Two-phase flow head losses across tube support plates in U-bend tube steam generators are classically evaluated from single phase head losses duly modified with a correction factor to account for two-phase effects. This communication reports upon a series of experiments to feed head loss models for clogged tube support plates under two-phase flow. By using a classical approach, a single phase head loss model is used together with a two-phase flow multiplier. The experiments cover a large span of clogging levels, up to the unrealistic limit case of 95% of clogging. Singular head loss due to the tube support plate is measured under single-phase flow for clean and clogged plates. The head loss factor is hence evaluated and compared to the prediction of some available models. Then the same experiment is repeated under two-phase flow condition. By combining the previously measured single-phase factor with the two-phase flow measurements, recommendations for predicting two-phase flow multiplier with existing models are given.

Flow-induced vibrations of Steam Generator tube bundles are a major concern for the operators of nuclear power plants. In order to predict damages due to such vibrations, EDF has developed the numerical tool GeViBus, which allows one to asses risk and thereafter to optimize the SG maintenance policy.The software is based on a semi analytical model of fluid dynamic forces and dimensionless fluid force coefficients which need to be assessed by experiment. The database of dimensionless coefficients is updated in order to cover all existing tube bundle configurations.Within this framework, a new test rig was presented in a previous conference with the aim of assessing parallel triangular tube arrangement submitted to a two-phase cross-flow. This paper presents the result of the first phase of the associated experiments in terms of force coefficients and two-phase flow excitation spectra for both in-plane and out-of-plane vibration.

The unsteady flow motions and the force distribution in a normal square tube array subject to cross-flow induced vibrations are investigated by means of large-eddy simulations. The flow configuration and the operating conditions are taken from the experiments of Gosse et al. (PVP Conference, 2001). The set-up is made of 63 (9 rows and 7 columns) straight tube bundle. The tubes are arranged in a square in line pattern, and a cell of 9 flexible tubes, located in the middle of the bundle, may translate in the drag and lift directions. The LES of cross-flow induced vibrations of a cell of 9 flexible tubes in a normal square tube array is performed. A fully-coupled fluid-structure calculation is hence achieved using Code_Saturne, an open source CFD tool. Turbulence modeling is achieved using the large-eddy simulation framework based on the so-called classical Smagorinsky model. The tube dynamics is modeled by simple mass-spring-damper systems, and the motions of the fluid domain is accounted for by a moving mesh technique (Arbitrary-Lagrangian-Eulerian formulation). The consistency of the calculations is demonstrated by comparing the numerical data to the experiments of Gosse et al. (PVP Conference, 2001) in terms of tube amplitude and flow-induced force spectra, for various gap velocities. Investigation of the spectra of the flow-induced forces then shows that the tube motions ignite the emergence of flow phenomena at constant Strouhal numbers. The fluid-structure interactions are also responsible for the existence of a series of tones at rather constant frequencies, corresponding to the vibrational modes of the flexible cell.

Flow-induced vibrations of Steam Generator (SG) tube bundles are a major concern for the operators of nuclear power plants. In order to predict damages due to such vibrations, EDF has developed the numerical tool GeViBus, which allows one to evaluate safety margins and thereafter to optimize the SG maintenance policy. The software is based on a semi analytical model of fluid dynamic forces and dimensionless fluid force coefficients which need to be assessed by experiment. The database of dimensionless coefficients is steadily updated in order to cover all tube bundle configurations found in EDF power plants. Within this framework, we present a new test rig dedicated to the parallel triangular tube arrangement submitted to a twophase cross-flow A new test loop is constructed as well, allowing fluid-elastic instability to be induced on the test rig for various qualities. The details of the experimental arrangement are presented together with the preliminary validation tests.

