## 1 Introduction  
In recent years, global warming has accelerated the melting of Arctic sea ice, enhancing the navigability of the region to some extent [1]. Simultaneously, the Arctic is abundant in natural gas resources; according to a report by the U.S. Geological Survey, the undeveloped natural gas reserves in the Arctic account for 30% of the global total [2]. As a result, navigation and resource development in the polar region have increasingly become a focal point of interest for countries worldwide. The vigorous development of polar resources is accompanied by significant risks for ships operating in polar regions, including material failure, harsh environmental conditions, structural ice accumulation, and other hazards. Due to the unique geographic environment of polar regions, structures such as ballast water tanks are prone to freezing phenomenon, and ballast water freezing is extremely hazardous to ships but is often easily ignored [3]. The freezing of ballast water will form the ice layer, and the ice layer will have an expansion effect on the structure; during the freezing process, it will be constrained by the bulkhead,which will exert a freezing expansion force on the structure, and when the temperature of the ice layer rises, the ice layer will exert a temperature expansion force, which will have a certain effect on the structure and reduce the service life of the structure [4; 5]. Additionally, ice accumulation increases the weight of the ship, raises its center of gravity, and prolongs the duration of transverse rocking, all of which compromise the safety and stability of the vessel and may lead to serious safety incidents [6]. Therefore, to ensure the safety of the ship and its crew, it is essential to conduct comprehensive studies on the icing of ballast tanks in LNG carriers operating in cold regions. Ballast water tank icing analysis can be mainly divided into temperature field analysis and ballast water freezing analysis. At this stage, the analysis of the temperature field in ballast water tanks has developed into a more comprehensive research framework. [PERSON] et al. conducted a study on the temperature field of floating LNG membrane tanks in harsh environments, analyzing the effects of various heating system states, double-row tank spacing, and water injection in both the middle and longitudinal compartments on the temperature field [7]. [PERSON] et al. employed finite element analysis software to investigate the temperature field distribution of the hull, support structure, and compartments of LNG ships. They identified the temperature field distribution patterns of the compartments under different structural configurations, providing valuable data for the low-temperature design of LNG ship compartments [8; 9; 10]. [PERSON] et al. utilized computational fluid dynamics (CFD) methods to examine the coupled heat transfer characteristics and temperature field distribution of the cargo sealing system (CCS) and the liquid cargo hold. By integrating the volume of fluid (VOF) model, they determined the variations in the temperature and velocity fields within the hold [11; 12; 13]. At present, basic research on the issue of ballast water freezing remains limited, and the research framework has yet to be fully developed. However, in the realm of freezing challenges related to marine structures--such as ice pools, wind turbine blades, and ships--scholars have conducted extensive studies and achieved significant results, which offer valuable insights for the investigation of ballast water freezing. In the area of ice pool freezing research, [PERSON] et al. developed a predictive model for ice growth based on ice pools in Hamburg, Germany, which provided data on the growth rate and final thickness of the ice [14]. [PERSON] et al. employed the finite volume method to numerically simulate the freezing process in a saltwater pond, obtaining the distribution characteristics of the ice thickness and temperature under varying water temperatures.