Fuel cell modeling method and device for metal hydrogen storage and liquid oxygen supply

Abstract

The invention discloses a metal hydrogen storage and liquid oxygen supply fuel cell modeling method and device. The method comprises the following steps: constructing a gas supply model; the gas supply model comprises a metal hydrogen storage and supply model and a liquid oxygen supply model; constructing an electric pile model; the galvanic pile model comprises an anode flow channel model, a cathode flow channel model, a transmembrane water transfer model and a voltage model; constructing a thermal management model; the thermal management model comprises a cooling water pump model, a radiator model and an electric pile temperature model; and performing parameter coupling on the gas supply model, the electric pile model and the thermal management model to form an overall dynamic model of the fuel cell. According to the invention, metal hydride hydrogen storage, liquid oxygen vaporization oxygen supply, galvanic pile electrochemical and hydrothermal coupling and system-level thermal management can be comprehensively considered, so that efficient and stable operation of the fuel cell in a special underwater environment is realized.

Description

Technical Field

[0001] This invention relates to the field of fuel cells, and more specifically to a method and apparatus for modeling a fuel cell with metal hydrogen storage and liquid oxygen supply. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) offer advantages such as high energy conversion efficiency, environmental friendliness, and fast response, and are widely used in automobiles, distributed energy, and power supply for special environments. In underwater applications, fuel cells face different technical challenges in fuel supply and thermal management compared to land-based applications: firstly, high-pressure hydrogen storage tanks pose safety risks and have insufficient volume utilization; secondly, conventional air-based oxygen supply methods are not feasible underwater. Therefore, using metal hydride hydrogen storage and liquid oxygen storage tanks for oxygen supply is an effective solution.

[0003] However, existing fuel cell modeling methods are mostly geared towards vehicle applications or conventional air-supply conditions, and the modeling objects are usually concentrated on the fuel cell stack itself or a single auxiliary subsystem, failing to form a system-level modeling framework covering hydrogen supply, oxygen supply, stack operation, and thermal management. Furthermore, the operation of a fuel cell stack involves multi-physics coupling behaviors such as electrochemical reactions, reactant gas mass transfer, heat transfer, and transmembrane water transport, making the modeling process inherently complex. Moreover, compared to terrestrial applications, underwater fuel cell systems must also consider the impact of external high-pressure environments on reactant gas flow and mass transfer characteristics, as well as the constraints on stack temperature control under limited heat dissipation conditions.

[0004] Therefore, in order to solve the problem that existing modeling techniques cannot meet the requirements for stable operation of fuel cells in special underwater environments, there is an urgent need for a fuel cell modeling method and device that can adapt to underwater application scenarios, and can comprehensively consider hydrogen storage by metal hydrides, oxygen supply by liquid oxygen vaporization, electrochemical and hydrothermal coupling of the fuel cell stack, and system-level thermal management, so as to achieve efficient and stable operation of fuel cells in special underwater environments. Summary of the Invention

[0005] In view of this, the purpose of this invention is to overcome the deficiencies in the prior art and provide a fuel cell modeling method and device for metal hydrogen storage and liquid oxygen supply, which can comprehensively consider metal hydride hydrogen storage, liquid oxygen vaporization oxygen supply, stack electrochemistry and hydrothermal coupling, and system-level thermal management, thereby achieving efficient and stable operation of fuel cells in special underwater environments.

[0006] The fuel cell modeling method for metal hydrogen storage and liquid oxygen supply of the present invention includes:

[0007] Construct a gas supply model; the gas supply model includes a metal hydrogen storage and hydrogen supply model and a liquid oxygen supply model;

[0008] A fuel cell stack model is constructed; the fuel cell stack model includes an anode flow channel model, a cathode flow channel model, a transmembrane water transport model, and a voltage model.

[0009] A thermal management model is constructed, which includes a cooling water pump model, a radiator model, and a fuel cell stack temperature model.

[0010] The gas supply model, stack model, and thermal management model are coupled with parameters to form an overall dynamic model of the fuel cell.

[0011] Furthermore, the metal hydrogen storage and supply model includes a metal hydrogen storage tank dynamics model, an electromagnetic proportional valve model, and a hydrogen circulation pump model.

[0012] The liquid oxygen supply model includes a liquid oxygen storage tank mass conservation model, a vaporizer energy balance model, and an automatic regulating valve model.

[0013] Furthermore, a dynamic model of a metal hydrogen storage tank is constructed based on the following formula:

[0014] ;

[0015] ;

[0016] ;

[0017] in, The pressure inside the tank; This refers to the density of gaseous hydrogen. It is the gas constant; for The reaction bed temperature of the material; The hydrogen mass exchange rate between the metal hydride and the gas phase is the rate of hydrogen absorption or desorption. These are dynamic constants; This is the activation energy for the dehydrogenation reaction; This is the density of the hydrogen storage material when it is completely bonded with hydrogen atoms. for Density of hydrogen storage materials; As the reference pressure; For the intercept term; This is the temperature slope term; The temperature of the metal hydride bed; The coefficient representing the degree of platform tilt; The bias coefficient for platform tilt; The shape factor; This represents the current hydrogen loading capacity; This refers to the saturated hydrogen content; Center position coefficient; This refers to the platform lag coefficient.

