Multi-physics field simulation method and medium for composite hydrogen storage reactor

Abstract

This application discloses a multiphysics simulation method and medium for a composite hydrogen storage reactor: A computational domain model of the composite hydrogen storage reactor is established based on parameters; a gas transport coupling model between a first region and a second region is constructed, as well as a solid-phase hydrogen absorption reaction model within the second region; segmented hydrogen charging boundary conditions for the composite hydrogen storage reactor are generated based on preset hydrogen charging inlet parameters; transient coupling solution is performed on the computational domain model to obtain the multiphysics simulation results during hydrogen storage; and the hydrogen storage simulation results of the composite hydrogen storage reactor are determined based on the multiphysics simulation results. This application aims to solve the problem of how to simultaneously consider the compressed hydrogen storage in the free gas region and the solid-phase hydrogen absorption reaction in the porous hydrogen storage medium region, as well as the gas transport coupling between them, in the hydrogen charging simulation of a high-pressure gas-solid composite hydrogen storage reactor, thereby accurately determining the gas phase hydrogen storage capacity, the solid phase hydrogen storage capacity, and the dynamic distribution relationship between gas phase hydrogen storage and solid phase hydrogen storage.

Description

Technical Field

[0001] This application relates to the field of hydrogen storage heat exchange, and in particular to a multiphysics simulation method and medium for a composite hydrogen storage reactor. Background Technology

[0002] High-pressure gaseous hydrogen storage offers advantages such as rapid hydrogen charging and discharging rates and high engineering maturity. However, increasing volumetric hydrogen storage density typically requires raising the storage pressure, which in turn increases compression energy consumption, tank costs, and safety constraints. Metal hydride hydrogen storage offers advantages such as high volumetric hydrogen storage density and low leakage risk, but its hydrogen absorption and desorption processes are limited by factors such as reaction heat, bed heat transfer, material plateau pressure, and hydrogen absorption kinetics. To combine the advantages of both, existing technologies have proposed hydrogen storage tanks or systems that combine high-pressure vessels with hydrogen storage alloys, such as metal hydride / high-pressure composite hydrogen storage tanks based on vanadium-based solid hydrogen storage alloys, or Ti-Cr-Fe-Mn-based hydrogen storage alloys suitable for high-pressure-metal hydride hydrogen storage. These approaches mainly focus on material or structural properties such as hydrogen storage alloy composition, plateau pressure, hydrogen storage capacity, fill rate, and tank hydrogen storage density. No simulation method has yet been established for the transient coupling evolution relationship between the free gas region, bed pore gas, and the metal hydride solid phase during high-pressure hydrogen charging.

[0003] In the simulation of metal hydride hydrogen storage tanks, existing multiphysics models typically focus on gas transport, hydrogen absorption kinetics, reaction heat release, and heat transfer processes within the metal hydride bed to calculate pressure, concentration, temperature, or reaction processes. However, conventional models often treat the metal hydride bed as a single homogeneous porous reactive medium, or simplify the free volume within the tank to boundary conditions, buffer spaces, or negligible cavities, failing to explicitly model the macroscopic free gas region as a functional hydrogen storage region alongside the porous reactive bed. In 10–20 MPa high-pressure gas-solid composite hydrogen storage reactors, the free gas region not only performs the function of compressed hydrogen storage but also participates in pressure propagation, gas supply, and heat and mass transfer; simultaneously, the bed also exhibits coupled behaviors such as hydrogen absorption and heat release, real gas compression, bed expansion, and changes in porosity and permeability. Therefore, traditional models are prone to unclear contributions from the gas phase hydrogen storage, inaccurate assessment of the driving force for solid-phase hydrogen absorption, and distortion of the gas-solid hydrogen storage coupling relationship.

[0004] Furthermore, actual high-pressure hydrogen charging processes typically involve a gradual transition from nominal mass flux supply to a pressure-limited charging stage constrained by a pressure ceiling. Inlet mass flux, reactor pressure, bed temperature, hydrogen absorption rate, and gas-solid hydrogen storage distribution interact over time. Existing simulation methods, if they do not simultaneously consider the gas transport coupling between the free gas region and the porous metal hydride region, real gas effects, solid-phase hydrogen absorption reactions, and segmented charging boundary conditions, struggle to accurately characterize the dynamic competition and compensation relationship between gas-phase and solid-phase hydrogen storage. This can lead to misjudgments of the impact of pressure ceiling, charging mass flux, and thermal management conditions on the total hydrogen storage capacity and hydrogen distribution. Therefore, there is an urgent need to establish a multiphysics simulation method for composite hydrogen storage reactors that can explicitly delineate the free gas region and the porous hydrogen storage medium region, and provide transient coupled solutions for gas transport, solid-phase hydrogen absorption reactions, and segmented charging boundaries. Summary of the Invention

[0005] This application aims to address how to simultaneously consider the compressed hydrogen storage in the free gas region and the solid-phase hydrogen absorption reaction in the porous hydrogen storage medium region, as well as the gas transport coupling between the two, in the hydrogen charging simulation of a high-pressure gas-solid composite hydrogen storage reactor, so as to accurately determine the amount of hydrogen stored in the gas phase, the amount of hydrogen stored in the solid phase, and the dynamic distribution relationship between the hydrogen stored in the gas phase and the hydrogen stored in the solid phase.

[0006] One aspect of this application provides a multiphysics simulation method for a composite hydrogen storage reactor, comprising:

[0007] Obtain the parameters of the composite hydrogen storage reactor to be simulated, and establish a computational domain model of the composite hydrogen storage reactor based on the parameters; the computational domain model includes a first region and a second region;

[0008] A gas transport coupling model is constructed between the first and second regions, and a solid-phase hydrogen absorption reaction model is constructed within the second region;

[0009] The segmented hydrogen charging boundary conditions of the composite hydrogen storage reactor are generated based on the preset hydrogen charging inlet parameters. The segmented hydrogen charging boundary conditions are used to transition the hydrogen charging inlet from the nominal mass flux supply state to the pressure-limited hydrogen charging state.

[0010] Based on the gas transport coupling model, the solid-phase hydrogen absorption reaction model, and the segmented hydrogen charging boundary conditions, the computational domain model is solved by transient coupling to obtain the multiphysics simulation results of the hydrogen storage process.

[0011] Based on the multiphysics simulation results, the hydrogen storage simulation results of the composite hydrogen storage reactor were determined. The hydrogen storage simulation results include the amount of hydrogen stored in the gas phase, the amount of hydrogen stored in the solid phase, and the hydrogen storage distribution results between the amount of hydrogen stored in the gas phase and the amount of hydrogen stored in the solid phase.

[0012] Another aspect of this application provides a computer-readable storage medium that stores computer instructions that, when executed by a processor, implement a multiphysics simulation method for a composite hydrogen storage reactor.

[0013] Compared to existing technologies, the advantages of this application are:

[0014] This application addresses the characteristics of free gas region, bed pore gas, and metal hydride solid phase jointly participating in and coupling with each other in a high-pressure gas-solid composite hydrogen storage reactor. The computational domain model is divided into a first region representing the free gas space and a second region representing the porous hydrogen storage medium. A gas transport coupling model between the two and a solid-phase hydrogen absorption reaction model within the second region are constructed. Transient coupling solutions are then performed using segmented hydrogen charging boundary conditions transitioning from nominal mass flux supply to pressure-limited hydrogen charging. This allows for the simultaneous characterization of high-pressure free gas compression hydrogen storage, inter-regional pressure propagation and mass exchange, and metal hydride solid-phase hydrogen absorption processes. It overcomes the problems of unclear gas-phase hydrogen storage contribution, distorted gas-solid hydrogen storage coupling, and misjudgment of hydrogen storage distribution caused by the weakening or neglect of the free gas region in traditional single homogeneous bed models. This provides reliable results for obtaining the pressure field, temperature field, gas-phase hydrogen storage capacity, solid-phase hydrogen storage capacity, and their dynamic distribution, offering a basis for evaluating the impact of pressure ceiling, hydrogen charging mass flux, and heat transfer conditions on composite hydrogen storage performance. Attached Figure Description

[0015] This application will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein:

[0016] Figure 1 A schematic diagram of the reactor configuration and computational domain decomposition of the high-pressure gaseous-solid composite hydrogen storage reactor provided in the embodiments of this application;

[0017] Figure 2 This is an exemplary flowchart of a multiphysics simulation method for a composite hydrogen storage reactor;

[0018] Figure 3 The following figures illustrate the model thermodynamic fitting, mesh independence test, and experimental verification results provided for embodiments of this application.

