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This paper is devoted to the validation of a two-fluid two-phase flow model in some highly unsteady situations involving strong rarefaction waves and shocks in water-vapor flows. The two-fluid model and its associated numerical method that were introduced in a previous work are first recalled, and details on the computational scheme and the verification of interfacial mass transfer terms are provided. Consistency with experimental data is checked in three configurations. First, a comparison with the speed of sound in a two-phase mixture is detailed. Afterwards, numerical approximations obtained with the two-fluid approach are discussed and compared with some experimental data documented in the Simpson water-hammer experiment and the high depressurization with flashing associated with Canon experiment.

International audience; The present paper is dedicated to the analysis of the fast transient mechanical consequences of the Loss Of Coolant Accident (LOCA) on the internal structures of a Pressurized Water Reactor (PWR). A complete methodology is described, based on a coupled 1D/3D representation of the entire primary loop of the reactor, with a robust and accurate approach for fluid–structure interaction inside the main vessel. A special attention is given to the modeling of small geometric details, such as perforated plates in the vicinity of the reactor core, through local impedance relations acting on the flow, which must be carefully calibrated for industrial purposes. The capabilities of the proposed framework are demonstrated with the application of the complete computational scheme to the simulation of the consequences of LOCA for a French 900 MW PWR, performed with EUROPLEXUS software.

Loss of coolant accident is characterized by a transient rarefaction wave propagating inside the primary loop after pipe break, resulting in fluid loading on internal structures, especially on the baffle surrounding the reactor core. In that case, loading comes from differences in rarefaction wave travel times, whether it propagates through the reactor core or through the by-pass between baffle and core barrel, yielding delays and pressure differences on both sides of baffle plates. Propagation is strongly influenced by geometric obstacles such as holes in baffle reinforcement plates, which cannot be represented in a numerical model of the whole primary loop and has then to be replaced by suitable impedance relations. A methodology to validate and calibrate such impedance models, based on specific experimental results and high-order CFD simulations, is thus proposed. Models are tested and integrated into EUROPLEXUS fast-transient fluid–structure dynamics software.

A high-order finite-difference algorithm is proposed in the aim of performing LES calculations for CAA applications. The subgrid scale dissipation is performed by the explicit high-order numerical filter used for numerical stability purpose. A shock-capturing non-linear filter is also used to deal with compressible discontinuous flows. In order to tackle complex geometries, an overset-grid approach is used. High-order interpolations make possible the communication between overlapping domains. The whole algorithm is first validated on canonical flow problems to illustrate both its properties for shock-capturing as well as for accurate wave propagation. Then, the influence of the multi-domain approach on the high-order spatial accuracy is assessed. Finally, a rod-airfoil configuration is studied to highlight the potential of the proposed algorithm to deal with multi-scale aeroacoustic applications.

We present in this paper some comparisons of numerical results and experimental data in some two-phase flows involving rather high pressure ratios. A two-fluid two-phase flow model has been used herein, but we also report a few results obtained with some simpler single-fluid two-phase flow models.

This contribution is dedicated to the latest methodological developments implemented in the fast transient dynamics software EUROPLEXUS (EPX) to simulate the mechanical response of fully coupled fluid-structure systems to accidental situations to be considered at reactor scale, among which the Loss of Coolant Accident, the Core Disruptive Accident and the Hydrogen Explosion. Time integration is explicit and the search for reference solutions within the safety framework prevents any simplification and approximations in the coupled algorithm: for instance, all kinematic constraints are dealt with using Lagrange Multipliers, yielding a complex flow chart when non-permanent constraints such as unilateral contact or immersed fluid-structure boundaries are considered. The parallel acceleration of the solution process is then achieved through a hybrid approach, based on a weighted domain decomposition for distributed memory computing and the use of the KAAPI library for self-balanced shared memory processing inside subdomains.

A pure tone phenomenon has been observed at 460 Hz on a piping steam line of a power plant. The source has been identified to be generated in a gate valve and to be of cavity noise type. This paper presents the investigations carried out on experimental models in order to analyze the problem. 2D and 3D axisymmetric models are used and lock-in situations between shear layer modes and acoustic duct modes are proven to give rise to powerful tones. Some counter measures are also tested with the objective of lowering the amplitude of pressure oscillations.Copyright © 2013 by ASME

Piping systems conveying gases at high pressure often generate high level of vibration and noise. These phenomena, in many cases, are initiated by the coupling between an unstable separated flow and an acoustic mode of the piping system. Various types of cavities in pipe flow are among the flow geometries which are known to be liable to the generation of tonal noise. Flow over cavities in ducts and piping systems has been investigated extensively for two and three dimensional situations. In this case, the feedback loop which generates the tonal noise is caused by the coupling between the instability of the shear layer forming at the cavity opening and an acoustic mode. This paper presents a study of tonal noise generation by subsonic pipe flows over a cavity formed inside a fully open gate valve. Previous 2D and 3D studies, presented in a companion paper, have shown that the presence of the valve-seat cavity is responsible for the generation of acoustic tonal noise. In this paper, the full 3D geometry of the valve, on a small scale model, is studied with experiments and using an unsteady compressible flow solver developed at EDF. Experimentally, the evolution of the fluid acoustic coupling in term of frequency and amplitude with the flow velocity is studied. Also, a modal analysis have been done to identify the frequency of acoustic mode of the valve. Numerically, the complex 3D geometry is meshed and computation is performed. The results show an acoustic tonal noise in a frequency range compatible with that experimentally. The study is underway, future analysis of the velocity and acoustic fields in the simulation may help to identify the shear layer and acoustic modes and to identify how they couple together.Copyright © 2013 by ASME

