Mechanistic Study on the Internal Thermodynamic Response of a Liquid Hydrogen Tank Under Support Thermal Bridge-Induced Non-Uniform Heat Input

Abstract

Support structures in liquid hydrogen tanks act as localized thermal bridges between the ambient temperature outer vessel and the cryogenic inner vessel. However, the difference between support thermal bridge-induced localized heat input and equivalent uniform heat input remains insufficiently clarified, especially regarding their effects on local thermal behavior and support position-dependent thermodynamic response. In this study, a gas–liquid two-phase CFD model was developed for a 37.4 m³ liquid hydrogen tank at a 50% filling ratio. Localized heat flux regions were used to represent support thermal bridges, and an equivalent uniform heat input case with the same total heat input was introduced for comparison. The results show that localized support heat input concentrates the high-temperature region near the support-corresponding wall area and induces stronger local natural convection with a maximum velocity of approximately 0.27 m/s, compared to approximately 0.14 m/s in the uniform heat input case. The uniform heat input case produces a slightly higher overall gas-phase pressure, but it cannot capture the local heat accumulation and flow field reconstruction caused by support thermal bridges. Circumferential support position variation mainly affects the relative position between the localized heat source, gas region, liquid region, and gas–liquid interface. Upper support position variation has a more pronounced influence on local peak temperature and flow intensity than lower support variation. Axial support position variation mainly shifts the local high-temperature and high-velocity regions along the tank length, while its influence on overall pressure response is limited. These results indicate that equivalent uniform heat input can approximate the overall pressurization trend, but localized support heat input boundaries should be retained when local temperature fields, flow structures, and support layout effects are of concern.

1. Introduction

Hydrogen has attracted increasing attention as a clean and flexible energy carrier for renewable energy utilization, large-scale energy storage, and transportation energy systems. Owing to its high gravimetric energy density and potential for coupling power generation, storage, and end-use energy conversion, hydrogen is considered an important pathway for improving the flexibility and sustainability of future energy systems [1]. Compared with compressed gaseous hydrogen, liquid hydrogen provides a higher volumetric storage density and is more suitable for long-distance transportation, centralized storage, and space-constrained mobile applications. As a key component in liquid hydrogen storage and transportation systems, the thermal management performance of liquid hydrogen tanks directly affects operational safety, pressure-control behavior, and medium loss characteristics.

Liquid hydrogen tanks are commonly designed as double-wall vacuum-insulated vessels. Nevertheless, external heat can still be transferred into the cryogenic inner vessel through the tank wall, piping interfaces, and support structures, leading to liquid hydrogen evaporation and gas-phase pressure rise, which is generally referred to as self-pressurization [2,3]. Among these heat transfer paths, the support structure connects the ambient temperature outer vessel to the cryogenic inner vessel. It therefore functions not only as a load transfer component, but also as a solid heat conduction path. Unlike the distributed heat leakage through multilayer insulation, support thermal bridges introduce localized heat input on the inner vessel wall. This localized heat input may alter the near-wall temperature gradient, buoyancy-driven flow path, phase change behavior near the gas–liquid interface, and gas-phase pressure response.

Previous studies have investigated liquid hydrogen tanks mainly from the perspectives of support structure design and heat leakage control. Lisowski et al. [4] reported that the thermal conduction characteristics of supports in double-wall cryogenic vessels affect the overall heat leakage. Nguyen et al. [5] proposed a portable cryogenic hydrogen storage tank using a porous adsorbent as the storage medium and a liquid-nitrogen cooling jacket, and demonstrated through finite element analysis the safety and lightweight potential of fiberglass-reinforced plastic supports under thermo-mechanical coupling. Yin et al. [6] suggested that the geometry, material, and connection configuration of support structures influence heat leakage and further affect the thermodynamic behavior of the gas–liquid two-phase system inside the tank. Wang [7] analyzed the stress distribution and heat leakage characteristics of an eight-point support structure under different operating conditions, showing that variations in support parameters can affect the thermal response of the vessel. Miao et al. [8] analyzed the mechanical loading and heat leakage of support structures between the inner and outer vessels of a liquid hydrogen container, further confirming the importance of support structures in heat leakage control for cryogenic vessels.

The self-pressurization process in liquid hydrogen tanks is closely associated with internal thermal stratification, buoyancy-driven natural convection, and interfacial phase change. Rossetti et al. [9] used CFD to investigate the thermodynamic response of cryogenic tanks under heat input and showed that wall heat flux affects temperature stratification near the liquid surface. Lan et al. [10] analyzed tank self-pressurization using a nodal model and indicated that turbulent mixing induced by heat leakage can modify thermal stratification. Liu et al. [11] investigated thermal stratification in liquid hydrogen tanks under different gravity conditions and found that stratification affects the internal temperature distribution and promotes pressure rise. Wang et al. [12] analyzed liquid hydrogen tank self-pressurization using a thermodynamic multi-zone model and identified interfacial heat transfer and evaporation rate as important factors governing gas-phase pressure evolution. Zhu et al. [13] further examined the coupling between transport-induced sloshing and thermal stratification, showing that sloshing enhances internal convective heat transfer and modifies the pressure response.

In recent years, increasing attention has also been paid to the effects of support layout and insulation structure on the thermal response of liquid hydrogen tanks. Wan et al. [14] designed and validated a horizontal onboard liquid hydrogen tank and analyzed how different insulation strategies affect heat leakage and loss-free storage duration. Qiu et al. [15] proposed a support strut with combined thermal insulation and vibration damping functions to reduce external heat intrusion and vibration-induced safety risks. Lee et al. [16] verified the structural safety of the inner and outer vessels of a liquid hydrogen tank trailer and emphasized that the support system is closely related to both structural integrity and thermal management performance. These studies provide an important basis for understanding heat leakage, thermal stratification, and self-pressurization in liquid hydrogen tanks. However, most existing studies have mainly focused on the total heat leakage level, structural safety of support systems, or self-pressurization under simplified wall heat input conditions. The localized heat input induced by support thermal bridges has not been sufficiently distinguished from an equivalent uniform heat input. In particular, the influence of support position on local heat accumulation, flow field reconstruction, and gas-phase pressure response remains unclear.

