## 1 Introduction
This research provides valuable insights for managing icing in ice ponds [15; 16]. [PERSON] et al. investigated the growth and disappearance of lake ice, using Lake Ulansu as a case study, and identified the patterns of change in ice thickness and temperature [17]. In the field of freezing research related to ship structures, [PERSON] et al. conducted experimental research and numerical simulations to analyze the distribution of wind turbine blade icing under offshore environmental conditions. They investigated the impact of icing on the aerodynamic performance of wind turbine blades [18; 19]. [PERSON] et al. performed experimental studies on the changes in the aerodynamic performance of wind turbine blades during dynamic icing, establishing a relationship between performance degradation due to ice accumulation and the blade model [20]. [PERSON] et al. examined the effects of ice crystal growth on the performance of heat exchangers under various dimensionless conditions, identifying the optimal environmental conditions for their operation [21]. [PERSON] et al. executed numerical simulations on the icing of ship superstructures and polar offshore platforms, determining the ice shape distribution and icing characteristics of different structures in polar environments [22; 23]. Given the complex environmental conditionswithin a ship's ballast water tank, this paper employs numerical simulation methods to study and analyze the freezing process in the ballast water tank. In summary, numerous scholars have conducted extensive research on the mechanisms, phenomena, and laws of icing. However, the study of ice shape evolution in the ballast tanks of polar ships remains limited, with many issues still requiring further investigation. Unlike the freezing processes observed in indoor ice pools, the environmental conditions in polar regions are complex and harsh. These conditions include significant temperature fluctuations, high humidity levels within the cabin, and the presence of various impurities in ballast water, all of which complicate the prediction of ice shape evolution. To explore the variation in the temperature field and the evolution of ice shape in ballast tanks under polar environmental conditions, this paper analyzes ice growth by integrating the volume fraction equation with a phase-change heat and mass transfer model. Additionally, it examines the temperature field variation in ballast tanks under different environmental parameters. Based on the characteristics of the temperature field, the trends and patterns of ice shape evolution are presented. This study focuses on the ballast tank of a polar LNG carrier as the research subject. Taking into account the environmental and climatic conditions in polar regions, we utilize Fluent 2022 fluid calculation software to integrate interphase mass, momentum, and heat transfer models into the Volume of Fluid (VOF) multiphase flow model. A numerical model for the freezing of ballast water is established, and the freezing process is simulated. The main research contents of this paper are as follows: Section 2 introduces the physical model of heat and mass transfer in the ballast tank. It elaborates on the fundamental theory and control equations used in the numerical calculations, as well as the boundary conditions for these calculations. Additionally, it outlines the numerical calculation process and verifies the reliability of the numerical model. Finally, Section 3 analyzes the variations in the temperature field and ice formation under different environmental parameters, revealing how changes in the temperature field influence the evolution of ice shape.