Structural Assessment of Independent Type-C Liquid Hydrogen Fuel Tank

Abstract

As environmental pollution has become a global concern, regulations on carbon emissions from maritime activities are being implemented, and interest in using renewable energy as fuel for ships is growing. Hydrogen, which does not release carbon dioxide and has a high energy density, can potentially replace fossil fuels as a renewable energy source. Notably, storage of hydrogen in a liquid state is considered the most efficient. In this study, a 0.7 m³ liquid hydrogen fuel tank suitable for small vessels was designed, and a structural analysis was conducted to assess its structural integrity. The extremely low liquefaction temperature of hydrogen at −253 °C and the need for spatial efficiency in liquid hydrogen fuel tanks make vacuum insulation essential to minimize the heat transfer due to convection. A composite insulation system of sprayed-on foam insulation (SOFI) and multilayer insulation (MLI) was applied in the vacuum annular space between the inner and outer shells, and a tube-shaped supporter made of a G-11 cryogenic (CR) material with low thermal conductivity and high strength was employed. The material selected for the inner and outer layers of the tank was STS 316L, which exhibits sufficient ductility and strength at cryogenic temperatures and has low sensitivity to hydrogen embrittlement. The insulation performance was quantitatively assessed by calculating the boil-off rate (BOR) of the designed fuel tank. Structural integrity evaluations were conducted for nine load cases using heat transfer and structural analyses in accordance with the IGF code.

1. Introduction

The exacerbated severity of global environmental pollution has led the International Maritime Organization (IMO) to actively regulate the carbon emissions of maritime vessels, whereby demand for eco-friendly fuels has increased [1]. Consequently, the interest in hydrogen energy, which has no carbon emissions, is on the rise [2].

The IMO regulations on SO_x and NO_x emissions have led to a notable increase in the demand for and usage of liquefied natural gas (LNG) as an eco-friendly fuel. However, LNG is not yet recognized as a completely eco-friendly fuel because it emits some carbon dioxide. Globally, there is a growing aspiration to achieve carbon neutrality by 2050, with numerous nations striving towards this goal by establishing policies with respect to carbon neutrality. This heightened focus on carbon neutrality has led to an interest in renewable energy sources with no carbon emissions.

Renewable energy sources, such as hydrogen, solar, and wind energies, are prominent examples of carbon-free energy. Although techniques for generating electricity through solar, wind, and hydropower eliminate carbon emissions during the energy production process, they are intermittent and unpredictable due to factors such as sunlight and wind availability [3]. Therefore, hydrogen energy, which is characterized by stable and consistent production, has received significant attention. Hydrogen is nontoxic and abundant in naturally occurring water and hydrocarbon forms [4]. When used as a fuel, hydrogen produces only water as a by-product, making it a sustainable energy resource and a recognized alternative to conventional fossil fuels [5]. Therefore, a transition from conventional fuels to hydrogen is anticipated. However, the practical application of hydrogen fuel in industrial settings depends heavily on the ability to store it safely and efficiently, highlighting the need for a thorough examination of hydrogen storage technologies [6].

Hydrogen can be stored using various physical and chemical methods. The physical methods for hydrogen storage include compressing hydrogen at high pressures (350–800 bar) to store it as a high-pressure gas, liquefying hydrogen at −253 °C to store it in a liquid state, and exposing hydrogen to low temperature and high pressure exceeding the critical point to store it as a supercritical fluid, as in the cryo-compressed method. Chemical methods for hydrogen storage include adsorption of materials such as carbon nanotubes or metals, chemical stabilization using materials such as metal hydrides, and utilization of alloyed metals to store hydrogen as interstitial hydrides [4,7,8,9].

Volumetric and gravimetric energy efficiencies are critical considerations in hydrogen storage. Hydrogen undergoes liquefaction at −253 °C, and its density in the gaseous state at 700 bar pressure is approximately 42 kg/m³, whereas in the liquid state at ambient pressure, its density reaches approximately 70.8 kg/m³.

Table 1. Energy density of liquid hydrogen, high-pressure gaseous hydrogen, and gaseous hydrogen at ambient pressure.

Type	Energy per Liter (MJ/L)	Energy per kg (MJ/kg)
Liquid hydrogen	10.1	143
Compressed hydrogen	5.6	143
Vapor hydrogen	0.0107	143

lists the energy densities of hydrogen in liquid, high-pressure gaseous, and ambient-pressure gaseous states, with liquid hydrogen exhibiting the highest energy density per unit volume [10]. Consequently, liquefaction of hydrogen for storage is widely acknowledged as the most practical and efficient method [11,12].

Effective management of storage and transport of cryogenic fluids at extreme temperatures necessitates storage methods that feature a robust thermal insulation performance. The experience acquired from using LNG, which involves liquefaction at −163 °C, can be utilized as a reference for storing liquid hydrogen, given the shared requirements of managing cryogenic fluids.

Considerable research has been conducted on type-C tanks designed for the storage of cryogenic fluids. Park et al. performed a structural integrity assessment of a type-C LNG fuel tank using finite element analysis and compared stainless steel and aluminum alloy as tank shell materials [13]. In addition to structural robustness, type-C tanks provide modular flexibility, simplified retrofitting of small vessels, and compatibility with high-efficiency insulation systems. Their ability to satisfy pressure vessel standards and integrate with vacuum or multilayer insulation systems makes them ideal for cryogenic hydrogen storage in the maritime sector [14].