Therefore, this study develops a gas–liquid two-phase CFD model for a 37.4 m³ liquid hydrogen tank to investigate the internal thermodynamic response under support thermal bridge-induced non-uniform heat input. The support thermal bridge effect is represented by localized heat flux regions on the inner vessel wall, and an equivalent uniform heat input case with the same total heat input is introduced for comparison. By comparing the localized and equivalent uniform heat input cases, this study evaluates whether support-induced localized heat leakage can be simplified as a uniform wall heat flux boundary. Furthermore, the circumferential and axial positions of the support heat input regions are varied to clarify how the relative position between the localized heat source, gas region, liquid region, and gas–liquid interface affects the temperature field, flow field structure, and gas-phase pressure response. The novelty of this work lies in revealing the mechanism by which localized support thermal bridges affect the internal thermodynamic response of a liquid hydrogen tank, rather than only evaluating the overall heat leakage magnitude. The results can provide guidance for thermal boundary simplification, support layout evaluation, and thermal management analysis of liquid hydrogen tanks.

2. Numerical Model and Simulation Setup

2.1. Research Object and Model Simplification

A 37.4 m³ liquid hydrogen tank was selected as the research object in this study. The liquid hydrogen tank is a mobile cryogenic pressure vessel used primarily for liquid hydrogen storage and transportation. As shown in Figure 1, the tank adopts a double-wall vacuum-insulated structure and consists of an inner vessel, an outer vessel, end heads, an interlayer insulation space, a support system, saddles, and related accessories. Figure 1 also shows the simplified relationship between the actual support structure and the support-equivalent heat input region used in the numerical model. In the actual tank, the support connects the outer vessel and the inner vessel through the vacuum insulation space. In the numerical model, the complete solid support structure was not explicitly resolved; instead, the heat transferred through the support thermal bridge was represented by a localized equivalent heat input region on the inner vessel wall. The inner vessel stores the liquid hydrogen medium, whereas the outer vessel bears external loads and maintains the sealing of the insulation interspace. A high-vacuum multilayer insulation system is arranged between the inner and outer vessels to reduce external heat transfer to the inner vessel. The tank has a geometric volume of 37.4 m³, a maximum filling ratio of 92%, an inner vessel diameter of 2150 mm, an outer vessel diameter of 2357 mm, and an inner vessel operating temperature of −253 °C. These structural features and parameters provide the basis for subsequent fluid domain modeling and thermal boundary condition specification.

The support structure connects the ambient-temperature outer vessel to the cryogenic inner vessel, serving both load transfer and heat transfer functions. Unlike the distributed heat leakage through MLI-covered regions, the support thermal bridge introduces localized heat input on the inner vessel wall, thereby affecting the internal temperature field, natural convection structure, and gas-phase pressure evolution. The tank considered in this study employs two sets of radial four-point supports at the front and rear, resulting in an eight-point support configuration. The front supports are fixed supports that mainly constrain the axial displacement and rotation of the inner vessel, whereas the rear supports are sliding supports used to release part of the axial deformation induced by cryogenic contraction. The circumferential support positions are classified into upper and lower supports. As shown in Figure 2, in the baseline case, the upper support is located approximately $45°$ from the vertical upward direction, while the lower support is located approximately $30°$ from the vertical downward direction. Compared with the simplified support-equivalent heat input representation in Figure 1 and Figure 2 further illustrates the actual circumferential arrangement of the support structures, outer vessel, vacuum space, MLI, and inner vessel. This support configuration determines the locations of localized heat input induced by support thermal bridges on the inner vessel wall.

To analyze the internal temperature field, flow field, and gas-phase pressure response under support-induced local heat input, the fluid domain was simplified while preserving the main geometric features and gas–liquid distribution characteristics. A three-dimensional Cartesian coordinate system was established with the geometric center of the liquid hydrogen tank as the origin. The X-axis is aligned with the vehicle forward direction, the Z-axis is opposite to the direction of gravity, and the Y-axis is defined according to the right-hand rule. The internal fluid domain of the liquid hydrogen tank has a horizontal cylindrical configuration.

Considering the symmetry of the model about the XOZ and YOZ planes, a quarter fluid domain model was adopted, with symmetry boundary conditions imposed on the two symmetry planes. Figure 3 shows the fluid domain geometry and the regions corresponding to the supports. This simplification preserves the free surface position, the main gas–liquid distribution characteristics, and the local heat input regions associated with the supports. In this simplified model, the front and rear support structures were treated using an equivalent symmetry assumption, and the support thermal bridge effect was represented by localized heat input regions on the inner vessel wall. This treatment reduces the computational cost and allows the analysis to focus on the influence of support-induced localized heat input on the internal thermodynamic response of the tank.

It should be noted that this simplification also introduces certain limitations. The equivalent symmetry assumption may neglect the difference in heat leakage between the actual front and rear supports. In addition, the detailed three-dimensional geometry and solid heat conduction process of the real support structures were not explicitly resolved. The present model also does not consider transport-induced vibration or sloshing effects, which may further affect the internal flow field and local heat transfer under actual operating conditions. Therefore, the present simplified model is mainly applicable to the comparative analysis of support-induced localized heat input under static conditions. Future work will further consider a full tank model, real support structures, coupled solid-fluid heat transfer, and sloshing-coupled effects to improve the engineering applicability of the numerical model.

The regions corresponding to the support thermal bridges were represented using equivalent heated areas. The total effective area of the eight support regions is $0.72 {\mathrm{m}}^2$, with each local support heat input region occupying 0.09 m². The equivalent area was determined according to the actual geometric size of the support structure and its corresponding heat transfer region on the inner vessel wall. In the numerical model, the detailed support geometry was simplified into an area-equivalent wall region, so that the localized heat input transferred through the support thermal bridge could be applied to the fluid domain boundary. Therefore, the equivalent heated area represents the effective thermal action area of the support on the inner vessel wall, rather than an arbitrarily assigned surface area. Each support heat input region was approximated as a circular heated area with an equivalent diameter of 338.5 mm. This circular approximation preserves the same equivalent area while simplifying the boundary definition and mesh generation of the local heat input region. In the baseline case, the axial position of the support is $x=3.085$ m. These regions were used to impose the localized heat flux boundary associated with the supports. Because the front and rear supports in the actual liquid hydrogen tank are not completely symmetric, their local heat leakage may differ. To accommodate the quarter fluid domain model, the front and rear supports were treated as equivalent symmetric components with respect to the YOZ plane, and the averaged local heat input was applied to the fluid domain wall.

2.2. Monitoring Point Arrangement

To quantitatively analyze the internal temperature distribution and thermal stratification evolution under support-induced local heat input, temperature monitoring points were arranged in the fluid domain. Since this study focuses on the internal thermodynamic response at a 50% filling ratio, the monitoring points were arranged based on the gas–liquid interface position corresponding to this filling condition, as shown in Figure 4. The monitoring points were arranged along the axial and vertical directions of the tank. Three representative axial sections were selected at $x=2.085$ m, $x=3.085$ m, and $x=4.085$ m. The section at $x=3.085$ m corresponds to the baseline support position and contains monitoring points P1–P7, whereas the sections at $x=2.085$ m and $x=4.085$ m are located on the two sides of the baseline support position and contain monitoring points P8–P14 and P15–P21, respectively. This arrangement enables comparison of temperature responses induced by localized support heat input at different axial positions.