[0019] Figure 4 Spatial distribution diagrams of seven representative cross sections when the average reactor pressure reaches 20 MPa, provided for embodiments of this application;

[0020] Figure 5 Spatial distribution diagram of the influence of the upper pressure limit on the temperature field during hydrogen charging, provided for embodiments of this application;

[0021] Figure 6 Spatial distribution diagram of the influence of the upper pressure limit on the hydrogen storage capacity of the metal hydride bed mass during hydrogen charging, provided for embodiments of this application;

[0022] Figure 7 Spatial distribution diagram of the influence of the upper pressure limit on the gas phase hydrogen density field during hydrogen charging, provided for embodiments of this application;

[0023] Figure 8 Global hydrogen charging behavior diagrams under different pressure upper limits provided in embodiments of this application;

[0024] Figure 9 Spatial distribution diagram of the influence of nominal inlet mass flux on the temperature field during hydrogen charging, provided for embodiments of this application;

[0025] Figure 10 Spatial distribution diagram of the influence of nominal inlet mass flux on the mass hydrogen storage capacity of metal hydride bed during hydrogen charging, provided for embodiments of this application;

[0026] Figure 11 Spatial distribution diagram of the influence of nominal inlet mass flux on gas phase hydrogen density field during hydrogen charging, provided for embodiments of this application;

[0027] Figure 12 Global hydrogen charging behavior diagrams under different nominal inlet mass fluxes provided in embodiments of this application;

[0028] Figure 13 This is a spatial distribution diagram showing the influence of heat exchange fluid velocity on the temperature field during hydrogen charging, provided in an embodiment of this application.

[0029] Figure 14 Spatial distribution diagram of the influence of heat exchange fluid flow rate on the hydrogen storage capacity of metal hydride bed mass during hydrogen charging, provided in the embodiments of this application;

[0030] Figure 15 Spatial distribution diagram of the influence of heat exchange fluid velocity on the gas phase hydrogen density field during hydrogen charging, provided in an embodiment of this application;

[0031] Figure 16 A graph showing the quantitative influence of heat exchange fluid flow rate on the hydrogen charging behavior of the composite hydrogen storage reactor, provided in an embodiment of this application.

[0032] Figure 17 Spatial distribution diagram of the influence of hydrogen absorption heat level on temperature field during hydrogen charging provided in the embodiments of this application;

[0033] Figure 18 Spatial distribution diagram of the influence of hydrogen absorption heat level on the hydrogen storage capacity of metal hydride bed mass during hydrogen charging, provided in the embodiments of this application;

[0034] Figure 19Spatial distribution diagram of the influence of hydrogen absorption heat level on gas phase hydrogen density field during hydrogen charging, provided in the embodiments of this application;

[0035] Figure 20 The global hydrogen charging response diagrams under different hydrogen absorption heat levels are provided for embodiments of this application. Detailed Implementation

[0036] The methods and systems provided in the embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0037] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0038] This application provides a multiphysics simulation method for a composite hydrogen storage reactor, particularly suitable for gas-solid composite hydrogen storage reactors operating under high pressure conditions of 10~20MPa. In this composite hydrogen storage reactor, hydrogen is simultaneously stored in compressed gaseous form in the free gas space and bed pores, and in solid hydride form in a metal hydride hydrogen storage medium.

[0039] Since the free gas space, bed pore gas, and metal hydride solid phase all participate in hydrogen storage during the hydrogen charging process, and there are coupled processes such as real gas compression, hydrogen absorption and heat release, bed expansion, changes in porosity and permeability, and switching of the pressure-limited hydrogen charging boundary, the embodiments of this application explicitly divide the computational domain of the composite hydrogen storage reactor into a free gas region and a porous hydrogen storage medium region, and perform transient coupling solutions on the gas transport, solid-phase hydrogen absorption reaction, and heat transfer processes between the two, thereby obtaining the pressure field, temperature field, velocity field, gas phase hydrogen storage capacity, solid phase hydrogen storage capacity, and hydrogen storage distribution results between the gas phase hydrogen storage capacity and the solid phase hydrogen storage capacity during the hydrogen storage process.

[0040] In one embodiment, such as Figure 1 As shown, the composite hydrogen storage reactor is a high-pressure gas-solid composite hydrogen storage reactor. Its reactor configuration and computational domain decomposition include experimental modules, reactor structure schematic, cross-sectional arrangement, and simplified computational domain partitioning. Figure 1 The reactor in the design includes a reactor vessel, hydrogen inlet, heat exchange fluid inlet, thermocouple inlet, external spiral heat exchange channel, free gas region, porous metal hydride bed, central heat exchange tube, internal fins, vessel wall, heat exchange fluid channel, free gas domain, porous metal hydride domain, solid wall domain, and heat exchange fluid domain. Figure 1 The computational domain decomposition shown can explicitly distinguish between the unfilled macroscopic free volume and the reactive porous metal hydride bed, so that the free gas region can participate in the calculation not only as a pressure propagation region, but also as a compressed hydrogen storage region for hydrogen storage statistics.

[0041] In one embodiment, the composite hydrogen storage reactor employs a dual-loop heat exchange configuration. The internal loop consists of a central heat exchange tube with longitudinal fins extending axially along the reactor, enhancing heat extraction or supply within the bed. The external loop is formed by spiral heat exchange channels arranged around the outer wall of the vessel, providing heat exchange access to the reactor periphery. The central heat exchange tube and internal fins shorten the heat transfer path within the porous hydrogen storage medium region, while the external spiral heat exchange channels extract or supply heat from the reactor periphery. The free gas region, porous metal hydride region, solid wall region, and heat exchange fluid region are treated in the computational domain as a compressible fluid domain, a reactive porous medium domain, a solid thermal conduction domain, and a heat exchange fluid domain, respectively. This configuration shortens the characteristic thermal conduction distance within the porous hydrogen storage medium region and improves the temperature field uniformity during transient operation.

[0042] In one embodiment, such as Figure 1 As shown, two representative temperature probe locations, denoted as TC1 and TC2, are set in the composite hydrogen storage reactor. TC1 is located in the porous metal hydride region, and TC2 is located in the free gas region. The radial positions of both are approximately one-third of the bed thickness. This setup allows for the characterization of the temperature response of the porous metal hydride bed and the free gas region during the hydrogen charging process, which can then be used for subsequent model validation.

[0043] Example 1

[0044] The hydrogen storage medium in this embodiment can be a Ti-Mn based AB2 type Laves phase metal hydride alloy, for example... The alloy undergoes a hydrogen absorption reaction within the porous hydrogen storage medium, thereby allowing some of the pore hydrogen to be absorbed by the solid-phase hydrogen storage medium and forming solid-phase hydrogen storage. For example... Figure 2 As shown:

[0045] S100: Obtain the parameters of the composite hydrogen storage reactor to be simulated, and establish the computational domain model of the composite hydrogen storage reactor based on the parameters.

[0046] In one embodiment, the parameters of the composite hydrogen storage reactor to be simulated include reactor geometric parameters, hydrogen storage medium parameters, heat exchange structure parameters, wall structure parameters, heat exchange fluid parameters, hydrogen inlet parameters, initial pressure, initial temperature, initial hydrogen storage capacity, and solution parameters.

[0047] The reactor geometry parameters are used to determine the free gas space, porous hydrogen storage medium filling space, heat exchange structure, and wall structure within the composite hydrogen storage reactor. The hydrogen storage medium parameters describe the hydrogen absorption thermodynamics, hydrogen absorption kinetics, bed porosity, permeability, thermal conductivity, and expansion characteristics of the metal hydride alloy in the porous hydrogen storage medium region. The heat exchange structure parameters determine the central heat exchange tube, internal fins, and external spiral heat exchange channels. The wall structure parameters determine the container wall and the solid thermally conductive region coupled with the heat transfer between the first and second regions.

[0048] In one embodiment, establishing a computational domain model of the composite hydrogen storage reactor based on parameters includes:

[0049] The free gas space, porous hydrogen storage medium filling space, heat exchange structure, and wall structure in the composite hydrogen storage reactor are determined based on the parameters.

[0050] The free gas space is divided into the first region, and the porous hydrogen storage medium filling space is divided into the second region.

[0051] Based on the heat transfer structure and wall structure, an auxiliary calculation region coupled with the heat transfer of the first and second regions is established; wherein, the auxiliary calculation region includes a solid heat conduction region and / or a heat transfer fluid region;

[0052] Based on the first region, the second region, and the auxiliary computational region, a computational domain model for solving transient multiphysics coupling is generated.

[0053] In the embodiments of this application, the first region is used to characterize the free gas space within the composite hydrogen storage reactor that is not filled with the hydrogen storage medium. This first region is not a negligible cavity, but rather an active functional region used to describe the compression and storage of free hydrogen, pressure propagation, gas supply, and heat and mass transfer processes during high-pressure hydrogen charging.

[0054] The second region is used to characterize the porous hydrogen storage medium region within the composite hydrogen storage reactor, where solid-phase hydrogen storage reactions can occur. This second region is filled with metal hydride alloy powder or particles, and pore hydrogen gas exists within the pore space. The solid-phase alloy can absorb the pore hydrogen gas and form solid hydrides.

