Lattice Boltzmann modeling of natural circulation loop with emphasis on non-Boussinesq mechanism

The natural circulation loop is crucial for the safe and stable operation of nuclear reactors and other applications. Traditional numerical algorithms, based on the Boussinesq approximation, have limitations when dealing with large temperature differences and density disparity, and they do not fully address fluid compressibility. This paper adopts the decoupled and stabilized lattice Boltzmann method (DSLBM) with a non-Boussinesq algorithm to study the natural circulation loop. The DSLBM provides a detailed flow description under large temperature and density differences, incorporating the pseudopotential multiphase model, temperature equation, and state equation, without relying on assumptions. The study examines the loop's performance under various temperature differences, central height differences, and heating source lengths, focusing on mass flow rate, driving head, and heating power. It reveals the energy performance, flow characteristics, and heat transfer properties of the loop, highlighting the physical mechanisms involved. Comparison with the empirical formulation of the incompressible equation from the theoretical aspect shows that when the temperature difference coefficient is lower than 0.15, the two methods are not much different from each other. When the temperature difference coefficient reaches 0.2, 0.3, and 0.4, the difference between the two methods is 9.47%, 19.11%, and 42.64%, respectively. Consequently, the Boussinesq approximation can be compensated by DSLBM, which proves the value of the application of the algorithm in exploiting the compressibility of fluids. The dimensionless fitting correlation with greater universality is obtained, which helps to predict the properties of the natural circulation loop with varying temperature differences, friction coefficients, and geometric structures. The research in this paper will lay the foundation for optimizing the system design of the natural circulation loop and improving energy utilization efficiency.