In previous research, Liu et al. conducted a parametric study to identify the optimal location of a vapor-cooled shield (VCS) in the insulation layer of rigid polyurethane foam for a large liquid hydrogen type-C tank made of STS 316L [15]. Choi et al. reviewed the codes and standards for designing liquid hydrogen fuel tanks for heavy-duty trucks and through structural and thermal analyses, verified that a liquid hydrogen fuel tank is suitable for 540 HP-grade heavy-duty trucks and satisfies the permissible limits of the codes and standards [16]. Winnefeld et al. presented a design tool for cryogenic hydrogen tanks in aircrafts and verified the significance of considering the hydrogen mass required for venting, using a specific mission for tank design based on an analysis of storage density sensitivity [17]. In this study, a fundamental investigation was conducted on the design of type-C liquid hydrogen fuel tanks applicable to small vessels such as ferries, and a finite element analysis was performed to assess the feasibility of designing a 0.7 m³ type-C liquid hydrogen fuel tank using a sprayed-on foam insulation (SOFI) and multilayer insulation (MLI) composite system. Although existing studies have explored either the thermal or structural aspects of liquid hydrogen storage [18], integrated analyses that use the finite element method (FEM) to evaluate composite insulation systems such as SOFI–MLI are rare, especially in small-scale marine applications. This study is therefore significant in addressing that gap by proposing a compact type-C LH₂ tank design that balances structural integrity and thermal efficiency for small vessels. Accordingly, this study aims to evaluate the structural and thermal feasibility of a 0.7 m³ type-C liquid hydrogen fuel tank for small marine vessels, using finite element analysis with a SOFI–MLI composite insulation system.

2. Design of Type-C Liquid Hydrogen Fuel Tank

Hydrogen is liquefied at −253 °C at ambient pressure; therefore, insulation is a critical factor in the storage of liquid hydrogen. Due to heat ingress, the internal liquid hydrogen evaporates and forms a gaseous boil-off gas (BOG). The BOG generation rate relative to the total volume of liquid hydrogen stored in the fuel tank is denoted as the boil-off rate (BOR). The BOG increases the pressure within the tank, and when the internal pressure exceeds a certain level, gaseous hydrogen is released, resulting in hydrogen loss. The quantity of heat input and the volume of BOG generated vary depending on the tank’s insulation performance, and a higher BOR can lead to significant economic losses [19].

An appropriate type of fuel tank is required to minimize the losses in liquefied gas fuel tanks. The IMO classifies the tanks used for the transport of liquefied gases into membrane-type integrated tanks and type-A, type-B, and type-C independent tanks. Type-A independent tanks are designed based on classical ship structure analysis, with the vapor pressure designed to be less than 0.07 MPa. Type-B independent tanks are designed using model tests and refined analytical methods, also with vapor pressure of less than 0.07 MPa. Type-B independent tanks are further divided into self-supporting prismatic shape type-B of the IHI Corporation (IHI SPB) or spherical-Moss type depending on the shape. A spherical shape can reduce sloshing effects. Type-C independent tanks are designed based on pressure vessel criteria, with a design vapor pressure of 0.2 MPa or higher. These pressure vessels enable efficient BOG management and are suitable for relatively small-capacity tanks with flexible utilization. Membrane-type integrated tanks that are commonly used in large vessels for long-distance transportation have a structure in which the internal hull supports the tank load.

Type-C independent tanks, commonly used as fuel tanks, are designed as spherical or cylindrical pressure vessels with vapor pressures exceeding 0.2 MPa. In this type of tank, the risk of fluid leakage is low because pressure is applied inside the tank, and a secondary barrier is not required. In addition, they facilitate BOG management, making them suitable for use in fuel tanks of small vessels.

Liquid hydrogen and LNG are similar because they are cryogenic fluids. However, when considering the design of liquid hydrogen fuel tanks compared to existing LNG fuel tanks, differences exist. A comparative analysis of liquid hydrogen and LNG is presented in

Table 2. Comparison of properties of liquid hydrogen and liquefied natural gas (LNG).

	Liquid Hydrogen	LNG
Boiling point	−252.8 °C (20 K)	−163 °C (110 K)
Liquid density	70.78 kg/m3	410–500 kg/m3
Gas density	0.084 kg/m3	0.717 kg/m3
Latent heat of vaporization	31 kJ/L (446 kJ/kg)	226 kJ/L (510 kJ/kg)
Lower heating value	119.93 MJ/kg	50.53 MJ/kg
Higher heating value	141.89 MJ/kg	45 MJ/kg
Volumetric energy density	10.1 MJ/L	22.2 MJ/L
Specific energy	143 MJ/kg	53.6 MJ/kg

. The boiling point of liquid hydrogen is −253 °C, whereas that of LNG is −163 °C, resulting in a difference of about 90 °C in liquefaction temperature. Furthermore, liquid hydrogen has a latent heat of vaporization of 31 kJ/L, whereas LNG has a much higher value of 226 kJ/L [20]. Consequently, the latent heat of liquid hydrogen is significantly lower than that of LNG.

Because of the lower boiling point and latent heat of vaporization, liquid hydrogen fuel tanks demand higher levels of thermal insulation than LNG tanks. However, applying insulation materials such as polyurethane foam, as commonly used in LNG insulation systems, for liquid hydrogen fuel tank insulation would require significantly thicker insulation, resulting in reduced spatial efficiency. Therefore, vacuum insulation is commonly applied to liquid hydrogen fuel tanks to reduce BOR while ensuring space efficiency [21]. To achieve vacuum insulation, a double-walled structure is applied, and a vacuum annular space is formed between the inner and outer shells. Typically, insulation materials, such as glass bubbles, SOFI, and MLI, among others, are placed within the vacuum annular space to enhance insulation performance.