[0055] In one embodiment, in a simplified computational geometry, approximately three-quarters of the internal hydrogen storage volume is allocated to the porous metal hydride region, with the remaining approximately one-quarter reserved as a macroscopic free gas region to accommodate bed expansion and compressed hydrogen storage. This partitioning is necessary for high-pressure composite hydrogen storage because hydrogen is stored not only in chemically bonded form within the metal hydride bed but also as a compressed gas within the bed pores and the free volume of the container.

[0056] In one embodiment, the computational domain model includes the following regions:

[0057] The free gas region, i.e., the first region;

[0058] Porous metal hydride region, i.e., the second region;

[0059] Solid wall region, including reactor wall, central heat exchange tube and internal fins;

[0060] The heat transfer fluid region, also known as the HTF region.

[0061] In this modeling approach, the container wall, central heat exchange tubes, and fins are treated as solid heat conduction domains; the metal hydride bed is treated as a reactive porous medium; the free gas region is treated as a compressible fluid domain; and the heat exchange fluid channels are treated as heat exchange fluid regions. Through this multi-domain modeling method, the gaseous hydrogen compression, porous medium reactive hydrogen storage, conjugate heat transfer, and transient pressure redistribution during high-pressure hydrogen absorption can be analyzed simultaneously.

[0062] In one embodiment, to reduce computational complexity while preserving the dominant physical processes of the composite hydrogen storage reactor, the computational domain model is established based on the following modeling assumptions:

[0063] The porous metal hydride bed is considered as an isotropic porous medium, and it is assumed that the solid alloy and the pore hydrogen are in a state of local thermal equilibrium.

[0064] In the high-pressure region, hydrogen is described using the real gas law to account for the deviations that may be introduced by the ideal gas assumption when the operating pressure is close to 20 MPa.

[0065] The structural evolution of the metal hydride bed during hydrogen absorption is characterized by dynamic changes in porosity and permeability.

[0066] The effective thermal conductivity of the porous metal hydride bed is described by the Zehner–Bauer–Schlünder model, and the contribution of gas phase thermal conductivity is corrected by Smoluchowski.

[0067] Hydrogen flow in the free gas region is considered as compressible flow, and hydrogen transport in the porous metal hydride bed is described within a porous media framework.

[0068] The heat transfer fluid is considered an incompressible fluid, and its turbulent flow is governed by the Reynolds-averaged Navier-Stokes equations and the standard equations. Turbulence model description;

[0069] The thermal contact resistance between the internal metal components is ignored.

[0070] Based on the above assumptions, it is possible to describe the coupling relationship between free gas compression, porous medium hydrogen absorption, bed structure evolution, and conjugate heat transfer while taking into account both numerical stability and computational efficiency.

[0071] S200, construct a gas transport coupling model between the first and second regions, and construct a solid-phase hydrogen absorption reaction model within the second region.

[0072] The multiphysics simulation method in this application includes thermodynamic relationships, reaction kinetic relationships, real gas equations of state, porous media structure evolution relationships, effective thermal conductivity models, free gas region governing equations, porous metal hydride region governing equations, solid wall heat transfer equations, and heat transfer fluid governing equations. These models are coupled through principal variables such as pressure field, temperature field, velocity field, gas density, and mass hydrogen storage capacity.

[0073] Specifically, the reference equilibrium pressure determined by the hydrogen absorption PCT isotherm, the equilibrium pressure obtained by the van't Hoff relation correction, the hydrogen absorption kinetic equation determined by local pressure and temperature, the mass source term and reaction heat source term determined by the hydrogen absorption rate, the real gas density determined by the Peng–Robinson equation of state, the porosity updated by the mass hydrogen storage capacity, the permeability updated by the porosity, and the effective thermal conductivity of the bed determined by the Smoluchowski correction and the ZBS model.

[0074] The pressure field drives hydrogen flow in both the free gas region and the porous metal hydride region, and also influences the equilibrium pressure and hydrogen absorption kinetics by incorporating the real gas law to determine gas density. The temperature field affects equilibrium pressure, reaction kinetics, gas density, and effective thermal conductivity, and is driven by the reaction heat source term. The velocity field controls convective mass transfer and convective heat transfer. The mass hydrogen storage capacity is updated by hydrogen absorption kinetics and further influences porosity, permeability, and effective thermal conductivity. Gas density is determined by the real gas law based on local pressure and temperature, and is incorporated into the mass conservation equation, momentum equation, and energy equation. This forms a transient coupling solution framework between thermodynamics, kinetics, flow, heat transfer, and hydrogen storage capacity.

[0075] In one embodiment, the gas transport coupling model is used to characterize free hydrogen transport in a first region, pore hydrogen transport in a second region, and pressure continuity, mass flux continuity, and gas exchange relationships between the first and second regions.

[0076] The solid-phase hydrogen absorption reaction model is used to characterize the absorption process of pore hydrogen by the hydrogen storage medium in the second region. Specifically, the solid-phase hydrogen absorption reaction model calculates the local hydrogen absorption rate based on the local pressure, local temperature, and local mass hydrogen storage capacity in the second region, and further obtains the gas mass change term and reaction heat source term caused by the solid-phase hydrogen absorption reaction.

[0077] In one embodiment, constructing a gas transport coupling model between the first region and the second region includes:

[0078] Construct a free hydrogen transport model within the first region;

[0079] Construct a porous hydrogen transport model within the second region;

[0080] Based on the pressure continuity, mass flux continuity, and gas exchange relationship between the first and second regions, a coupled gas transport model is obtained by coupling the free hydrogen transport model and the pore hydrogen transport model.

[0081] Among them, the gas transport coupling model is used to characterize the effects of solid-phase hydrogen absorption reaction, real gas compression effect, and the evolution of porous hydrogen storage medium structure on pore hydrogen transport in the second region.

[0082] In this embodiment, hydrogen in the first region is modeled as a compressible fluid; gas transport in the second region is described using a compressible Brinkman form that includes Darcy resistance. The Brinkman form preserves viscous stress effects and provides a smooth transition between the free gas region and the porous metal hydride region.

[0083] S210, Construct a free hydrogen transport model within the first region.

[0084] In one embodiment, the free hydrogen transport model includes a continuity equation and a momentum equation for hydrogen in a first region.

[0085] The continuity equation is:

[0086] ;

[0087] The momentum equation is:

[0088] ;

[0089] in, The density of hydrogen gas in the first region is given in units of 1000 kJ / m³. t represents the transient solution time, in seconds. The velocity vector of hydrogen gas in the first region, in units of ; This represents the hydrogen pressure in the first region, in Pa. Let be the viscous stress tensor of hydrogen gas in the first region, in Pa. For spatial gradient operators; It is the spatial divergence operator.

[0090] The hydrogen density in the first region The local pressure p and local temperature T in the first region are determined according to the Peng–Robinson real gas equation of state.

[0091] In one embodiment, local molar volume The values ​​are obtained from the local pressure p and temperature T using the Peng–Robinson real gas equation of state:

[0092] ;

[0093] The corresponding hydrogen density is calculated as follows:

[0094] ;

[0095] Where R is the universal gas constant, in J / (mol·K); T is the temperature, in K; This is the molar volume of hydrogen, in units of . ; This represents the molar mass of hydrogen, expressed in kg / mol. b uses the standard Peng–Robinson expression based on the critical properties of hydrogen and the eccentricity factor. In a specific implementation, the above real gas parameters can be determined by calling the built-in thermophysical property library of the simulation software.

[0096] S220, construct a porous hydrogen transport model in the second region.

[0097] In one embodiment, the pore hydrogen transport model includes a continuity equation and a momentum equation for pore hydrogen in a second region.

[0098] The continuity equation is:

[0099] ;

[0100] The momentum equation is:

[0101] ;

[0102] in, is the porosity of the second region, and is a dimensionless parameter; The hydrogen density within the pore space of the second region, in units of t represents the transient solution time, in seconds. The apparent velocity vector of hydrogen gas in the pores of the second region is given in m / s. This represents the change in gas mass caused by the solid-phase hydrogen absorption reaction in the second region, in units of... p represents the pore hydrogen pressure in the second region, in Pa. The viscous stress tensor of pore hydrogen in the second region in Brinkman form is expressed in Pa. This is the dynamic viscosity of hydrogen, expressed in Pa⋅s. The penetration rate of the second region is expressed in units of... .

[0103] Among them, the quality change item The local hydrogen absorption rate is determined as follows:

[0104] ;

[0105] in, This refers to the alloy density, in units of... ; Local mass hydrogen storage capacity, in units of ; Local hydrogen absorption rate, in units of .

[0106] In one embodiment, to account for reaction-induced alloy bed expansion, the porosity of the second region is updated based on the local mass hydrogen storage capacity:

[0107] ;

[0108] in, The initial bed porosity; The coefficient of thermal expansion; The saturated mass hydrogen storage capacity is expressed in units of... .

[0109] Bed permeability is updated using the following formula:

[0110] ;

[0111] in, Initial penetration rate, in units of .

