate the impact of different boundary conditions on the flow field developing around a tilted rectangular cylinder. We are mainly interested in analyzing the changes in force coefficients and in the vortex shedding Strouhal number due to the proximity of the cylinder to a bottom plate (placed at various distances from the cylinder) at different angles of attack. The angle of attack ranges between −30° and +30° and the cylinder elevation above the bottom wall is varied between almost zero and 200 mm. The effects of the different boundary conditions on the vortex shedding phenomenon are investigated by considering the Strouhal number of the vortex shedding as the key controlling parameter. The experimental results mimicking the unbounded conditions (relative large elevation of the cylinder above the solid wall) are in close agreement with those already found in literature. On the contrary, remarkable differences occur when the elevation of the cylinder is decreased. A large body of experimental results is related to the small elevation conditions at different attack angles, where the presence of the wall has a non-negligible effect on the behavior of the force coefficients and Strouhal number of the vortex shedding.

Effect of Shock Loading on Food Processing

In the food industry, it is hoping high value-aided product and the increase in efficiency of food processing. On the other hand, we get an experimental result that the load of the shock wave improves an extraction of food, and soften food. But, the safe and high efficiency pressure vessel for the processing is necessary to apply these technologies to the food processing field actually. Therefore, we are planning the development of the pressure vessel for food processing. The fundamental data of the shock loading to food are necessary in order to make suitable vessel. As for these data, it is variety the specifications required by the kind of food and effect to expect. We report the result that shock wave loading was done to various food.