[0018] Construct an electromagnetic proportional valve model based on the following formula:

[0019] ;

[0020] in, This represents the mass flow rate of hydrogen. For flow coefficient; The effective flow area of ​​the valve port; , These are the pressures before and after the valve, respectively. It is the gas constant; Absolute temperature; Specific heat ratio;

[0021] Construct a hydrogen circulation pump model based on the following formula:

[0022] ;

[0023] in, This refers to the mass flow rate of the hydrogen circulation pump. For relational functions, This refers to the speed of the hydrogen circulation pump. The pressure difference of the hydrogen circulation pump; These are empirical parameters.

[0024] Furthermore, a mass conservation model for the liquid oxygen storage tank is constructed based on the following formula:

[0025] ;

[0026] in, The mass of liquid oxygen in the liquid oxygen storage tank; The liquid oxygen outlet mass flow rate used for tank pressurization; The mass flow rate of liquid oxygen at the outlet of the oxygen supply equipment;

[0027] Construct a vaporizer energy balance model based on the following formula:

[0028] ;

[0029] in, This represents the total heat capacity of the vaporizer and the oxygen gas within it. The temperature at which gaseous oxygen exits the vaporizer; The temperature at which liquid oxygen enters the vaporizer; The specific heat of gaseous oxygen; The specific heat of liquid oxygen; Thermal resistance; The logarithmic mean temperature difference; The mass flow rate of gaseous oxygen exiting the vaporizer; The mass flow rate of liquid oxygen into the vaporizer; For time;

[0030] Construct an automatic control valve model based on the following formula:

[0031] ;

[0032] in, To regulate the flow rate at a certain opening degree of the valve; To regulate the inlet pressure of the regulating valve; To regulate the outlet pressure of the valve; The throttling cross-sectional area; The resistance coefficient of the regulating valve; For fluid density;

[0033] ; This represents the maximum flow area of ​​the valve. The relative opening of the control valve, that is, the stroke of the control valve at a certain opening degree. Travel when fully open The ratio; The adjustable ratio of the valve.

[0034] Furthermore, the anode flow channel model is constructed based on the following formula:

[0035] - ; ;

[0036] in, This refers to the amount of hydrogen gas in the anode channel. This refers to the anode inlet flow rate; This represents the anode outlet flow rate. The molar flow rate of hydrogen consumed in the reaction. , For the effective reaction area, It is Faraday's constant; Current density; The relative humidity at the anode outlet; This refers to the partial pressure of water vapor at the anode. t is the saturated vapor pressure; t is time.

[0037] Construct the cathode flow channel model based on the following formula:

[0038] ;

[0039] in, The amount of oxygen in the cathode channel; The molar flow rate of oxygen at the cathode inlet; The molar flow rate of oxygen at the cathode outlet; This refers to oxygen consumption. ;

[0040] A transmembrane water transport model is constructed based on the following formula:

[0041] ;

[0042] in, This represents the total amount of water that migrates across the membrane. This refers to the number of individual cells in the fuel cell stack. The molar mass of water vapor. The activated area of ​​a single cell; The electroosmotic coefficient; Current density; It is Faraday's constant; The membrane water diffusion coefficient; For concentration gradient; The concentration of water inside the membrane; Equivalent penetration rate; The equivalent dynamic viscosity of water in the membrane; For pressure gradient;

[0043] Construct a voltage model based on the following formula:

[0044] ;

[0045] in, This refers to the output voltage of the fuel cell stack. ; Standard reversible voltage; , These are the partial pressures of hydrogen and oxygen, respectively. Standard pressure;

[0046] ; For exchange current density, For the transmission coefficient, The number of electrons in the reaction;

[0047] ; For film thickness, For membrane conductivity;

[0048] ; ; Where is the diffusion coefficient. For phase concentration, For surface concentration, The thickness is the diffusion layer.

[0049] Furthermore, a cooling water pump model is constructed based on the following formula:

[0050] ;

[0051] ;

[0052] in, This refers to the mass flow rate of the cooling water pump. This is the pump flow coefficient; This refers to the pump speed; This is the pressure difference influence coefficient; The pressure difference across the pump; This indicates the amount of heat removed from the fuel cell stack by the cooling water pump per unit time; This refers to the specific heat capacity of the coolant. and These are the inlet and outlet temperatures of the coolant, respectively.

