A method for calculating residual effective hydrogen reserves of a vehicle-mounted liquid hydrogen system and an evaluation model

Abstract

This invention relates to a method and evaluation model for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system. It models the heat exchange between the storage tank and the environment, temperature changes, liquid hydrogen evaporation and vaporization, and gaseous hydrogen pressure changes. It comprehensively considers the heat transfer from the actual vehicle operating conditions, including radiative heat transfer, convective heat transfer, gas heat transfer, and solid heat transfer, as well as the heat loss from the environment to the liquid hydrogen storage tank, coupled with liquid hydrogen consumption, refueling, and overpressure emissions. This invention offers high computational efficiency and accuracy with minimal computational resource consumption. It can be deployed in real-world vehicle environments, replacing level gauges to provide effective hydrogen storage capacity information for vehicles equipped with on-board liquid hydrogen systems. This reduces the "thermal bridge" effect caused by level gauges, decreasing heat loss from the liquid hydrogen storage tank and the self-evaporation rate of liquid hydrogen. For on-board liquid hydrogen systems equipped with level gauges, this invention provides dual protection for vehicle operation, reducing the operational risks caused by level gauge failure.

Description

Technical Field

[0001] This invention relates to a method and evaluation model for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system. Background Technology

[0002] Liquid hydrogen has a density of approximately 70.8 kg / m³, about 1.8 times that of gaseous hydrogen at 70 MPa high pressure, giving it significant advantages in storage, transportation, refueling, and use. However, liquid hydrogen is a cryogenic medium, with a temperature range primarily around 20K, making it highly volatile and prone to vaporization. In practical applications, liquid hydrogen is stored in vacuum-insulated containers to prevent external heat sources from penetrating, reducing the vaporization rate of the liquid hydrogen within the tank and mitigating the risk of overpressure. Currently, vehicle-mounted liquid hydrogen systems use level gauges to monitor the remaining liquid hydrogen storage tank. These gauges primarily monitor liquid hydrogen, but the vaporized gaseous hydrogen at low temperatures is not adequately assessed. This results in inaccurate measurements of the remaining effective hydrogen storage in the vehicle-mounted liquid hydrogen system. Furthermore, the presence of level gauges increases the contact points between the tank liner and the external environment, potentially creating thermal bridges and increasing heat leakage. Level gauges also have a certain risk of failure, making maintenance difficult after failure. Summary of the Invention

[0003] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0004] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution:

[0005] A method for calculating the remaining effective hydrogen storage capacity of an onboard liquid hydrogen system includes the following steps:

[0006] Step 1: Establish a finite volume simulation model of the liquid hydrogen storage tank and calculate the key parameters of heat transfer area and volume for different insulation layers;

[0007] Step 2: Establish a heat transfer simulation model using convective heat transfer, radiative heat transfer, solid heat transfer, and gas heat transfer methods, and determine the physical parameters of the spacer material, reflective material, and vacuum level of the liquid hydrogen storage tank.

[0008] Step 3: Calculate the net heat flow rate between different insulation layers under actual operating conditions of different vehicle speeds, ambient temperatures, and ambient wind speeds;

[0009] Step 4: Calculate the temperature changes between different insulation layers based on the net flow rate, insulation layer volume, and heat exchange surface area, and update the temperature accordingly.

[0010] Step 5: Calculate the heat leakage from the operating environment to the liquid hydrogen storage tank. Calculate the mass of liquid hydrogen vaporization based on the properties of liquid hydrogen and the heat leakage. Obtain the liquid hydrogen mass flow rate, liquid hydrogen filling flow rate, and gaseous hydrogen emission flow rate during actual vehicle operation. Use the Kalman filter algorithm to process the noise in the sensor observations. Finally, calculate the total mass of liquid hydrogen vaporization and the pressure and volume of the gas phase space after liquid hydrogen vaporization.

[0011] Step 6: Calculate the mass of gaseous hydrogen emitted to the outside and the actual mass of liquid hydrogen used. Finally, obtain the mass of remaining liquid hydrogen inside the liquid hydrogen storage tank and the mass of hydrogen in the gas phase space. The effective hydrogen balance is the sum of the mass of remaining liquid hydrogen and the mass of hydrogen in the gas phase space.

[0012] Furthermore, the specific details of step one are as follows:

[0013] A vacuum multilayer insulation numerical simulation model was established based on the finite volume method. The vacuum multilayer insulation liquid hydrogen storage tank is mainly composed of an inner liner, spacer material, reflective material, and outer liner. The spacer material and reflective material are combined in multiple layers and then evacuated to form an insulation barrier. The vacuum multilayer insulation numerical simulation model mainly calculates the volume and heat transfer surface area of ​​the spacer material and reflective material between different layers. In the model calculation, one layer of spacer material and one layer of reflective material are treated as a whole for calculation. The storage tank is simplified as a cylinder for calculation.