[0112] Initial permeability can be estimated using the Kozeny-Carman relationship for an equivalent granular packed bed:

[0113] ;

[0114] in, The value represents the diameter of the alloy powder particles, expressed in meters (m).

[0115] S230, construct a solid-phase hydrogen absorption reaction model in the second region.

[0116] In one embodiment, the absorption process of pore hydrogen by the hydrogen storage medium in the second region is described by a pressure- and temperature-dependent kinetic expression. The local mass hydrogen storage capacity of the alloy in the second region is denoted as w, in wt.%. Based on the alloy pressure-composition-temperature characteristics measured within the operating range considered in this embodiment, the saturated mass hydrogen storage capacity is taken as:

[0117] ;

[0118] The hydrogen absorption rate is:

[0119] ;

[0120] in, Local hydrogen absorption rate, in units of ; Pre-exponential factors, in units of ; Activation energy, unit: R is the universal gas constant, with units of 1000 ppm. T is the local temperature in K; p is the local hydrogen pressure in the second region in Pa. To balance the pressure, the unit is Pa.

[0121] The equilibrium pressure is determined by alloy thermodynamics, using a reference PCT isotherm and a van't Hoff temperature correction.

[0122] ;

[0123] in, For reference equilibrium pressure, the unit is Pa, which is the mass hydrogen storage capacity. The function, and determined by the reference temperature. The measured hydrogen absorption PCT isotherm was obtained by interpolation; This represents the absolute value of the enthalpy change upon hydrogen absorption, in units of 1. .

[0124] In one embodiment, the reaction heat source term in the second region is determined by the local hydrogen absorption rate as follows:

[0125] ;

[0126] in, This is the heat source term for the reaction, in units of... ; This is the absolute value of the enthalpy change upon hydrogen absorption, in units of 1. ; The molar mass of hydrogen is given by 1000 ppm. .

[0127] S300, establish a heat transfer coupling model.

[0128] In one embodiment, although the core steps in the claims mainly include a gas transport coupling model and a solid-phase hydrogen absorption reaction model, in order to fully describe the multiphysics simulation process of the composite hydrogen storage reactor, the embodiments of this application also perform coupled modeling of heat transfer in the first region, the second region, and the auxiliary calculation region.

[0129] In the first region, the energy equation is:

[0130] ;

[0131] in: ;

[0132] in, This is the isobaric specific heat capacity of hydrogen, in units of... ; Thermal conductivity, unit: ; Here is the thermal conductivity of hydrogen, in units of 1000 ppm. ; For heat sources related to pressure work, the unit is . ; For heat sources related to viscous dissipation, the unit is... .

[0133] In the second region, under the assumption of local thermal equilibrium between the gas and solid phases, the energy equation is:

[0134] ;

[0135] in, The effective volumetric heat capacity of the porous bed is expressed in units of... ; The effective thermal conductivity of the metal hydride bed is expressed in units of 1000 kJ / m². .

[0136] The effective volumetric heat capacity is calculated as follows:

[0137] ;

[0138] in, Specific heat capacity of the alloy, in units of .

[0139] In the heat transfer fluid region, the heat transfer fluid flow is modeled using the RANS equations and closed by the standard k−ϵk−ϵ turbulence model. In one embodiment, the HTF flow field is treated as quasi-steady state, while the temperature field is solved transiently to capture the thermal response during hydrogen absorption. The momentum equation is:

[0140] ;

[0141] The corresponding energy equation is written as:

[0142] ;

[0143] in, HTF density, in units of ; This is the HTF velocity vector, in m / s. HTF pressure, in Pa; HTF dynamic viscosity, in units of ; Turbulent viscosity, in units of ; HTF temperature, in Kelvin (K). HTF is the specific heat capacity at constant pressure, in units of ; HTF thermal conductivity, in units of ; This is the turbulent thermal conductivity, in units of... .

[0144] For solid structure regions, the heat transfer description is as follows:

[0145] ;

[0146] in, For solid density, For specific heat capacity, is the thermal conductivity.

[0147] In one embodiment, the effective thermal conductivity of the second region is calculated using the Zehner–Bauer–Schlünder model, i.e., the ZBS model, and the gas phase contribution is corrected using the Smoluchowski model.

[0148] The ZBS model is:

[0149] ;

[0150] in, The effective thermal conductivity of the gas phase in the pore space; The thermal conductivity of the alloy skeleton; The ratio of gas to solid thermal conductivity is defined as: ;

[0151] B is the shape factor, given by the following formula: ;

[0152] To account for the reduction in gas thermal conductivity caused by gas-wall interaction within confined pores, the gas phase thermal conductivity entering the ZBS model is corrected using the Smoluchowski relation:

[0153] ;in, is the bulk thermal conductivity of hydrogen; Smoluchowski coefficient;

[0154] Let Knudsen number be defined as: ;in, The mean free path of the hydrogen molecule. The characteristic aperture is denoted by .

[0155] For external surfaces exposed to the environment, heat transfer is represented by natural convection boundary conditions:

[0156] ;

[0157] in, It is the outward normal unit vector; The outer wall temperature; The ambient temperature.

[0158] Natural convection heat transfer coefficient External natural convection correlation assessment:

[0159] ;

[0160] in, The thermal conductivity of the ambient fluid; Characteristic outer diameter; For based on Rayleigh number; The Prandtl number is the number of the environmental fluid.

[0161] S400 generates segmented hydrogen charging boundary conditions for the composite hydrogen storage reactor based on preset hydrogen charging inlet parameters.

[0162] In one embodiment, the preset hydrogen inlet parameters include the nominal inlet mass flux and the upper limit of the hydrogen pressure inside the composite hydrogen storage reactor.

[0163] The segmented hydrogen charging boundary conditions for the composite hydrogen storage reactor are generated based on preset hydrogen charging inlet parameters, including:

[0164] Obtain the preset hydrogen charging inlet parameters, which include the nominal inlet mass flux and the upper limit of the hydrogen pressure inside the composite hydrogen storage reactor;

[0165] Based on the nominal inlet mass flux, generate the inlet hydrogen supply boundary of the hydrogen charging inlet during the nominal mass flux supply phase;

[0166] Based on the pressure limit, the inlet pressure limit boundary of the hydrogen charging inlet during the pressure-limited hydrogen charging stage is generated;

[0167] Based on the pressure state inside the composite hydrogen storage reactor, the transition range from the inlet hydrogen supply boundary to the inlet pressure limiting boundary is determined;

[0168] Within the transition zone, the actual inlet mass flux of the hydrogen charging inlet is adjusted to obtain the segmented hydrogen charging boundary conditions.

[0169] In one embodiment, a smooth pressure and time-dependent mass flux boundary condition is applied at the hydrogen inlet:

[0170] ;

[0171] in, This represents the actual inlet quality flux, in units of... ; The nominal mass flux is defined in units of... ; and These are the regularization Heaviside functions for pressure and time, respectively; This is the upper limit of pressure, expressed in Pa. Startup time, in seconds.

[0172] With the above-mentioned segmented hydrogen charging boundary conditions, the reactor operates at a specified flux in the early stage; when the bed can still accommodate the specified hydrogen supply, the actual inlet mass flux is basically equal to the nominal inlet mass flux; when the internal hydrogen absorption capacity is insufficient or the local pressure is close to the specified pressure limit, the actual inlet mass flux gradually deviates from the nominal setting and continuously decreases, thereby transitioning the hydrogen charging process from the nominal mass flux supply state to the pressure-limited hydrogen charging state.

[0173] At the hydrogen inlet, the temperature at which hydrogen enters is specified as a constant. .

[0174] For the HTF region, the inlet boundary is determined by the HTF inlet temperature. The inlet flow rate is specified, and the outlet boundary is set as a pressure outlet with zero gauge pressure. At the HTF-solid interface, the flow field adopts a no-slip boundary condition, while heat transfer is subject to temperature continuity and heat flux continuity conditions.

[0175] S500, based on the gas transport coupling model, the solid-phase hydrogen absorption reaction model, and the segmented hydrogen charging boundary conditions, performs transient coupling solution on the computational domain model to obtain multi-physics simulation results of the hydrogen storage process.

[0176] In one embodiment, based on a gas transport coupling model, a solid-phase hydrogen absorption reaction model, and segmented hydrogen charging boundary conditions, a transient coupling solution is performed on the computational domain model to obtain multiphysics simulation results of the hydrogen storage process, including:

[0177] Based on the segmented hydrogen charging boundary conditions, an inlet hydrogen supply condition is applied to the hydrogen charging inlet of the computational domain model;

[0178] Based on the gas transport coupling model, the free hydrogen transport in the first region and the pore hydrogen transport in the second region are coupled and solved.

[0179] Based on the solid-phase hydrogen absorption reaction model, the solid-phase hydrogen absorption reaction state in the second region is determined according to the pressure and temperature in the second region, and the gas mass change term and reaction heat source term in the second region are updated according to the solid-phase hydrogen absorption reaction state.