[0053] Construct a heat sink model based on the following formula:

[0054] ;

[0055] in, The convective heat transfer coefficient; For heat exchange area; This refers to the average temperature of the coolant. Air temperature;

[0056] The fuel cell stack temperature model is constructed based on the following formula:

[0057] ;

[0058] in, For the heat capacity mass of the fuel cell stack; Specific heat capacity; This refers to the temperature of the fuel cell stack. For heat generation power, , For current, It is a reversible voltage. This is the actual voltage; The heat carried away by the cooling water , , These are the specific enthalpy of the coolant inlet and outlet, respectively. This is due to heat loss from the environment.

[0059] Furthermore, parameter coupling is performed on the gas supply model, the fuel cell stack model, and the thermal management model, specifically including:

[0060] Changes in the control variables of the gas supply model cause changes in inlet flow rate or pressure, which in turn change the flow channel pressure and relative humidity of the anode or cathode. The humidity state, together with the stack temperature and current, determines the transmembrane water flux and membrane water content in the stack model, and further affects the effective partial pressure of reactants and voltage output. Voltage and current determine the heat generation of the stack. The thermal management model adjusts the cooling heat dissipation through cooling water pumps and radiators to obtain the stack temperature. The stack temperature then feeds back to the gas state and membrane transport parameters to achieve closed-loop coupling.

[0061] A fuel cell modeling device for metal hydrogen storage and liquid oxygen supply includes a gas supply module, a stack module, a thermal management module, and a coupling module.

[0062] The gas supply module is used to construct a gas supply model; the gas supply model includes a metal hydrogen storage and supply model and a liquid oxygen supply model.

[0063] The fuel cell stack module is used to construct a fuel cell stack model; the fuel cell stack model includes an anode flow channel model, a cathode flow channel model, a transmembrane water transport model, and a voltage model.

[0064] The thermal management module is used to construct a thermal management model; the thermal management model includes a cooling water pump model, a radiator model, and a fuel cell stack temperature model.

[0065] The coupling module is used to couple the parameters of the gas supply model, the stack model, and the thermal management model to form an overall dynamic model of the fuel cell.

[0066] The beneficial effects of this invention are as follows: The fuel cell modeling method and apparatus for metal hydrogen storage and liquid oxygen supply disclosed in this invention constructs an overall dynamic model covering gas supply, stack electrochemical reaction, and thermal management through a combination of modularization and parameter coupling. By establishing a metal hydrogen storage and supply model and a liquid oxygen supply model, and introducing the dynamics of the metal hydrogen storage tank, the energy balance of liquid oxygen vaporization, and valve pump regulation characteristics, the hydrogen and oxygen supply process in an airless underwater environment is realistically reflected. By comprehensively considering the anode and cathode flow channels, transmembrane water transfer, and voltage characteristics, electrochemical and water management modeling is achieved. A thermal management model is constructed through cooling water pump, radiator, and stack temperature models, and parameter coupling is performed with the aforementioned models. This enables a systematic and accurate description of the dynamic response and multiphysics coupling behavior of the fuel cell under underwater operating conditions, providing reliable technical support for fuel cell performance analysis, control strategy design, and optimization. Attached Figure Description

[0067] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0068] Figure 1 This is a schematic diagram of the fuel cell modeling method of the present invention;

[0069] Figure 2 This is a schematic diagram of the gas supply model principle of the present invention;

[0070] Figure 3 This is a schematic diagram of the fuel cell stack model of the present invention;

[0071] Figure 4 This is a schematic diagram illustrating the principle of the thermal management model of the present invention;

[0072] Figure 5 This is a schematic diagram of the overall dynamic model principle of the fuel cell of the present invention. Detailed Implementation

[0073] The present invention will be further described below with reference to the accompanying drawings, as shown in the figures:

[0074] This embodiment discloses a fuel cell modeling method for metal hydrogen storage and liquid oxygen supply, including the following steps:

[0075] Construct a gas supply model; the gas supply model includes a metal hydrogen storage and hydrogen supply model and a liquid oxygen supply model;

[0076] A fuel cell stack model is constructed; the fuel cell stack model includes an anode flow channel model, a cathode flow channel model, a transmembrane water transport model, and a voltage model.

[0077] A thermal management model is constructed, which includes a cooling water pump model, a radiator model, and a fuel cell stack temperature model. The thermal management model is used to accurately characterize the heat transfer and temperature distribution characteristics of the fuel cell stack under different operating conditions.

[0078] The gas supply model, stack model, and thermal management model are coupled with parameters to form an overall dynamic model of the fuel cell.

[0079] In this embodiment, as Figure 2 As shown, the gas supply model includes a metal hydrogen storage and supply model and a liquid oxygen supply model; the metal hydrogen storage and supply model includes a metal hydrogen storage tank dynamics model, an electromagnetic proportional valve model, and a hydrogen circulation pump model; the liquid oxygen supply model includes a liquid oxygen storage tank mass conservation model, a vaporizer energy balance model, and an automatic regulating valve model.