[0014] The volume calculation formulas for different insulation layers are as follows:

[0015] (1)

[0016] The formulas for calculating the surface area of ​​different insulation layers are as follows:

[0017] (2)

[0018] in The number of different insulation layers; This corresponds to the thickness of the insulation layer spacer material; This corresponds to the thickness of the reflective material in the insulation layer; This refers to the length of the inner liner of the liquid hydrogen storage tank. Let be the radius of the inner liner of the liquid hydrogen storage tank.

[0019] Furthermore, the specific details of step two are as follows:

[0020] Set the physical property parameters of the reflective material and the spacer material, as well as the vacuum degree simulation parameters, and establish a heat exchange module. The heat exchange mainly includes radiation heat transfer, convection heat transfer, gas heat transfer and solid heat transfer. The main influencing factors of convection heat transfer are the vehicle speed, ambient wind speed and ambient temperature of the vehicle equipped with the on-board liquid hydrogen system.

[0021] The formulas for calculating the heat flow rate of different heat exchange methods are as follows:

[0022] Radiative heat transfer: (3)

[0023] in Boltzmann's constant; and These are the temperatures of the corresponding insulation layers; and These represent the emissivity of the reflective materials of adjacent insulation layers at the corresponding temperatures;

[0024] Convection heat transfer: (4)

[0025] in Temperature of the outer liner of the storage tank; The ambient temperature; The convective heat transfer coefficient is calculated using the following formula:

[0026] (5)

[0027] (6)

[0028] (7)

[0029] (8)

[0030] in The thermal conductivity of a fluid at a given temperature; For Nusselt numbers; The characteristic length of the fluid in the flow direction; It is the Reynolds number; For flow rate; The kinematic viscosity of the fluid; For fluid density; The dynamic viscosity of the fluid; It is a Prandtl number; The specific heat capacity at constant pressure of the fluid;

[0031] Heat transfer in rarefied gases under vacuum conditions: (9)

[0032] in These are empirical constants; Vacuum pressure; This refers to the gas adaptability coefficient;

[0033] Solid heat transfer: (10)

[0034] in These are empirical constants; The thickness of the spacer material between adjacent insulation layers and the vacuum pressure; The degree of looseness of the spacer material; It represents the thermal conductivity of the material separating adjacent insulation layers.

[0035] Furthermore, step three, in detail, is as follows:

[0036] Calculation of heat flux of different insulation layers;

[0037] The outer liner of the liquid hydrogen storage tank is separated from the multi-layer insulation material by a high-vacuum gap. The heat exchange occurs through radiation and rarefied gas transfer in a vacuum environment. The heat exchange with the environment is through convection and radiation. The formula for calculating the net heat flow rate of heat exchange to the outer liner is as follows:

[0038] (11)

[0039] in Heat transferred from the environment to the outer shell; This refers to the heat transferred from the outer liner to the outermost insulation material.

[0040] The formula for calculating the net heat flow rate for the outermost insulation material is as follows:

[0041] (12)

[0042] The innermost layer of insulation material is in direct contact with the inner liner of the storage tank. The heat transfer to the inner liner is the final heat loss, which directly causes changes in the temperature of liquid hydrogen and vaporization. The formula for calculating the net heat flow rate of heat loss from the external environment to the storage tank is:

[0043] (13)

[0044] in The temperature of the inner liner of the storage tank can be simplified to the temperature of the liquid hydrogen inside the storage tank. The emissivity of the material inside the storage tank;

[0045] For insulation materials in other locations, the formula for calculating the net heat flow rate is:

[0046] (14).

[0047] Furthermore, step four, in detail, is as follows:

[0048] Temperature update calculation between different insulation layers: The calculation process uses one layer of spacer material and one layer of reflective material as a calculation unit;

[0049] The formula for updating the interlayer temperature of different insulation layers is as follows:

[0050] (15)

[0051] in The temperature of the corresponding calculation unit; This corresponds to the heat flux rate of the calculation unit; For heat exchange surface area; Total volume; This refers to the composite specific heat capacity at the corresponding temperature. Composite density;

[0052] For materials with specific heat capacity, such as common spacer and reflective materials, the specific heat capacity varies with temperature. The specific heat capacity of the two materials is fitted with a polynomial, and the composite specific heat capacity is calculated based on the mass fraction in the calculation unit.