In each axial section, the monitoring points were distributed vertically to cover the upper gas region, the vicinity of the gas–liquid interface, and the lower liquid region. Taking the $x=3.085$ m section as an example, P1–P3 are located in the gas region to characterize gas-phase temperature variation and heat accumulation, P4 is located near the gas–liquid interface to characterize the interfacial temperature response, and P5–P7 are located in the liquid region to reflect bulk liquid temperature variation. P8–P14 and P15–P21 correspond spatially to P1–P7 and were used to analyze the propagation and migration of local thermal disturbances along the tank length when the axial support position was varied.

2.3. Mathematical Formulation

To describe the thermodynamic response of the liquid hydrogen tank under non-uniform heat input induced by support thermal bridges, a gas–liquid two-phase flow numerical model was established. The liquid hydrogen and hydrogen vapor were treated as two immiscible phases. The vapor–liquid interface was captured using the volume of fluid (VOF) method, and the evaporation and condensation processes near the interface were described using the Lee phase change model. The governing equations for mass, momentum, and energy conservation were solved in ANSYS Fluent 2024 R1, together with the corresponding interfacial force, phase change source terms, and turbulence closure.

2.3.1. Governing Equations

The flow and heat transfer processes in the computational domain were governed by the conservation equations of mass, momentum, and energy. The continuity equation is expressed as:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla \left(\rho \overrightarrow{v}\right)=\dot{m}$$

(1)

where $\rho$ is the density, $\overrightarrow{v}$ is the velocity vector, and $\dot{m}$ is the mass source term introduced by phase change.

The momentum conservation equation is written as:

$${\displaystyle \frac{\partial \left(\rho \overrightarrow{v}\right)}{\partial t}}+\nabla \left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla p+\nabla \left[{\mu }_{\mathrm{eff}}\left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^T\right)\right]+\rho \overrightarrow{g}+{\overrightarrow{F}}_{\mathrm{vol}}$$

(2)

where p is the pressure, ${\mu }_{\mathrm{eff}}$ is the effective viscosity, g is the gravitational acceleration, and ${\overrightarrow{F}}_{\mathrm{vol}}$ denotes volumetric body forces, including surface tension contributions.

The energy conservation equation is expressed as:

$${\displaystyle \frac{\partial \left(\rho E\right)}{\partial t}}+\nabla \left[\overrightarrow{v}(\rho E+p)\right]=\nabla \left(k_{\mathrm{eff}}\nabla T\right)+S_h$$

(3)

where E is the total energy per unit mass, $k_{\mathrm{eff}}$ is the effective thermal conductivity, T is the temperature, and $S_h$ represents the volumetric energy source term associated with evaporation and condensation.

2.3.2. VOF Interface Tracking Model

The VOF method was used to track the vapor–liquid interface by solving the transport equation of phase volume fraction. In each computational cell, the volume fractions of all phases satisfy:

$$\sum _q{\alpha }_q=1$$

(4)

where ${\alpha }_q$ is the volume fraction of phase q. The mixture density and other mixture properties were calculated from the volume-fraction-weighted average of the corresponding phase properties:

$$\rho =\sum _q{\alpha }_q{\rho }_q,\varphi =\sum _q{\alpha }_q{\varphi }_q$$

(5)

where ${\rho }_q$ and ${\varphi }_q$ denote the density and general thermophysical property of phase q, respectively. This treatment ensures the conservation of phase volume fractions and maintains the continuity of mixture properties across the vapor–liquid interface.

For the liquid phase, the volume fraction transport equation can be written as

$${\displaystyle \frac{\partial {\alpha }_l}{\partial t}}+\overrightarrow{v}·\nabla {\alpha }_l={\displaystyle \frac{{\dot{m}}_{cond}-{\dot{m}}_{evap}}{{\rho }_l}}$$

(6)

where ${\alpha }_l$ is the liquid-phase volume fraction, ${\rho }_l$ is the liquid density, and ${\dot{m}}_{cond}$ and ${\dot{m}}_{evap}$ are the mass source terms caused by evaporation and condensation, respectively.

2.3.3. Lee Phase Change Model

The Lee phase change model was used to describe the interfacial mass transfer between liquid hydrogen and hydrogen vapor. In this model, evaporation occurs when the local temperature is higher than the saturation temperature, while condensation occurs when the local temperature is lower than the saturation temperature. The corresponding mass source terms are expressed as

$${\dot{m}}_{\mathrm{evap}}=r{\rho }_l{\displaystyle \frac{T-T_{\mathrm{sat}}}{T_{\mathrm{sat}}}},T>T_{\mathrm{sat}}$$

(7)

$${\dot{m}}_{\mathrm{cond}}=r{\rho }_v{\displaystyle \frac{T_{\mathrm{sat}}-T}{T_{\mathrm{sat}}}},T<T_{\mathrm{sat}}$$

(8)

where ${\rho }_l$ and ${\rho }_v$ are the densities of the liquid and vapor phases, respectively, $T_{\mathrm{sat}}$ is the saturation temperature, and r is the phase change intensity factor in the Lee model.

The latent heat effect was introduced into the energy equation through the source term:

$$S_h=\dot{m}{L}_v$$

(9)

where $L_v$ is the latent heat of vaporization of liquid hydrogen.

The saturation temperature was expressed as a pressure-dependent polynomial correlation fitted from the NIST REFPROP database:

$$\begin{array}{c}\hfill T_{sat}=11.80388+(2.02106E-4)\times P-(2.14773E-9)\times P^2+\\ \hfill (1.37275E-14)\times P^3-(4.50977E-20)\times P^4+(5.9173E-26)\times P^5\end{array}$$

(10)

The phase change intensity factor in the Lee model controls the interfacial mass transfer rate during evaporation and condensation. Therefore, its value can affect the predicted evaporation rate and gas-phase pressure evolution. To justify the coefficient used in this study, a coefficient-sensitivity comparison was conducted based on the validation case of the low-heat flux liquid hydrogen self-pressurization experiment. Three commonly used coefficients, namely 0.1, 0.01, and 0.001, were tested under the same initial conditions, boundary conditions, and solver settings. The comparison showed that the coefficient of 0.1 provided the best agreement with the experimental pressure evolution, whereas the smaller coefficients led to a weaker phase change response and a larger deviation from the experimental pressure curve. Therefore, the Lee phase change coefficient was set to 0.1 in this study.