[0180] Perform heat transfer coupling solution for the first region, the second region, and the auxiliary calculation region that is heat-coupled with the first region and the second region;

[0181] Based on the updated gas transport state, solid-phase hydrogen absorption reaction state, and heat transfer state, iterative solutions are performed to obtain multiphysics simulation results of the hydrogen storage process.

[0182] The multiphysics simulation results include pressure field, temperature field, velocity field, gas density field, mass hydrogen storage capacity field, gas phase hydrogen storage in the first and second regions, and solid phase hydrogen storage in the second region.

[0183] In one embodiment, the model is initialized as a transient hydrogen absorption process. At t=0, the initial conditions for the gas region and the metal hydride region are:

[0184] ;

[0185] ;

[0186] ;

[0187] ;

[0188] in, Indicates spatial location; This represents the gas velocity vector within the free gas region. The apparent gas velocity is within the porous metal hydride region.

[0189] In one embodiment, the baseline operating conditions are defined as: ;

[0190] The same temperature is assigned to the ambient temperature, HTF inlet, and hydrogen inlet simultaneously. The initial pressure is set as follows: ;

[0191] Initial mass hydrogen storage capacity Instead of being set to zero, the initial hydrogen storage capacity is determined based on the equilibrium hydrogen content corresponding to 293.15 K and 0.1 MPa, according to the measured PCT isotherm. In one embodiment, the initial mass hydrogen storage capacity is: ;

[0192] This treatment is because under ambient temperature and pressure conditions, some hydrogen remains in the alloy and cannot be completely released. Therefore, initialization by the corresponding equilibrium state is more representative of actual operating conditions.

[0193] In one embodiment, the initial temperature of the HTF domain is also taken as... The HTF flow field is considered to be quasi-steady, and therefore is not initialized from a static state.

[0194] In one embodiment, the model is implemented in COMSO Lultiphysics. The computational domain is discretized using an unstructured tetrahedral mesh, with local refinement at the hydride bed, free gas region, HTF region, and critical interface boundaries. Two boundary layer meshes are generated in the flow domain. Transient simulation coverage is provided. The backward difference formula (BDF) scheme with adaptive time step is adopted, with a maximum BDF order of 2 and a relative tolerance of 0.001. To improve numerical stability, a separate solution strategy is used: first, the hydride state variables are solved, followed by the flow and pressure variables, and finally the temperature field. The solver sequence uses an algebraic multigrid (AMG) module and a direct solver module, with PARDISO selected as the direct solver module.

[0195] In one embodiment, the materials and model parameters used in the numerical model are shown in Table 1.

[0196] Table 1. Materials and model parameters used in the numerical model

[0197]

[0198] The initial volume filling density can be expressed as:

[0199] ;

[0200] The characteristic pore size is estimated from the representative particle diameter and initial porosity as follows:

[0201] ;

[0202] In this embodiment, when , At that time, we obtained: ;

[0203] S600, based on the multiphysics simulation results, determines the hydrogen storage simulation results of the composite hydrogen storage reactor.

[0204] In one embodiment, determining the hydrogen storage simulation results of the composite hydrogen storage reactor based on multiphysics simulation results includes:

[0205] S610, based on the multiphysics simulation results, determine the amount of gaseous hydrogen storage in the first region and the second region respectively, and determine the amount of solid hydrogen storage in the second region.

[0206] S620 determines the total hydrogen storage capacity of the composite hydrogen storage reactor and the hydrogen storage distribution between the gas phase and solid phase based on the gas phase hydrogen storage capacity and the solid phase hydrogen storage capacity.

[0207] The amount of gaseous hydrogen stored in the first region can be determined by integrating the hydrogen density in the first region onto the volume of the first region.

[0208] The amount of gaseous hydrogen stored in the second region can be determined by integrating the hydrogen density and porosity in the pore space of the second region over the volume of the second region.

[0209] The solid-phase hydrogen storage capacity in the second region can be determined based on the local mass hydrogen storage capacity w and alloy density within the second region. And the determination of the solid volume fraction of the bed;

[0210] In one embodiment, the gaseous hydrogen storage capacity of the composite hydrogen storage reactor includes the mass of gaseous hydrogen in the free gas space of the first region and the mass of gaseous hydrogen in the pore space of the second region. The solid-phase hydrogen storage capacity of the composite hydrogen storage reactor is the mass of hydrogen absorbed by the metal hydride alloy in the second region. The total hydrogen storage capacity is the sum of the gaseous hydrogen storage capacity and the solid-phase hydrogen storage capacity. The hydrogen storage allocation result may include the proportion of gaseous hydrogen storage capacity in the total hydrogen storage capacity, the proportion of solid-phase hydrogen storage capacity in the total hydrogen storage capacity, and the evolution relationship between the two with time or pressure.

[0211] Example 2

[0212] In one embodiment, the established multiphysics simulation method for the composite hydrogen storage reactor is subjected to model thermodynamic fitting, grid independence testing, and experimental verification.

[0213] like Figure 3 As shown in (a), the hydrogen absorption PCT curves at 273.15 K, 293.15 K, 313.15 K, and 333.15 K were obtained. The equilibrium pressure increases with increasing temperature across the entire mass hydrogen storage capacity range. Figure 3 (b) gives The linear fit relationship between 1 / T and its linear correlation coefficient The value of 0.9999 indicates that the use of the van't Hoff type temperature correction to describe the equilibrium pressure has good applicability.

[0214] like Figure 3 (c) and Figure 3 As shown in (d), the temperature and mean pressure histories under different grid densities are tested for grid independence. The number of test grid cells includes... Multiple levels. Using the finest grid as a reference, for... Cell mesh and A comparison of representative TC1 temperature histories across different cell grids yielded a mean absolute error of 0.55 K and a root mean square error of 0.76 K. This result indicates that further mesh refinement has minimal impact on the computational results. Therefore, in one embodiment, subsequent calculations employ approximately... An unstructured tetrahedral mesh of individual units is used to balance computational accuracy and efficiency.

[0215] like Figure 3 (e) and Figure 3 As shown in (f), the model can reproduce the temporal evolution trends of TC1 temperature, TC2 temperature, average pressure, and total hydrogen storage measured experimentally. In the verification experiment, although the reactor design could be used for operation at 20 MPa, the upper limit of the verification experiment pressure was set to 10 MPa due to experimental conditions and safety factors. Before hydrogen charging, the heat exchange fluid circulated in the heat exchange loop at an inlet temperature of 293.15 K and an inlet velocity of 0.4 m / s until the reactor temperature field stabilized; subsequently, hydrogen absorption began at an inlet hydrogen temperature of 293.15 K and a specified inlet hydrogen mass flow rate of 0.634 g / s. For TC1 and TC2, the mean absolute errors between the simulated and experimental temperatures were 1.54 K and 1.11 K, respectively, and the root mean square errors were 1.75 K and 1.23 K, respectively. The predicted final total hydrogen storage was close to the experimental measurement, with a relative error of 4.5%. The above results demonstrate that the multiphysics simulation method of this application can reliably capture the coupled behavior between thermodynamics, gas transport, reactive hydrogen absorption, and hydrogen storage evolution in the composite hydrogen storage reactor.

[0216] In another baseline hydrogen charging simulation, the upper pressure limit was increased from 10 MPa to 20 MPa, while other conditions remained the same as those used in the validation experiment: both the HTF inlet temperature and the hydrogen inlet temperature were 293.15 K, the HTF inlet velocity was 0.4 m / s, and the specified hydrogen inlet mass flow rate was 0.634 g / s, corresponding to an inlet mass flux of... .

[0217] like Figure 4 As shown, under reference hydrogen charging conditions, when the average pressure of the reactor reaches 20 MPa, the spatial distribution of gas velocity, temperature, gas density, and mass hydrogen storage capacity at seven representative cross sections is extracted.

[0218] like Figure 4As shown in (a), the gas velocity field indicates that hydrogen transport is mainly concentrated in the free gas region and the region directly connected to the main flow channel, while the gas velocity is significantly lower in most areas of the porous metal hydride bed. This result suggests that under high-pressure hydrogen charging conditions, the free gas region is the main channel for rapid gas transport and pressure propagation, while the flow inside the porous bed is constrained by permeation resistance. Therefore, explicitly analyzing the free gas region as the first region helps to accurately characterize the local gas supply and pressure propagation processes within the reactor.

[0219] like Figure 4 As shown in (b), significant temperature inhomogeneity exists within the porous metal hydride bed. Radially, the temperature is lower near the heat transfer enhancement structures and outer boundaries, while the internal regions further away from the cooling surfaces are warmer. Axially, the cross-sections near the hydrogen inlet and heat exchange fluid inlet are generally cooler, as the lower temperatures of the hydrogen and heat exchange fluid entering the reactor suppress local heat accumulation. This temperature distribution affects the local hydrogen uptake rate, as higher temperatures increase the equilibrium pressure and weaken the thermodynamic driving force for hydrogen uptake.