[0053] (16)

[0054] in This refers to the specific heat capacity of the corresponding spacer material or reflective material; These are the fitting coefficients; The current calculated temperature;

[0055] (17)

[0056] in For composite specific heat capacity; For the quality of the corresponding material; Density of the spacer material; For the volume of the spacer material; Density of the reflective material; The volume of the reflective material; This refers to the specific heat capacity of the material at a given temperature.

[0057] (18)

[0058] in Composite density; This represents the density of the corresponding material.

[0059] Furthermore, step five, in detail, is as follows:

[0060] Liquid hydrogen vaporization and evaporation and gas pressure calculation:

[0061] Mass of liquid hydrogen vaporization:

[0062] (19)

[0063] in The mass of liquid hydrogen vaporized due to heat leakage; The net heat flow rate from the external environment to the storage tank; For heat exchange area; This represents the latent heat of vaporization of liquid hydrogen under the corresponding conditions.

[0064] Calculation of gas pressure inside the liquid hydrogen storage tank after vaporization:

[0065] (20)

[0066] in The mass of gaseous hydrogen in the original gas phase space; where is the molar mass of hydrogen; is Gas phase space volume; It is the ideal gas constant; The current calculation temperature is assumed to be the same as the liquid hydrogen temperature.

[0067] (twenty one)

[0068] in This represents the remaining mass of liquid hydrogen. This represents the density of liquid hydrogen under the corresponding conditions. This refers to the water volume of the liquid hydrogen storage tank.

[0069] Furthermore, step six, in detail, is as follows:

[0070] Calculation of changes in liquid hydrogen reserves;

[0071] There are three main ways for hydrogen to be sourced and consumed in vehicle-mounted liquid hydrogen systems: liquid discharge from the outlet, liquid filling from the inlet, and overpressure relief of gaseous hydrogen.

[0072] The formula for calculating the mass of liquid hydrogen in a liquid hydrogen storage tank is:

[0073] (twenty two)

[0074] in The mass of liquid hydrogen in its initial state; This refers to the mass flow rate of liquid hydrogen during the refueling process; The mass flow rate at the liquid outlet during operation is positively correlated with vehicle speed and fuel cell system operating power.

[0075] The formula for calculating gaseous hydrogen reserves is:

[0076] (twenty three)

[0077] in This refers to the mass of gaseous hydrogen inside the storage tank. This represents the initial mass of gaseous hydrogen. The mass of liquid hydrogen vaporization caused by heat leakage; The mass of gaseous hydrogen discharged by the safety valve after overpressure;

[0078] The calculation formulas are as follows:

[0079] (twenty four)

[0080] in The initial pressure inside the tank. and These represent the mass and density of liquid hydrogen in its initial state; This represents the initial temperature inside the storage tank.

[0081] (25)

[0082] in The pressure difference before and after the safety valve opens and closes; and These represent the mass and density of liquid hydrogen in the liquid hydrogen storage tank, respectively. The temperature inside the storage tank during the release;

[0083] The final formula for calculating the remaining effective hydrogen balance in the onboard liquid hydrogen system is as follows:

[0084] (26)

[0085] In practical application, the above process , , The values ​​are the observations from the relevant sensors. To ensure accuracy, they are processed by the Kalman filter algorithm to remove observation noise and then input into equations (20) to (26) for calculation.

[0086] Furthermore, the main steps of the Kalman filter algorithm are as follows:

[0087] Initialize state variables and covariance

[0088] (27)

[0089] (28)

[0090] State prediction

[0091] (29)

[0092] Observation and prediction

[0093] (30)

[0094] Covariance matrix prediction

[0095] (31)

[0096] Kalman gain calculation

[0097] (32)

[0098] Status update

[0099] (33)

[0100] Covariance Update

[0101] (34)

[0102] In the above steps, the subscript Represented as the state parameters at the corresponding time; subscript " "and" "" represents the state parameters before and after the update at the corresponding time point; the meanings of each parameter are as follows:

[0103] This is the state vector at the initial moment; These are the state variables at the initial moment; Let k be the state vector before the update. Let be the updated state vector at time k;

[0104] The mathematical expectation of the relevant computation matrix;

[0105] This is the state transition matrix; This is the transpose of the state transition matrix;

[0106] The state control input matrix is ​​used to describe the transformation relationship between the states at different times and the state at the next time.