The evaporation source term, condensation source term, and phase change temperature were implemented using user-defined functions and coupled with the VOF interface tracking model. In addition, the thermophysical properties of both gas and liquid phases, including density, enthalpy, and specific heat capacity, were obtained from the REFPROP database [17]. This treatment ensures consistency in the thermophysical properties used in the governing equations and maintains the compatibility of the phase change calculation with equilibrium thermodynamics under cryogenic conditions.

2.3.4. Surface Tension Model

Surface tension was considered because interfacial forces affect the morphology and stability of the vapor–liquid interface under cryogenic conditions. The continuum surface force (CSF) model was used to represent the surface tension force near the interface:

$${\overrightarrow{F}}_{vol}={\sigma }_{lv}{\kappa }_l\nabla {\alpha }_l$$

(11)

$${\kappa }_l=-\nabla ·\left({\displaystyle \frac{\nabla {\alpha }_l}{|\nabla {\alpha }_l|}}\right)$$

(12)

where $\sigma$ is the surface tension coefficient and ${\kappa }_l$ is the local interface curvature.

2.3.5. Turbulence Model

The self-pressurization process of the liquid hydrogen tank involves thermal stratification and buoyancy-driven natural convection. Therefore, the realizable $k-\epsilon$ turbulence model with enhanced wall treatment was used to describe the internal flow. The transport equations for turbulent kinetic energy k and dissipation rate $\epsilon$ are given as:

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+\nabla ·\left(\rho k\overrightarrow{v}\right)=\nabla ·\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right)\nabla k\right]+G_k+G_b-\rho \epsilon -Y_M$$

(13)

$${\displaystyle \frac{\partial \left(\rho \epsilon \right)}{\partial t}}+\nabla ·\left(\rho \epsilon \overrightarrow{v}\right)=\nabla ·\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right)\nabla \epsilon \right]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}(G_k+C_3{G}_b)-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}$$

(14)

The turbulent viscosity is calculated as

$${\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^2}{\epsilon }}$$

(15)

where $\mu$ is the dynamic viscosity, ${\mu }_t$ is the turbulent viscosity, $G_k$ is the generation of turbulent kinetic energy caused by the mean velocity gradient, $G_b$ is the generation of turbulent kinetic energy induced by buoyancy, and $Y_M$ represents the contribution of fluctuating dilatation in compressible turbulence. The model constants were adopted from the default Realizable $k-\epsilon$ formulation in Fluent.

To further justify the selection of the turbulence model, the Reynolds number and Rayleigh number were estimated for the buoyancy-driven flow inside the liquid hydrogen tank. At a 50 percent filling ratio, the characteristic length was taken as the vertical height of the gas region, which is approximately equal to the inner radius of the tank. The characteristic velocity was obtained from the simulated velocity field under localized support heat input. Based on the thermophysical properties of gaseous hydrogen near the initial cryogenic state, the Reynolds number was estimated to be on the order of ${10}^{-5}$, indicating that the internal flow induced by localized support heat input belongs to a turbulent flow regime. In addition, the Rayleigh number was estimated to be on the order of ${10}^{-11}$, indicating that the buoyancy force caused by the local temperature difference is sufficiently strong to induce turbulent natural convection.

Therefore, a turbulence model was required to describe the internal flow field under support thermal bridge-induced non-uniform heat input. Compared with the Standard $k-\epsilon$ model, the Realizable $k-\epsilon$ model improves the formulation of turbulent viscosity and is more suitable for flows involving strong strain, streamline curvature, rotation, and buoyancy effects. These characteristics are consistent with the local thermal plume, near-wall flow acceleration, and recirculation structures generated by localized support heat input. In addition, the realizable $k-\epsilon$ model maintains good numerical stability and computational efficiency in transient multiphase simulations. Therefore, it was selected as the turbulence closure method in this study to capture the main turbulent natural convection structure and flow field reconstruction inside the liquid hydrogen tank.

2.4. Initial and Boundary Conditions

Initially, the liquid hydrogen tank was set to a 50% filling ratio. The liquid-phase volume fraction was 50%, and the remaining space was occupied by pure hydrogen vapor. The initial liquid temperature was set to 20.369 K, while the initial gas temperature was set to 20.369–20.370 K with a linear distribution opposite to the direction of gravity. The initial absolute gas-phase pressure was set to 1.0 atm, corresponding to the saturation state of liquid hydrogen. Under these conditions, the gas and liquid phases inside the tank were assumed to be in quasi-thermodynamic equilibrium. The external ambient pressure and temperature were set to 1.0 atm and 300 K. A transient simulation was performed with a time step of 0.001 s and a total physical time of 2000 s. The time step was determined based on preliminary calculations. With this time step, the volume fraction near the gas–liquid interface varied smoothly, the gas-phase pressure curve showed no obvious numerical oscillation, and the residuals of the governing equations satisfied the convergence criteria within each time step. The computational domain included only the liquid hydrogen and gaseous hydrogen fluid regions and the thermal boundaries at the contacting walls, while the outer vessel, insulation layer, and solid support structures were not explicitly modeled, so that the analysis focused on phase change mass transfer, natural convection, and gas-phase pressure response induced by localized support heat input.

The effects of gravitational body force and surface tension were included in the model. The gravitational acceleration was set to $9.81 {\mathrm{m/s}}^2$ in the vertical downward direction, and the wall contact angle was set to $5°$ to describe the wettability of liquid hydrogen near the metal wall. The gaseous hydrogen density was described using the compressible ideal gas equation of state, whereas the liquid hydrogen density was treated using the Boussinesq approximation to represent buoyancy-driven flow caused by density variations under small temperature differences. No-slip boundary conditions were applied to the walls, and symmetry boundary conditions were imposed on the two symmetry planes to satisfy the geometric and physical symmetry of the quarter fluid domain model. To represent the non-uniform heat input induced by support thermal bridges, the inner vessel wall was divided into support conduction regions and MLI-covered regions, to which equivalent heat flux boundary conditions were separately applied. The support conduction regions were defined according to the corresponding support locations on the inner vessel wall to represent the localized thermal bridges formed by fiberglass supports. Based on steady-state heat transfer test data for the support structure provided by Zhangjiagang Hydrogen Energy Research Institute, the equivalent heat flux in the region corresponding to the fiberglass support was set to $32.603 {\mathrm{W/m}}^2$. This value was used to characterize the localized heat input transferred to the inner vessel wall through the support thermal bridge. A low heat flux of $0.725 {\mathrm{W/m}}^2$ was applied to the MLI-covered regions to represent distributed heat leakage under multilayer insulation conditions [18]. The equivalent heat flux for the uniform heat input case was obtained by converting the total heat input of the local heat input case; specifically, the total heat input from the support conduction regions and the MLI-covered regions was kept unchanged and uniformly distributed over the inner vessel wall, yielding an equivalent heat flux of $2.496 {\mathrm{W/m}}^2$.