International audience; We examine in this paper the accuracy of some approximations of the Baer-Nunziato two-phase flow model. The governing equations and their main properties are recalled, and two distinct numerical schemes are investigated, including a classical second-order extension relying on symmetrizing variables. Shock tube cases are considered, and two simple Riemann problems based on well-balanced initial data are detailed. These enable to recover the expected convergence rates. However, it is shown that these simple cases are indeed very difficult and that the accuracy of basic schemes is rather poor.

International audience

The influence of the filter shape on the effective scale separation and the numerical accuracy of large-eddy simulations based on relaxation filtering (LES-RF) is investigated. The simulation of the turbulent flow development of a high-Reynolds number low-subsonic compressible mixing layer is performed using the LES-RF procedure, for discrete filters of order 2–10. A reference solution is first obtained using high-order numerical algorithms and shows a good agreement with experimental data found in the literature. Discrete filters of order 2, 4, 6, 8 and 10 are then considered to study the influence of the filter shape on numerical results. The 2nd-order scheme turns out to be too dissipative and prevents the emergence of unsteady motions within the mixing layer. For higher order schemes, from 4th- to 10th-order, the flow solutions are turbulent but exhibit mean flows and turbulent intensities depending on the filter. The investigation of the one-dimensional kinetic energy spectra then shows that the 4th-order filter may still be too dissipative whereas large scales remain unaffected using the 6th-, 8th- and 10th-order filters. A further study of the kinetic energy spectra nonetheless demonstrates that the effective spatial bandwidth of the LES increases with the order of the filtering scheme. Simulations using the 6th-, 8th- and 10th-order filters, with mesh sizes chosen to provide the same effective LES cut-off wavenumber, are performed and yield similar results. It is hence found that the value of the effective LES cut-off wavenumber, rather than to the filter shape itself, is mainly responsible for the discrepancies between the flow statistics obtained using different filters. One may conclude that filter shape independence is consequently achieved in the present LES of a mixing layer.

A chained method to compute the single mode vibration of mistuned bladed disk assemblies is proposed. Aerodynamic coupling effects are first evaluated by computing unsteady aerodynamic coefficients for a quasi-3D geometry. The code is parallelized with a decomposition domain method and validated with the 4th Aeroelastic Standard Configuration. Aerodynamic coefficients are then included in a mass-spring model of the bladed disk assembly. The chained method is applied to the last row blades of a low pressure steam turbine in which localized high levels of vibrations have been observed. The phenomenon of vibration localization found by experiments is predicted with a reasonably good accuracy. Numerical results indicate that aerodynamic coupling is predominant and highly influences mistuning sensitivity. It is also shown that the mistuned row is very sensitive to structural damping. Intentional mistuning is used as a mean to reduce the amplitude magnification on the mistuned assembly. Modifying the frequency of every two blades of the assembly has proved to efficiently reduce localization. A very similar result is obtained by locally modifying the characteristics of a few blades located in high magnification zones.Copyright © 2006 by ASME

High levels of vibrations have been observed on the last row blades of a low pressure steam turbine for nominal operating conditions. A self-excited phenomenon known as flutter is suspected to be the cause of the vibrations for non-stall transonic conditions. The non-homogeneous distribution of vibratory levels on the row is attributed to mistuning effects. They are beyond the scope of our study. A time-dependent ALE formulation of Euler equations is derived on a quasi-3D domain and coupled with a one-degree-of-freedom structural model. The work-by-cycle (WBC) method is performed in order to analyse the stability of the vibrating blades in the surrounding flowfield, for a perfectly tuned assembly. On the top part of the blades, the flow is transonic and fully attached. It is shown that, for these operating conditions, the cascade aeroelastic behaviour is linear. By using the influence coefficient method, an instability region is exhibited. The effects of the flowfield on the vibrating blades are discussed. They are expressed in terms of added damping and stiffness in order to be used as the input data of a structural mistuning analysis.Copyright © 2005 by ASME

Solving the Linear Euler Equations (LEE) is the reference method that allows to take into account all the phenomena involved in Outdoor Sound Propagation. However, the huge size of the problems to be treated is still a great limitation to the practical application of this method. The concept of multi domain computations associated with the use of massively parallel computers now pushes the limits away. The code SAFARI, recently developed by EDF, solves LEE with high order numerical schemes on structured grids. To deal with complex and large geometries, a multi domain approach is used. The computational domain is composed of several partially overlapping grids (overset grids). Computations are parallelized by domain decomposition to be runned on cluster facilities. The presentation means to show the capability of SAFARI to deal with propagation over realistic 3D domains. The strategy used to carry out the calculations is detailed. The new perspectives of this kind of method are finally given.

