Science and Technology of Nuclear Installations

Volume 2018, Article ID 4053254, 10 pages

https://doi.org/10.1155/2018/4053254

## Development of a Coupled Code for Steady-State Analysis of the Graphite-Moderated Channel Type Molten Salt Reactor

^{1}Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China^{2}CAS Innovative Academy in TMSR Energy System, Chinese Academy of Sciences, Shanghai 201800, China^{3}University of Chinese Academy of Sciences, Beijing 100049, China

Correspondence should be addressed to Wei Guo; nc.ca.panis@iewoug and Xiang-Zhou Cai; nc.ca.panis@zxiac

Received 15 March 2018; Accepted 20 May 2018; Published 2 July 2018

Academic Editor: Stephen M. Bajorek

Copyright © 2018 Long He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The molten salt reactor (MSR) is one of the six advanced reactor concepts selected by Generation IV International Forum (GIF) because of its inherent safety and the promising capabilities of TRU transmutation and Th-U breeding. In this study, a three-dimensional thermal-hydraulic model (3DTH) is developed for evaluating the steady-state performance of the graphite-moderated channel type MSR. The coupled code is developed by exchanging the power distribution, temperature, and fuel density distribution between SCALE and 3DTH. Firstly, the thermal-hydraulic model of the coupled code is validated by RELAP5 code. Then, the mass flow distribution, temperature field, , and power density distribution for a conceptual design of the 2MWt experimental molten salt reactor are calculated and analyzed by the coupled code under both normal operating situation and the central fuel assembly partly blocked situation. The simulated results are conductive to facilitate the understanding of the steady behavior of the graphite-moderated channel type MSR.

#### 1. Introduction

The research on MSR concept can date back to the 1940s-1960s with the project of the aircraft reactor experiment (ARE) [1] and the molten salt reactor experiment (MSRE) [2, 3] in Oak Ridge National Laboratory (ORNL). The successful design, construction, and operation of MSRE established the basic technologies, provided experimental data for MSR, and led to a conceptual design of the 1000MWe molten salt breeder reactor (MSBR) [4] at ORNL in the 1970s. After that, a series of studies on MSR for Th-U breeding or TRU transmutation were done by France [5], Japan [6], Russia [7], and China [8–10] since the 1980s. With the advantages of inherent safety, excellent neutron economy, and the capabilities of online reprocessing, MSR was selected as one of the six advanced reactors in GIF [11]. In 2011, Chinese Academy of Sciences (CAS) launched the Thorium-based Molten Salt Reactor (TMSR) nuclear system project. It aims to build a 2MWt graphite-moderated liquid fuel molten salt reactor and to solve the key technical problems of TMSR [12].

Unlike the solid fuel reactors, the primary coolant of MSR is a liquid molten salt mixture of carrier salt and fissile material (such as U or Th), which serves as fuel at the same time. The graphite-moderated channel type MSRs generally adopt graphite as neutron moderator. In this type of MSR, most of the fission energy is released directly into the salt [13], and only a small part of energy is deposited in the graphite moderator due to gamma rays and fast neutron slowdown. The fuel salt flowing through the fuel channel transfers the fission energy out of the core and cools the graphite moderator and reflector. The thermal coupling of fuel salt in this type of MSR is achieved through heat conduction in the graphite moderator. Considering the above-mentioned characteristics, detailed understanding of the thermal-hydraulic behavior of MSR is important for its design.

Efforts on the development of suitable simulation tools for the graphite-moderated channel type MSR were made by different authors for different purposes. In ORNL, Engel et al. calculated the fuel salt and graphite temperature distributions of MSRE by an analytical method [14], in which the fuel assembly was equivalent to a hollow cylinder and the radial one-dimensional heat conduction equation was solved analytically. Zhang et al. performed the steady-state analysis for the MSRE by a multiple-channel analysis model, in which the distribution of the velocity and temperature was obtained [15]. Guo et al. developed a multiple-channel analysis code and coupled it with MCNP4c to analyze the steady-state behavior of the MSRE [16]. Křepel et al. developed the DYN1D-MSR [17] code and DYN3D-MSR [18] code for the dynamic analysis of graphite-moderated channel type MSR. The neutron diffusion model was adopted for neutronics calculation. And the one-dimensional single-phase flow model was adopted for the thermal-hydraulic calculation. Kópházi developed a three-dimensional analysis codes DT-MSR [19]. The neutronic physics part of DT-MSR is based on the neutron diffusion model, which extended a term to consider the drift of delayed neutron precursors (DNPs). For the thermal-hydraulic part, the temperature of fuel salt was calculated by the one-dimensional heat convection equation. And the temperature field in the graphite moderator was calculated by the three-dimensional heat conduction equation on a structured mesh. In DT-MSR, the heat conduction in the graphite moderator was coupled to the temperature of fuel salt and the thermal coupling between fuel assemblies was initiatively realized.

Although many tools have been developed for the graphite-moderated channel type MSR, most of them only adopt the one-dimensional heat conduction model for the moderator and neglect the thermal coupling of the adjacent assemblies. Some tools like DT-MSR can simulate the three-dimensional temperature field, but they are based on the structured mesh and need equivalent geometry modification. Therefore, one objective of the present work is to develop an accurate three-dimensional thermal-hydraulic model (named 3DTH hereinafter), which can calculate the temperature field in complex geometries on an unstructured mesh and consider the thermal coupling between different assemblies. Then, a coupled code is developed through exchanging the data between 3DTH and the reactor criticality safety analyses software SCALE [20] and is applied to the steady-state analysis of a conceptual design of the 2MWt experimental molten salt reactor (named 2MW-MSR hereinafter) [21].