The simulations were performed using ANSYS Fluent. Pressure–velocity coupling was handled using the coupled algorithm, and time discretization was performed using a first-order implicit scheme. The convection terms were discretized using a second-order upwind scheme, whereas the turbulent kinetic energy and dissipation rate equations were discretized using first-order schemes. Convergence within each time step was considered achieved when the residuals of the continuity, momentum, and energy equations decreased below ${10}^{-6}$, ${10}^{-3}$, and ${10}^{-6}$, respectively.

2.5. Grid Independence Verification

To reduce the influence of mesh size on the numerical results, a grid independence verification was conducted for the fluid domain model. Figure 5 presents the typical mesh used in the numerical simulation. The fluid domain was discretized using a polyhedral mesh, which can better adapt to the cylindrical tank wall and end-head geometry while maintaining mesh quality and computational efficiency. Considering that the support heat input regions, near-wall regions, and gas–liquid interface are key areas where large temperature gradients, velocity gradients, and phase change mass transfer variations may occur, local mesh refinement was applied in these regions, while the remaining fluid domain was meshed relatively uniformly. Under identical initial conditions, boundary conditions, and solver settings, four mesh sizes of 40 mm, 35 mm, 30 mm, and 25 mm were tested, corresponding to 245,327, 518,219, 782,616, and 1,158,345 cells, respectively. Gas-phase pressure was selected as the evaluation metric for grid independence because it reflects the combined effects of temperature variation, phase change mass transfer, and gas-phase mass variation inside the tank. Figure 6 shows the gas-phase pressure evolution under different mesh sizes.

Figure 6 indicates that the gas-phase pressure curves obtained with the 40 mm and 35 mm meshes still differ to some extent, suggesting that coarse meshes are insufficient for resolving local temperature gradients, natural convection structures, and phase change processes. When the mesh size was reduced to 30 mm, the gas-phase pressure evolution became stable. Further reducing the mesh size to 25 mm produced only minor changes in gas-phase pressure, while increasing the cell number from 782,616 to 1,158,345 and substantially increasing the computational cost. Considering both accuracy and computational efficiency, the 30 mm mesh was selected for subsequent simulations of the support-induced local heat input cases.

2.6. Model Validation

To validate the applicability of the gas–liquid two-phase flow numerical model for simulating self-pressurization, the low-heat flux liquid hydrogen experiment conducted by Hasan et al. [19] was selected for comparison. In that experiment, a flightweight liquid hydrogen vessel with an effective volume of $4.89 {\mathrm{m}}^3$ was used to measure gas-phase pressure evolution and gas–liquid thermal stratification under closed heating conditions in normal gravity. Three constant heat flux conditions, namely $0.35 {\mathrm{W/m}}^2$, $2.0 {\mathrm{W/m}}^2$, and $3.5 {\mathrm{W/m}}^2$, were tested, with an initial liquid filling ratio of approximately 83%. During the experiment, the vent valve was closed, and the gas-phase pressure evolution was recorded. The $3.5 {\mathrm{W/m}}^2$ heat flux condition was selected for validation, and the initial state, boundary conditions, and thermophysical parameters of the numerical model were specified according to the experimental conditions. Figure 7 compares the experimental and simulated gas-phase pressure results.

Figure 7 shows that the simulation results capture the overall experimental trend of gas-phase pressure increasing with time. In the early stage, the gas-phase pressure increases rapidly, mainly due to gas-region heating and enhanced liquid hydrogen evaporation induced by external heat input; thereafter, the pressure continues to rise, indicating that the model can describe the self-pressurization process of a closed liquid hydrogen vessel under low heat flux conditions. The simulation results agree well with the experimental data, with the overall maximum relative error kept within 8.4%. These results indicate that the present numerical model is suitable for subsequent analysis of the internal temperature field, flow field, and gas-phase pressure response of the liquid hydrogen tank under non-uniform heat input induced by support thermal bridges.

3. Results and Discussion

3.1. Simulation Case Setup

To investigate the effects of non-uniform heat input induced by support thermal bridges and its spatial distribution on the internal thermodynamic response of the liquid hydrogen tank, simulation cases were designed at a 50% filling ratio. Except for the spatial distribution of heat input, the circumferential support position, or the axial support position, all cases used the same initial conditions, boundary conditions, solver settings, and total heat input. In the baseline case, localized heat input boundaries were applied to the support regions, with the upper support angle set to $45°$, the lower support angle set to $30°$, and the axial support position set to $x=3.085$ m. In the local heat input case, the heat flux applied to the support conduction regions was $32.603 {\mathrm{W/m}}^2$, while that applied to the MLI-covered regions was $0.725 {\mathrm{W/m}}^2$. In the uniform heat input case, the total heat input was kept unchanged, and a uniform heat flux of $2.496 {\mathrm{W/m}}^2$ was applied to the inner vessel wall. The detailed simulation cases are listed in

Table 1. Simulation cases under 50% filling ratio.

Case	Upper Support Angle	Lower Support Angle	Axial Position	Heat Input Type
Baseline case	${45}^{°}$	${30}^{°}$	3.085 m	Local heat input
Upper support variation	${15}^{°}$	${30}^{°}$	3.085 m	Local heat input
	${30}^{°}$	${30}^{°}$	3.085 m	Local heat input
Lower support variation	${45}^{°}$	${15}^{°}$	3.085 m	Local heat input
	${45}^{°}$	${45}^{°}$	3.085 m	Local heat input
Axial-position variation	${45}^{°}$	${30}^{°}$	2.085 m	Local heat input
	${45}^{°}$	${30}^{°}$	4.085 m	Local heat input
Uniform heat input case	—	—	—	Uniform heat input

.

In the table, the uniform heat input case was used to compare the response differences between an ideal uniform heat flux boundary and the localized heat input boundary induced by support thermal bridges. The circumferential support position cases were divided into upper support variation and lower support variation cases. The upper support angle was set to $15°$, $30°$, and $45°$, while the lower support angle was also set to $15°$, $30°$, and $45°$. These cases were used to analyze the temperature field, flow field, and gas-phase pressure response when the relative position of the localized support heat input to the gas region, liquid region, and gas–liquid interface was changed. For the axial support position cases, the circumferential positions of the upper and lower supports were kept unchanged, and only the axial support position was varied as $x=2.085$ m, $x=3.085$ m, and $x=4.085$ m. These cases were used to compare the differences in the internal thermodynamic response caused by the movement of localized thermal disturbance along the tank length.