[0080] The kinetic model of the metal hydrogen storage tank is based on the ideal gas law and hydrogen absorption and release kinetics. Its hydrogen release rate satisfies the relationship between the tank pressure, the material reaction bed temperature, the kinetic constant, and the activation energy, and is used to calculate the rate of change of gaseous hydrogen mass and the outlet mass flow rate. The kinetic model of the metal hydrogen storage tank is constructed according to the following formula:

[0081] ;

[0082] ;

[0083] ;

[0084] in, The pressure inside the tank; This refers to the density of gaseous hydrogen. It is the gas constant; for The reaction bed temperature of the material; The hydrogen mass exchange rate between the metal hydride and the gas phase is the rate of hydrogen absorption or desorption. These are dynamic constants; This is the activation energy for the dehydrogenation reaction; This is the density of the hydrogen storage material when it is completely bonded with hydrogen atoms. for Density of hydrogen storage materials; As the reference pressure; For the intercept term; This is the temperature slope term; The temperature of the metal hydride bed; The coefficient representing the degree of platform tilt; The bias coefficient for platform tilt; The shape factor; This represents the current hydrogen loading capacity; This refers to the saturated hydrogen content, i.e., the maximum loading capacity. Center position coefficient; This represents the platform lag coefficient.

[0085] Electromagnetic proportional valves are used to precisely regulate the supply flow rate of hydrogen. Based on the gas orifice flow mechanism, the relationship between valve opening and gas flow rate is calculated using the mass flow rate of hydrogen. With valve opening and the pressure difference across the valve The relationship, i.e., valve opening. Hydrogen supply flow rate The relationship is a monotonically increasing function, and an electromagnetic proportional valve model is established based on the following formula:

[0086] ;

[0087] in, This represents the mass flow rate of hydrogen. For flow coefficient; The effective flow area of ​​the valve port; , These are the pressures before and after the valve, respectively. It is the gas constant; Absolute temperature; Specific heat ratio.

[0088] According to the pressure rise characteristic curve and flow equation of the pump, a hydrogen circulation pump model is established to re-transport the unreacted hydrogen at the anode outlet back to the anode inlet to improve the hydrogen utilization rate. The hydrogen circulation pump model is constructed according to the following formula:

[0089] ;

[0090] where, is the mass flow rate of the hydrogen circulation pump; is the relational function, is the rotational speed of the hydrogen circulation pump, is the pressure difference of the hydrogen circulation pump; is an empirical parameter, not a fixed value, related to the structure, type and design parameters of the pump. For pumps supporting small-power (10–30 kW) fuel cells, can take 1.5×10 ; For pumps supporting large-power (60–120 kW) fuel cells, can take 3.0×10 −8 ∼4.5×10 −8 .

[0091] In this embodiment, combined with the mass conservation equation, the gas-phase state equation is used to characterize the relationship between the gas-phase pressure and temperature of the liquid oxygen storage tank, and the vaporizer is modeled in combination with the energy conservation equation. Among them, the state equation of the gas phase space of the liquid oxygen storage tank is differentiated to simplify the model, and the following formula is formed to represent the mass conservation model of the liquid oxygen storage tank:

[0092] ;<​​​​​​​​​​​​​​​​​​​​​​​​​​​The specific heat of liquid oxygen; Thermal resistance; The logarithmic mean temperature difference; The mass flow rate of gaseous oxygen exiting the vaporizer; The mass flow rate of liquid oxygen into the vaporizer; For time;

[0097] Automatic regulating valves are used to periodically adjust the flow rate in liquid oxygen delivery pipelines to maintain the stable operation of the liquid oxygen delivery system. An automatic regulating valve model is established based on the orifice flow mechanism. The model is constructed according to the following equation:

[0098] ;

[0099] in, To regulate the flow rate at a certain opening degree of the valve; To regulate the inlet pressure of the regulating valve; To regulate the outlet pressure of the valve; The throttling cross-sectional area; The resistance coefficient of the regulating valve; For fluid density;

[0100] ; This represents the maximum flow area of ​​the valve. The relative opening of the control valve, that is, the stroke of the control valve at a certain opening degree. Travel when fully open The ratio; The adjustable ratio of the valve.