2.1. Design Pressure

Type-C fuel tanks can withstand high levels of internal pressure, making BOG management easier. However, the increase in internal pressure due to BOG can potentially lead to cracking or damage to the tank. Therefore, determining the appropriate pressure and tank thickness is important during the design process. For the liquid hydrogen fuel tanks discussed in this study, vacuum insulation and a double-wall structure were adopted to effectively enhance thermal insulation performance. A vacuum insulation space was created between the inner and outer shells. Consequently, when performing pressure calculations, the application range of the internal and external pressures must be considered along with the pressure caused by the vacuum.

2.1.1. Internal Pressure

The minimum internal pressure applied inside the tank is the sum of the vapor pressure caused by the evaporation of liquid hydrogen and liquid pressure caused by the motion of the ship induced by the movement of the internal fluid, as expressed in Equation (1). To ensure that the surface-generated cracks do not progress beyond half the tank thickness over the operational lifespan of the fuel tank, the minimum value of the design vapor pressure can be calculated using Equations (2) and (3). When the fuel tank is filled with fluid, the internal motion of the liquid generates liquid pressure within the tank as the ship accelerates. This liquid pressure can be calculated using Equation (4).

$$P_{eq}=P_0+P_{gd}$$

(1)

$$P_0=0.2+AC({\rho }_r{)}^{1.5}$$

(2)

$$A=0.00185{\left({\displaystyle \frac{{\sigma }_m}{\mathsf{\Delta }{\sigma }_A}}\right)}^2$$

(3)

$$P_{gd}={\alpha }_{\beta }{Z}_{\beta }{\displaystyle \frac{\rho }{1.02\times 10^5}}$$

(4)

where $C$ is the characteristic tank dimensions; ${\rho }_r$ is the relative density of the cargo for fresh water at the designed temperature; ${\sigma }_m$ is the primary membrane stress or maximum allowable stress designed; $\mathsf{\Delta }{\sigma }_A$ is the allowable dynamic membrane stress such that when the specified design life of a tank is 108, this value is equal to 55 MPa for ferritic–pearlitic, martensitic, and austenitic steel and 25 MPa for aluminum alloy; and ${\alpha }_{\beta }$ is the dimensionless acceleration due to gravitation and the dynamic loads in an arbitrary direction $\beta .$ The acceleration ellipsoid is shown in Figure 1a. $Z_{\beta }$ is the largest liquid height above the liquid height for which the pressure point was determined (Figure 1b), and $\rho$ is the maximum cargo density at the design temperature.

The acceleration components acting on the tank according to the ship motion are expressed in terms of the vertical component $a_z$, transverse component $a_y$, and longitudinal component $a_x$ depending on the direction. The maximum dimensionless acceleration in each direction can be calculated based on Equations (5)–(9).

$$a_z=\pm a_0\sqrt{1+{\left(5.3-{\displaystyle \frac{45}{L_0}}\right)}^2{\left({\displaystyle \frac{x}{L_0}}+0.05\right)}^2{\left({\displaystyle \frac{0.6}{C_B}}\right)}^{1.5}+{\left({\displaystyle \frac{0.6y{K}^{1.5}}{B}}\right)}^2}$$

(5)

$$a_y=\pm a_0\sqrt{0.6+2.5{\left({\displaystyle \frac{x}{L_0}}+0.05\right)}^2+K{\left(1+0.6K{\displaystyle \frac{z}{B}}\right)}^2}$$

(6)

$$a_x=\pm a_0\sqrt{0.06+A^2-0.25A}$$

(7)

$$A=\left(0.7-{\displaystyle \frac{L_0}{1200}}+5{\displaystyle \frac{z}{L_0}}\right)\left({\displaystyle \frac{0.6}{C_b}}\right)$$

(8)

$$a_o=k_p\left(0.2{\displaystyle \frac{V}{\sqrt{L_0}}}+{\displaystyle \frac{34-\left(\frac{600}{L_0}\right)}{L_0}}\right)$$

(9)

where $k_p$ is the load factor for adjusting the probability of exceedance, which is 1.0 for yielding and buckling strength assessment and 0.5 for fatigue strength assessment; $L_0$ is the length of the ship for scantling determination, as defined by recognized standards; $C_B$ is the block coefficient of the ship; $B$ is the greatest molded breadth of the ship; $x$ is the longitudinal distance from amidships to the center of gravity of the tank with contents; $y$ is the transverse distance from the vessel center to the center of gravity of the tank; $z$ is the vertical distance from the actual waterline of the vessel to the center of gravity of the tank with contents; $K$ is 1 in general; and $V$ is the service speed (10 knots for yielding and buckling strength assessment, and 75% of the design speed for fatigue strength assessment).

2.1.2. External Pressure

The external pressure to apply to the external tank of the fuel tank is calculated during design using Equation (10).

$$P_e=P_1+P_2+P_3+P_4$$

(10)

where $P_1$ is the setting value of the vacuum relief valves; $P_2$ is the set pressure of the pressure relief valves for completely closed spaces containing pressure vessels; $P_3$ is the compressive action in or on the shell under the weight and contraction of tank components; and $P_4$ is the external pressure from the water head in the pressure vessel.