3.2. Comparison Between Local Heat Input and Uniform Heat Input

To analyze the effect of non-uniform heat input induced by support thermal bridges on the internal thermodynamic response of the liquid hydrogen tank, the local heat input case was compared with the uniform heat input case. The two cases maintained the same total heat input, and only the spatial distribution of heat input on the inner vessel wall was changed. The local heat input case was used to represent concentrated heat leakage caused by support thermal bridges, whereas the uniform heat input case was used to represent an ideal uniform heat flux boundary. By comparing the temperature field, flow field, and gas-phase pressure variation, it can be determined whether the localized heat input induced by support thermal bridges can be equivalent to a uniform heat input.

Figure 8 shows the temperature evolution at the monitoring points under the two heat input cases. In both cases, the temperatures of the monitoring points in the gas region increased with time, whereas those in the liquid region changed only slightly. This behavior is mainly related to the difference in thermal response between the gas and liquid phases. The gas region has a smaller heat capacity and is therefore more sensitive to wall heat input. In contrast, the liquid region has a larger heat capacity, and liquid-phase convection further weakens the local temperature rise. Comparison of the two heat input cases shows that the temperatures of the gas-region monitoring points were generally higher in the uniform heat input case than in the local heat input case. This difference is not caused by the total heat input, because the two cases have the same total heat input, but by the different spatial distribution of wall heating. In the uniform heat input case, heat continuously enters the gas region and the near-wall region along a larger portion of the inner vessel wall, resulting in a larger effective heated area in the gas phase. In the local heat input case, the support region produces a higher local heat flux and stronger local thermal disturbance, but the heated area is more concentrated. Therefore, its contribution to the overall gas-phase temperature rise is relatively limited, although it may have a stronger effect on the local temperature gradient and flow field development near the support region.

Figure 9 and Figure 10 show the temperature distributions on the circumferential support section and the axial section under the two heat input cases, respectively. In both cases, gas–liquid thermal stratification was formed inside the liquid hydrogen tank, with the gas region showing a higher temperature than the liquid region. However, the spatial distribution and formation mechanism of the high-temperature region differed between the two cases. In the local heat input case, the high-temperature region was mainly concentrated near the wall corresponding to the support region, where the local temperature gradient was relatively large. This is because the support thermal bridge introduces heat into a limited wall area, thereby enhancing local heat accumulation and promoting upward thermal transport under buoyancy. In the uniform heat input case, the high-temperature region was more continuously distributed along the upper gas region, and the overall temperature level of the gas region was higher. This occurs because the same total heat input is distributed over a larger wall area, allowing the gas region to be heated more uniformly. These results indicate that local heat input mainly changes the near-wall temperature gradient and local heat accumulation near the support region, whereas uniform heat input mainly enhances the overall temperature rise in the gas region.

Figure 11 compares the velocity vector distributions under the two heat input cases. Natural convection induced by wall heating was observed in both cases, but the flow intensity and local flow structure differed. In the local heat input case, the large temperature gradient near the support region caused the heated fluid to rise along the wall and induced local recirculation near the gas–liquid interface. This is because the localized support heat input produces a stronger local density gradient, which strengthens the buoyancy-driven thermal plume and promotes interaction between the rising flow and the gas–liquid interface. The maximum velocity inside the tank was approximately 0.27 m/s. In the uniform heat input case, the wall heat input was more uniformly distributed, the local temperature gradient was smaller, and the natural convection structure was more gradual, with a maximum velocity of approximately 0.14 m/s. In this case, the thermal plume was less concentrated because the same total heat input was distributed over a larger wall area. This indicates that, under the same total heat input, localized heat input induced by support thermal bridges is more likely to generate strong local natural convection and local flow field reconstruction near the support region.

Figure 12 shows the gas-phase pressure evolution under the two heat input cases. In both cases, the gas-phase pressure increased with time, indicating that continuous heat input promoted liquid hydrogen evaporation and gas-phase pressure accumulation. Since the total heat input was kept the same in the two cases, the difference in pressure response mainly resulted from the spatial distribution of wall heat input rather than the heat input magnitude itself. The gas-phase pressure in the uniform heat input case was slightly higher than that in the local heat input case. This is because uniform heat input enlarged the heated area in the upper gas region and increased the overall gas-phase temperature. The difference between the two pressure curves was mainly reflected in the early-stage pressure level. After the internal heat transfer and natural convection structures gradually developed, the pressurization rates of the two cases became close to each other. Although local heat input enhanced natural convection near the support region, its heating area was more concentrated, and its contribution to the overall gas-phase temperature rise and pressure increase was relatively limited. Therefore, uniform heat input can approximately capture the overall pressurization trend, but it cannot accurately describe the local heat accumulation and flow field reconstruction induced by support thermal bridges. This is because gas-phase pressure is mainly governed by the total heat input, average gas-phase thermal state, and phase change mass transfer, whereas the local velocity field and near-wall temperature gradients are more sensitive to the spatial distribution of heat input. Thus, pressure evolution reflects the integral thermodynamic response of the tank, while the local temperature and velocity fields reflect the localized effect of support thermal bridges.

3.3. Effect of Circumferential Support Position Variation

To analyze the effect of circumferential support position variation on the internal thermodynamic response of the liquid hydrogen tank, upper support variation and lower support variation cases were designed. In the upper support variation cases, the lower support angle was kept at $30°$, while the upper support angle was set to $15°$, $30°$, and $45°$. In the lower support variation cases, the upper support angle was kept at $45°$, while the lower support angle was set to $15°$, $30°$, and $45°$. These cases were used to compare the differences in temperature field, flow field, and gas-phase pressure response caused by changes in the relative position between the localized support heat input and the gas region, liquid region, and gas–liquid interface.

Figure 13 shows the temperature evolution at P1–P3 under different circumferential support positions. The temperature differences among the cases mainly appeared in the upper gas region, while the temperature variation near the gas–liquid interface was relatively small. When the lower support angle was kept at $30°$, the maximum temperature differences at P1 and P2 caused by upper support position variation were about 0.03 K and 0.02 K, respectively, whereas the temperature difference at P3 was less than 0.01 K. This indicates that the thermal disturbance induced by upper support position variation was mainly concentrated in the upper gas region and gradually weakened toward the gas–liquid interface. When the upper support angle was kept at $45°$, lower support position variation caused a smaller temperature difference, with the maximum differences at P1 and P2 being about 0.02 K and 0.01 K, respectively.