[0107] The system process noise vector corresponding to time k; This is the observation noise vector corresponding to time k;

[0108] Let be the observation matrix at time k, representing the linear transformation relationship from the system state to the observed values; This is the transpose of the observation matrix at time k;

[0109] and These are process noise and observation noise, respectively. Process noise represents the dynamic error introduced by the model, while observation noise is the error introduced by sensor observation, which varies depending on the sensor accuracy.

[0110] The estimated covariance under the initial conditions;

[0111] The calculation relationship between system state observation noise; The prediction of the system state at time k is calculated based on the state at the previous time step.

[0112] is the Kalman gain at time k, used to evaluate the reliability of prediction and observation data.

[0113] Furthermore, the calculation process uses the effective hydrogen mass, liquid hydrogen mass, and gas phase mass in the storage tank as state variables, and the mass flow rates at the liquid hydrogen storage tank outlet, inlet, and gas phase emission flow sensor values ​​as input quantities. The corresponding matrices in the Kalman filter algorithm are as follows:

[0114] , , , ,

[0115] in The sampling interval is denoted as .

[0116] An evaluation model for calculating the remaining effective hydrogen storage capacity of an onboard liquid hydrogen system is established, the model comprising:

[0117] The module for calculating key parameters is used to establish a finite volume simulation model of a liquid hydrogen storage tank and calculate the key parameters of heat transfer area and volume for different insulation layers.

[0118] The vacuum degree determination module is used to establish a heat transfer simulation model using convective heat transfer, radiative heat transfer, solid heat transfer, and gas heat transfer methods, and to determine the physical parameters of the spacer material, reflective material, and vacuum degree of the liquid hydrogen storage tank.

[0119] The net heat flow rate calculation module is used to calculate the net heat flow rate between different insulation layers under actual operating conditions of different vehicle speeds, ambient temperatures, and ambient wind speeds.

[0120] The temperature update module is used to calculate the temperature change between different insulation layers based on the net flow rate, insulation layer volume, and heat exchange surface area, and to update the temperature accordingly.

[0121] The module calculates the conversion amount of gaseous hydrogen after heat absorption and the pressure of the gas phase space. It is used to calculate the heat leakage from the operating environment to the liquid hydrogen storage tank. Based on the properties of liquid hydrogen and the heat leakage, it calculates the mass of liquid hydrogen vaporization. It obtains the liquid hydrogen mass flow rate, liquid hydrogen filling flow rate and gaseous hydrogen emission flow rate during actual vehicle operation. The sensor observation values ​​are noise-processed by Kalman filtering algorithm. Finally, it calculates the total mass of liquid hydrogen vaporization and the pressure and volume of the gas phase space after liquid hydrogen vaporization.

[0122] The module for calculating the effective hydrogen reserve is used to calculate the mass of gaseous hydrogen emitted to the outside and the actual mass of liquid hydrogen used, and finally obtains the mass of liquid hydrogen remaining inside the liquid hydrogen storage tank and the mass of hydrogen in the gas phase space. The effective hydrogen reserve is the sum of the mass of the remaining liquid hydrogen and the mass of hydrogen in the gas phase space.

[0123] Compared with the prior art, the beneficial effects of the present invention are:

[0124] This invention comprehensively considers various forms of heat transfer between the storage tank and the environment (radiative heat transfer, convective heat transfer, gas heat transfer, solid heat transfer), liquid hydrogen evaporation and vaporization, and temperature and pressure changes. It also couples in actual operating conditions such as liquid hydrogen consumption, refueling, and overpressure discharge to construct a full-process effective hydrogen storage assessment model. The algorithmic model achieves accurate calculation of the remaining effective hydrogen storage. This method can replace a level gauge working independently, reducing the contact points between the tank liner and the outside environment and avoiding the formation of thermal bridges; or it can be used in conjunction with an on-board liquid hydrogen system equipped with a level gauge to provide dual storage monitoring for vehicle operation, improving system reliability and reducing the risk of level gauge failure and high maintenance difficulty. Simultaneously, the model features high computational efficiency and low resource consumption, allowing direct deployment in real-vehicle environments. It balances assessment accuracy with the operational performance of the on-board system, demonstrating engineering application feasibility.

[0125] This invention couples real-world vehicle operating scenarios (temperature, speed, hydrogen consumption, etc.) to real-time run and quantify the effective storage capacity of liquid and gaseous hydrogen, temperature changes in the insulation layer, and pressure changes within the storage tank. By replacing some hardware monitoring functions with an algorithm model, it can reduce heat leakage to a certain extent, providing technical support for the lightweight and integrated design of onboard liquid hydrogen systems. At the same time, this method can reduce the high-difficulty maintenance work after level gauge failure, reduce the probability of vehicle downtime due to hardware failure, further improve the operational stability of onboard liquid hydrogen systems under complex operating conditions, and provide accurate data support and technical assurance for vehicle range prediction and hydrogen energy dispatch. Attached Figure Description

[0126] The invention will now be further described with reference to the accompanying drawings:

[0127] Figure 1 A simplified diagram of the structure and heat exchange of a vacuum multilayer insulated liquid hydrogen storage tank.

