# Experimental and Numerical Study of Orifice Coefficient of Cargo Tank Design of LNG Vessels
## 1 Introduction
The basic concept of this study is to examine in an experimental and numerical method whether the design formula applied at the design stage is reasonable if cracks occur in LNG tanks. It is an  
Figure 1: Configuration of independent liquefied natural gas (LNG) tank with drip tray. experimental review, especially of the parameters used in the design equation, orifice coefficient. Even in hydrodynamics, orifice flow is based on simplified flow and fluid properties. Since it is difficult to consider the effects of complex multidimensional viscosity of fluid flow, it is generally reflected in empirical form. This theory is also applied in the design of the drip tray of LNG tanks. In the study related to the orifice of fluid, the fluid leakage is generally found in a variety of studies of physical and apparent losses associated with accidents. These orifice cases have a significant impact on the economic and operational management of the relevant systems. Therefore, because there are significant failures and manifestations, various research cases can be found (e.g., actual fluid burst) [10; 11; 12; 13; 14; 15]. Even in these studies, for estimating the liquid losses deriving from the events, hydraulic characterization of the leakage is required, such as the relation between the leak outflow and the hydraulic head, the geometric features of the hole, and the mechanical characteristics of the tank. In addition, for compressible fluids, an empirical expansion factor is applied to the discharge coefficient equation to adjust for the fluid density variation due to changes in pressure upstream and downstream of the orifice plate. Thus, the orifice coefficient should be dependent on the different conditions [5]. This study examined the orifice rate calculation method proposed by the Det Norske Veritas (DNV) class guidance as an international guidebook for the estimation of the orifice rate in the design process of the LNG tank. However, it is impossible to measure the amount of liquid cargo leakage in an LNG tank where the actual crack occurred. Therefore, experimental equipment was installed in the similar condition of the operating conditions of the LNG vessels, and the orifice flow weight was measured using crack specimens. In addition, the crack specimens applied to the flow-rate measurement have too many cases to consider the actual crack geometry and have experimental limitations in processing them. Therefore, the size of the crack was assumed and applied in a rectangular shape based on the typical crack area applied in the LNG CCS strength assessment. In order to simulate the loading condition of the LNG tanks, pressure containers were manufactured, and the internal pressure conditions of the container were adopted to the design pressures of LNG vessels. In the experiment, the internal pressure of the pressure container was adjusted, and the liquid effects were reflected by using water. In order to reflect the effects of LNG, a series of numerical analyses were performed through CFD (Computing Fluid Dynamics) simulations to approach reasonable results [10; 11; 16; 17]. In order to investigate the validity of CFD model, the leakage flow weight and analysis results were compared through experiments using water first, and the CFD model assuming the incompressible fluid was confirmed to be reasonable. Therefore, simulations applied with the fluid characteristics of LNG were carried out using the proven CFD model. Then, the results were analyzed to confirm orifice characteristics of LNG in the tank. The purpose of this study is to provide the basis for the review of the orifice coefficient applied in the design of the LNG tank. Therefore, the flow rate of liquid leakage was simulated when cracks occurred in LNG tanks through experiments and CFD analysis. To simulate several leakage states, an incomprehensible CFD model was applied, which assumes that the mass flow rate through an orifice is based on mass conservation [17; 18].