# Experimental and Numerical Study of Orifice Coefficient of Cargo Tank Design of LNG Vessels
## 1 Introduction  
The designing liquefied natural gas (LNG) tanks to be installed in LNG vessels requires a high level of design and safety evaluation to transport the cryogenic fluid cargo. The type of tank system is representative of a membrane type prismatic tank (type A) and independent tank (type B) [1]. In the case of the independent tanks, since they have structures that are vulnerable to a fatigue damage, they are designed in consideration of high safety for cracks. There have been many studies on the membrane cargo containment systems (CCS) due to widespread application [1, 2]. However, the independent CCS has not been used primarily in the past, and demand has been increasing in recent years. Therefore, there is little research related to the design technology of the independent CCS. The independent LNG tanks (type B) are designed and manufactured through precise design verification stages, such as wave load calculation, detailed stress analysis, fatigue analysis, and thermal stress analysis [3]. In addition, there is a possibility of fatal damage if the LNG leakage is during operation time of the LNG vessels. Therefore, design techniques are needed to prevent cracking and catastrophic damage in the initial design stage [4]. The LNG CCS sets up primary and secondary barriers for storing liquid cargo in order to ensure safety cargo transportation. This shallbe designated as a regulation by the international maritime organization (IMO), an international regulation [1]. Furthermore, a second barrier with a drip tray system is installed to store discharged liquid cargo for a predetermined period and ensure the safety of the tank for a period of operating time [3; 4]. This design method is generally known as the leak before failure (LBF) concept. In the event of a crack in the tank as shown in Figure 1, the leakage of LNG cargo from the containment system is safely stored in the drip tray even if it does not spread rapidly within the specified days (15 days) [1]. This is designated as an international regulation that must be applied when designing an LNG cargo containment system (CCS) [1]. During the design of the containment system, the leakage rate (primary barrier) through cracks in the external shell plate shall be generally determined for the size of cracks in the cargo tank. However, the international regulations also state that the CCS design process is generally determined by the orifice formula presented in hydrodynamics. In particular, the orifice coefficient uses 0.1 as the experimental result presented by the design guidance [1]. This is the main factor in the drip tray capacity design for safe storage of discharged fluid cargo. Therefore, in the drip tray design stage, the leakage rate for representative crack size should be calculated and its capacity calculated to determine the volume of the drip tray. The assessment of liquid cargo leakage in the tank system represents an important aspect, which is determined by the orifice coefficient [1]. In the conservative view of the general design process, taking into account the greater leakage of LNG liquid is a general approach to dimensioning the size of the leak protection system. The general design process for the LNG tanks presented by the design guidance and shipyard engineer is based on a simple theoretical and empirical method of calculating the orifice coefficient of liquid cargo based on hydrodynamic theory [5; 6; 7; 8; 9; 10]. The equation presented in this guidance is the same theory as the equation presented in consideration of the flow of fluid mechanics and the geometric characteristics of orifice shapes [1; 5]. However, in the case of the LNG tank loaded with the fluid cargo, the crack size and operating conditions vary for the conditions under which the leakage occurs, so it will be necessary to apply several approaches with an experiment or numerical analysis method considering the leakage characteristics of the fluid for various operating conditions.