[0101] In this embodiment, as Figure 3 As shown, the fuel cell stack model includes an anode flow channel model, a cathode flow channel model, a transmembrane water transfer model, and a voltage model. The anode flow channel model is established based on mass conservation, using the transmembrane water velocity, anode inlet flow rate, anode relative humidity, anode pressure, and ambient temperature as inputs, and the relative humidity on the anode side of the proton exchange membrane and the anode reactant outlet pressure as outputs. The following assumptions can be used during its establishment: the anode outlet valve variable is zero, there is no liquid water retention at the anode, and the mass of gaseous water at the anode is less than or equal to the mass of water corresponding to the anode saturated water vapor pressure. That is, the anode flow channel model is constructed according to the following formula:

[0102] - ; ;

[0103] in, This refers to the amount of hydrogen gas in the anode channel. This refers to the anode inlet flow rate; This represents the anode outlet flow rate. The molar flow rate of hydrogen consumed in the reaction. , For the effective reaction area, It is Faraday's constant; Current density; The relative humidity at the anode outlet; This refers to the partial pressure of water vapor at the anode. t is the saturated vapor pressure; t is time. This indicates the rate of change of the amount of hydrogen in the anode channel over time.

[0104] The cathode flow channel model is established based on mass conservation, using the transmembrane velocity of water through the proton exchange membrane, the cathode inlet flow rate, the cathode relative humidity, the cathode pressure, the ambient temperature, and the gas composition as inputs, and the relative humidity on the cathode side of the proton exchange membrane and the cathode reactant outlet pressure as outputs. When establishing the model, an upper limit approximation of the internal liquid water capacity of the cathode can be used, and the inlet and outlet flow rates can be calculated using approximate linear or logarithmic approximations. That is, the cathode flow channel model is constructed according to the following formula:

[0105] ;

[0106] in, The amount of oxygen in the cathode channel; The molar flow rate of oxygen at the cathode inlet; The molar flow rate of oxygen at the cathode outlet; This refers to oxygen consumption. ; This indicates the rate of change of the amount of oxygen in the cathode channel over time.

[0107] The transmembrane water transport model is used to describe the migration behavior of water across the proton exchange membrane during the operation of the stack. Assuming that the water content and water flux distribution on the proton membrane surface are uniform and the membrane volume remains constant, water transport in the proton membrane mainly includes three pathways: electroosmotic drag, concentration gradient back diffusion, and pressure gradient osmosis.

[0108] Transmembrane water flux is denoted as (mol / s), its total amount can be expressed as the sum of three parts:

[0109] ;in, For electroosmotic drag water flux, For anti-diffusion water flux, Water flux is driven by pressure difference.

[0110] Among them, electroosmotic dragging: when hydrogen protons migrate through the membrane under the influence of an electric field, they drag water molecules from the anode to the cathode. The water flux is related to the current density and the electroosmotic coefficient. ; This refers to the amount of water that migrates from the anode to the cathode under the dragging effect of hydrogen proton electroosmosis. Let be the electroosmotic coefficient. The electroosmotic coefficient can be expressed as a function of the membrane's water content: ;

[0111] Concentration gradient back diffusion: Water generated at the cathode results in a higher water concentration on the cathode side than on the anode side. Water then diffuses back from the cathode to the anode, and the flux can be expressed as: ; The amount of water that migrates under the effect of anti-diffusion. The diffusion coefficient of water concentration in the proton exchange membrane. This represents the concentration gradient between the anode and cathode.

[0112] The water concentration diffusion coefficient varies with different water contents and temperatures, as expressed by the formula:

[0113] ;

[0114] in, The size is related to the water content in the membrane; under different water content ranges... The function is:

[0115] ;

[0116] The water concentration gradient is a function of the water concentrations at the anode and cathode, and is also affected by the thickness of the proton exchange membrane.

[0117] ;

[0118] The changes in water concentration at the cathode and anode inside the fuel cell stack satisfy the following:

[0119] ;

[0120] in, The density of the proton exchange membrane under dry conditions. The equivalent weights of the proton exchange membrane under dry conditions. Indicates the anode. Indicates cathode, This refers to the proton membrane.

[0121] Pressure gradient permeation: Due to the pressure difference between the anode and cathode (generally, the cathode pressure is higher than the anode pressure), water migrates from the high-pressure side to the low-pressure side under the influence of the pressure difference; this flux can be expressed using the pressure difference-driven expression derived by Bernardi. ;

[0122] The pressure gradient across the membrane can be expressed as a function of the pressure on both sides and the membrane thickness: ;

[0123] In summary, a transmembrane water transport model is constructed based on the following formula:

[0124] ;

[0125] in, This represents the total amount of water that migrates across the membrane. This refers to the number of individual cells in the fuel cell stack. The molar mass of water vapor. The activated area of ​​a single cell; The electroosmotic coefficient; Current density; It is Faraday's constant; The membrane water diffusion coefficient; For concentration gradient; The concentration of water inside the membrane; Equivalent penetration rate; The equivalent dynamic viscosity of water in the membrane; For pressure gradient;

[0126] Based on the characteristics that the external voltage is positively correlated with the reversible voltage and negatively correlated with activation loss, ohmic loss, and concentration loss, the voltage model consists of the reversible voltage, activation loss, ohmic loss, and concentration loss. Therefore, the voltage model is constructed according to the following equation:

[0127] ;

[0128] in, This refers to the output voltage of the fuel cell stack. ; It is a reversible voltage; Standard reversible voltage; , These are the partial pressures of hydrogen and oxygen, respectively. Standard pressure;

[0129] ; For activation loss; For exchange current density, For the transmission coefficient, The number of electrons in the reaction;

[0130] ; For ohm loss; For film thickness, For membrane conductivity;

[0131] ; For concentration loss; , The limiting current density; Where is the diffusion coefficient. For phase concentration, For surface concentration, The thickness is the diffusion layer.