[0220] like Figure 4 As shown in (c), the gas density field varies across the free gas region, the porous metal hydride region, and different axial positions. The increase in gas density directly reflects the contribution of compressed gas hydrogen storage to the total hydrogen storage under 20 MPa operating conditions. Meanwhile, the non-uniform density distribution indicates differences in local pressure states and local hydrogen absorption driving forces throughout the reactor. Under similar pressure conditions, cooler regions maintain higher hydrogen density, while hotter regions exhibit lower pore gas density due to the decrease in gas density with increasing temperature.

[0221] like Figure 4 As shown in (d), the local mass hydrogen storage capacity w in the porous metal hydride bed also exhibits spatial inhomogeneity. In regions with favorable mass and heat transfer conditions, the hydrogen absorption process proceeds rapidly; however, in regions far from the heat exchange structure or with low gas supply efficiency, the hydrogen absorption reaction lags behind. Higher local mass hydrogen storage capacity mainly occurs at locations with lower temperatures and easier access to hydrogen supply. These results indicate that hydrogen charging behavior under 20 MPa conditions is controlled by the coupling of gas transport, heat transfer, and reaction processes.

[0222] Example 3

[0223] In one embodiment, to examine the effect of the upper pressure limit on the hydrogen charging behavior of the composite hydrogen storage reactor, the upper pressure limit is compared under reference hydrogen charging conditions. Three operating conditions.

[0224] The initial bed, ambient, HTF inlet, and hydrogen inlet temperatures were all 293.15 K; the initial pressure was 0.1 MPa; the HTF inlet velocity was 0.4 m / s; and the nominal hydrogen inlet mass flux was [missing value]. The corresponding mass flow rate is 0.634 g / s.

[0225] In one embodiment, such as Figure 5 As shown, compare the upper pressure limit. Temperature field distributions at 2000s, 4000s, 6000s, 8000s, and 10000s during hydrogen charging are shown. The three operating conditions exhibit similar temperature distributions in the early and middle stages, with significant differences mainly appearing in the later stages. At 10000s, the 20MPa condition maintains a relatively high bed temperature, the 10MPa condition shows more thorough cooling, and the 15MPa condition falls between the two. The spatial pattern of heat accumulation remains largely consistent, but its intensity and duration increase with the upper pressure limit. This is because a higher pressure limit prolongs the effective hydrogen charging time, allowing the hydrogen absorption and exothermic process to continue for a longer period.

[0226] In one embodiment, such as Figure 6 As shown, the mass hydrogen storage capacity of porous metal hydride beds under different pressure upper limits is compared. Distribution. Increasing the upper pressure limit can slightly promote solid-phase hydrogen absorption, making... The pressure increases, but its impact is relatively limited. The three operating conditions are quite similar for most of the hydrogen charging period, with significant differences mainly appearing in the later stages. The 20MPa condition can achieve a slightly higher final pressure. This is because a higher pressure upper limit maintains the hydrogen absorption driving force for a longer time; however, as the alloy gradually approaches saturation, The increase is still relatively small.

[0227] In one embodiment, such as Figure 7 As shown, the gaseous hydrogen density field under different pressure limits is compared. Between 2000 and 6000 s, the various operating conditions have not yet clearly entered the pressure-limiting stage, and the density distribution is relatively similar; between 8000 and 10000 s, the differences gradually become significant. At 10000 s, the hydrogen density is highest at 20 MPa, followed by 15 MPa and 10 MPa. This result reflects the stronger hydrogen compression in the free gas region and bed pore space under higher pressure limits. Compared with the solid-phase mass hydrogen storage capacity, the gaseous hydrogen density responds more directly to the pressure limit.

[0228] In one embodiment, such as Figure 8 As shown, the global hydrogen charging behavior under different pressure upper limits is compared. Figure 8(a) shows that the three pressure limit conditions follow almost the same pressure rise process in the early stage, followed by a rapid divergence in the later stage. The average pressure reaches 10 MPa, 15 MPa, and 20 MPa at approximately 8230 s, 8840 s, and 9350 s, respectively. Therefore, the initial 10 MPa pressure rise takes approximately 8300 s, while the subsequent rise from 10 MPa to 20 MPa takes only approximately 1050 s. This nonlinear pressure rise process indicates that the pressure increase in the low-pressure stage is strongly buffered by the hydrogen absorption of metal hydrides, while in the high-pressure stage, as the bed gradually approaches saturation, a larger proportion of the incoming hydrogen accumulates as compressed gas in the free gas region and pore space, resulting in a significantly faster pressure rise.

[0229] like Figure 8 As shown in (b), the inlet hydrogen flow rate remains essentially constant until the average pressure approaches the specified upper pressure limit, after which it decreases rapidly. The 10 MPa condition exhibits a wider flow transition zone, while the 20 MPa condition shows a significantly narrower flow transition zone. This difference stems from the different rates of pressure increase in the later stages: when the pressure approaches the limit more slowly, the same smooth pressure window corresponds to a longer time interval, thus forming a wider transition zone; when the pressure increase is steeper in the later stages, the transition is compressed into a shorter time interval.

[0230] like Figure 8 (c) and Figure 8 As shown in (d), the differences in average temperature and average solid-phase hydrogen storage capacity under different pressure upper limits are moderate. In contrast, as Figure 8 As shown in (e), the total hydrogen storage capacity increases more significantly with the increase of the upper pressure limit. At 10,000 s, the total hydrogen storage mass increases from about 5.18 kg at 10 MPa to about 5.58 kg at 15 MPa, and further increases to about 5.89 kg at 20 MPa.

[0231] like Figure 8 As shown in (f), the gas-phase hydrogen storage, solid-phase hydrogen storage, and total hydrogen storage over time are extracted along the 20 MPa hydrogen charging trajectory. Since the 10 MPa, 15 MPa, and 20 MPa operating conditions have almost identical pressure, temperature, and hydrogen storage histories before reaching their respective pressure limits, the 20 MPa trajectory can be used to extract the gas-solid hydrogen storage distribution relationship at different pressure levels. Table 2 shows the gas-solid hydrogen storage distribution at representative pressure levels along the representative 20 MPa hydrogen charging trajectory.

[0232] Table 2. Gas-solid hydrogen storage distribution at representative pressure levels along the 20MPa hydrogen charging trajectory.

[0233]

[0234] Table 2 shows that when the average pressure increases from 5 MPa to 20 MPa, the amount of gaseous hydrogen increases from 0.27 kg to 0.88 kg, and its proportion in the total hydrogen storage mass increases from 6.4% to 14.9%; the amount of solid hydrogen increases from 3.95 kg to 5.01 kg, gradually approaching saturation. This result indicates that the additional capacity gained by increasing the pressure upper limit increasingly comes from compressed gas hydrogen storage, rather than a proportional increase in solid hydrogen storage. Therefore, under the combined hydrogen storage conditions at 20 MPa, the free gas region is not a negligible passive cavity, but rather a functional region that quantitatively contributes to the hydrogen storage capacity.

[0235] Example 4

[0236] In one embodiment, at a fixed pressure upper limit Next, examine the nominal inlet quality flux. The impact on the hydrogen charging behavior of the combined hydrogen storage reactor. Three mass flux levels are considered: The initial conditions and thermal boundary conditions are the same as those of the reference condition.

[0237] In one embodiment, such as Figure 9 As shown, the nominal inlet mass flux is compared. The evolution of the temperature field over time. Increasing the nominal inlet mass flux significantly advances the emergence of the high-temperature region. Under operating conditions, a significant temperature rise was observed at 4000s, and was most pronounced around 6000s, after which the high-temperature region gradually weakened; Under the given conditions, heat accumulation was delayed, mainly occurring between 6000 and 8000 s; while under the 0.008 kg / (m²²·s) condition, only a relatively mild temperature rise was observed at 10000 s. These results indicate that a higher inlet mass flux accelerates early hydrogen absorption and reaction exotherm, but also pushes the reactor into the pressure-limiting phase earlier, causing subsequent exothermic decay to occur sooner.

[0238] In one embodiment, such as Figure 10 As shown, the evolution of the mass hydrogen storage capacity *w* in porous metal hydride beds under different nominal inlet mass fluxes is compared. Higher inlet mass fluxes can significantly accelerate the increase of *w*. Under operating conditions, most areas of the bed reach a relatively high w level between 4000s and 6000s, and approach saturation after 8000s; The operating conditions follow a similar trend, but with a significant delay; The operating condition still retains a large low-w region at 10000s. Therefore, increasing the inlet mass flux mainly improves the solid-phase hydrogen charging rate, while the final solid-phase hydrogen storage gain becomes limited as the alloy approaches saturation.