The different temperature responses can be explained by the relative position between the localized support heat input and the gas–liquid distribution. The upper support is closer to the gas region, where the heat capacity is smaller and local heat accumulation is more likely to occur. Therefore, changes in the upper support position can more directly affect the temperature response of the upper gas region. In contrast, the lower support is closer to the liquid region. The liquid phase has a larger heat capacity and stronger thermal buffering ability, so the local thermal disturbance introduced by the lower support is more readily diffused and weakened before it affects the upper gas region. Therefore, circumferential support position variation mainly affects the upper gas temperature, and upper support position variation has a more pronounced influence than lower support position variation.

Figure 14 shows the axial temperature distributions under different circumferential support position combinations. In the angle notation used in Figure 14 and the following discussion, the angle before the hyphen denotes the upper support angle, whereas the angle after the hyphen denotes the lower support angle. In all cases, the temperature variation in the bulk liquid region was small and remained within 20.39–20.42 K, indicating that the bulk liquid region had a strong thermal buffering effect under localized support heat input. The temperature differences were mainly concentrated near the top region corresponding to the support location. When the lower support angle was fixed at $30°$, as the upper support angle increased from $15°$ to $30°$ and $45°$, the local peak temperature near the upper support region decreased from 22.09 K to 21.50 K and 20.90 K, with a maximum decrease of about 1.19 K. This indicates that when the upper support heat input is closer to the top gas region, local heat accumulation is more likely to form. This is mainly because the upper gas region has a smaller heat capacity, and the localized heat input can be more easily accumulated near the top wall. As the upper support position moves downward along the side wall, the concentration of the local high-temperature region near the top is weakened. In this case, the localized heat source becomes closer to the gas–liquid interface, and part of the heat is transported by buoyancy-driven flow and interface-adjacent convection, which weakens the temperature accumulation in the upper gas region. In contrast, when the upper support angle was fixed at $45°$, the local peak temperatures near the top region were approximately 20.93 K, 20.90 K, and 20.94 K for lower support angles of $15°$, $30°$, and $45°$, the maximum temperature difference caused by lower support position variation was only about 0.04 K. Since the lower support heat input is closer to the liquid region, the larger heat capacity of the liquid phase and local convection weaken its influence on the temperature distribution in the upper gas region. Therefore, the circumferential position of the upper support has a more direct influence on local heat accumulation in the gas region, whereas the effect of lower support position variation is more easily buffered by the liquid phase.

Figure 15 shows the velocity vector distributions under different circumferential support position combinations. Variation in the circumferential support position changes the location of the localized heat input relative to the gas region and the gas–liquid interface, thereby affecting the natural convection structure. This influence is essentially related to the coupling between the localized thermal plume and the interface-adjacent recirculation region. When the lower support angle was kept at $30°$, the maximum velocity inside the tank increased from approximately 0.16 m/s to 0.23 m/s and 0.27 m/s as the upper support angle increased from $15°$ to $30°$ and $45°$. This indicates that the local peak temperature and the overall natural convection intensity are not fully synchronized. As the upper support position moves downward along the side wall, the relative distance between the local heat source and the gas–liquid interface, as well as the buoyancy-driven flow path, changes. Although the local peak temperature near the upper region decreases, the localized heat source becomes more favorable for driving the heated fluid toward the gas–liquid interface. The rising thermal plume can interact more directly with the interface-adjacent recirculation structure, thereby enhancing local momentum exchange and increasing the velocity peak. Meanwhile, local heat accumulation in the upper gas region is weakened, resulting in a decrease in the peak temperature. In contrast, when the lower support angle was varied, the maximum velocity remained approximately 0.27 m/s. This is because the lower support heat input mainly acts on the liquid region, where the thermal disturbance is more readily diffused by liquid-phase convection; the larger heat capacity and stronger thermal buffering effect of the liquid phase weaken the upward propagation of the thermal disturbance. Therefore, variation in the lower support circumferential position has a weaker effect on the overall flow intensity.

Figure 16 shows the gas-phase pressure evolution under different circumferential support position combinations. In all cases, the gas-phase pressure increased with time, and the overall increasing trend was similar. This similarity indicates that the pressure response was mainly governed by the total heat input, average gas-phase thermal state, and phase change mass transfer. The pressure differences caused by upper support position variation mainly developed during the early stage of the calculation. After approximately 600 s, the pressure curves became nearly parallel, and the average pressurization rate in the later stage was about 0.039 Pa/s. This indicates that the change in support angle mainly caused an early-stage pressure level shift, but did not significantly affect the late-stage pressurization rate. At the end of the calculation, the maximum gas-phase pressure difference among the different upper support angle cases was about 55 Pa. The pressure difference induced by lower support position variation was smaller, with a maximum pressure difference of about 10 Pa at the end of the calculation. These small pressure differences can be attributed to the identical total heat input used in all circumferential support position cases. Since gas-phase pressure is mainly controlled by the overall energy accumulation and the average gas-phase thermal state, changing the support angle only modifies the local heat input distribution without significantly changing the global pressurization behavior. Therefore, the small pressure differences indicate a limited influence of support position variation on the overall pressure response, rather than numerical error. Since the total heat input was kept constant in all cases, circumferential support position variation mainly affected the pressure level shift caused by early-stage local thermal disturbance, rather than significantly changing the overall pressurization trend.

3.4. Effect of Axial Support Position Variation

To analyze the effect of axial support position variation on the internal thermodynamic response of the liquid hydrogen tank, the axial support position was set to $x=2.085$ m, $x=3.085$ m, and $x=4.085$ m while keeping the circumferential positions of the upper and lower supports unchanged. Among these positions, $x=3.085$ m was taken as the baseline support position, whereas $x=2.085$ m and $x=4.085$ m correspond to cases in which the localized support heat input was shifted by 1 m in the negative and positive axial directions of the tank, respectively.

Figure 17 shows the axial temperature distributions under different axial support positions. In all three cases, gas–liquid thermal stratification was formed inside the liquid hydrogen tank, with the gas region showing a higher temperature than the liquid region, while the temperature variation in the bulk liquid region remained small. Variation in the axial support position did not significantly change the overall temperature distribution. Its effect was mainly reflected in the migration of the high-temperature region associated with the localized support heat input along the tank length. When the axial support position changed from $x=2.085$ m to $x=3.085$ m and $x=4.085$ m, the maximum difference in local peak temperature near the top region was only about 0.01 K. This result indicates that axial support position variation mainly changes the axial location of the localized heat input, while having only a weak effect on the local peak temperature and the intensity of gas–liquid thermal stratification. For a horizontal liquid hydrogen tank, the dominant stratification and buoyancy-driven flow are controlled by the gravity direction. Since axial displacement does not change the height of the localized heat source relative to the gas–liquid interface, its effect is mainly reflected in the axial migration of the local high-temperature region rather than in a change in the overall thermal stratification pattern.

