Loss Of Coolant Accident causes the propagation of a transient rarefaction wave within the primary circuit that generates a transient pressure load on the baffle surrounding the reactor core. This is the result of nonidentical travel times of the rarefaction wave between the two sides of the baffle: the reactor core on one side and the bypass between the baffle and core barrel on the other. The two zones have different geometrical characteristics, in particular the perforated reinforcement plates in the by-pass significantly influence wave propagation. Representing these obstacles in numerical simulations of the primary circuit requires the use of simplified models. A study on the accuracy of these models is hereby proposed, through a detailed comparison between numerical simulations realized with the EUROPLEXUS software and experimental results obtained on the MADMAX facility. The numerical models investigated are both quite reliable for the simulation of the case study under consideration. Both models imply a simplified representation of the real geometry of the experimental device, but despite this they can be considered quite valid. Lastly, the Fluid-Structure Interaction calculations enable us to comprehensively assess the phenomenon of cavitation and provide an initial evaluation of the deformations and mechanical stresses experienced by the structure.

This paper describes a novel approach to alleviate the carbuncle phenomenon which consists in adding to any carbuncle prone Riemann solver an extra viscosity term in tangential momentum flux and its contribution to the energy conservation equation. This term contains one numerical parameter only, a scalar viscosity, which is reduced using a face-based shear detector to preserve shear waves.The idea stems from the investigation of some of the existing Riemann solvers, also presented in the paper. Indeed, when splitting the numerical flux into the face normal and tangential components, we observe that all the carbuncle free Riemann solvers present in the tangential part a numerical viscosity which scales with the sound speed when the normal flow velocity becomes zero. Opposite, in the carbuncle prone solvers this viscosity scales with the normal flow velocity. In particular the carbuncle free HLLCM scheme proposed by Shen et al. can be written by adding to the carbuncle prone HLLC scheme a tangential artificial viscosity term. Then the same can be done for any other Riemann solver, which renders the approach easy to implement in CFD codes for compressible flows.Numerical experiments shows the efficiency of the approach in computing carbuncle free single-component and multi-material flows.

The present paper focuses on the simulation of compressible three-component flows interacting with surrounding deformable and immersed structures. For this purpose, a barotropic three-component model assuming instantaneous kinematic and mechanical equilibria is discussed. The mathematical properties of the system, the structure of the waves, the expression of the Riemann invariants and the existence of a mathematical entropy are thus examined. The link between the present model and the extension to three components of the Kapila model is discussed. An HLLC-type solver for the present threecomponent model based on the mathematical structure of the system is then described. The multi-fluid solver used is coupled with an updated Lagrangian approach used for the structural domain. Arbitrary Lagrangian-Eulerian (ALE) approach and Immersed Boundary Method (IBM) are here considered and compared for their capability to account for fluidstructure interactions (FSI). A series of Riemann problems with available analytical solutions are regarded to assess the used numerical approaches: Eulerian on fixed grids, ALE on moving grids and IBM with independent fluid and structure meshes. Finally, ALE and IBM methods are used to simulate an experimental configuration involving complex FSI problems with a multi-material flow and structural plastic deformations. The numerical results presented show a good agreement with the experimental data.(c) 2023 Elsevier Inc. All rights reserved.

Fluid–structure interaction in fluid-filled flexible pipelines is modeled here with a time explicit nonlinear 1-D coupled approach. The internal steam–water fluid is modeled using a homogeneous equilibrium model where kinematic, mechanical, thermal, and thermodynamic equilibrium between liquid and steam water is assumed. As a consequence, the nonlinear convective effects are taken into account as well as the temperature variations in the fluid model. The mechanical behavior of the pipelines is obtained following the Euler–Bernoulli beam theory. This leads to structural equations taking into account axial, flexural, lateral, and torsional pipe motion. In addition, plasticity is also considered in the structural behavior. Thus, the overall model corresponds to the nonlinear extension of the so-called seven degree-of-freedom fluid–structure interaction model. Furthermore, radial expansion of the pipe cross section due to the internal fluid pressure loading is also taken into account, while the pipe radial motion is neglected. Both junction and friction coupling mechanisms are considered in the present model, whereas the Poisson coupling is ignored in this study. An explicit finite-volume method is used for approximating the fluid equations and is coupled with an explicit finite-element approach used for the structural beam equations. This leads to an explicit two-way coupling approach for fluid–structure interactions which is assessed on a selection of several experiments involving non-isothermal steam–water behavior or significant FSI effects during fast-transient events. Comparisons are given with the experimental data on all considered experiments, which clearly demonstrates the ability of the present approach to be efficient and representative.

Loss Of Coolant Accident causes the propagation of a transient rarefaction wave within the primary circuit that generates a transient pressure load on the baffle surrounding the reactor core. This is the result of nonidentical travel times of the rarefaction wave between the two sides of the baffle: the reactor core on one side and the by-pass between the baffle and core barrel on the other. The two zones have different geometrical characteristics, in particular the perforated reinforcement plates in the by-pass significantly influence wave propagation. Representing these obstacles in numerical simulations of the primary circuit requires the use of simplified models. A study on the accuracy of these models is hereby proposed, through a detailed comparison between numerical simulations realized with the EUROPLEXUS software and experimental results obtained on the MADMAX facility.

