Jean-François Sigrist

Fluid-Structure Interaction Effects Modeling for the Modal Analysis of a Nuclear Pressure Vessel

The present paper deals with the modal analysis of a nuclear reactor with fluid-structure interaction effects. The proposed study aims at describing various fluid-structure interaction effects using several numerical approaches. The modeling lies on a classical finite element discretization of the coupled fluid-structure equation, enabling the description of added mass and added stiffness effects. A specific procedure is developed in order to model the presence of internal structures within the nuclear reactor, based on periodical homogenization techniques. The numerical model of the nuclear pressure vessel is developed in a finite element code in which the homogenization method is implemented. The proposed methodology enables a convenient analysis from the engineering point of view and gives an example of the fluid-structure interaction effects, which are expected on an industrial structure. The modal analysis of the nuclear pressure vessel is then performed and highlights of the relative importance of FSI effects for the industrial case are evaluated: the analysis shows that added mass effects and confinement effects are of paramount importance in comparison to added stiffness effects.

Hydroelastic Responses of a Flexible Hydrofoil in Turbulent, Cavitating Flow

The objective of this work is to develop and validate a robust method to simulate the hydroelastic responses of flexible hydrofoil in turbulent, cavitating flow. A two degrees-of-freedom (2-DOF) model is used to simulate the plunging and pitching motion at the foil tip due to bending and twisting deformation of a 3-D cantilevered hydrofoil. The 2-DOF model is loosely coupled with the commercial computational fluid dynamics (CFD) solver STAR-CCM+ to efficiently simulate the fluid-structure interaction (FSI) responses of a cantilevered, rectangular hydrofoil. The numerical predictions are compared with experimental measurements for cases with and without cavitation. The experimental studies were conducted in the cavitation tunnel at the French Naval Academy (IRENav), France. Only quasi-steady cases with Reynolds number (Re) of 750,000 are shown in this paper. In general, the numerical results agree well with the experimental measurements and observations. The results show that elastic deformation of the POM polyacetate (flexible) hydrofoil lead to increases in the angle of attack, which resulted in higher lift and drag coefficients, lower lift to drag ratio, and longer cavities compared to the stainless steel (rigid) hydrofoil. Whereas only stable cavitation cases are considered in this paper, significant interaction effects were observed during experiments for cases with unstable cavitation due to interations between the foil natural frequencies and the cavity shedding frequencies. Transient analysis of the FSI responses of 3-D elastic hydrofoils in turbulent, cavitating flow is currently under work.Copyright

Numerical Simulation of Vortex Shedding Past a Circular Cylinder in a Cross-Flow at Low Reynolds Number With Finite Volume-Technique: Part 1 — Forced Oscillations

This paper is the sequel of the work exposed in a companion publication dealing with forced oscillations of a circular cylinder in a cross-flow. In the present study, oscillations of the cylinder are now directly induced by the vortex shedding process in the wake and therefore, the former model used for forced oscillations has been modified to take into account the effects of the flow in order to predict the displacement of the cylinder. The time integration of the cylinder motion is performed with an explicit staggered algorithm whose numerical damping is low. In the first part of the paper, the performances of the coupling procedure are evaluated in the case of a cylinder oscillating in a confined configuration for a viscous flow. Amplitude and frequency responses of the cylinder in a cross-flow are then investigated for different reduced velocities U* ranging from 3 to about 15. The results show a very good agreement at Re = 100 and the vortex shedding modes have also been related to the frequency response observed. Finally, some perspectives for further simulations in the turbulent regime (at Re = 1000) with structural damping are presented.Copyright

Investigation of Numerical Methods for Modal Analysis of a Tube Bundle With Fluid-Structure Interaction