[0128] Figure 2This is a flowchart of the method for calculating the remaining effective hydrogen storage capacity of the on-board liquid hydrogen system described in this invention.

[0129] Figure 3a A schematic diagram showing the temperature changes of each layer of a liquid hydrogen storage tank when the vehicle is stationary.

[0130] Figure 3b A schematic diagram of the hydrogen mass in the gas phase space of a liquid hydrogen storage tank when the vehicle is stationary.

[0131] Figure 3c A schematic diagram showing the mass of hydrogen in the liquid phase space of a liquid hydrogen storage tank when the vehicle is stationary.

[0132] Figure 3d A schematic diagram showing the effective hydrogen balance in the liquid hydrogen storage tank when the vehicle is stationary.

[0133] Figure 4a A schematic diagram of the vehicle's cyclic operating condition vt curve;

[0134] Figure 4b This is a schematic diagram showing the temperature changes of each layer of a liquid hydrogen storage tank under cyclic operating conditions.

[0135] Figure 4c A schematic diagram of the hydrogen mass in the liquid phase space of a liquid hydrogen storage tank under cyclic operating conditions;

[0136] Figure 4d A schematic diagram of the hydrogen mass in the gas phase space under cyclic operating conditions;

[0137] Figure 4e This is a schematic diagram showing the effective hydrogen reserve in a liquid hydrogen storage tank under cyclic operating conditions. Detailed Implementation

[0138] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of this invention. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The embodiments of this invention will be described in detail below with reference to the accompanying drawings.

[0139] In the description of this invention, it should be understood that the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this invention.

[0140] The present invention will now be described in detail with reference to the accompanying drawings:

[0141] like Figure 1 As shown, this invention relates to a precise assessment model and calculation method for the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system. It models issues such as heat exchange between the storage tank and the environment, temperature changes, liquid hydrogen evaporation and vaporization, and gaseous hydrogen pressure changes. It comprehensively considers the heat transfer from the actual vehicle operating conditions, including radiative heat transfer, convective heat transfer, gas heat transfer, and solid heat transfer, to the liquid hydrogen storage tank. It also couples liquid hydrogen consumption, refueling, and overpressure emissions to provide a calculation model and method for the effective hydrogen storage capacity of an on-board liquid hydrogen system. This method has high computational efficiency and accuracy, consumes few computational resources, and can be deployed in real-world vehicle environments. It replaces level gauges to provide effective hydrogen storage capacity information for vehicles equipped with on-board liquid hydrogen systems, reducing the "thermal bridge" effect caused by level gauges and decreasing heat leakage from the liquid hydrogen storage tank and the self-evaporation rate of liquid hydrogen. For on-board liquid hydrogen systems equipped with level gauges, the method described in this invention provides dual protection for vehicle operation, reducing the operational risks caused by level gauge failure.

[0142] Overall process: Based on the finite volume method, the volume, heat transfer surface area, and other parameters of different insulation layers in a vacuum multilayer insulated storage tank are calculated to establish the foundation for a numerical simulation model.

[0143] Subsequently, the physical properties of the reflective material and spacer material, as well as simulation parameters such as vacuum level, were set.

[0144] Subsequently, a heat exchange module was established, with heat exchange methods including radiation heat exchange, convection heat exchange, gas heat transfer, and solid heat transfer.

[0145] Based on a finite-volume vacuum multilayer insulation numerical simulation model, the heat loss from the ambient temperature to the liquid hydrogen storage tank was calculated.

[0146] Then, based on the physical properties of liquid hydrogen, such as temperature and density, the changes in liquid hydrogen temperature, density, mass, vaporization mass, and gas phase pressure under real-time heat leakage conditions are calculated.

[0147] The mass of hydrogen emitted under overpressure, the flow rate of liquid hydrogen outlet, and the flow rate of liquid hydrogen refueling outlet are then obtained through the hydrogen consumption and refueling module, and the effective hydrogen storage capacity of the on-board liquid hydrogen system under real-time conditions is finally calculated.

