## 1 Introduction  
Carbon dioxide (CO\({}_{2}\)) is one of the most significant greenhouse gases; however, it is still emitted into the environment from large industrial facilities. Carbon capture and storage (CCS) technologies have been developed as an option to stabilize the concentration of CO\({}_{2}\) in the atmosphere [1]. Generally, the CCS chain consists of three stages: capture, transportation, and storage [2]. Ocean storage is becoming the most promising approach to sequestering CO\({}_{2}\) due to the large capacity of deep saline aquifers [3]. Although pipelines have recently been developed for transporting CO\({}_{2}\), there are major obstacles related to the initial installation, as well as maintenance costs [4]. Alternatively, CO\({}_{2}\) shipping vessels (or water carriers) are more attractive alternatives when considering maintenance costs [5]. To be specific, the capacity of a CO\({}_{2}\) transport ship is determined by the daily production of CO\({}_{2}\) and the sailing period of the ship [6]. Much effort to build CO\({}_{2}\) transport ships has been conducted in the Republic of Korea, because Korea is a peninsula surrounded by the sea [7]. Currently, CO\({}_{2}\) transport is still in the development stage but, because of its importance, a persistent effort is being made regarding the better design of transport ships.  
In general, gaseous CO\({}_{2}\), compressed and liquefied, is stored in tanks for efficient transportation [8]. Because the tanks are used for transportation on the ocean [9], the possibility of gas leakage should be examined for confirming the safety of the transportation facilities [10]. The transport ships may be damaged if an accidental CO\({}_{2}\) leak occurs in the container during sailing [11]. When an accidental leak occurs, liquefied CO\({}_{2}\) undergoes rapid vaporization and expansion, causing a significant pressure rise [12]. Even if CO\({}_{2}\) is not classified as a dangerous substance, two important factors clearly affect safety, one of which is the occurrence of personal injury such as suffocation by workers exposed to an environment with a high CO\({}_{2}\) concentration [13]. The other is associated with thermal damage to the tank structure during leakage, because very cold CO\({}_{2}\) gas might impinge on the cargo walls, causing a local change in solid temperature and thermal deformation [14]. Thus, we need a good deal of information on thermal characteristics depending on different scenarios of gas leakage.  
In spite of its importance, as noted above, it is very hard to directly measure temperature and CO\({}_{2}\) concentration in a real-scale cargo to obtain information on thermal behavior during leakage. As an alternative, the computational fluid dynamics (CFD) simulation is a promising way to get useful information on the variations in concentration and thermal characteristics during the leakage of CO\({}_{2}\) gas. Thus, to provide a better understanding when designing CO\({}_{2}\) cargo facilities, the present study aims to numerically investigate CO\({}_{2}\) propagation characteristics inside a container and to examine thermal effects on the cargo walls on which thermal damage might occur. We also suggest a new engineering model with an effective area concept to consider the phase change during leakage. Moreover, the influence of crack size on the transient evolution of CO\({}_{2}\) concentration and structure temperature is analyzed.