Figure 18 shows the velocity vector distributions under different axial support positions. In all three cases, natural convection induced by localized support heat input was formed. The fluid near the support region was heated and rose along the wall, inducing local recirculation near the gas–liquid interface. This indicates that the basic flow mechanism was still controlled by buoyancy-driven thermal plume development, rather than by the axial location of the support alone. The main differences among the cases were reflected in the axial locations of the local high-velocity region and recirculation structure, while the overall flow intensity changed only slightly. The maximum velocity in all three axial support position cases was approximately 0.27 m/s. This further indicates that axial support movement mainly changes the spatial position of the velocity disturbance, but has little influence on the strength of the natural convection. When the support was located at $x=2.085$ m and $x=4.085$ m, the velocity disturbance region shifted toward the front and rear of the tank, respectively. When the support was located at $x=3.085$ m, the local high-velocity region was mainly concentrated near the support section. Therefore, the axial support position primarily determines where the local flow disturbance occurs along the tank length, while the dominant buoyancy-driven flow pattern remains almost unchanged.

Figure 19 shows the gas-phase pressure evolution under different axial support positions. In all three cases, the gas-phase pressure increased with time, and the overall trend was nearly the same. At the end of the calculation, the maximum gas-phase pressure difference among the three axial-position cases was about 24 Pa. This difference was smaller than that caused by circumferential support position variation, indicating that axial support position variation has a relatively limited influence on the gas-phase pressure response. Unlike circumferential support variation, axial support variation does not change the height of the localized heat source relative to the gas–liquid distribution. It mainly shifts the local heat input region along the tank length. Therefore, its influence on the overall pressure evolution is weak, and the small pressure difference should be interpreted as a limited physical effect rather than numerical error.

3.5. Mechanism of Localized Support Heat Input

The non-uniform heat input induced by support thermal bridges mainly affects the internal thermodynamic response by changing the local temperature gradient and buoyancy-driven flow structure. Compared with equivalent uniform heat input, localized support heat input acts on a limited wall area and therefore produces stronger local heat accumulation near the support-corresponding region. The heated fluid rises along the wall under buoyancy and further induces local recirculation near the gas–liquid interface. As a result, localized heat input has a more pronounced effect on the near-wall temperature field and local velocity field, although its contribution to the average gas-phase temperature rise is relatively limited.

The influence of support position depends on the relative location between the localized heat source and the gas–liquid distribution. Circumferential support variation changes the height of the heat input region relative to the gas region, liquid region, and gas–liquid interface, so it has a more direct influence on local heat accumulation and natural convection development. The upper support mainly affects the gas region and interface-adjacent flow, whereas the effect of the lower support is weakened by the larger heat capacity and thermal buffering effect of the liquid phase. In contrast, axial support variation mainly changes the longitudinal location of the local thermal disturbance, without changing the vertical relationship between the heat source and the gas–liquid interface. Therefore, its influence is mainly reflected in the axial migration of the local high-temperature and high-velocity regions.

Under the same total heat input, the gas-phase pressure response is mainly governed by the overall energy accumulation, average gas-phase thermal state, and phase change mass transfer. Therefore, support position variation mainly causes a pressure level difference in the early stage, while the later-stage pressurization rates tend to be consistent. The small pressure differences among different support position cases indicate that support position has a limited influence on the overall pressure response, rather than numerical error. Overall, localized support heat input boundaries should be retained when local temperature distribution, flow field reconstruction, and support layout effects are of concern.

4. Conclusions

In this study, a gas–liquid two-phase CFD model was established to investigate the internal thermodynamic response of a liquid hydrogen tank under support thermal bridge-induced non-uniform heat input. The effects of localized support heat input, equivalent uniform heat input, circumferential support position variation, and axial support position variation were analyzed. The main conclusions are as follows.

(1) The support thermal bridge produces a localized heat input effect that cannot be fully represented by an equivalent uniform heat input boundary. Although the two heat input forms have the same total heat input, they lead to different local temperature and flow field characteristics. Localized support heat input strengthens the near-wall temperature gradient and promotes local heat accumulation near the support-corresponding region, whereas equivalent uniform heat input mainly increases the average thermal level of the upper gas region. This indicates that the spatial distribution of heat input is important when local thermal behavior is concerned.

(2) The localized heat input changes the buoyancy-driven flow mechanism inside the tank. Heat introduced through the support-corresponding wall region reduces the local fluid density and drives the heated fluid to rise along the wall, forming a thermal plume and inducing recirculation near the gas–liquid interface. This mechanism explains why localized support heat input can produce stronger local flow field reconstruction than equivalent uniform heat input, even when the overall heat input remains unchanged.

(3) The influence of support position is mainly controlled by the relative location between the localized heat source and the gas–liquid distribution. Circumferential support variation has a more direct effect on local heat accumulation and natural convection development because it changes the height of the heat input region relative to the gas region, liquid region, and gas–liquid interface. In contrast, axial support variation mainly shifts the local thermal disturbance along the tank length and has a weaker influence on the overall thermal stratification pattern and gas-phase pressure response.

(4) The gas-phase pressure response is less sensitive to support position variation than the local temperature and velocity fields. Under the same total heat input, the overall pressure increase trend is mainly governed by the average gas-phase thermal state and phase change mass transfer. Therefore, an equivalent uniform heat input model may be acceptable when only the overall pressure increase trend is estimated. However, it is not sufficient for predicting local hot spots, near-wall temperature gradients, and support-induced flow field reconstruction.

The main contribution of this study is to clarify the applicability boundary between localized support heat input modeling and equivalent uniform heat input simplification. For engineering applications, localized support heat input boundaries should be retained in analyses involving support thermal protection, support layout optimization, local hotspot identification, and temperature monitoring point arrangement. In contrast, the uniform heat input model can be used as a simplified approximation for preliminary estimation of the overall pressure increase trend.

This study still has some limitations. The present work focuses on a 50% filling ratio and represents the support thermal bridge using equivalent localized heat input regions. The detailed solid heat conduction inside the support structure, different filling ratios, dynamic transportation conditions, and experimental validation of local thermal stratification still require further investigation. Future work will consider coupled solid–fluid heat transfer and broader operating conditions to improve the engineering applicability of the model.