Laura Matteo

The French Alternative Energies and Atomic Energy Commission (CEA) works on Brayton cycles modeling and design for the reactor energy conversion systems. Within this framework, the Code for Analysis of Thermal-Hydraulics during an Accident of Reactor and safety Evaluation (CATHARE) is used as computational tool is used to perform thermal-hydraulic calculations. It is a transient two-phase flow six-equation model closed by physical closure laws and solved using a Newton-Raphson iterative method. It is able to reproduce various fluids (such as water, sodium, hydrogen or air) with their real properties like their compressibility and to simulate different flow regimes. Diverse possibilities for simulating turbomachinery exist at several scales in the code: a nodal non-predictive 0D model and a 1D transient predictive model. This 1D model is fast in terms of CPU time, is used for pre-design studies and can be included in a full system scale computation without deteriorating the global calculation time. A complete description of the modeling can be found in the Ph.D thesis of L. Matteo. The development of the model includes various validation cases. It is able to predict the performances of a machine on a wide flow rate range (typically [10%QN - 150%QN]), at various rotational speeds with a relative error generally lower than 10%. This 1D model considers a mean streamline adopted by the fluid on each element of the machine. As a result, it allows to have an internal representation of the machine as all the thermal-hydraulic quantities can be post-processed on each mesh using the CATHARE code (pressure and velocity profiles can be obtained on each element of the machine, fixed and rotating parts). This model has so far been mostly applied to hydraulic machines and to a one low-speed compressor where compressibility effects are not clearly visible. The aim of this work is to extend the model on a high-speed compressor to match the needs of the Brayton cycles. For example, it could be used to model the low pressure compressor of the Pebble Bed Micro Model (PBMM) where the rotational speed of the machine is around 60000 rpm. The studied turbomachine is the NASA's CC3 compressor. This is a 4:1 pressure ratio centrifugal compressor with a nominal rotational speed of 21789 rpm. The geometry is fully described by McKain and Skoch as well as the experimental performances. The first task is to collect all the data necessary for the model (geometric specifications, hydraulic parameters, experimental conditions...) and to establish for verification purposes a calculation under ideal conditions to compare it to Euler's theory. Then a work is carried out to predict the performances in real conditions, on the various rotational speeds available in order to check the similarity laws. The developments and improvements useful for the modeling of this particular machine are described, especially the the management of a compressible fluid.

A predictive transient two-phase flow rotodynamic pump model has been developed in the Code for Analysis of THermalhydraulics during an Accident of Reactor and safety Evaluation (CATHARE-3). Flow inside parts of the pump (suction, impeller, diffuser and volute) is computed according to a one-dimensional discretisation following a mean flow path. Transient governing equations of the model are solved using an implicit resolution method and integrated along the curvilinear abscissa of the element. This model has been previously qualified at the component scale by comparison to an existing experimental database. The present study aims at extending the validation at the system scale: a whole experimental test loop is modelled. The ability of the transient pump model to predict flow rate, head and torque as a function of time during a 1-s pump fast start-up is evaluated. The transient evolution of the pressure upstream and downstream from the centrifugal pump is well predicted by the simulation compared to the measurements. Local quantities such as pressure and velocity inside elements of the circuit are analysed. In the considered case, inertial effects of the global circuit are dominant when compared to pump inertial effects due to the high characteristic lengths of the pipes. The main perspective of this work consists in the simulation of similar pump transients, in cavitating conditions.

For reactor design and safety purposes, the French Alternative Energies and Atomic Energy Commission (CEA) is currently working on the implementation of a predictive transient two-phase flow 4-quadrant rotodynamic pump model in the CATHARE-3 code (Code for Analysis of THermalhydraulics during an Accident of Reactor and safety Evaluation). This paper presents the pump model and its validation in single-phase first quadrant conditions at component scale. Explanations are first given on code architecture, meshing, equations to solve and how to switch from fixed frame to rotating frame and vice versa at impeller endpoints. Then, verification results in an ideal case are compared to Euler equations. Finally, validation results on real cases including the prediction of single-phase first quadrant steady performance curves and the simulation of a fast startup transient are presented.

For reactor design and safety purposes, the French Alternative Energies and Atomic Energy Commission (CEA) is currently working on Sodium Fast Reactor (SFR) thermal-hydraulics. A SFR is a system composed of three circuits (primary and secondary: liquid sodium and tertiary: nitrogen gas or water) and designed to both produce electricity and optimize nuclear fuel cycle. In such SFR systems, primary pumps are associated as a parallel circuit. Then, throughout primary pump seizure transients, cavitation may occur in non-affected pumps because of the induced hydraulic resistance drop. Studying sodium flow cavitation occurring in simple geometries such as a Venturi tube (converging/diverging tube) is the first step to better understand the phenomenon and its sensitivities. The long term aim is to validate the flashing model used for sodium applications in the CATHARE-3 code in order to be confident when simulating more complex geometries. In this article, a Venturi tube test section experimented in the CANADER facility at CEA Cadarache in the 1980s and its modelling are presented. Cavitation is obtained by flow rate variation at fixed tank pressure and circuit temperature conditions. Several computations are made in order to study the sensitivity of results to numerical and physical parameters. A set of parameters supposed to constitute the most representative case is defined and comparison of the predicted Thoma number against the experimental one is made. Detailed results of quantities of interest as profiles along the test section and evolutions during the transient are also presented.