Transactions of the Korean Nuclear Society Virtual Spring Meeting July 9-10, 2020 Study about the impact of Pr effect on the validity of Boussinesq approximation in molten salt natural circulation Dong Hun Lee, In Cheol Bang* Department of Nuclear Engineering., Ulsan National Institute of Science and Technology (UNIST)., 50 UNIST-gil., Ulju-gun., Ulsan., Republic of Korea *Corresponding author: +82-52-217-2915, +82-52-217-2429, icbang@unist.ac.kr 1. Introduction (2) The variation of all other fluid properties with temperature and pressure is negligible. Natural circulation that has been studied as a key (3) Neglecting viscosity dissipation phenomenon for a purely passive safety occurs owing to the buoyancy resulting from density differences Although it is usually valid when the temperature between the heat source and heat sink that system can differences are small, unique characteristics of molten become independent of the external pumping power salt induce large temperature sensitivity of fluid even in severe accidents. thermophysical properties in the thermal boundary layer. There have been several studies about natural And under the natural circulation, it has a weak driving circulation in the molten salt to investigate the flow force compared to that of forced circulation that characteristics for improving heat transfer effectively thermal-hydraulic characteristics are strongly affected and passive safety as a heat transfer fluid. [1-3] Molten by geometrical features and thermophysical properties. Salt reactor (MSR) is an innovative system that uses the It is important to predict the temperature and velocity concept of liquid fuel, and they are highly safe and field accurately to predict the power level or decay heat useful reactor which is understudying in many countries. in the MSR system due to the strong coupling of On the one hand, molten salt has high heat capacity, thermal-hydraulic and neutronics [4]. But distortions of high boiling temperature, and low vapor pressure that velocity and temperature distribution can occur as it can be efficiently operated at a high temperature. On the involves drastic temperature changes near the wall other hand, a pump is not required owing to the low because of the high Pr of molten salt, making the mass flow rate when using natural circulation in passive numerical analysis difficult. This can trigger the wrong safety. estimation of power peak distribution of molten salt The molten salt in the reactor is a typical high Prandtl reactor that can induce hot spots due to the deposition of number fluid that has a high heat capacity, viscosity, fuel on the wall which is an important failure and low thermal conductivity, which induce large phenomenon in MSR. temperature gradients in the boundary layers. The In this work, we aim to comprehensively analyze the Prandtl number Pr (1) is the ratio of the momentum effect of the assumptions of the Boussinesq diffusivity ν to the heat diffusivity α and is a key approximation, i.e., that the properties change only in thermal-hydraulic dimensionless number that the gravitational term and that viscous dissipation can determines the heat transfer mechanism, i.e., the be neglected, on the molten salt’s natural circulation contributions of convection and conduction in the fluid. w/wo internal heat generation (IHG). The heat transfer and flow characteristics in the laminar natural circulation loop were investigated numerically and (1) analytically. To study about thermohydraulic behavior of molten salt w/wo IHG and the validity of the In a high-Pr fluid, heat is mainly transferred by aforementioned assumption will improve the accuracy convection. This implies that in the natural circulating of the analysis of molten salt, contributing to the flow of molten salt, a thin thermal boundary layer and a reduction in the uncertainties of the system and the high-temperature gradient appear near the wall as the optimal design of molten salt reactors in the future. fluid passes through the heater or cooler. This study purpose on the study of the validity of the 2. Natural Circulation Modeling Boussinesq approximation in a molten salt natural circulation with the different heating conditions. This For the simulation, a vertical heater and vertical approximation was mostly used in the analysis of cooler (VHVC) configuration design as shown in Fig. 1 natural circulation not only typical fluid but also in were selected for neglecting flow instability issues [5], molten salt for saving time with applied three and a HITEC (KNO3-NaNO3-NaNO2) nitrite molten assumptions in the analysis: salt was selected as the heat transfer medium. The flow and temperature fields of the molten salt were analyzed (1) Density variations as a linear function of the using the open-source CFD package OpenFOAM [6]. thermal expansion coefficient only in the body force term
Transactions of the Korean Nuclear Society Virtual Spring Meeting July 9-10, 2020 Initial temperature 573 K 3. Results and Discussions This section discusses flow and temperature behavior and the validity of the Boussinesq approximation of the molten salt natural circulation with different heating condition. Figs. 2 and 3 showed the temperature and velocity fields of both models in 1250 W external heating conditions in radial direction of pipe. Both models showed the thin thermal boundary layer, which is characteristic of high Pr fluids. The flow characteristics of molten salt were induced due to the high-temperature gradients near the wall, which cause a local density gradient that flows near the wall region and drags the bulk region. Velocity profile s reflected this fluid’s motion; the velocity of the fluid near the wall became faster than in the bulk region when molten salt passed the heater inlet to the outlet. Significant velocity gradients between near the wall and the bulk region was generated because of an effect of the viscous shearing Fig. 1. Molten Salt VHVC domain for analysis forces due to high viscous characteristics. To investigate the temperature sensitivity of thermophysical properties The CFD analysis of molten salt was conducted to near the wall, each field of the temperatures and understand the single-phase flow characteristics of velocities of both models was compared. Both models natural circulation in the high-Pr fluid. The pre-built showed a very similar temperature trend. However, the solver buoyantSimpleFoam for steady-state, buoyant, velocity difference between the two models was turbulent flows were selected with different significant near the wall. The magnitude of bulk region thermophysical properties model. To analyze the velocity is similar in both cases but, the significant validity of the Boussinesq approximation for molten overshoot in the velocity profile is observed near the salt’s natural circulation, simulat ions with both models wall region in the non-Boussinesq case. This means that for the mass, momentum, and energy equations were the weak driving force of natural circulation is easily conducted. The boundary and initial conditions of the affected by the temperature sensitivity of simulation are listed in Table I. The initial temperature thermophysical properties that affect the performance of was set to 573 K, which is above the melting point of the natural circulation near-wall region. Rapid change of HITEC (~415K), and the loop was operated at 1 atm. temperature in the thermal boundary layer induces a Various values of uniform external heat flux in the large variation of viscosity, it means that the non- heater and internal heat generation were set, and the Boussinesq model showed more high viscosity in the heat sink was specified as a constant wall temperature. near-wall region. High viscosity induced more shear viscous stress effect in the near-wall region, it generated TABLE I: CFD initial and boundary conditions the velocity differences of the bulk region and the near- wall region were bigger than the constant model. Domain Further increase of buoyancy forces enhances the Value parameter differences in the core and the viscous layer, which means that the Boussinesq model showed less heat Working fluid HITEC (KNO3-NaNO3-NaNO2) transfer. Therefore, the application of the Boussinesq approximation in the analysis of the natural circulation External uniform heat flux, Heating Condition Internal Heat Generation (1250 – 2500 W) of molten salts shows distortion occurring at heat transfer, especially in the velocity fields near the wall. Cooler condition Constant wall temperature
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