A novel beam model is proposed in order to consider deformations of its cross-section in the context of straight thin-walled tubes. For this purpose, the straight beam kinematics is enriched by addition of orthogonal shell-type displacement field of the tube section. Linear strain in terms of displacement is considered in conjunction with the non-linear coupling between local deformation of the section and its global rotation. Both Euler-Bernoulli and Love-Kirchhoff hypotheses for beam and shell kinematics, respectively, are adopted as well as the thin-walled assumption. First-order shear deformation for the radial variable and Fourier expansion in terms of the circumferential variable are also considered for the mid-surface displacement field. Then, the stress tensor is obtained under plane stress conditions. The virtual power principle is finally used to obtain the equations of motion satisfied by the correspond-ing generalized forces. Afterwards, an explicit updated Lagrangian Finite-Element approach using a lumped mass matrix is proposed for solving the tube governing equations and the stability condition of the time integration is given. Test-cases are then chosen to assess the present tube finite-element. Both static and dynamic problems are considered. First, the proposed model is compared to analytical solutions. Finally, a tube subjected to a distributed patch loading is studied. The influence of the number of Fourier modes, of warping and coupling terms is examined. The proposed model makes it possible to retrieve classical shell solution of the cross-section deformation with significant computational savings.& COPY; 2023 Published by Elsevier Ltd.

A 1D/3D Finite-Volume coupling is proposed for the Euler/Homogeneous Equilibrium Model equations. The present approach is based on the Finite-Volume framework making it possible to tackle general equations of state. A special attention is given to the conservation of mass, momentum and energy at the common 1D/3D interface. For fluid–structure interaction induced by fast-transient phenomena occurring in pipelines, the present 1D/3D fluid coupling is also associated with a beam/shell elements coupling to deal with the mechanical pipe behavior. A series of test-cases involving both purely fluid, purely structural and coupled fluid–structure problems with available analytical or experimental references is considered to demonstrate the performance of the present 1D/3D coupling.

This work is devoted to the simulation of single- and two-phase shock-tubes. In particular, the interaction between pressure waves and an abrupt change of area (sudden expansion and sudden contraction) is also considered. For this purpose, the quasi 1-D Finite-Volume approach recently developed by the authors for compressible flows in pipelines is used and assessed on a variety of test-cases. The numerical solutions are compared with other numerical solutions obtained with codes as RELAP-5, WAHA or RELAP-7 or analytical solutions when available. Finally, the experimental pressure waves propagation in a network experiments is also considered. The carefully chosen test-cases assess the ability of the present approach to predict the complex dynamics of single-and two-phase pressure wave phenomena with satisfactory accuracy and efficiency.

A low-diffusion self-adaptive flux-vector splitting method is presented for the Euler equations. The fluxvector is here split into convective and acoustic parts following the formulation recently proposed by the authors. This procedure is based on the Zha-Bilgen (or previously Baraille et al. for the Euler barotropic system) approach enriched by a dynamic flow-dependent splitting parameter based on the local Mach number. As a consequence, in the present self-adaptive splitting, the convective and acoustic parts decouple in the low-Mach number regime whereas the complete Euler equations are considered for the sonic and highly subsonic regimes. The low diffusive property of the present scheme is obtained by adding anti-diffusion terms to the momentum and the energy components of the pressure flux in the acoustic part of the present splitting. This treatment results from a formal invariance principle preserving the discrete incompressible phase space through the pressure operator. Numerical results for several carefully chosen one- and two-dimensional test problems are finally investigated to demonstrate the accuracy and robustness of the proposed scheme for a wide variety of configurations from subsonic to highly subsonic flows. (C) 2020 Elsevier Ltd. All rights reserved.

A novel Finite-Volume scheme for the numerical computations of compressible two-phase flows in pipelines is proposed for the fully non-equilibrium Baer–Nunziato model. The present FV approach is the extension of the method proposed in Daude and Galon (2018) in the context of the Euler equations to the Baer–Nunziato model. In addition, proper approximations of the non-conservative terms are proposed to consider jumps of volume fraction as well as jumps of cross-section in order to respect uniform pressure and velocity profiles preservation. In particular, focus is given to the numerical treatment of abrupt changes in area and to networks wherein several pipelines are connected at junctions. The proposed method makes it possible to avoid the use of an iterative procedure for the solution of the junction problem. The present approach can also deal with general Equations Of State. In addition, the fluid–structure interaction of compressible fluid flowing in flexible pipes is also considered. The proposed scheme is then assessed on a variety of shock-tubes and other transient flow problems and experiments demonstrating its capability to resolve such problems efficiently, accurately and robustly.