[0148] like Figure 2 The specific steps are as shown:

[0149] 1. A numerical simulation model of vacuum multilayer insulation is established based on the finite volume method. A simplified structural diagram of the vacuum multilayer insulation liquid hydrogen storage tank is shown in the figure below. It mainly consists of an inner liner, spacer materials, reflective materials, and an outer liner. The insulation barrier is formed by multiple layers of spacer and reflective materials combined and then evacuated. This module mainly calculates the volume and heat transfer surface area of ​​the spacer and reflective materials between different layers. During the model calculation, one layer of spacer material and one layer of reflective material are treated as a single unit. In the example calculation, the storage tank is simplified as a cylinder for calculation.

[0150] The volume calculation formulas for different insulation layers are as follows:

[0151] (1)

[0152] The formulas for calculating the surface area of ​​different insulation layers are as follows:

[0153] (2)

[0154] in The number of different insulation layers; This corresponds to the thickness of the insulation layer spacer material; This corresponds to the thickness of the reflective material in the insulation layer; This refers to the length of the inner liner of the liquid hydrogen storage tank. Let be the radius of the inner liner of the liquid hydrogen storage tank.

[0155] 2. Set the physical properties of the reflective material and the spacer material, as well as the vacuum degree and other simulation parameters, and establish a heat exchange module. The heat exchange mainly includes radiation heat transfer, convection heat transfer, gas heat transfer and solid heat transfer. The main influencing factors of convection heat transfer are the vehicle speed, ambient wind speed and ambient temperature of the vehicle equipped with the onboard liquid hydrogen system.

[0156] The formulas for calculating the heat flow rate of different heat exchange methods are as follows:

[0157] Radiative heat transfer: (3)

[0158] in Boltzmann's constant; and These are the temperatures of the corresponding insulation layers; and These represent the emissivity of the reflective materials of adjacent insulation layers at the corresponding temperatures.

[0159] Convection heat transfer: (4)

[0160] It is positively correlated with vehicle speed;

[0161] in Temperature of the outer liner of the storage tank; For ambient temperature, The convective heat transfer coefficient is calculated using the following formula:

[0162] (5)

[0163] (6)

[0164] (7)

[0165] (8)

[0166] in The thermal conductivity of a fluid at a given temperature; For Nusselt numbers; The characteristic length of the fluid in the flow direction; It is the Reynolds number; For flow rate; The kinematic viscosity of the fluid; For fluid density; The dynamic viscosity of the fluid; It is a Prandtl number; The specific heat capacity at constant pressure of the fluid;

[0167] Heat transfer in rarefied gases under vacuum conditions: (9)

[0168] in These are empirical constants; Vacuum pressure; This refers to the gas adaptability coefficient;

[0169] Solid heat transfer: (10)

[0170] in These are empirical constants; The thickness of the spacer material between adjacent insulation layers and the vacuum pressure; The degree of looseness of the spacer material; It represents the thermal conductivity of the material separating adjacent insulation layers.

[0171] 3. Calculation of heat flux of different insulation layers

[0172] For the outer liner of the liquid hydrogen storage tank, there is a high-vacuum gap between it and the multi-layer insulation material. The heat exchange forms are radiation heat transfer and rarefied gas heat transfer in a vacuum environment. The heat exchange with the environment is convective heat transfer and radiation heat transfer. The formula for calculating the net heat flow rate of heat exchange to the outer liner is:

[0173] (11)

[0174] in Heat transferred from the environment to the outer shell; This refers to the heat transferred from the outer liner to the outermost insulation material.

[0175] Similarly, the formula for calculating the net heat flow rate of the outermost insulation material is as follows:

[0176] (12)

[0177] For the innermost insulation material, which is in direct contact with the inner liner of the storage tank, the heat transfer from it to the inner liner is the final heat loss, which directly leads to changes in the temperature and vaporization of liquid hydrogen. The formula for calculating the net heat flow rate of heat loss from the external environment to the storage tank is:

[0178] (13)

[0179] For insulation materials in other locations, the formula for calculating the net heat flow rate is:

[0180] (14)

[0181] 4. Temperature update calculation between different insulation layers: The calculation process is performed using one layer of spacer material and one layer of reflective material as a calculation unit.

[0182] The formula for updating the interlayer temperature of different insulation layers is as follows:

[0183] (15)

[0184] in The temperature of the corresponding calculation unit; This corresponds to the heat flux rate of the calculation unit; For heat exchange surface area; Total volume; This refers to the composite specific heat capacity at the corresponding temperature. Composite density;

[0185] For materials with specific heat capacity, such as common spacer and reflective materials like polyurethane foam and aluminum foil, the specific heat capacity varies with temperature. The specific heat capacity of the two materials is fitted with a polynomial, and the composite specific heat capacity is calculated based on the mass fraction in the calculation unit.