2.1.3. Vacuum Pressure

A liquid hydrogen fuel tank with vacuum insulation experiences the influence of vacuum pressure within the inner and outer shells of the tank. The vacuum pressure can be expressed as the difference between atmospheric pressure and the pressure corresponding to the degree of vacuum. Under standard conditions, the atmospheric pressure is approximately 0.1 MPa. The pressure in a perfect vacuum where no gas is present is considered to be 0 MPa. Therefore, the maximum value of the vacuum pressure considered in the design corresponds to the difference between a perfect vacuum state and atmospheric pressure, which is 0.1 MPa. Thus, a value of 0.1 MPa was used as the design vacuum pressure. The direction of the action of the vacuum pressure on both the inner and outer shells is illustrated in Figure 2. Vacuum pressure acts in the same direction as the internal pressure on the inner shell and in the same direction as the external pressure on the outer shell. Therefore, during the design process, vacuum pressure is incorporated into the design by adding 0.1 MPa to the internal and external designed pressures.

2.2. Material Selection and Tank Shell Thickness Calculation

Type-C fuel tanks must possess structural integrity to withstand the pressure exerted by the gas resulting from the evaporation of the internal fluid. Therefore, after selecting the appropriate steel material, the appropriate thickness for a fuel tank under pressure must be calculated using the internal and external pressures obtained for the design in the previous section.

Hydrogen diffusing into a metal can cause a decrease in the ductility and strength of the metal, which is known as hydrogen embrittlement. Therefore, when selecting materials for storing liquid hydrogen, resistance to hydrogen embrittlement must be considered in addition to ductility and strength at cryogenic temperatures.

The materials used for cryogenic applications, including LNG storage, include the 300 series of austenitic stainless steels, such as 304 and 316, aluminum alloys, such as Al 5083, Invar, 9% nickel steels, and high-manganese steels. Materials with face-centered cubic (FCC) structures, such as austenitic stainless steels and aluminum alloys, are generally considered suitable for hydrogen environments, whereas nickel is susceptible to hydrogen embrittlement; 9% nickel steel, with a body-centered cubic (BCC) structure, has a ductile-to-brittle transition temperature near −200 °C and is therefore not suitable for storing liquid hydrogen. Invar, a nickel alloy with a nickel content of 36%, exhibits an FCC structure. However, the hydrogen embrittlement characteristics of Invar have not been extensively researched, and because of the susceptibility of nickel to hydrogen embrittlement, there is no basis for using Invar for liquid hydrogen storage. High-manganese steel is unsuitable for hydrogen storage containers because of its susceptibility to hydrogen embrittlement, whereas Al 5083 is suitable for use as a material for liquid hydrogen storage containers because it neither has a ductile-to-brittle transition temperature (DBTT) nor exhibits hydrogen embrittlement, but its strength is relatively low; therefore, the tank wall may be thick. Instead, 316L austenitic stainless steel is used for liquid hydrogen storage tanks and is considered suitable for type-C liquid hydrogen fuel tanks, which experience less deformation. Therefore, in this study, STS 316L was used as the material for the liquid hydrogen fuel tank.

In this study, the required thickness for a type-C liquid hydrogen fuel tank was calculated in accordance with the American Bureau of Shipping (ABS) rules. The required thickness of the cylindrical shell under the ABS rules was calculated according to Equations (11) and (12), whereas Equations (13) and (14) were used to calculate the required thickness of the ellipsoidal heads. The components and dimensions of the type-C liquid hydrogen fuel tank design in this study are listed in

Table 3. Components and dimensions of liquid hydrogen fuel tanks.

Inner shell	Inner diameter	700 mm
	Shell length	1600 mm
	Shell thickness	4 mm
	Head type	2:1 Ellipsoidal
	Head thickness	4 mm
Outer shell	Inner diameter	808 mm
	Shell length	1600 mm
	Shell thickness	4 mm
	Head type	2:1 Ellipsoidal
	Head thickness	4 mm
Vacuum annular space	Thickness	50 mm
Saddle	Distance between saddles	1000 mm
	Width	200 mm
	Thickness	5 mm

.

$$T={\displaystyle \frac{WR}{fSE-(1-y)W}}+C$$

(11)

$$T={\displaystyle \frac{WD}{2fSE+2yW}}+C\mathrm{for}W\ge 6.9\mathrm{b}\mathrm{a}\mathrm{r}$$

(12)

$$T={\displaystyle \frac{WDK}{2fSE-0.2W}}+C$$

(13)

$$K={\displaystyle \frac{1}{6}}\left[2+{\left({\displaystyle \frac{D}{2h}}\right)}^2\right]$$

(14)

where $f$ is a factor for units of measure, and is 10 for SI units; $W$ is the maximum allowable working pressure; $S$ is the maximum allowable working stress at the design temperature of the material; $E$ is the efficiency of the longitudinal joint; $R$ is the inner radius of the weakest course of the shell; $D$ is the outer diameter of the header; $C$ denotes the corrosion allowance and is not less than one-sixth of the calculated thickness; $y$ is a coefficient with the value listed in

Table 4. Value of $y$ used to calculate the required thickness.

	≤482 °C	510 °C	538 °C	566 °C	593 °C	621 °C
Ferritic steel	0.4	0.5	0.7	0.7	0.7	0.7
Austenitic steel	0.4	0.4	0.4	0.4	0.5	0.7

; $h$ is the inside depth of the tank head; and $D$ is the inner diameter of the tank head.

2.3. Insulation and Thermal Performance

The liquid hydrogen fuel tank studied in this research has a double-walled structure consisting of an inner shell and an outer shell, with a vacuum insulation between these two shells with a pressure of 0.1 mTorr. A composite insulation system, SOFI-MLI, was applied between these two shells. Heat transfer mechanisms included conduction, convection, and radiation. Vacuum insulation enhances the insulation performance by minimizing the effects of convection and conduction.