[0132] In this embodiment, as Figure 4 As shown, the thermal management model includes a cooling water pump model, a radiator model, and a fuel cell stack temperature model. The coolant flow rate can be obtained by considering the pressure difference between the coolant before and after the pump input and the pump speed. A cooling water pump model is then established using thermodynamic formulas. This model takes the fuel cell stack temperature, pump speed, and inlet coolant temperature as inputs and the heat dissipation of the cooling water as the output. Therefore, the cooling water pump model is constructed according to the following formula:

[0133] ;

[0134] ;

[0135] in, This refers to the mass flow rate of the cooling water pump. This is the pump flow coefficient; This refers to the pump speed; This is the pressure difference influence coefficient; The pressure difference across the pump; This indicates the amount of heat removed from the fuel cell stack by the cooling water pump per unit time, i.e., the heat dissipation of the cooling water pump. This refers to the specific heat capacity of the coolant. and These are the inlet and outlet temperatures of the coolant, respectively.

[0136] A radiator model is constructed based on the convective heat transfer between air and coolant, according to the first law of thermodynamics for open systems. This model takes coolant flow rate and coolant inlet temperature as inputs and coolant outlet temperature as outputs. The radiator model is then constructed according to the following equation:

[0137] ;

[0138] in, The convective heat transfer coefficient; For heat exchange area; This refers to the average temperature of the coolant. Air temperature;

[0139] Using the enthalpy of the coolant inlet and outlet, the enthalpy of the gas entering and exiting the cathode or anode, and the heat generated by the fuel cell stack as inputs, the output is the fuel cell stack temperature, which is used to adjust temperature-related terms. The heat generated by the fuel cell stack mainly comes from irreversible reaction losses. Therefore, the fuel cell stack temperature model is constructed based on the following formula:

[0140] ;

[0141] in, For the heat capacity mass of the fuel cell stack; Specific heat capacity; This refers to the temperature of the fuel cell stack. For heat generation power, , For current, It is a reversible voltage. This is the actual voltage; The heat carried away by the cooling water , , These are the specific enthalpy of the coolant inlet and outlet, respectively. This is due to heat loss from the environment.

[0142] In this embodiment, parameter coupling is performed on the gas supply model, the fuel cell stack model, and the thermal management model, specifically including: the control variables of the gas supply model. Changes in flow rate or pressure (such as valve opening / pump speed) cause changes in inlet flow rate or pressure, which in turn alter the flow channel pressure at the anode or cathode. and relative humidity The humidity level, along with the stack temperature and current, determines the transmembrane water flux in the stack model. With membrane water content This further affects the effective partial pressure of the reactants and the voltage output. Voltage and current determine the heat generated by the fuel cell stack. The thermal management model regulates the cooling heat dissipation through cooling water pumps and radiators. The temperature of the fuel cell stack was obtained. The temperature of the fuel cell stack is fed back to the gas state and membrane transport parameters to achieve closed-loop coupling.

[0143] Among them, such as Figure 5 As shown, The gas supply side control parameters are used to determine the flow rate and inlet pressure boundaries at the anode and cathode inlets. The anode or cathode flow channel model is established based on mass conservation, and takes transmembrane water flux, inlet flow rate, relative humidity, pressure, and ambient temperature as inputs, outputting the corresponding outlet relative humidity and reactant outlet pressure, thereby obtaining the flow channel pressure state. With humidity status The transmembrane water transfer model uses anode relative humidity, cathode relative humidity, stack temperature, and operating current as inputs, and outputs membrane water content. and transmembrane water flux ; It can be determined by both electroosmosis and diffusion transport generated by the water concentration gradient, and used to couple and correct the water vapor states on both sides. This serves as a key input to the voltage model to correct for membrane conductivity and ohmic loss. The voltage model takes reactant partial pressure and temperature as inputs, and performs decomposition calculations based on reversible voltage, activation loss, ohmic loss, and concentration loss to output the stack voltage. Further combining current and voltage yields the heat generation of the fuel cell stack. And the cooling output from the thermal management model removes heat. Together they determine the stack temperature The temperature Feedback then affects saturated vapor pressure, humidity state, and membrane transport parameters, achieving multi-physics closed-loop coupling.

