### 1. Introduction

_{x}), nitrogenoxides (NO

_{x}), and carbondioxide (CO

_{2}).

_{x}regulation, the sulfur content in fuels used in an emission control area (ECA) is limited to 0.5% as of 2020, and according to the NO

_{x}regulation, it should satisfy the “Tier II” level in general waters and “Tier III” in the ECA as of 2016. In addition, regulations on CO

_{2}emissions have been gradually applied by introducing the energy efficiency design index (EEDI). The EEDI refers to the amount of CO

_{2}(gCO

_{2}/t·mile) generated by a new ship that carries one ton of cargo for one mile. The EEDI has been proposed by the IMO’s Marine Environmental Protection Committee (MEPC) and requires a 10% reduction in CO

_{2}emissions at each phase as of 2008 (Ivica and Ante, 2015). In the MEPC 72nd conference in May 2018, it was proposed to advance to Phase II (20% CO

_{2}reduction) in 2020 and to Phase III (30% CO

_{2}reduction) in 2025. Furthermore, it was proposed to advance to Phase IV (40% CO

_{2}reduction) in 2030 instead of 2040 (IMO, 2018).

_{x}, NO

_{x}, and CO

_{2}, which are pollutants emitted from ships. According to Alternative Fuels Insight (AFI) provided by DNV-GL, there are 170 LNG-operated ships and 147 LNG-propelled ships as of October 2019, and 55 more ships will be built by 2020 (DNV-GL, 2019).

*k*

*) and the heat flux (*

_{e}*q*) according to the vacuum level have been verified through experiments with various insulation materials (Fesmire, 2015).

### 2. Optimum Shape Design of LNG Fuel Tank of Tugboat

### 2.1 LNG fuel tank space in tugboat

^{3}even if the cylinders are simply stacked. In contrast, for the LPV designed in this study, the volume is 37.5 m

^{3}because it can utilize most of the fuel tank space. In other words, the LPV is approximately 55% more space-efficient than cylinder tanks. In addition, the maintenance of the cylindrical tank is complicated because each tank is equipped with pipes and safety valves for fuel movement, whereas the maintenance of the LPV is relatively simple because it is equipped with fewer pipes and safety valves. Therefore, the LPV will incur lower maintenance cost.

### 2.2 Lattice pressure vessel shape design

*σ*

_{m}= primary general membrane stress

*σ*

_{L}= primary local membrane stress

*σ*

_{b}= primary bending stress

*σ*

_{g}= secondary stress

*σ*

_{UTS}= ultimate tensile strength

*σ*

_{Y}= yield strength

### 3. Analysis of BOG Generation by Insulation

### 3.1 Insulation Information

### 3.2 BOG generation analysis

*t*) can be determined from the insulation thickness (

*k*), thermal conductivity (

*A*), and cross-sectional area (

*R*). Eq. (9) helps calculate the heat intrusion (

*q*). Dividing the thermal resistance (

*T*

*) obtained from Eq. (8) by the difference between the external temperature (*

_{amb}*R*) and the temperature of the LNG (

*T*

*) results in thermal intrusion (*

_{LNG}*q*). The equation for calculating the BOG, or the LNG evaporating due to heat intrusion (

*q*), is shown in Eq. (10). The BOG calculated using Eq. (10) is the amount of the LNG that evaporates during a day and is calculated by the ratio of the heat intrusion (

*q*) and the latent heat of evaporation of the LNG (

*h*

_{fg}). Finally, to calculate the boil-off rate (BOR), the BOG relative to the amount of the LNG in the fuel tank should be calculated using Eq. (11). The LNG in the fuel tank is obtained by multiplying the density of the LNG (

*ρ*

*), the volume of the fuel tank (*

_{LNG}*V*), and the liquid fraction (

*LLF*). where

*t*insulation thickness (m)*k*conductivity (W/m·K)*A*surface area (m^{2})*R*thermal resistance (K/W)*T*ambient temperature (K)_{amb}*T*temperature (K)_{LNG}*q*heat ingress (kW)*h*_{fg}heat of vaporization (kJ/kg)*LLF*liquid level fraction*ρ*density (kg/m^{3})*V*volume (m^{3})*BOG*boil off gas (kg/day)*BOR*boil off rate (%/day)

### 4. Results and Discussion

### 4.1 Shape design result of fuel tank

^{3}and 25.37 ton, respectively. Table 4 shows the materials, density, physical properties, allowable stress, design pressure, and LNG density information in the design. The load conditions used in the design include internal pressure, the weight of the LNG, and gravity.

### 4.2 BOG generation result

### 5. Conclusion

^{3}and a fuel tank is designed with rounded corners to minimize surface area. The surface area of the fuel tank was 79.8 m

^{2}when the LPV was applied, and the volume efficiency in the same fuel tank space was increased by 55% compared with that of the cylindrical pressure vessel. The finite element analysis considering the fuel tank internal pressure, weight of the LNG, and gravity resulted in a von Mises stress of 204.3 MPa, which is within the allowable stress and thus confirmed the safety of the design.