The insulating material MLI comprises multiple layers of highly reflective material, such as aluminum foil, and a spacer with low thermal conductivity, such as a glass fiber mat. MLI is known to be an excellent insulating material for storing cryogenic fluids because it can effectively shield heat transfer by radiation in a vacuum environment where the effects of convection and conduction are limited [22]. The use of MLI combined with high vacuum in this study ensured a superior insulation performance, with thermal conductivities as low as 0.001–0.01 W/m·K. Compared to rigid polyurethane (PU) foam and pearlite systems widely adopted in LNG vessels, the MLI–vacuum system minimizes boil-off but requires meticulous vacuum integrity management and higher cost. Their integration is particularly advantageous in small-scale cryogenic tanks for marine applications [23]. However, MLI may not be suitable for use under typical atmospheric conditions with high humidity, and its insulating performance can deteriorate in low-vacuum environments [24]. Therefore, if vacuum loss occurs due to tank damage during ship operations or other reasons, the insulation performance of the fuel tank can degrade, leading to a sudden increase in boil-off and a rapid rise in internal tank pressure. Constructing a composite insulation system of MLI and SOFI enables a consistent insulation performance even when the vacuum level is lowered. SOFI is a foam insulation material with low density and significantly reduces heat transfer through conduction while negligibly affecting convection and radiation, providing a good insulation performance even at low vacuum levels.

For the 0.7 m³ type-C liquid hydrogen fuel tank in this study, a 50 mm vacuum annular space with a vacuum pressure of 0.1 mTorr was established. Additionally, 25.4 mm of SOFI and 40 layers of MLI with a total thickness of 15.5 mm were applied.

Table 5. Effective thermal conductivity of insulation at 0.1 mTorr CVP and boundary temperatures of 78 K and 293 K.

	Thickness [mm]	Density [kg/m3]	${\mathbf{k}}_{\mathbf{e}}$ [mW/m·K]
SOFI	25.4	42	7.75
MLI (40 layers)	15.5		0.040
Vacuum only	9.1		12

displays the effective thermal conductivity at cold vacuum pressure (CVP) of 0.1 mTorr and boundary temperatures of 78 K and 293 K [25].

In addition to heat ingress through insulation, heat influx through support occurs in fuel tanks. Because of the substantial proportion of heat ingress attributed to support, selecting support materials with low thermal conductivity is essential for effective insulation. Glass fiber-reinforced plastic (GFRP), which is a composite structural material of glass fibers and epoxy, possesses a low thermal conductivity and coefficient of thermal expansion, making it suitable for cryogenic fuel tanks as a support material [26]. In this study, G-11 CR material was employed for support, with a total of ten supports placed, five at each location where the centers are aligned with two saddles.

The insulation performance of a liquid hydrogen fuel tank can be quantitatively expressed by calculating the BOR of a liquid hydrogen fuel tank. The BOR can be calculated as the ratio of the total heat ingress transmitted from the outside of the liquid hydrogen fuel tank to the inside of the tank through insulation and support, at a certain pressure, considering the latent heat required to vaporize the entire amount of liquid hydrogen contained in the tank. The heat ingress was calculated according to Fourier’s law using Equation (15), and the associated thermal resistance was calculated using the effective thermal conductivity of the materials at the corresponding vacuum degree according to Equation (16).

$$Q=k\cdot A\cdot {\displaystyle \frac{\mathsf{\Delta }T}{t}}$$

(15)

$$R={\displaystyle \frac{t}{k\cdot A}}$$

(16)

where $Q$ is the heat ingress (W); $k$ is the thermal conductivity (W/mK); $A$ is the area (m²); $\mathsf{\Delta }T$ is the temperature difference (K); and $t$ is thickness (m). The total heat ingress was calculated by summing the heat ingress through the insulation and support, and the heat ingress through the insulation was calculated using the serial thermal resistance of the composite insulation layers. For the 0.7 m³ liquid hydrogen fuel tank studied in this research, the calculation according to Equations (17)–(21) yielded a BOR of 4% per day.

The calculated BOR of approximately 4% per day is consistent with reported values in similar small-scale LH₂ systems without active re-liquefaction [27]. From an operational perspective, this translates to a vaporized mass of roughly 2 kg/day for a 0.7 m³ tank, which can be reused for auxiliary loads or fuel cell applications [28]. Although this imposes a limitation on idle storage time, it also opens up opportunities for onboard energy recovery. Several studies have found that BOR levels below 5% per day remain operationally feasible for coastal and short-distance vessels, particularly when coupled with effective BOG utilization systems [29].

$$Q_{Total}=Q_{Insulation}+Q_{Support}$$

(17)

$$R_{Insulation}=R_{Innershell}+R_{SOFI}+R_{MLI}+R_{Outershell}$$

(18)

$$Q_{Insulation}={\displaystyle \frac{T_{Ambient}-T_{L{H}_2}}{R_{Insulation}}}$$

(19)

$$Q_{Support}={\displaystyle \frac{T_{Ambient}-T_{L{H}_2}}{R_{Support}}}$$

(20)

$$BOR={\displaystyle \frac{Q_{Total}}{\rho \cdot V\cdot H}}\cdot 3600\cdot 24\cdot 100$$

(21)

where $\rho$ is the density of liquid hydrogen (kg/m³); $V$ is the volume of liquid hydrogen (m³); $H$ is the latent heat for vaporization of liquid hydrogen (kJ/kg); and $R$ denotes thermal resistance (K/W).