The cross flow induced vibrations in water of a single flexible tube in a normal square array of rigid tubes are investigated by means of large-eddy simulations, based on the classical Smagorinsky model. The flow configuration and the operating conditions are taken from the experiments of Granger et al. (J. Fluid Struct., 1993). A fully-coupled fluid-structure calculation is hence performed: the tube dynamics is modeled by a mass spring-damper system, and the motion of the fluid domain is accounted for by a moving mesh technique.The numerical results are compared to the experimental data in terms of amplitude and frequency of the flexible tube oscillations, for various inflow velocities. In addition, characteristics of the flow-induced forces are discussed: features of the power spectral densities of lift and drag forces, such as the envelope spectrum or the spanwise correlation length are investigated.

Corrosion product deposits in the secondary side of nuclear power plant Steam Generators may result in Tube Support Plate flow blockage, and tube fouling. In order to simulate those two phenomena in the whole Steam Generator, a solid deposit growth model has been developed by the EDF R&D Division. This model is implemented in the frame of THYC, which is the EDF's reference code for the modeling of two-phase thermal-hydraulic phenomena at the subchannel scale. A new deposit process, based on Tube Support Plate flow blockage studies, has been developed and implemented in the model, and is presented in this work. It can be defined by two main steps: particle deposition, and strengthening process called "flashing" due to soluble species precipitation in the pores of the particle deposit. The relevance of this process is tested by comparing the simulation results to the actual levels of flow blockage observed in some nuclear plants. Two dominant trends are showed in this work: the flow blockage is more important on the hot leg than on the cold leg and at the top than at the bottom of the Steam Generators. Moreover the flow blockages at the upper Tube Support Plate have the special feature to be more important at the periphery than at the center. The "flashing" phenomenon allows one to underline the magnetite solubility dependence, so the pH dependence, of flow blockage phenomenon. A pH elevation of the secondary circuit seems to be a interesting remedy which is currently considered on EDF fleet. (C) 2013 Elsevier B.V. All rights reserved.

The computation of the dynamic response of a structure subjected to a fluid flow requires the knowledge of the fluid forces acting on the structure At least three classes of these forces can be distinguishedfluid-elastic forces due to the coupling between fluid flow and structure displacementrandom forces due to the turbulent nature of the flow. In cases of two-phase fluid configurations, such as those occurring in steam generators of nuclear power plants, forces due to the two-phase nature of the fluid are also assumed to be part of this type of excitationsfluid forces due to coherent structures in the flow, such as Von Karman vortex-streets downstream of a single tube in cross-flowIn this paper we focus on the numerical study of this last class of excitations. We propose here a method to compute the dimensionless spectrum of those forces as a function of a scaled parameter called "reduced frequency" [1]. We perform CFD (Computational Fluid Dynamics) calculations with the EDF (Electricite De France) CFD software Code_Saturne (R)[2], using a U-RANS (Unsteady-Reynolds Averaged Navier Stokes) approach, and a k-omega SST (Shear Stress Transport) model. Tube wall fluid stresses are derived and post-processed into spectra. This numerical methodology allows one to distinguish the drag from the lift component in overall fluid force.The paper includes three parts:In the first part, the numerical method of our study is presented : the k-omega SST model developed to solve U-RANS equations [2] is described. We then detail the post-processing used to compute the dimensionless spectrum starting from fluid stresses at tube walls.In the second part, k-omega SST model's implementation is validated on the case of a single rigid tube in an upwards cross-flow of water. CFD results are compared to experimental measurements [3].Eventually the study of a 2D rigid tube bundle subjected to a two-phase cross-flow modeled by an equivalent single phase flow is presented. A sensitivity analysis is carried out to study the influence of bundle's bulk and the Reynolds number. Wall pressures are post-processed to derive the dimensionless spectrum associated with fluid forces due to coherent structures.

