Thermo-Hydrodynamics of Internally Heated Molten Salts for Innovative Nuclear Reactors

The problem of heat transfer in pipe flow has been extensively investigated in the past. Many different models have been proposed and adopted to predict the velocity profile, the eddy diffusivity, the temperature distributions, the friction factor and the heat transfer coefficient (Kays et al., 2004; Schlichting & Gersten, 2000). However, the majority of such studies give a description of the problem for non-internally heated fluids. Models regarding fluids with internal heat generation have been developed more than 50 years ago (Kinney & Sparrow, 1966; Poppendiek, 1954; Siegel & Sparrow, 1959), giving in most cases a partial treatment of the problem in terms of boundary conditions and heat source distribution, and relying on a turbulent flow treatment that does not seem fully satisfactory in the light of more recent investigations (Churchill, 1997; 2002; Kays, 1994; Zagarola & Smits, 1997). Internally heated fluids are of great interest in the current development of Molten Salt Reactors (MSR) (LeBlanc, 2010), included as one of the six innovative nuclear reactors selected by the Generation IV International Forum (GIF-IV, 2002) for a more sustainable version of nuclear power. MSRs are circulating fuel reactors (Nicolino et al., 2008), which employ a non-classical (fluid-type) fuel constituted by a molten halide (fluoride or chloride) salt mixture playing the distinctive role of both heat source and coolant. By adopting classical correlations for the Nusselt number (e.g., Dittus-Boelter), the heat transfer coefficient of the MSR fuel can be overestimated by a non-negligible amount (Di Marcello et al., 2008). In the case of thermal-neutron-spectrum (graphite-moderated) MSRs (LeBlanc, 2010), this has significant consequences on the core temperature predictions and on the reactor dynamic behaviour (Luzzi et al., 2011). Such influence of the heat source within the fluid cannot be neglected, and thus required proper investigation. The present chapter deals with this critical issue, first summarizing the main modelling efforts carried out by the authors (Di Marcello et al., 2010; Luzzi et al., 2010) to investigate the thermo-hydrodynamics of internally heated fluids, and then focusing on the heat transfer coefficient prediction that is relevant for analysing the molten salt behaviour encountered in MSRs. The chapter is organized as follows. Section 2 provides a brief description of the Molten Salt Reactors, focusing on their distinctive features, in terms of both sustainability (i.e., reduced radioactive waste generation, effective use of natural resources) and safety, with respect to the traditional configuration of nuclear reactors. Section 3 deals with the study of molten salt heat transfer characteristics, which represent a key issue in the current development of MSRs. In particular, a "generalized approach" to evaluate the steady-state temperature distribution in a representative power channel of the reactor core is presented. This approach incorporates recent formulations of turbulent flow and convection (Churchill, 1997; 2002), and is built in order to carefully take into account the molten salt mixture specificities, the reactor core power conditions and the heat transfer in the graphite core structure. In Section 4, a preliminary correlation for the Nusselt number prediction is advanced in the case of simultaneous uniform wall heat flux and internal heat generation, on the basis of the results achieved by means of the presented generalized approach. In Section 5, the main conclusions of the present study are summarized

Development of a Reduced Order Model for Fuel Burnup Analysis

Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed

Convergence Analysis and Criterion for Data Assimilation with Sensitivities from Monte Carlo Neutron Transport Codes

Sensitivity coefficients calculated with Monte Carlo neutron transport codes are subject to statistical fluctuations. The fluctuations affect parameters that are calculated with the sensitivity coefficients. The convergence study presented here describes the effects that statistically uncertain sensitivities have on first-order perturbation theory, uncertainty quan-tification, and data assimilation. The results show that for data assimilation, posterior nuclear data were remarkably uninfluenced by fluctuations in sensitivity mean values and by sensitivity uncertainties. Posterior calculated values computed with first-order perturbation theory showed larger dependence on sensitivity mean-value convergence and small uncertainty arising from the sensitivities' uncertainties. A convergence criterion is proposed for stopping simulations once the sensitivity means are sufficiently converged and their uncertainties are sufficiently small. Employing this criterion economizes computational resources by preventing an excess of particle histories from being used once convergence is achieved. The criterion's advantage is that it circumvents the need to set up the full data assimilation procedure, but is still applicable to data assimilation results

A new approach to the stabilization and convergence acceleration in coupled Monte Carlo–CFD calculations: The Newton method via Monte Carlo perturbation theory

This paper proposes the adoption of Monte Carlo perturbation theory to approximate the Jacobian matrix of coupled neutronics/thermal-hydraulics problems. The projected Jacobian is obtained from the eigenvalue decomposition of the fission matrix, and it is adopted to solve the coupled problem via the Newton method. This avoids numerical differentiations commonly adopted in Jacobian-free Newton–Krylov methods that tend to become expensive and inaccurate in the presence of Monte Carlo statistical errors in the residual. The proposed approach is presented and preliminarily demonstrated for a simple two-dimensional pressurized water reactor case study

NUCLEAR DATA UNCERTAINTY QUANTIFICATION IN MOLTEN SALT REACTORS WITH XGPT

In the framework of the European project SAMOFAR, a preliminary uncertainty propagation and quantification is carried out, focusing the attention on the influence of nuclear data uncertainty on some relevant neutronic parameters. Relying on the recently developed nuclear data sampler code SANDY and on the xGPT capabilities implemented in the Monte Carlo code SERPENT-2, the uncertainty contributions to the effective neutron multiplication factor, keff, due to the fissile and breeder nuclides can be quantified using a first-order sandwich rule. In order to verify the consistency of the uncertainty propagation performed with xGPT, the study is also performed with legacy GPT approach, available in SERPENT-2

Modelling and analysis of the MSFR transient behaviour

Molten Salt Reactors (MSRs) were conceived at the early stages of nuclear energy in view of the favourable features fostered by a liquid fuel. They were developed as graphite-moderated thorium-fuelled breeder reactors till the seventies, when studies on this reactor concept were mostly abandoned in favour of the liquid–metal fast breeder concepts. A decade ago, the MSRs were included among the six GEN-IV systems and a core optimization process allowing for the GEN-IV main objectives led toward a fast-spectrum MSR concept (MSFR – Molten Salt Fast Reactor). Albeit advantageous in terms of U-233 breeding and/or radio-active waste burning, the new concept lacks the notable know-how available for the thermal-spectrum MSR technology. The present paper preliminarily investigates the MSR dynamics, based on the conceptual MSFR design currently available. A primary objective is to benchmark two different models of the MSFR primary circuit, both of them including a detailed and fully-coupled (node-wise) representation of turbulent fuel-salt flow, neutron diffusion, and delayed-neutron precursor diffusion and convection. A good agreement is generally observed between the adopted models, though some discrepancies exist in the temperature-field, with ensuing mild impacts on the reactor dynamics. The performed analyses are also used for a preliminary characterization of the MSFR steady-state and accidental transient response. Some points of enhancement needed in the MSFR conceptual design are identified, mainly related to in-core velocity and temperature fields. The reactor response following major accidental transient initiators suggests a generally benign behaviour of this reactor concept