3. Results and Discussion

The independent type-C liquid hydrogen fuel tank exists independently of the vessel’s hull; therefore, the hull strength condition need not be satisfied. Instead, structural stability assessments should be performed to evaluate the response to the static and dynamic loads that occur during operation. Accordingly, finite element analysis was performed to assess the structural stability of an independent type-C liquid hydrogen fuel tank under suitable load conditions.

As shown in Figure 3, an FEM-based evaluation framework was developed to assess the structural stability of an independent type-C liquid hydrogen fuel tank. The methodology consists of two key stages: thermal and structural analysis, which are both essential because of the extreme cryogenic environment of LH₂ (–253 °C) and dynamic loads encountered in marine operations. First, a heat transfer analysis was conducted to compute the thermal gradient across the tank walls and insulation boundaries, using the temperature conditions of the internal LH₂ and external ambient air. The resulting thermal distribution was applied as a boundary condition for subsequent structural analysis. Next, a structural analysis was performed under multiple load scenarios, including maximum acceleration conditions (representing ship motion), a heeled condition (30° inclination), and collision-induced loads (forward and aft impacts). The stress responses obtained for each condition were compared with the allowable stress criteria specified by the classification rules of ABS. If all the criteria were satisfied, the design was considered structurally sound, proceeding onto the final safety assessment stage.

3.1. Finite Element Model

Finite element analysis was performed using ANSYS (version R18.1, Ansys Inc., Canonsburg, PA, USA), a commercial finite element analysis program. Modeling was performed in accordance with the design described in the previous section. The structure was modeled to incorporate inner and outer shells, both made of STS 316L, with a vacuum annular space of 50 mm in between. The vacuum annular space consisted of layers of SOFI, MLI and a vacuum-only section. Within the structure, supports made of GFRP were positioned at the center of the saddles to support the inner shell. The entire tank was supported by two saddles with centers spaced 1200 mm apart and made of AH 36 material, each having a central angle of 120° and a width of 200 mm. Between the outer shell and saddles, there were plates made of AH 36 material, each with a central angle of 136° and a width of 260 mm. The anti-floating device connected to the plate prevented the tank from floating by contacting the saddle with the anti-floating wood blocks. The geometry of the 0.7 m³ liquid hydrogen fuel tank is illustrated in Figure 4 and Figure 5.

Contact conditions are necessary for supports that connect the inner and outer tanks, or saddles that support the tank. The inner shell of the tank experiences thermal contraction and expansion under the influence of the cryogenic fluids. To accommodate these thermal deformations, the contact condition on one side of the support was set as “fixed” and the other side as “sliding”. The thermal deformation of the inner tank was handled by the sliding contact conditions applied to the supports. Therefore, the saddles, which support the entire tank do not have to adapt to severe thermal deformations. So, both sides of the saddles were assigned a “fixed” contact condition.

To construct an appropriate mesh for the finite element analysis, a mesh convergence study was conducted on the inner shell of the tank. The results of this study are presented in Figure 6. Various element sizes of 80, 60, 50, 40, 30, 25, 20, 15, 10, and 8 mm were considered in this study. Two layers of elements were constructed in the thickness direction for each case. The maximum equivalent stress in the mesh convergence study is the result of the analysis under a vertical acceleration load applied to the inner shell.

Based on the results of the mesh convergence study, the mesh size was maintained at or below 10 mm to ensure accuracy. In the thickness direction, two mesh layers were used to assess the bending effects. A total of 638,331 elements and 946,313 nodes were used in the entire structural model to perform heat transfer and structural analyses, including 637,657 hex-type and 674 wedge-type meshes. Figure 7 illustrates the finite element analysis model with the constructed mesh, and

Table 6. Material properties of tank components used in finite element analysis.

Material Properties	STS 316L	AH 36	GFRP	Wood
Density (kg/m3)	7980	7800	1956	1350
Elastic modulus (MPa)	193,000	206,000	31,100	6500
Poisson’s ratio	0.3	0.3	0.2	0.14
Thermal conductivity (W/mK)	14.78	59.0	0.3	0.24
Thermal expansion (10−6/K)	10.3 (20 K) 15.2 (280 K)	12.0	21.0	8.0

lists the material properties employed in the finite element analysis.

3.2. Heat Transfer Analysis

A heat transfer analysis was conducted for the transient thermal analysis. The inner shell, which contains liquid hydrogen, was set to a temperature of −253 °C, reflecting the temperature of the liquid hydrogen, whereas the external temperature was set to 5 °C, following the International Code of Safety for ships using gas or other low-flashpoint fuels (IGF code). Insulation materials such as SOFI and MLI have effective thermal conductivities at 0.1 mTorr vacuum pressure. By performing a heat transfer analysis, the temperature distribution inside the tank can be confirmed, and the thermal stress due to the temperature difference between the inside and outside can be calculated. The thermal stress and temperature distribution of the structural components of the tank are subsequently linked to the structural analysis. Figure 8 illustrates the temperature distribution of the tank obtained through heat transfer analysis, and the temperature distribution at the supports is shown in Figure 9.

3.3. Structural Analysis

Structural analysis was conducted, and the load conditions were applied based on the IGF code. The inner shell of the liquid hydrogen fuel tank, which contained liquid hydrogen, was subjected to the following loads: liquid pressure, vapor pressure resulting from the vaporization of liquid hydrogen, and weight of liquid hydrogen. The outer shell was subjected to an external pressure. Additionally, both the inner and outer shells experienced vacuum pressure with a vacuum between them; a vacuum pressure of 0.1 MPa was used in all cases. Vapor pressure was consistent across the load cases and was set to a design pressure of 0.9 MPa. Liquid pressure was applied using the maximum dimensionless acceleration calculated in the previous section, taking into account the density of liquid hydrogen. The filling limit was not considered in the calculation of liquid pressure. Different conditions were applied to each load case.