[0186] (16)

[0187] in This refers to the specific heat capacity of the corresponding spacer material or reflective material; These are the fitting coefficients; The current temperature;

[0188] (17)

[0189] in Total specific heat capacity; For the quality of the corresponding material; Density of the spacer material; For the volume of the spacer material; Density of the reflective material; The volume of the reflective material; This refers to the specific heat capacity of the material at a given temperature.

[0190] (18)

[0191] in Composite density; This represents the density of the corresponding material.

[0192] 5. Liquid hydrogen vaporization and evaporation and gas pressure calculation:

[0193] Mass of liquid hydrogen vaporization:

[0194] (19)

[0195] in The mass of liquid hydrogen vaporization; The net heat flow rate from the external environment to the storage tank; For heat exchange area; This represents the latent heat of vaporization of liquid hydrogen under the corresponding conditions.

[0196] Calculation of gas pressure inside the liquid hydrogen storage tank after vaporization:

[0197] (20)

[0198] in The mass of gaseous hydrogen in the original gas phase space; where is the molar mass of hydrogen; is Gas phase space volume; It is the ideal gas constant; The temperature inside the storage tank is assumed to be the same as the temperature of the liquid hydrogen in the gas phase space.

[0199] (twenty one)

[0200] in This represents the remaining mass of liquid hydrogen. This represents the density of liquid hydrogen under the corresponding conditions. This refers to the water volume of the liquid hydrogen storage tank.

[0201] 6. Calculation of changes in liquid hydrogen reserves

[0202] For vehicle-mounted liquid hydrogen systems, there are three main ways to source and consume hydrogen: liquid outlet, liquid inlet filling, and gaseous hydrogen overpressure relief.

[0203] The formula for calculating the mass of liquid hydrogen in a liquid hydrogen storage tank is:

[0204] (twenty two)

[0205] in The mass of liquid hydrogen in its initial state; This refers to the mass flow rate of liquid hydrogen during the refueling process; This is the mass flow rate at the liquid outlet during operation, which is positively correlated with vehicle speed and fuel cell system operating power.

[0206] The formula for calculating gaseous hydrogen reserves is:

[0207] (twenty three)

[0208] in This refers to the mass of gaseous hydrogen inside the storage tank. This represents the initial mass of gaseous hydrogen. The mass of liquid hydrogen vaporization caused by heat leakage; The mass of gaseous hydrogen discharged by the safety valve after overpressure;

[0209] The calculation formulas are as follows:

[0210] (twenty four)

[0211] in The initial pressure inside the tank. and These represent the mass and density of liquid hydrogen in its initial state; This represents the initial temperature inside the storage tank.

[0212] (25)

[0213] in The pressure difference before and after the safety valve opens and closes; and These represent the mass and density of liquid hydrogen in the liquid hydrogen storage tank, respectively. The temperature inside the storage tank during the release;

[0214] The final formula for calculating the remaining effective hydrogen balance in the onboard liquid hydrogen system is as follows:

[0215] (26)

[0216] In practical application, the above process , , The values ​​are the observations from the relevant sensors. To ensure accuracy, they are processed by the Kalman filter algorithm to remove observation noise and then input into equations (20) to (26) for calculation.

[0217] The main steps of the Kalman filter algorithm are as follows:

[0218] Initialize state variables and covariance;

[0219] (27)

[0220] (28)

[0221] Among them are:

[0222] State prediction;

[0223] (29)

[0224] Observation and prediction;

[0225] (30)

[0226] Covariance matrix prediction;

[0227] (31)

[0228] Kalman gain calculation;

[0229] (32)

[0230] Status update;

[0231] (33)

[0232] Covariance update;

[0233] (34)

[0234] In the above steps, the subscript Represented as the state parameters at the corresponding time; subscript " "and" "" represents the state parameters before and after the update at the corresponding time point; the meanings of each parameter are as follows:

[0235] This is the state vector at the initial moment; These are the state variables at the initial moment; Let k be the state vector before the update. Let be the updated state vector at time k;

[0236] The mathematical expectation of the relevant computation matrix;

[0237] This is the state transition matrix; This is the transpose of the state transition matrix;

[0238] The state control input matrix is ​​mainly used to describe the transformation relationship between states at different times and the next time.

[0239] The system process noise vector corresponding to time k; This is the observation noise vector corresponding to time k;

[0240] Let be the observation matrix at time k, representing the linear transformation relationship from the system state to the observed values; This is the transpose of the observation matrix at time k;

[0241] and These are process noise and observation noise, respectively. Process noise represents the dynamic error introduced by the model, while observation noise is the error introduced by sensor observation, which varies depending on the sensor accuracy.