[0239] In one embodiment, such as Figure 11As shown, the gas-phase hydrogen density field is compared under different nominal inlet mass fluxes. The gas-phase hydrogen density field responds significantly to the hydrogen charging rate. Under operating conditions, a large-scale high-density area had already formed by 6000s; Under operating conditions, similar density increases mainly occur between 8000s and 10000s; for Even at 10,000 s, the overall gas density remains relatively low. This is because higher flux conditions reach higher solid-phase hydrogen storage capacity earlier, and subsequently a larger proportion of the supplied hydrogen accumulates as compressed gas in the free gas region and pore space.

[0240] In one embodiment, such as Figure 12 As shown, the average pressure, inlet hydrogen flow rate, average temperature, average solid-phase hydrogen storage, gaseous hydrogen mass, and total hydrogen storage are compared under different nominal inlet mass fluxes. Figure 12 (a) shows that the mean pressure rises slowly in the early stages and then rises rapidly in the later stages. The operating pressure reaches 20 MPa at approximately 6000 seconds. The operating pressure reaches 20 MPa at approximately 9300s, while The pressure was still only about 4 MPa at 10,000 s. This nonlinear pressure increase phenomenon is due to the fact that most of the hydrogen supplied in the early stage is absorbed by the alloy. As the bed approaches saturation, a larger proportion of hydrogen accumulates in the free gas region and pore space in the form of compressed gas.

[0241] like Figure 12 As shown in (b), the inlet hydrogen flow rate remains close to the nominal value until the average pressure approaches 20 MPa, after which it drops rapidly. Therefore, a higher nominal inlet mass flux causes the reactor to reach the pressure ceiling earlier and triggers inlet flow rate decay sooner. Figure 12 (c) and Figure 12 As shown in (d), with the increase of nominal inlet mass flux, the increase in both temperature peak and average solid-phase hydrogen storage capacity occurs earlier. At 10000 s, The average mass hydrogen storage capacity under operating conditions is approximately 1.48, 1.86, and 1.88 wt.%, respectively. Therefore, the mass flux from... Increase to It can significantly improve solid-phase hydrogen adsorption within 10,000 s, and further increase it to It only brings limited additional benefits.

[0242] like Figure 12 (e) and Figure 12 As shown in (f), at 10000s, The mass of gaseous hydrogen under the operating conditions is approximately 0.25, 0.87, and 0.82 kg, corresponding to a total hydrogen storage mass of approximately 4.20, 5.90, and 5.91 kg, respectively. Therefore, the mass flux is increased from... Increase to It will significantly increase the hydrogen storage mass during the simulation period; and further increase it to At this point, the total hydrogen storage mass hardly increases any further. The slightly lower gaseous hydrogen mass under the highest flux condition is because it reaches the 20 MPa pressure limit earlier, reducing subsequent hydrogen input and causing later reactions and gas accumulation to decay earlier. Therefore, at the 20 MPa pressure limit, the nominal inlet mass flux primarily determines the rate at which the reactor progresses from the reaction-driven hydrogen charging phase to the pressure-limiting gas accumulation phase. Once the mass flux is sufficient to allow the reactor to reach the pressure limit during hydrogen charging, further increasing the mass flux has limited effect on the final total hydrogen storage.

[0243] Example 5

[0244] In one embodiment, at a fixed nominal inlet mass flux and pressure limit Next, examine the HTF entry speed. The impact on the hydrogen charging behavior of the combined hydrogen storage reactor. Three rate levels are considered: .

[0245] In one embodiment, such as Figure 13 As shown, the temperature field evolution is compared under different heat transfer fluid inlet velocities. Compared to the 0 m / s condition, forced HTF circulation significantly suppresses the high-temperature region inside the bed and weakens the subsequent heat accumulation. Increasing the HTF velocity from 0.4 m / s to 0.8 m / s further improves the temperature field, but the improvement is less than that obtained by increasing it from 0 m / s to 0.4 m / s, indicating that under the current operating conditions, heat transfer enhancement has a diminishing returns effect.

[0246] In one embodiment, such as Figure 14 As shown, the mass hydrogen storage capacity in porous metal hydride beds is compared under different heat exchange fluid flow rates. The evolution. Under the condition of 0 m / s, high The heat transfer zone primarily expands from the outer areas towards the interior of the bed, with a longer lag time in the central area. After adopting forced HTF circulation, multi-lobed high-temperature condensation appears around the internal heat exchange structure. The region indicates that hydrogen absorption is promoted not only by heat extraction at the outer boundary but also by heat transfer through the internal heat exchange structure. At 10000 s, the bed structure is closer to a uniform height under the operating conditions of 0.4 m / s and 0.8 m / s. The state is as described, while the 0m / s condition still retains a more pronounced low speed. area.

[0247] In one embodiment, such as Figure 15 As shown, the gas-phase hydrogen density field is compared under different heat exchange fluid velocities. Without forced HTF circulation, the bed temperature is higher, and solid-phase hydrogen absorption is suppressed. More hydrogen is retained in the free gas region and pore space in the early and middle stages, thus the gas density increases earlier at 0 m / s. When the HTF velocity increases, the lower bed temperature promotes solid-phase hydrogen absorption, thus delaying gas-phase accumulation in the early stages. However, in the later stages, the gas-phase hydrogen mass at 0.4 m / s and 0.8 m / s increases again with the increase of total hydrogen storage mass. Therefore, the effect of HTF velocity on gas-phase hydrogen storage is indirect, mainly reflecting the hydrogen redistribution between compressed gas hydrogen storage and solid-phase hydride hydrogen storage.

[0248] In one embodiment, such as Figure 16 As shown, the global hydrogen charging response is compared under different heat exchange fluid flow rates. Figure 16 (a) and Figure 16 (b) shows that increasing the HTF flow rate delays the time it takes for the reactor mean pressure to reach the specified upper limit and prolongs the nominal mass flux hydrogen charging phase. This is because stronger heat extraction lowers the bed temperature, allowing more incoming hydrogen to be absorbed by the solid phase before the gas phase pressure builds up rapidly. Figure 16 (c) and Figure 16 (d) shows that higher HTF velocities reduce the average bed temperature and increase the average mass hydrogen storage capacity in porous metal hydride beds. However, the improvement from increasing the HTF velocity from 0.4 m / s to 0.8 m / s is relatively small, indicating diminishing returns to further flow enhancement.

[0249] Furthermore, such as Figure 16 (d) to Figure 16 As shown in (f), at higher HTF flow rates, the solid-phase hydrogen storage capacity increases slightly, while the gas-phase hydrogen mass decreases slightly, resulting in only a marginal change in the total hydrogen storage mass. Therefore, under the current operating conditions, additional cooling primarily redistributes hydrogen from compressed gas storage to solid-phase hydride storage, rather than significantly increasing the overall hydrogen storage capacity.

[0250] Example 5: The Influence of Initial Bed Temperature and HTF Inlet Temperature on Hydrogen Storage Simulation Results

[0251] In one embodiment, at a fixed nominal inlet mass flux and pressure limit The influence of thermal conditions on the hydrogen charging behavior of the composite hydrogen storage reactor is investigated below. This indicates the specified heat of hydrogen absorption, where the initial bed temperature and the HTF inlet temperature are set to the same value. In one embodiment, consider:

[0252] ;

[0253] In one embodiment, such as Figure 17 As shown, comparing different The effect on the temperature field. The results show that changing... This primarily causes the overall reactor temperature to shift upwards or downwards, while the spatial pattern and temporal evolution trend of heat accumulation remain similar. (Higher) This will keep the bed temperature high throughout the hydrogen charging process.

[0254] In one embodiment, such as Figure 18 As shown, comparing different Evolution of the mass hydrogen storage capacity w in a porous metal hydride bed. (Lower) This is more conducive to solid-phase hydrogen absorption because lower temperatures reduce equilibrium pressure and enhance the thermodynamic driving force for hydrogen absorption. With Rise, High As regional propagation weakens, the average solid-phase hydrogen storage capacity eventually decreases.

[0255] In one embodiment, such as Figure 19 As shown, comparing different The gaseous hydrogen density field at that temperature. Compared to lower temperature conditions, the higher... This will suppress solid-phase hydrogen absorption and allow a larger proportion of the supplied hydrogen to remain in the free gas region and pore space. Therefore, higher The accumulation in the lower gas phase is more significant, reflecting the redistribution of hydrogen from solid-phase hydride storage to compressed gas storage.

[0256] In one embodiment, such as Figure 20 As shown, for different The average pressure, inlet hydrogen flow rate, average temperature, average solid-phase hydrogen storage, gaseous hydrogen mass, and total hydrogen storage were compared. Figure 20 (a) and Figure 20 (b) shows that it is higher. The reduced solid-phase hydrogen absorption means a larger proportion of the supplied hydrogen remains in the gas phase, causing the reactor pressure to rise more rapidly in the early stages. However, in the later stages, the lower temperature conditions approach solid-phase saturation earlier, so the time required for different conditions to reach the pressure limit stage remains relatively similar, and the difference in inlet flow rate transition is also smaller.