The load conditions listed in

Table 7. Conditions of load cases.

Load Case	Condition	Type of Load
1	Standard	Maximum vertical acceleration
2	Standard	Maximum transverse acceleration
3	Standard	Maximum longitudinal acceleration
4	Standard	Heeling 30° + Maximum vertical acceleration
5	Standard	Heeling 30° + Maximum transverse acceleration
6	Standard	Heeling 30° + Maximum longitudinal acceleration
7	Accidental	Collision forward
8	Accidental	Collision aftward

include the maximum acceleration in each direction, maximum acceleration when 30° heeling occurs, collision in forward or aftward directions, and flooding when submerged in water. In general, most vessels reach their maximum righting lever (GZ) between the heel angles of 25° and 35°, beyond which the restoring moment significantly decreases, thereby increasing the risk of instability. Thus, a 30° heel is commonly recognized as a practical upper bound for stability assessments under intact conditions. In line with this, the IMO Intact Stability Code [30], 3.1.2, stipulates that the angle used for stability criteria must be “30° or the angle of downflooding, whichever is less,” thereby setting a conservative boundary to ensure structural and hydrodynamic safety near the threshold of capsize initiation [31,32].

Load cases 1–6 are based on the typical operating conditions of a general vessel and categorized as standard. Load cases 7–8 are based on situations involving accidents and categorized as accidental.

Table 8. Types of loads applied to each load case.

Case	Self-Weight	Thermal Load	External Pressure	Vapor Pressure	Vacuum Pressure	Heeling 30°	Buoyant Load	Liquid Pressure			Collision
								ax	ay	az	0.5 g	−0.25 g
1	O	O	O	O	O					O
2	O	O	O	O	O				O
3	O	O	O	O	O			O
4	O	O	O	O	O	O				O
5	O	O	O	O	O	O			O
6	O	O	O	O	O	O		O
7	O	O	O	O	O						O
8	O	O	O	O	O							O

lists the types of loads applied in each load case.

3.4. Allowable Stresses Criteria

Because type-C fuel tanks may experience various loads during their lifetime, calculating the allowable stress during the design is important to prevent excessive deformation or failure. To evaluate the stresses occurring in the type-C fuel tank, the stress was divided into primary and secondary stresses based on the ASME Boiler and Pressure Vessel Code (BPVC) Section 8 Division 2. Primary stress is the stress generated to maintain equilibrium in the presence of an externally applied load. It has no self-limiting property; therefore, if a high primary stress is applied, failure may occur because of excessive deformation. Secondary stress is the stress generated by constraints to maintain the continuity of the structure and is self-limiting; stress reduction occurs through local yielding or deformation [33]. Primary stress can be further categorized into general membrane, local membrane, and bending stresses. The primary general membrane stress occurs uniformly in the thickness direction of the tank and does not exhibit a stress reduction. This can lead to significant plastic deformation when yielding occurs. Primary local membrane stress occurs at discontinuities and can lead to a redistribution of stress, causing deformation in the process. Primary bending stress refers to stress that varies linearly in the thickness direction. The permissible criteria for each stress are specified in Equation (22). The calculated stress values for STS 316L and carbon steel (AH 36) components of the type-C fuel tank must not exceed certain criteria based on $f$. The value of $f$ was 113 MPa for STS 316L and 163 MPa for AH 36.

$$\begin{gathered} {\sigma }_m\le f \\ {\sigma }_L\le 1.5f \\ {\sigma }_b\le 1.5f \\ {\sigma }_L+{\sigma }_b\le 1.5f \\ {\sigma }_m+{\sigma }_b\le 1.5f \\ {\sigma }_m+{\sigma }_b+{\sigma }_g\le 3.0f \\ {\sigma }_L+{\sigma }_b+{\sigma }_g\le 3.0f \end{gathered}$$

(22)

where ${\sigma }_m$ is the equivalent primary general membrane stress; ${\sigma }_L$ is the equivalent primary local membrane stress; ${\sigma }_b$ is the equivalent primary bending stress; and ${\sigma }_g$ is the equivalent secondary stress.

3.5. Results of Structural Analysis

In previous sections, the structural analysis on the 0.7 m³ liquid hydrogen fuel tank was presented. The structural integrity was evaluated for each load case to determine whether the applied loads were within the allowable stress. Structural analysis was performed for various load conditions, including the maximum acceleration in each direction, maximum acceleration when 30° heeling occurs, collisions occurring in the forward and aftward directions, and flooding when submerged in water. The stress evaluation involved classifying stress based on the material of the tank components and assessing whether the calculated stress was within the allowable range according to the allowable stress criteria. In each case, the calculated stress was below the allowable stress, indicating that the allowable stress criteria were satisfied. Detailed results for all load cases, including membrane, bending, and secondary stresses, can be found in Appendix A. Specifically, STS 316L was selected for the inner and outer shells of the cryogenic tank, and stresses in these primary pressure components were decomposed according to the ASME BPVC VIII-2 classification, which includes membrane, local membrane, bending, and secondary stress components (${\sigma }_m$, ${\sigma }_L$, ${\sigma }_b$, ${\sigma }_g$). This level of classification is essential for evaluating the components exposed to internal pressure and thermal gradients. In contrast, carbon steel and G-11CR were used for secondary structural supports, such as saddles and anti-floating devices, for which assessing structural adequacy based on the overall von Mises stress or compressive strength is sufficient.