Seismic analysis of tube bundle is of paramount importance in the safety assessment of nuclear installations. These analyses require in particular the calculation of frequency, mode shape and effective mass of the system eigenmodes. As fluid-structure interaction effects can significantly affect dynamic behaviour of immersed structures, the numerical modeling of the tube bundle has to take into account FSI. A complete modeling of heat exchangers (including pressure vessel, tubes and fluid) is not accessible to the engineer for industrial design studies. In the past decades, homogenization methods have been studies and developed in order to model tubes and fluid through an equivalent continuous media, thus avoiding the tedious task to mesh all structure and fluid sub-domains within the tube bundle. Few of these methods have nonetheless been implemented in industrial finite element codes. In previous papers (Sigrist & Broc, Pressure Vessel and Piping, Vancouver, July 2006), a homogenization method has been developed and applied to an industrial case for the modal analysis of a nuclear rector with internal structures and coupling effects modeling. The present paper aims at investigating the application of the proposed method for the dynamic analysis of tube bundle. The homogenization method is compared with direct and indirect fluid-structure coupled methods for the calculation of eigenmode frequencies, shapes and modal masses.Copyright

Benchmark of Numerical Codes for Coupled CSD/CFD Computations on an Elementary Vortex Induced Vibration Problem

Numerical simulation of vortex-induced-vibrations (VIV) of an elastically supported rigid circular cylinder in a fluid cross-flow has been thoroughly studied over the past years, both from the experimental and numerical points of view, because of its theoretical and practical interest in the understanding of flow-induced vibrations problems. In this context, the present paper aims at exposing a numerical study based on a coupled fluid-structure simulation, compared with previously published studies [34], [36]. The computational procedure relies on a partitioned method ensuring the coupling between fluid and structure solvers. The fluid solver involves a moving mesh formulation for simulation of the interface motion. Energy exchanges between both systems are ensured through convenient coupling schemes. The present study is devoted to a low Reynolds number configuration ( Re = 100). Cylinder motion magnitude, hydrodynamic forces, oscillation frequency and fluid vortex shedding modes are investigated with the intention to observe the “lock-in” phenomenon. These numerical simulations are proposed for code validation purposes prior to industrial applications to tube bundle configurations [4].Copyright

Fluid Structure Interaction Analysis on a Transient Pitching Hydrofoil

In this paper, the structural behavior of a deformable hydrofoil in forced pitching motion is analyzed through an experimental approach. The experimental study is based on the measurement in a hydrodynamic tunnel of the foil displacement obtained with a video camera. Tip section displacement is compared to the hydrodynamic loading obtained on a rigid hydrofoil using wall pressure measurement. The structural response appears to be strongly linked to hydrodynamic phenomena such as laminar to turbulent transition and leading edge vortex shedding. The influence of pitching velocity is discussed. Finally, the paper presents displacement measurements in cavitating flows.Copyright

Seismic Analysis of a Nuclear Reactor With Fluid Structure Interaction

In the framework of the studies on the seismic behaviour of the PWR reactor cores, models have been built to describe the dynamic behaviour of one fuel assembly, one assembly row or of the whole core. Behaviour models currently restrain the study to the central row of the core. These “One Row Models” (2D vertical models) use beam models for the assemblies and do not consider interactions between the assemblies by the fluid. Recent models consider the whole core (2D horizontal models), with the objective to describe the interactions between the different rows by the fluid. This paper presents a new step to build a complete 3D whole core model, with calculations of vertical fluid flow that can take place in a 2D “one row model”. These vertical flows leads to interactions between the assemblies, even if only one row is considered.Copyright

Tackling FSI Simulation for FIV Problems in Tube Bundle Systems With POD Approach