[0144] By combining the gas supply model, the fuel cell stack model, and the thermal management model, and dynamically coupling and optimizing the input and output quantities, an overall dynamic model of the fuel cell is constructed, thereby achieving efficient and stable operation of the fuel cell in the special underwater environment.

[0145] The present invention also relates to a fuel cell modeling device for metal hydrogen storage and liquid oxygen supply, which can be understood as a modeling device for implementing the fuel cell modeling method of the above embodiments. The modeling device includes a gas supply module, a stack module, a thermal management module and a coupling module.

[0146] The gas supply module is used to construct a gas supply model; the gas supply model includes a metal hydrogen storage and supply model and a liquid oxygen supply model.

[0147] The fuel cell stack module is used to construct a fuel cell stack model; the fuel cell stack model includes an anode flow channel model, a cathode flow channel model, a transmembrane water transport model, and a voltage model.

[0148] The thermal management module is used to construct a thermal management model; the thermal management model includes a cooling water pump model, a radiator model, and a fuel cell stack temperature model.

[0149] The coupling module is used to couple the parameters of the gas supply model, the stack model, and the thermal management model to form an overall dynamic model of the fuel cell.

[0150] The fuel cell modeling device is suitable for simulating fuel cell power systems in underwater or enclosed environments. It takes into account special boundary conditions such as hydrothermal management, liquid oxygen extrusion oxygen supply, and metal hydride hydrogen storage, and can be used for underwater operations.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for modeling a fuel cell with metal hydrogen storage and liquid oxygen supply, characterized in that: include: Construct a gas supply model; the gas supply model includes a metal hydrogen storage and hydrogen supply model and a liquid oxygen supply model; A fuel cell stack model is constructed; the fuel cell stack model includes an anode flow channel model, a cathode flow channel model, a transmembrane water transport model, and a voltage model. A thermal management model is constructed, which includes a cooling water pump model, a radiator model, and a fuel cell stack temperature model. The gas supply model, stack model, and thermal management model are coupled with parameters to form an overall dynamic model of the fuel cell.

2. The fuel cell modeling method for metal hydrogen storage and liquid oxygen supply according to claim 1, characterized in that: The metal hydrogen storage and supply model includes a metal hydrogen storage tank dynamics model, an electromagnetic proportional valve model, and a hydrogen circulation pump model. The liquid oxygen supply model includes a liquid oxygen storage tank mass conservation model, a vaporizer energy balance model, and an automatic regulating valve model.

3. The fuel cell modeling method for metal hydrogen storage and liquid oxygen supply according to claim 2, characterized in that: A dynamic model of a metal hydrogen storage tank is constructed based on the following formula: ； ； ； in, The pressure inside the tank; This refers to the density of gaseous hydrogen. It is the gas constant; for The reaction bed temperature of the material; The hydrogen mass exchange rate between the metal hydride and the gas phase is the rate of hydrogen absorption or desorption. These are dynamic constants; This is the activation energy for the dehydrogenation reaction; This is the density of the hydrogen storage material when it is completely bonded with hydrogen atoms. for Density of hydrogen storage materials; As the reference pressure; For the intercept term; This is the temperature slope term; The temperature of the metal hydride bed; The coefficient representing the degree of platform tilt; The bias coefficient for platform tilt; The shape factor; This represents the current hydrogen loading capacity; This refers to the saturated hydrogen content; Center position coefficient; This refers to the platform lag coefficient. Construct an electromagnetic proportional valve model based on the following formula: ； in, This represents the mass flow rate of hydrogen. For flow coefficient; The effective flow area of ​​the valve port; , These are the pressures before and after the valve, respectively. It is the gas constant; Absolute temperature; Specific heat ratio; Construct a hydrogen circulation pump model based on the following formula: ； in, This refers to the mass flow rate of the hydrogen circulation pump. For relational functions, This refers to the speed of the hydrogen circulation pump. The pressure difference of the hydrogen circulation pump; These are empirical parameters.

4. The fuel cell modeling method for metal hydrogen storage and liquid oxygen supply according to claim 2, characterized in that: Construct a mass conservation model for a liquid oxygen storage tank based on the following formula: ； in, The mass of liquid oxygen in the liquid oxygen storage tank; The liquid oxygen outlet mass flow rate used for tank pressurization; The mass flow rate of liquid oxygen at the outlet of the oxygen supply equipment; Construct a vaporizer energy balance model based on the following formula: ； in, This represents the total heat capacity of the vaporizer and the oxygen gas within it. The temperature at which gaseous oxygen exits the vaporizer; The temperature at which liquid oxygen enters the vaporizer; The specific heat of gaseous oxygen; The specific heat of liquid oxygen; Thermal resistance; The logarithmic mean temperature difference; The mass flow rate of gaseous oxygen exiting the vaporizer; The mass flow rate of liquid oxygen into the vaporizer; For time; Construct an automatic control valve model based on the following formula: ； in, To regulate the flow rate at a certain opening degree of the valve; To regulate the inlet pressure of the regulating valve; To regulate the outlet pressure of the valve; The throttling cross-sectional area; The resistance coefficient of the regulating valve; For fluid density; ; This represents the maximum flow area of ​​the valve. The relative opening of the control valve, that is, the stroke of the control valve at a certain opening degree. Travel when fully open The ratio; The adjustable ratio of the valve.