[0257] like Figure 20 As shown in (c), the average temperature curves differ mainly at the overall temperature level, while the temporal evolution trend remains similar. Figure 20 (d) and Figure 20 (e) shows that, with As the concentration increases, the average mass hydrogen storage capacity in porous metal hydride beds decreases, while the mass of gaseous hydrogen increases. Figure 20 (f) further indicates that, despite the higher The mass of hydrogen in the gas phase is slightly higher, but the difference in total hydrogen mass remains relatively small. This behavior differs from traditional pure solid-state hydrogen storage systems, where temperature typically has a strong impact on the total hydrogen storage capacity. However, in the high-pressure gas-solid hybrid hydrogen storage system of this application embodiment, the high-pressure hydrogen charging conditions and nominal mass flux supply allow the increase in gas-phase hydrogen storage to partially offset the decrease in solid-phase hydrogen absorption. Therefore, the thermal conditions have a limited impact on the total hydrogen storage capacity, but they significantly alter the distribution relationship between solid-phase and gas-phase hydrogen storage.

[0258] As can be seen from the above embodiments, the multiphysics simulation method for the composite hydrogen storage reactor provided in this application can simultaneously describe high-pressure gas compression hydrogen storage, pore gas transport, solid-phase hydrogen absorption reaction, hydrogen absorption heat release, bed expansion, porosity and permeability evolution, and segmented hydrogen filling boundary switching process by explicitly coupling the macroscopic free gas region characterized by the first region and the reactive porous metal hydride region characterized by the second region.

[0259] Under 20 MPa hydrogen charging conditions, gaseous hydrogen accounts for nearly 15% of the total hydrogen storage, indicating that the free gas region has a significant contribution to hydrogen storage in high-pressure composite hydrogen storage. The method described in this application can further quantitatively evaluate the impact of pressure ceiling, hydrogen charging mass flux, and thermal management conditions on gaseous hydrogen storage, solid-phase hydrogen storage, total hydrogen storage, and hydrogen distribution, thus providing a basis for the structural design, pressure ceiling selection, charging rate setting, and thermal management optimization of composite hydrogen storage reactors.

[0260] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of this application.

Claims

1. A multiphysics simulation method for a composite hydrogen storage reactor, characterized in that, include: Obtain the parameters of the composite hydrogen storage reactor to be simulated, and establish a computational domain model of the composite hydrogen storage reactor based on the parameters; the computational domain model includes a first region and a second region; A gas transport coupling model is constructed between the first and second regions, and a solid-phase hydrogen absorption reaction model is constructed within the second region; The segmented hydrogen charging boundary conditions of the composite hydrogen storage reactor are generated based on the preset hydrogen charging inlet parameters. The segmented hydrogen charging boundary conditions are used to transition the hydrogen charging inlet from the nominal mass flux supply state to the pressure-limited hydrogen charging state. Based on the gas transport coupling model, the solid-phase hydrogen absorption reaction model, and the segmented hydrogen charging boundary conditions, the computational domain model is solved by transient coupling to obtain the multiphysics simulation results of the hydrogen storage process. Based on the multiphysics simulation results, the hydrogen storage simulation results of the composite hydrogen storage reactor were determined. The hydrogen storage simulation results include the amount of hydrogen stored in the gas phase, the amount of hydrogen stored in the solid phase, and the hydrogen storage distribution results between the amount of hydrogen stored in the gas phase and the amount of hydrogen stored in the solid phase.

2. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 1, characterized in that: The first region is used to characterize the free gas space within the composite hydrogen storage reactor that is not filled with the hydrogen storage medium. The second region is used to characterize the porous hydrogen storage medium region in the composite hydrogen storage reactor that can undergo solid-phase hydrogen storage reaction. The gas transport coupling model is used to characterize the free hydrogen transport in the first region, the pore hydrogen transport in the second region, and the pressure continuity, mass flux continuity and gas exchange relationship between the first and second regions. The solid-phase hydrogen absorption reaction model is used to characterize the absorption process of pore hydrogen by the hydrogen storage medium in the second region.

3. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 2, characterized in that: A computational domain model of the composite hydrogen storage reactor is established based on the parameters, including: The free gas space, porous hydrogen storage medium filling space, heat exchange structure, and wall structure in the composite hydrogen storage reactor are determined based on the parameters. The free gas space is divided into the first region, and the porous hydrogen storage medium filling space is divided into the second region. Based on the heat transfer structure and wall structure, an auxiliary calculation region coupled with the heat transfer of the first and second regions is established; wherein, the auxiliary calculation region includes a solid heat conduction region and / or a heat transfer fluid region; Based on the first region, the second region, and the auxiliary computational region, a computational domain model for solving transient multiphysics coupling is generated.

4. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 2, characterized in that: Constructing a gas transport coupling model between the first and second regions, including: Construct a free hydrogen transport model within the first region; Construct a porous hydrogen transport model within the second region; Based on the pressure continuity, mass flux continuity and gas exchange relationship between the first and second regions, the free hydrogen transport model and the pore hydrogen transport model are coupled to obtain the coupled gas transport model. Among them, the gas transport coupling model is used to characterize the effects of solid-phase hydrogen absorption reaction, real gas compression effect, and the evolution of porous hydrogen storage medium structure on pore hydrogen transport in the second region.

5. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 4, characterized in that: The free hydrogen transport model includes the continuity equation and momentum equation for hydrogen in the first region; The continuity equation is: ； The momentum equation is: ； in, The hydrogen density in the first region is given by t; the transient solution time is given by t. This represents the hydrogen velocity vector within the first region. The hydrogen pressure in the first region; Let be the viscous stress tensor of hydrogen gas in the first region; For spatial gradient operators; It is the spatial divergence operator.

6. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 5, characterized in that: The pore hydrogen transport model includes the continuity equation and momentum equation for pore hydrogen in the second region; The continuity equation is: ； The momentum equation is: ； in, The porosity of the second region; is the hydrogen density in the pore space of the second region; t is the transient solution time. The apparent velocity vector of hydrogen gas in the pores of the second region; denoted as the gas mass change term caused by the solid-phase hydrogen absorption reaction in the second region; p is the pore hydrogen pressure in the second region. This represents the viscous stress tensor of pore hydrogen in the second region in Brinkman form. The dynamic viscosity of hydrogen; This represents the penetration rate in the second region.

7. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 2, characterized in that: The segmented hydrogen charging boundary conditions for the composite hydrogen storage reactor are generated based on preset hydrogen charging inlet parameters, including: Obtain the preset hydrogen charging inlet parameters, which include the nominal inlet mass flux and the upper limit of the hydrogen pressure inside the composite hydrogen storage reactor; Based on the nominal inlet mass flux, generate the inlet hydrogen supply boundary of the hydrogen charging inlet during the nominal mass flux supply phase; Based on the pressure limit, the inlet pressure limit boundary of the hydrogen charging inlet during the pressure-limited hydrogen charging stage is generated; Based on the pressure state inside the composite hydrogen storage reactor, the transition range from the inlet hydrogen supply boundary to the inlet pressure limiting boundary is determined; Within the transition zone, the actual inlet mass flux of the hydrogen charging inlet is adjusted to obtain the segmented hydrogen charging boundary conditions.

8. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 6, characterized in that: Transient coupling solution of the computational domain model yields multiphysics simulation results for hydrogen storage, including: Based on the segmented hydrogen charging boundary conditions, an inlet hydrogen supply condition is applied to the hydrogen charging inlet of the computational domain model; Based on the gas transport coupling model, the free hydrogen transport in the first region and the pore hydrogen transport in the second region are solved in a coupled manner. Based on the solid-phase hydrogen absorption reaction model, the solid-phase hydrogen absorption reaction state in the second region is determined according to the pressure and temperature in the second region, and the gas mass change term and reaction heat source term in the second region are updated according to the solid-phase hydrogen absorption reaction state. The heat transfer coupling solution is performed on the first region, the second region, and the auxiliary calculation region where the heat transfer is coupled between the first region and the second region; Based on the updated gas transport state, solid-phase hydrogen absorption reaction state, and heat transfer state, the multiphysics simulation results of the hydrogen storage process are obtained by iterative solution. The multiphysics simulation results include pressure field, temperature field, velocity field, and solid-phase hydrogen storage capacity in the second region.

9. The multiphysics simulation method for the composite hydrogen storage reactor according to claim 2, characterized in that: Based on the multiphysics simulation results, the hydrogen storage simulation results of the composite hydrogen storage reactor were determined, including: Based on the multiphysics simulation results, the amount of gaseous hydrogen storage in the first region and the second region were determined, and the amount of solid hydrogen storage in the second region was also determined. Based on the hydrogen storage capacity in the gas phase and the hydrogen storage capacity in the solid phase, the total hydrogen storage capacity of the composite hydrogen storage reactor and the hydrogen storage distribution between the gas phase and the solid phase are determined.

10. A computer-readable storage medium storing computer instructions that, when executed by a processor, implement the method as described in any one of claims 1 to 9.

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