On a low Mach nuclear core model

Dellacherie, Stéphane

doi:10.1051/proc/201235005

Cited by 17 publications

(47 citation statements)

References 11 publications

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“…As detailed in [1,4], this system may be expressed differently in order to highlight that one of the variables (ρ, h, v,p) might be considered as a parameter through the equation of state: hence one has to choose to select one variable in (ρ, h). We decided to keep (h, v,p) as main variables.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Let us make a few comments about these results. First of all, we recover steady solutions from [4] when h e is constant. Indeed y * is an unbounded monotone-increasing function of t which implies that, for a given y ∈ (0, L), we can find t large enough such that y * (t) > y.…”

Section: Constant Power Density and Constant Inlet Velocitymentioning

confidence: 99%

“…The Lmnc model is an initial boundary value problem derived in [4]. As the Mach number of the flow is assumed to be very small, an asymptotic expansion (wrt to the Mach number) can be performed in the compressible Navier-Stokes equations similarly to [10].…”

Section: A 1d Single-phase Low-mach Modelmentioning

confidence: 99%

“…In [4], the author formally derives a low Mach number model (called Lmnc for Low Mach Nuclear Core model ) describing the evolution of the coolant (in liquid phase) inside a nuclear reactor core. This system of PDEs includes a source term (power density) modelling the heating due to fission reactions as well as inlet and outlet boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In the framework of safety evaluations in nuclear reactor cores, several models have been derived [4,5] in order to better understand the evolution of physical variables (like temperature) within the reactor. Let us first present the normal functioning of a PWR (Pressurized Water Reactor) -see Fig.…”

Section: Introductionmentioning

confidence: 99%

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Study of a low Mach nuclear core model for single-phase flows

et al. 2012

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Abstract. This paper deals with the modelling of the coolant (water) in a nuclear reactor core. This study is based on a monophasic low Mach number model (Lmnc model) coupled to the stiffened gas law for a single-phase flow. Some analytical steady and unsteady solutions are presented for the 1D case. We then introduce a numerical scheme to simulate the 1D model in order to assess its relevance. Finally, we carry out a normal mode perturbation analysis in order to approximate 2D solutions around the 1D steady solutions.Résumé. Dans cet article, nous nous intéressonsà la modélisation de l'écoulement de l'eau dans le circuit primaire d'un réacteur nucléaire. Pour cela, nous utilisons un modèle bas-Mach monophasique (modèle Lmnc) pour une loi d'état de type gaz raidi. Nous présentons des solutions analytiques 1D stationnaires et instationnaires pour certains types de données. Nous simulons ensuite le modèle afin d'évaluer sa pertinence. La dernière partie est consacréeà une analyse de pertubations en modes normaux réalisée pour approcher les solutions 2Dà partir des solutions stationnaires 1D.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Constant Power Density and Constant Inlet Velocitymentioning

confidence: 99%

Section: A 1d Single-phase Low-mach Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Study of a low Mach nuclear core model for single-phase flows

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A combined finite volumes ‐ finite elements method for a low‐Mach model

Calgaro

Colin

Creusé

2019

Numerical Methods in Fluids

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Summary In this paper, we develop a finite volumes ‐ finite elements method based on a time splitting to simulate some low‐Mach flows. The mass conservation equation is solved by a vertex‐based finite volume scheme using a τ‐limiter. The momentum equation associated with the compressibility constraint is solved by a finite element projection scheme. The originality of the approach is twofold. First, the state equation linking the temperature, the density, and the thermodynamic pressure is imposed implicitly. Second, the proposed combined scheme preserves the constant states, in the same way as a similar one previously developed for the variable density Navier‐Stokes system. Some numerical tests are performed to exhibit the efficiency of the scheme. On the one hand, academic tests illustrate the ability of the scheme in term of convergence rates in time and space. On the other hand, our results are compared to some of the literature by simulating a transient injection flow as well as a natural convection flow in a cavity.

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Une solution explicite monodimensionnelle d’un modèle simplifié de couplage stationnaire thermohydraulique–neutronique

Dellacherie

Lafitte

2016

Ann. Math. Québec

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Une solution explicite monodimensionnelle d'un modèle simplifié de couplage stationnaire thermohydraulique-neutronique Stéphane Dellacherie, Olivier Lafitte To cite this version: Stéphane Dellacherie, Olivier Lafitte. Une solution explicite monodimensionnelle d'un modèle simplifié de couplage stationnaire thermohydraulique-neutronique. 2016. hal-01263642v2 Une solution explicite monodimensionnelle d'un modèle simplifié de couplage stationnaire thermohydraulique-neutronique Résumé Nousétudions un système stationnaire monodimensionnel couplant un modèle simplifié de thermohydrauliqueà un modèle simplifié de neutronique dans l'approximation par la diffusionà un groupe enénergie. Nous montrons que ce modèle de couplage non-linéaire peutêtre abordé sous deux angles différents et qu'il peutêtre ramenéà la résolution d'uneéquation différentielle ordinaire non-linéaire scalaire autonome d'ordre 1. Il est ainsi possible d'obtenir une solution explicite sans passer par un algorithme itératif résolvant successivement la thermohydraulique et la neutronique. De plus, nous obtenons une solution analytique dans un cas simple. Les résultats explicites obtenus avec nos solutions analytiques confirment les résultats numériques obtenus avec l'algorithme itératif classique de couplage thermohydraulique-neutronique.Mots clés :Équation différentielle ordinaire, spectre d'opérateur, thermohydraulique, neutronique, couplage de modèles. AbstractWe study a monodimensional stationary system coupling a simplified thermohydraulic model to a simplified neutronic model based on the diffusion approximation with one energy group. We observe that this nonlinear coupled model can be studied under two points of view and we show that solving this model is equivalent to the resolution of a non-linear scalar autonomous ordinary differential equation of order 1. As a consequence, it is possible to obtain an explicit solution without using an iterative coupling algorithm solving successively the thermohydraulics and the neutronics. Moreover, we obtain an analytic solution in a simple case. The explicit results obtained with our analytical solutions confirm the numerical results obtained with the iterative classical thermohydraulics-neutronics algorithm.

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On a low Mach nuclear core model

Cited by 17 publications

References 11 publications

Study of a low Mach nuclear core model for single-phase flows

Study of a low Mach nuclear core model for single-phase flows

A combined finite volumes ‐ finite elements method for a low‐Mach model

Une solution explicite monodimensionnelle d’un modèle simplifié de couplage stationnaire thermohydraulique–neutronique

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