In this paper, Section 2 will focus on the neutronic model, thermal-hydraulic model, and coupling code. In Section 3, the correctness of 3DTH will be validated. Section 4 will briefly introduce the 2MW-MSR. In Section 5, the distributions of mass flow, temperature, and power density of the 2MW-MSR under both normal operating situation and central fuel assembly partly blocked situation will be calculated and discussed. Finally, the conclusions are given in Section 6.

#### 2. Theoretical Model

##### 2.1. The Neutronic Model

SCALE [20] is widely used for calculating the criticality, depletion, and reaction rates distribution of reactor core. The TRITON computer code is a multipurpose SCALE control module for transport, depletion, and sensitivity and uncertainty analysis. In this work, the TRITON module is adopted for calculation of criticality and power distribution with a 238-group ENDF/B-VII cross-section data library. However, the TRITON module can only calculate the power of a material number. In order to obtain the power distribution of the fuel salt and graphite, the fuel assemblies are divided into several units in the axial direction, and each unit is labeled with a unique material number. Similar to the calculation of axial power distribution, the radial power distribution is also calculated with different material numbers.

It should be noted that the power distribution calculated by SCALE has not considered the drift of DNPs and decay heat. Since the fuel salt is circulated in the primary loop, the fission products (DNP and the products which generate decay heat) move towards the outlet of the reactor due to the fuel salt flow. For a reactor operating a long time, about 7% of the reactor power is generated in the form of decay heat. The drift of decay heat slightly changes the power distribution in the active core and causes a fraction of decay heat released in the primary loop [22], which will slightly influence the temperature rise and the temperature distribution in the core and primary loop. Because the fraction of delayed neutron (DN) is relatively small, the drift of delayed neutron precursors does not obviously affect the neutron fluxes and the power distribution under the steady-state condition [16, 23].

##### 2.2. The Thermal-Hydraulic Model

A three-dimensional thermal-hydraulic model 3DTH is developed for the graphite-moderated channel type MSR. The temperature distribution in the solid region which includes the graphite of fuel assembly, reflector, and reactor vessel is calculated by the three-dimensional heat conduction model. The steady heat conduction equation can be written as

*λ*_{s} and* T*_{s} are the thermal conductivity and temperature of the solid region, respectively;* Q*_{s} is the power density deposited in the solid region. The outer wall of the solid region and the inner wall of fuel channel employ the adiabatic boundary condition and convective heat transfer boundary condition, respectively.

The fuel salt in the channel is described by the one-dimensional single-phase flow model. Under steady-state condition, the governing equations are momentum, mass, and energy conservation equations:

*v*, *ρ*,* T*_{f},* C*_{p} are the velocity, density, temperature, and heat capacity of the fuel salt, respectively;* A* and* P*_{e} are the flow area and perimeter of the fuel channel, respectively;* P*_{f} is the frictional pressure drop;* Q*_{f} represents the volumetric heat released in the fuel salt;* Q*_{h} denotes the convective heat transfer at the wall of the fuel channel.

The Darcy formula is adopted to calculate frictional pressure drop, which can be written as

*f* and* D*_{e} are the friction coefficient and diameter of the fuel channel, respectively. For the laminar flow* f* can be written as

The thermal coupling of fuel salt and solid region is built by the convective heat transfer boundary condition at the inner wall of the fuel channel. The heat flux* Q*_{h} (in (4)) can be described as

*λ*_{f} and* Nu* are the thermal conductivity of fuel salt and Nusselt numbers, respectively. The empirical correlation provided by ORNL’s experiment is adopted in the 3DTH to calculate the Nusselt numbers [24]. For the laminar flow, the empirical correlation can be written as

*Re*,* Pr*, and* L* are the Reynolds number, Prandtl number, and length of the channel, respectively. In (8), *μ*_{f} and *μ*_{s} are the dynamic viscosity of fuel salt calculated using fuel salt temperature and wall temperature, respectively.

In the 3DTH, the mass flow in each fuel channel is calculated based on the assumption of equal pressure drop over all channels. The line integral of momentum conservation equation (2) along the axial direction of fuel channel can be written as

*ΔP*_{a} is the acceleration pressure drop along the fuel channel;* ΔP*_{f} and* ΔP*_{g} are the friction and gravity pressure drop of the fuel channel, respectively;* ΔP*_{i} and* m*_{i} are the total pressure drop and the mass flow for the fuel channel numbered with i, respectively;* ΔP*_{k_in} is the local pressure drop at the inlet of each fuel channel, which describes the pressure drop caused by the resistance of the flow distribution plate in the bottom plenum;* ΔP*_{k_out} is the local pressure drop at the outlet of each fuel channel, which describes the pressure drop caused by the form resistance of top plenums.* ΔP*_{k_in} and* ΔP*_{k_out} have the form of

is resistance coefficient, which is inputted for each channel.

The average pressure drop of reactor is defined as

In the process of mass flow calculation, the mass flow of each fuel channel will be adjusted according to the deviation between* ΔP*_{i} and* ΔP*_{av} before the condition is met [25], as shown in Figure 1.