Tube bundles in steam boilers of nuclear power plants and nuclear on-board stokehold are known to be exposed to high levels of vibrations under flowing fluid. This coupled fluid-structure problem is still a challenge for engineers, first because of the difficulty to fully understand it, second because of the complexity for setting it up numerically. Although numerical techniques could help the understanding of such a mechanism, a complete simulation of a fluid past a whole elastically mounted tube bundle is currently out of reach for engineering purposes. To get round this problem, the use of a reduced-order model has been proposed with the introduction of the widely used Proper Orthogonal Decomposition (POD) method for a flow past a fixed structure [M. Pomarede, E. Liberge, A. Hamdouni, E.Longatte, & J.F. Sigrist - Simulation of a fluid flow using a reduced-order modelling by POD approach applied to academic cases; PVP2010, July 18–22, Seattle]. Interesting results have been obtained for the reconstruction of the flow. Here a first step is to propose to consider the case of a flow past a fixed tube bundle configuration in order to check the good reconstruction of the flow. Then, an original approach proposed by Liberge (E. Liberge; POD-Galerking Reduction Models for Fluid-Structure Interaction Problems, PhD Thesis, Universite de La Rochelle, 2008) is applied to take into account the fluid-structure interaction characteristic; the so-called “multiphase” approach. This technique allows applying the POD method to a configuration of a flow past an elastically mounted structure. First results on a single circular cylinder and on a tube bundle configuration are encouraging and let us hope that parametric studies or prediction calculations could be set up with such an approach in a future work.© 2011 ASME

Simulation of Fluid Flow Using Reduced-Order Modeling by POD Approach Applied to a Fixed Tube Bundle System

Tube bundles in steam boilers of nuclear power plants and nuclear on-board stokehold are known to be exposed to high levels of vibrations. This coupled fluid-structure problem is very complex to numerically set up, because of its three-dimensional characteristics and because of the large number of degrees of freedom involved. A complete numerical resolution of such a problem is currently not viable, all the more so as a precise understanding of this system behaviour needs a large amount of data, obtained by very expensive calculations. We propose here to apply the now classical reduced order method called Proper Orthogonal Decomposition to a case of 2D flow around a tube bundle. Such a case is simpler than a complete steam generator tube bundle; however, it allows observing the POD projection behaviour in order to project its application on a more realistic case. The choice of POD leads to reduced calculation times and could eventually allow parametrical investigations thanks to a low data quantity. But, it implies several challenges inherent to the fluid-structure characteristic of the problem. Previous works on the dynamic analysis of steam generator tube bundles already provided interesting results in the case of quiescent fluid [J.F. Sigrist, D. Broc; Dynamic Analysis of a Steam Generator Tube Bundle with Fluid-Structure Interaction; Pressure Vessel and Piping, July 27–31, 2008, Chicago]. Within the framework of the present study, the implementation of POD in academic cases (one-dimensional equations, 2D-single tube configuration) is presented. Then, firsts POD modes for a 2D tube bundle configuration is considered; the corresponding reduced model obtained thanks to a Galerkin projection on POD modes is finally presented. The fixed case is first studied; future work will concern the fluid-structure interaction problem. Present study recalls the efficiency of the reduced model to reproduce similar problems from a unique data set for various configurations as well as the efficiency of the reduction for simple cases. Results on the velocity flow-field obtained thanks to the reduced-order model computation are encouraging for future works of fluid-structure interaction and 3D cases.© 2010 ASME

Overview of DCNS Methodology on Fluid-Structure Interaction Modelling in Nuclear Pressure Vessels

The design of nuclear pressure vessel requires the description of various dynamic effects, among which fluid-structure interaction. The present paper gives on overview of DCNS RD importance of FSI in the dynamic behaviour of a nuclear reactor are underlined by a fully coupled analysis. 2) The dynamic analysis of a steam generator with FSI is made possible by the implementation of an homogenisation technique within the CASTEM code [J.F. Sigrist, D. Broc, Dynamic Analysis of a Tube Bundle with Fluid-Structure Interaction Modelling Using a Homogenisation Method, Computer Methods in Applied Mechanics and Engineering, 197 (9–12), 1080–1099, 2008] allowing the description of the interactions between the confined fluid and inner structures and tube bundle in a straightforward manner.Copyright