In order to model flow phenomena involving interactions between aerodynamics and acoustics, it is necessary to use Direct Noise Computation (DNC) instead of hybrid methods that are not suitable to take into account the feedback of acoustics on the flow. The methods that are now available in the field of Computational AeroAcoustics (CAA) allows us to deal with DNC in realistic configurations. The numerical code SAFARI (Simulation of Aeroacoustics in Fluids And with Resonance and Interactions) has been developed for this goal. The set of equations are the compressible 3‐D Navier‐Stokes equations. High order finite difference schemes are used. Multidomain capabilities are implemented in order to deal with complex geometries. Block decomposition is used in order to take advantage of parallel processing on large clusters Validation cases are presented: diffraction by a cylinder, shock tube. Results on realistic configurations are also shown: ducted cavity, transonic sudden enlargment, airfoil interactions.

A high-order finite-difference algorithm is proposed in the aim of LES and CAA applications. The subgrid scale dissipation is performed by the explicit high-order numerical filter used for numerical stability purpose. A shock-capturing non-linear filter is also implemented to deal with compressible discontinuous flows. In order to tackle complex geometries, an overset-grid approach is used. High-order interpolations make it possible to ensure the communication between overlapping domains. The whole algorithm is first validated on canonical flow problems to illustrate both its properties for shock-capturing as well as for accurate wave propagation. Then, the influence of the multi-domain approach on the high-order spatial accuracy is assessed. Afterwards, the algorithm is extended to dynamic mesh applications with overlapping grids. Finally, two industrial cases are presented to highlight the potential of the proposed algorithm.

The propagation of a transient wave through an orifice is investigated for applications to Loss Of Coolant Accident in nuclear plants. An analytical model is proposed for the response of an orifice plate and implemented in the EUROPLEXUS fast transient dynamics software. It includes an acoustic inertial effect in addition to a quasi-steady dissipation term. The model is experimentally validated on a test rig consisting in a single pipe filled with pressurized water. The test rig is designed to generate a rapid depressurization of the pipe, by means of a bursting disk. The proposed model gives results which compare favourably with experimental data.Copyright © 2011 by ASME

The sound radiated by an airfoil in the wake of a rod is predicted by means of compress- ible large-eddy (LES) simulation. The LES strategy is based on high-order spectral-like numerical methods to allow the direct noise calculation of the sound sources. Owing to the complexity of the geometry, an overset grid approach is implemented in order to tackle with turbulent flows around multiple solid bodies. The aerodynamic data as well as the acoustic far-field are thoroughly compared to the experimental data of Jacob et al. (J. Theoret. Comput. Fluid Dyn., 19(3), 2005) in order to demonstrate the accuracy of the present simulation.

Strong tonal noise can be found on the main steam lines of power plants. The source of noise was identified to be located at the gate valves present on the steam lines. Analysis of on-site measurements showed that the source of noise was due to the cavity that forms the valve seat at the bottom of the valve body. The valve in its open position is then composed of this bottom cavity over which an unstable shear layer develops but also of the top cavity where the gate is stored in open position. The valve is of course also connected to the pipe. All these elements are good candidates for flow-acoustic phenomena. The development of the shear layer over the cavity gives rise to self-sustained flow oscillations and noise radiation. The vortices convected in the shear layer which develops from the upstream corner of the cavity interact with the downstream corner of the cavity. A pressure disturbance is then generated and acts as a feedback loop on the separation point at the upstream corner. Due to the phase relationship between the generation of the disturbance downstream and its influence upstream, this pressure feedback selection amplifies the shear layer and preferred modes of oscillation are then produced. It is also well known that at low Mach number these pressure oscillations in the cavity remain weak. However, in ducted configurations, powerful tones can be generated even at low Mach number when pressure oscillations in the shear layer couple with the acoustical response of the duct. In order to study these phenomena in configurations close to the industrial ones, both numerical and experimental approaches are carried out. A high-order numerical code has been developed in order to capture aeroacoustic interactions in turbulent flows. An experimental test rig has been built in order to study aeroacoustic phenomena in small scale models of control flow devices present on steam pipes of power plants. A vacuum pump is used instead of a ventilator for creating the flow through the test rig in order to study high pressure loss devices. The present paper aims at handling the flow-acoustic phenomena in the case of a fully 3D geometry of the gate valve. Both numerical and experimental investigation methods are used. In the second section of the paper, industrial problem and previous study are recalled. In the third section, the small scale model that is used for both numerical and experimental investigations is presented. In the fourth section, the numerical methods used in this paper are presented. In the fifth section, the experimental device and the measurements techniques are presented. In the sixth section, results of the acoustic modal analysis of the valve are analysed. In the seventh section, results of the flow-acoustic analysis of phenomena in the valve are analysed.