In Pressurized Water Reactors (PWR), Steam Generator (SG) tubes constitute one of the three barriers which preserve the environment from radioactivity. Excessive tube vibrations under fluid forces, due to the steam-water mixture flow across the tube bundle, can lead to the failure of some tube. Several methods have been proposed to estimate some upper bounds for these forces. These bounds are applicable at the design stage and are helpful to avoid tube failures. Most of the available methods are based on experimental results that have been obtained on tube bundles installed in scaled test-facilities. Unlike this popular test-based approach, one combines here Computational Fluid Dynamics (CFD) to High Performance Computing (HPC), in order to estimate fluid forces in a simple case by applying the Direct Numerical Simulation (DNS) method to solve the Navier-Stokes equations. In the first paragraph, one summarizes the general standard method which allows one to derive the auto-power spectral density of the displacement response at any point of an SG tube, departing from the cross-power spectral densities of fluid forces between any two points along the tube. In the second paragraph, one recalls the equivalent dimensionless spectrum, which was proposed by Axisa et al. in the early nineties, and which still remains a useful reference in the domain. One then applies DNS to the test case of a single infinite cylinder, which is submitted to a single phase cross-flow in a rectangular channel. The Reynolds number is equal to 3900. One presents the time dependent tensors of fluid pressure and viscous stresses, and uses this tensor to estimate the field of non stationary forces that are applied by the fluid, per unit length, at a set of equidistant locations along the tube. Even if they do still require experimental validations, our computation results are more abundant and detailed than standard experimental results, as well as more flexible to use. They therefore provide an interesting additional source of information. They already allow us to try to get new insights into quantities that would be, in any case, very difficult to obtain experimentally. Lift, drag, and even the forces acting in the direction of the tube axis, are computed, and can be distinguished one from the other. Fluid forces due to viscous stresses can also be compared to the ones caused by pressure. The degree of correlation of the forces along the tube can also be examined.

Computation of the dynamic response of a structure submitted to a fluid flow requires the knowledge of the spectrum of fluid forces acting on the structure. In order to get that spectrum, one usually proceeds by rescaling a dimensionless envelope spectrum, which has been previously elaborated by applying safety margins to the most conservative of all spectra derived from a set of scaled experimental configurations. When designing nuclear steam generator tube bundles to minimize flow-induced vibrations, one of the most popular dimensionless envelope spectra is the one proposed by Axisa et al..(1985,1990) In his papers, Axisa proposed a method that allows one to experimentally derive the dimensionless spectrum as a function of a dimensionless parameter, the "reduced frequency". Although Axisa initially applied his method to derive turbulent buffeting forces, we here propose to use it to derive the dimensionless spectrum of fluid forces due to vortex shedding. We consider the case of a single rigid tube in an upwards water cross-flow. Tube wall fluid stresses are derived by using Code_Saturne (R) which is EDF CFD reference code. The paper includes four parts. In the first part, we present the two laboratory configurations "AMOVI" and "DESider", which provide the experimental data used in the framework of the present study.. In the second part. we detail the post-processing that we used to derive the dimensionless spectrum from the computed tube wall fluid stresses. In the third part, we validate the CFD simulations on the basis of the "DESider" air case, for which several fluid dynamics experimental results are available. In the fourth part, we post-process tube wall pressures to derive the fluid force dimensionless spectrum in the "AMOVI" water case. We also perform a sensitivity study of our results, with respect to both boundary conditions and Reynolds number value. Numerical methodology allows one to readily distinguish the drag from the lift component in the overall fluid force.

During the normal cycle of a pressurized water reactor, boron concentration is reduced in the core until fuel burns up. A stretch out of the normal cycle is however possible afterwards, provided primary coolant temperature is reduced. In those stretch out periods, nuclear operators want to keep constant thermal power exchanged in the steam generator, in order to preserve its performances. Under that constraint, the required reduction in primary coolant temperature involves both a decrease of secondary cooling system pressure and an increase of tube bundle vibrations. Since neither pressure nor vibrations should exceed some given thresholds in order to preserve component integrity, the reduction of primary coolant temperature has to be limited. Nuclear plant operators thereafter need an operating diagram, i.e. a diagram that provides minimum allowed primary coolant temperature versus power rate. In that context, we propose a method to derive such a diagram, by combining, on the one hand a code for simulating primary and secondary fluid flows in steam generators and, on the other hand, a software that allows one to predict fluid elastic tube bundle instabilities. That method allows one to take into account both tube fouling and plugging. It is now used by French utility “Electricite´ De France”, in order to check or supplement the analysis that are provided by steam generator manufacturers.