Comparing each load case, the most critical load case corresponded to the highest stress being applied to both the inner and outer shells, when the tank experienced 30° heeling with maximum transverse acceleration. In this load case, the equivalent primary general membrane stress in the inner shell was 76.75 MPa, and the sum of the membrane, bending, and secondary stresses was 167.71 MPa. The stress distribution results for the critical load case are shown in Figure 10. For further comparison, the bar chart in Figure 11 illustrates the calculated stress values for the inner shell and inner head, along with the allowable stress. The structural integrity of the tank was verified by comparing the calculated stress values with the allowable stress values. A temperature gradient was observed between the cryogenic fluid inside the tank at –253 °C and the ambient external temperature of approximately 5 °C. This gradient induces thermal contraction in the inner shell, which may lead to localized thermal stress concentrations and potential structural vulnerabilities under fluctuating temperature conditions. However, in the present design, these concentrated stresses are effectively mitigated by implementing a sliding support system that accommodates thermal deformation. Consequently, the maximum thermal stress was limited to approximately 56 MPa, indicating minimal structural impact. The stress results obtained in this study were consistent with the findings of Kim et al., who conducted a comprehensive structural integrity assessment of a large-scale 5.75 K-class type-C liquefied hydrogen cargo tank using finite element analysis [18]. In their work, the stress evaluation also followed the ASME-based classification method, and the most critical condition, accidental collision, resulted in a localized peak stress of 272 MPa at the support connection of the inner shell, with the general primary membrane stress reaching 112 MPa. Both values remain within the allowable limits specified for SUS 304 L material. These results collectively support the conclusion that type-C tank designs, whether for small- or large-scale hydrogen applications, can achieve adequate structural reliability under combined thermal and mechanical loading conditions with appropriate design procedures and material selection.

4. Conclusions

In this study, a fundamental investigation was conducted on the design of type-C liquid hydrogen fuel tanks, and its feasibility was verified by performing finite element analysis. The shape of the fuel tank was chosen as a type-C pressure vessel, which is primarily used as a fuel tank for low mobility, allowing easy BOG management. The material chosen for the fuel tank was STS 316L, which is known for its compatibility with liquid-hydrogen environments. The minimum design pressures applied within and outside the tank were calculated in accordance with the IGF code and served as the basis for selecting an appropriate design pressure. Based on the design pressure, the required thicknesses of the inner and outer shells of STS 316L were calculated in accordance with the ABS rule. To ensure adequate insulation performance, a combination of 0.1 mTorr vacuum insulation and a SOFI-MLI composite insulation system was applied, resulting in a calculated BOR of approximately 4% per day.

Heat transfer analysis was conducted on the designed liquid hydrogen fuel tank to examine the temperature distribution in the tank. The insulation resulted in temperatures above zero on the tank exterior. The thermal contraction of the inner shell in the presence of cryogenic fluids can be managed by allowing one side of the support structure to slide. The influence of thermal stress can be mitigated by permitting thermal contraction-induced deformation. A structural analysis was performed for load conditions corresponding to the maximum acceleration in each direction, maximum acceleration in the presence of 30° heeling, collisions occurring in the forward and aftward directions, and flooding when submerged in water. The analyses considered a range of loads such as self-weight, temperature-induced thermal stress, vapor pressure within the tank, liquid pressure, external pressure, vacuum pressure between the inner and outer shells, and buoyant loads when submerged. It was confirmed that all components, including the tank made of STS 316L, satisfied the allowable stress criteria for all load cases.

The originality of this research lies in its integrated design evaluation for small-scale type-C LH₂ tanks, applying finite element analysis to incorporate both structural and thermal aspects using a composite SOFI–MLI insulation system. Unlike most previous studies that focused on large-scale tanks or separate evaluation domains, this study introduces a compact and integrative approach for vessel-level feasibility. In future studies, the proposed design should be validated experimentally through physical prototyping to assess its real-world performance under marine operating conditions. Investigations into fatigue resistance under cyclic loading, sloshing behavior, and operational safety during bunkering are crucial for verifying their practical applicability. However, several technical limitations and challenges remain. These include the complexity of fabricating composite insulation layers, the potential for undetected microleakage under long-term cryogenic exposure, material degradation because of thermal cycling, hydrogen embrittlement, and pressure instability caused by insulation failure over time [34,35,36]. Additionally, the regulatory landscape is continuously evolving. Although this study complies with the IGF code and ABS rules, emerging global standards must also be considered. The IMO Interim Guidelines (MSC.1/Circ.1647) adopted in 2022 outline the specific requirements for hydrogen containment, ventilation, and safety monitoring in fuel-cell power systems [37]. These, along with the broader regulatory framework detailed by Moretto and Quong (2022), are becoming increasingly vital for the development of next-generation marine hydrogen storage systems [38]. In addition, long-term maintenance and safety considerations must be incorporated into the operational planning of cryogenic hydrogen tanks. Periodic inspection of vacuum insulation performance, nondestructive testing (NDT) of structural components, and continuous monitoring of hydrogen leakage are essential to ensure sustained performance and regulatory compliance over time [39,40].

Overall, this study offers promising insights into the early-stage engineering of cryogenic hydrogen storage for maritime applications. However, it must be emphasized that simulation-based evaluation should be followed by physical testing. The findings presented in this study provide a foundation for future development. However, further prototyping and system-level qualification testing are necessary to enable practical implementation.