5. The fuel cell modeling method for metal hydrogen storage and liquid oxygen supply according to claim 1, characterized in that: Construct the anode flow channel model based on the following formula: - ； ； in, This refers to the amount of hydrogen gas in the anode channel. This refers to the anode inlet flow rate; This represents the anode outlet flow rate. The molar flow rate of hydrogen consumed in the reaction. , For the effective reaction area, It is Faraday's constant; Current density; The relative humidity at the anode outlet; This refers to the partial pressure of water vapor at the anode. t is the saturated vapor pressure; t is time. Construct the cathode flow channel model based on the following formula: ； in, The amount of oxygen in the cathode channel; The molar flow rate of oxygen at the cathode inlet; The molar flow rate of oxygen at the cathode outlet; This refers to oxygen consumption. ; A transmembrane water transport model is constructed based on the following formula: ； in, This represents the total amount of water that migrates across the membrane. This refers to the number of individual cells in the fuel cell stack. The molar mass of water vapor. The activated area of ​​a single cell; The electroosmotic coefficient; Current density; It is Faraday's constant; The membrane water diffusion coefficient; For concentration gradient; The concentration of water inside the membrane; Equivalent penetration rate; The equivalent dynamic viscosity of water in the membrane; For pressure gradient; Construct a voltage model based on the following formula: ； in, This refers to the output voltage of the fuel cell stack. ; Standard reversible voltage; , These are the partial pressures of hydrogen and oxygen, respectively. Standard pressure; ; For exchange current density, For the transmission coefficient, The number of electrons in the reaction; ; For film thickness, For membrane conductivity; ; ; Where is the diffusion coefficient. For phase concentration, For surface concentration, The thickness is the diffusion layer.

6. The fuel cell modeling method for metal hydrogen storage and liquid oxygen supply according to claim 1, characterized in that: Construct a cooling water pump model based on the following formula: ； ； in, This refers to the mass flow rate of the cooling water pump. This is the pump flow coefficient; This refers to the pump speed; This is the pressure difference influence coefficient; The pressure difference across the pump; This indicates the amount of heat removed from the fuel cell stack by the cooling water pump per unit time; This refers to the specific heat capacity of the coolant. and These are the inlet and outlet temperatures of the coolant, respectively. Construct a heat sink model based on the following formula: ； in, The convective heat transfer coefficient; For heat exchange area; This refers to the average temperature of the coolant. Air temperature; The fuel cell stack temperature model is constructed based on the following formula: ； in, For the heat capacity mass of the fuel cell stack; Specific heat capacity; This refers to the temperature of the fuel cell stack. For heat generation power, , For current, It is a reversible voltage. This is the actual voltage; The heat carried away by the cooling water , , These are the specific enthalpy of the coolant inlet and outlet, respectively. This is due to heat loss from the environment.

7. The fuel cell modeling method for metal hydrogen storage and liquid oxygen supply according to claim 1, characterized in that: The parameters of the gas supply model, the fuel cell stack model, and the thermal management model are coupled, specifically including: Changes in the control variables of the gas supply model cause changes in inlet flow rate or pressure, which in turn change the flow channel pressure and relative humidity of the anode or cathode. The humidity state, together with the stack temperature and current, determines the transmembrane water flux and membrane water content in the stack model, and further affects the effective partial pressure of reactants and voltage output. Voltage and current determine the heat generation of the stack. The thermal management model adjusts the cooling heat dissipation through cooling water pumps and radiators to obtain the stack temperature. The stack temperature then feeds back to the gas state and membrane transport parameters to achieve closed-loop coupling.

8. A fuel cell modeling device for metal hydrogen storage and liquid oxygen supply, characterized in that: It includes a gas supply module, a fuel cell stack module, a thermal management module, and a coupling module; The gas supply module is used to construct a gas supply model; the gas supply model includes a metal hydrogen storage and supply model and a liquid oxygen supply model. The fuel cell stack module is used to construct a fuel cell stack model; the fuel cell stack model includes an anode flow channel model, a cathode flow channel model, a transmembrane water transport model, and a voltage model. The thermal management module is used to construct a thermal management model; the thermal management model includes a cooling water pump model, a radiator model, and a fuel cell stack temperature model. The coupling module is used to couple the parameters of the gas supply model, the stack model, and the thermal management model to form an overall dynamic model of the fuel cell.

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