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler–Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

Water-hammer with column-separation induced by cavitation is investigated numerically. The vapor–water flow is modeled using the Homogeneous Equilibrium Model in conjunction with the 1984 NBS/NRC Steam Tables. The discretization is done with the quasi 1-D Finite-Volume approach recently developed by the authors for compressible flows in pipelines. The ability of the present approach to tackle cavitating flows is first assessed. Then, comparisons with experimental results of water-hammer with column-separation demonstrate consistency with the present computations. Based on the obtained numerical results, focus is given to the dynamics of the liquid column-separation and to the associated physics such as cavitation, vapor growth and collapse, generation of the secondary water-hammer peak and the interaction of the primary and secondary pressure waves. The influence of the initial flow velocity before valve closure on the duration and size of the cavity and on the magnitude of the secondary water-hammer is examined.

The method presented below focuses on the numerical approximation of the Euler compressible system. It pursues a two-fold objective: being able to accurately follow slow material waves as well as strong shock waves in the context of low Mach number flows. The resulting implicit–explicit(IMEX) fractional step approach leans on a dynamic splitting designed to react to the time fluctuations of the maximal flow Mach number. When the latter rises suddenly, the IMEX scheme, so far driven by a material-wave Courant number, turn into a time-explicit approximate Riemann solver constrained by an acoustic-wave Courant number. It is also possible to enrich the dynamic splitting in order to capture high pressure jumps even when the flow Mach number is low. One-dimensional low Mach number test cases involving single or multiple waves confirm that the present approach is as accurate and efficient as an IMEX Lagrange-Projection method. Besides, numerical results suggest that the stability of the present method holds for any Mach number if the Courant number related to the convective subsystem arising from the splitting is of order unity.

Herein, a Mach-sensitive fractional step approach is proposed for Euler-like systems. The key idea is to introduce a time-dependent splitting which dynamically decouples convection from acoustic phenomenon following the fluctuations of the flow Mach number. By doing so, one seeks to maintain the accuracy of the computed solution for all Mach number regimes. Indeed, when the Mach number takes high values, a time-explicit resolution of the overall Euler-like system is entirely performed in one of the present splitting step. On the contrary, in the low-Mach number case, convection is totally separated from the acoustic waves production. Then, by performing an appropriate correction on the acoustic step of the splitting, the numerical diffusion can be significantly reduced. A study made on both convective and acoustic subsystems of the present approach has revealed some key properties as hyperbolicity and positivity of the density and internal energy in the case of an ideal gas thermodynamics. The one-dimensional results made on a wide range of Mach numbers using an ideal and a stiffened gas thermodynamics show that the present approach is as accurate and CPU-consuming as a state of the art Lagrange-Projection-type method.

The present paper is dedicated to the simulation of fast transient phenomena involving multi-component flows with fluid–structure interaction and ALE grid motion, where the fluid interfaces are tracked using the VOFIRE anti-dissipative scheme for unstructured meshes. It introduces an extension of the existing scheme in EUROPLEXUS software, written for liquid–gas flows only, to handle a combination of stiffened gases as equations of state for the fluid components, thus increasing its genericity and overcoming some limitations, at the cost of significantly modifying its implementation. The proposed methodology is proven to achieve its goals through validation examples with fluid only, such as the sloshing of a liquid in a decelerated tank or a gas–gas interaction with Richtmyer–Meshkov instability. Two large scale three-dimensional examples with full fluid–structure interaction are then provided to fully demonstrate the capabilities and the robustness of the complete proposed computational framework.

This paper is devoted to the computation of the fast depressurization of water using a two-fluid model. Such application, which is extensively studied in the nuclear field, involves many interactions between two phenomena, the mass transfer and the propagation of pressure waves. A simple but physically-based modelling of the mass transfer for the depressurization of water is proposed, which relies on the work of Bilicki & Kestin [1] in the homogeneous frame. Four different experiments have been chosen to assess the proposed model. Three of them study the depressurization of hot water in a pressurized pipe. The comparison between converged numerical results and the experimental data shows a good agreement and demonstrates the ability of the two-fluid-model to capture the proper mass transfer for a wide range of thermodynamical conditions. The last test-case is the HDR experiment which considers the depressurization of a full-scale vessel under the hypothesis of a Loss Of Coolant Accident. The results of an ALE computation show the ability of the proposed model to retrieve experimental data in both structure and fluid. (C) 2017 Elsevier Ltd. All rights reserved.

In steady-state regimes, water circulating in the nuclear power plants pipes behaves as a low Mach number flow. However, when steep phenomena occur, strong shock waves are produced. Herein, a fractional step approach allowing to decouple the convective from the acoustic effects is proposed. The originality is that the splitting between these two parts of the physics evolves dynamically in time according to the Mach number. The first one-dimensional explicit and implicit numerical results on a wide panel of Mach numbers show that this approach is as accurate and CPU-consuming as a state of the art Lagrange-Projection-type method.

This paper is devoted to the comparison of three two-fluid models in steam-water applications involving phase transition and shock waves. The three models are presented in a common formalism that helps to underline their shared properties. A numerical method based on previous work is extended to all models and to more complex Equations Of State. Particular attention is paid to the verification of every step of the method so that convergence studies can be carried out. Afterwards, models are compared with each other and with experimental data in two different cases of steam-water transients. The first one is Simpson water-hammer experiment and the second one is a rapid depressurization with flashing studied in Canon experiment.