Phenomenology of liquid metal thermal-hydraulics

The cooling system of the Energy Amplifier (EA) is based on a Lead flow driven by natural circulation [1]. In the Energy Amplifier Demonstration Facility (EADF) a Lead-Bismuth eutectic is used and natural circulation, although enhanced through a gas injection system, is the pumping force for the cooling of both the target (only in the case of the window-type target) and the primary circuit[2]. Numerical simulation is extensively used for the design and analysis of these flows, using both commercial and in-house codes. However, liquid metals properties are very different from that of common fluids, so the physical models to be used in the simulations should be carefully assessed. In general the numerical simulation of any kind of flow requires: (i) the thermodynamic modelling of the fluid; (ii) the fluid dynamics governing equations; (iii) the turbulence modelling. In this work the thermodynamic model for heavy liquid metals is presented, starting with the derivation of the equations of state for a general fluid from the basic laws of thermodynamics. This thermodynamic model is then used for the analysis of a one-dimensional natural convection loop, in order to put in evidence the main physical mechanisms governing this particular kind of flow and the simplifications that can be applied to the one dimensional governing equations. An extensive analysis of the tree-dimensional fluid dynamic governing equations and of the turbulence models for liquid metal flows can be found in [7] and [8] respectively

Numerical methodologies for the simulation of liquid metal flows

The fluid-dynamic modelling for the simulation of the Lead-Bismuth flow in the EADF was reviewed. The general form of the non-dimensional governing equation was derived, and the analysis of the orders of magnitude of the different terms in the case of a the liquid metal flows in the EADF was performed, through a flow-Mach number asymptotic analysis. It was found that the resulting form of the equations is the one commonly used in commercial CFD codes for the simulation of liquid flows, which can then be used for our applications. The most common numerical methods for flow-Mach number applications were also presented. These methods are general and can be applied to liquid metal flows without any modification. The peculiarity of the numerical simulation of liquid metal flows lies in the modelling of the turbulent heat transfer, due to the flow Prandtl number of this type of fluids. This subject is discussed in [21]

Integration of numerical tools for the combined thermal-hydraulics and structural analysis of energy amplifier components

The CRS4 R&D activity on the Energy Amplifier Demonstration Facility (EADF) [1] concerns the thermal fluid-dynamic and structural computational analysis in support to the design of some of the crucial components of the machine. We are currently studying the operating conditions of the spallation target [2-3] and the sub-critical core [4-5], including steady state, transient [31-32] and accidental conditions. The simulation activity also includes the analysis of multi-phase (liquid-gas systems with high void fractions) [6-7] and free surface Liquid Metal (LM) flows [8-9]. A parallel activity of benchmarking of numerical codes on LM experiments is in progress [10-12, 33-34], joined with a critical theoretical review of numerical models applied to LM flows [13-15]

Numerical studies related to the design of the beam target of the energy amplifier prototype

The Centre for Advanced Studies, Research and Development in Sardinia (CRS4) is participating in an Italian R&D program, together with Ansaldo, ENEA and INFN, devoted to the design of a 80 MW prototype of the Energy Amplifier proposed by C. Rubbia et al.. The use of advanced numerical tools has been of practical support in the design of critical elements of the machine such as the fuel element and the beam target. The aim of this work is to show the design and optimization of the Liquid Metal Spallation Target, which consists in an axial-symmetric vertical cylinder, where a Pb-Bi eutectic, in a natural convection driven flow regime, works at the same time as spallation material and coolant for the target and the beam window. The most critical part of the target is the window itself, where the highest temperatures and thermal stresses are reached. The minimization of such temperatures and stresses is the goal of the optimization. The main geometrical dimensions of the target (i.e. beam pipe, beam window and external container) are somehow fixed since they are related to the proton beam distribution and to the EA core design. The optimization therefore acts on the suitable design of the flow guide which separates the hot rising flow from the cold one. In the region where the flow is heated by the proton beam the flow guide has a funnel shape which accelerates the liquid metal. The numerical simulations are performed by using three different tools. The FLUKA Montecarlo code is used to calculate the heat source distribution in the window and in the coolant generated by the interaction with the proton beam. The results of these calculations are used as input data for the thermal fluid dynamic simulations performed with the STAR-CD commercial software. The resulting temperature and pressure fields are finally introduced in the NASTRAN code used for the structural analysis of the solid components

Thermo-mechanical stresses on the beam window

The Centre for Advanced Studies, Research and Development in Sardinia (CRS4) is participating to an Italian R&D program, together with Ansaldo, ENEA and INFN, devoted to the design of a 80 MW prototype of the Energy Amplifier proposed by C. Rubbia. The use of advanced numerical tools has been of practical support in the design of critical elements of the machine such as the fuel element and the beam target. The aim of this work is to study the sensitivity of beam window stresses to the beam distribution, size and interruption. In order to compute thermal stresses, the heat deposition in the window and in the coolant generated by the interaction with the proton beam is calculated and used as input data for the fluid dynamic simulation of the natural convection flow of the target coolant