[0242] The estimated covariance under the initial conditions;

[0243] The calculation relationship between the system state observation noise is given by equation (29); The prediction of the system state at time k is calculated based on the state at the previous time step.

[0244] The Kalman gain at time k is used to evaluate the reliability of the predicted and observed data;

[0245] The formulas involved in the main steps of the Kalman filter algorithm are mainly used to correct the calculated values ​​of the model based on the actual sensor data during vehicle operation, suppress sensor noise and sensor error, and ensure the accuracy of model operation. The main application scope is to pass the corrected parameters to formulas (22), (23), and (24), and finally apply them to formula (26). Formulas (20) to (26) are the methods for calculating the hydrogen balance, and formula (26) is the final calculation result.

[0246] The calculation uses the effective hydrogen mass, liquid hydrogen mass, and gaseous mass in the storage tank as state variables, and the mass flow rates at the liquid hydrogen storage tank outlet, inlet, and gaseous emission flow rate sensors as inputs. The corresponding matrices in the Kalman filter algorithm are as follows:

[0247] , , , ,

[0248] in The sampling interval is denoted as .

[0249] The present invention provides another embodiment of an evaluation model for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system, including a key parameter calculation module: used to establish a finite volume simulation model of a liquid hydrogen storage tank and calculate the heat transfer area and volume key parameters of different insulation layers;

[0250] Vacuum Degree Determination Module: Used to establish heat transfer simulation models using convective heat transfer, radiative heat transfer, solid heat transfer, and gas heat transfer methods, and to determine the physical parameters of the spacer material, reflective material, and vacuum degree of the liquid hydrogen storage tank;

[0251] Net heat flow rate calculation module: used to calculate the net heat flow rate between different insulation layers under actual operating conditions of different vehicle speeds, ambient temperatures, and ambient wind speeds;

[0252] Temperature update module: used to calculate the temperature change between different insulation layers based on net flow rate, insulation layer volume and heat exchange surface area, and to update the temperature.

[0253] The module for calculating the conversion amount of gaseous hydrogen after heat absorption and the pressure of the gas phase space is used to calculate the heat leakage from the operating environment to the liquid hydrogen storage tank, calculate the mass of liquid hydrogen vaporization based on the properties of liquid hydrogen and the heat leakage, obtain the liquid hydrogen mass flow rate, liquid hydrogen filling flow rate and gaseous hydrogen emission flow rate during actual vehicle operation, process the noise of sensor observations through Kalman filtering algorithm, and finally calculate the total mass of liquid hydrogen vaporization and the pressure and volume of the gas phase space after liquid hydrogen vaporization.

[0254] The module for calculating the effective hydrogen reserve is used to calculate the mass of gaseous hydrogen emitted to the outside and the actual mass of liquid hydrogen used, and finally obtains the mass of liquid hydrogen remaining inside the liquid hydrogen storage tank and the mass of hydrogen in the gas phase space. The effective hydrogen reserve is the sum of the mass of the remaining liquid hydrogen and the mass of hydrogen in the gas phase space.

[0255] Example test results:

[0256] During the example operation, the ambient temperature is stable at 25℃, the water volume of the storage tank is 1.25m3, the maximum tooling pressure of the liquid hydrogen storage tank is 1.05MPa, the safety valve opening pressure is 1.25 times the maximum working pressure, the closing pressure is 0.9 times the maximum working pressure, and the initial liquid hydrogen filling volume is at the maximum liquid level, with an initial pressure of 0.95MPa.

[0257] 1. In a static state: such as Figure 3a , Figure 3b , Figure 3c , Figure 3d As shown.

[0258] 2. Under operating conditions: such as Figure 4a , Figure 4b , Figure 4c , Figure 4d , Figure 4e As shown.

[0259] The example cases mainly present the calculation results of the remaining effective hydrogen balance of the on-board liquid hydrogen system under the corresponding operating conditions, which are used to demonstrate the effectiveness of the method.

[0260] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be included within the scope of protection of the present invention. Furthermore, all content not described in detail in this specification is prior art known to those skilled in the art.

Claims

1. A method for calculating the remaining effective hydrogen storage capacity of an onboard liquid hydrogen system, characterized in that, Includes the following steps: Step 1: Establish a finite volume simulation model of the liquid hydrogen storage tank and calculate the key parameters of heat transfer area and volume for different insulation layers; Step 2: Establish a heat transfer simulation model using convective heat transfer, radiative heat transfer, solid heat transfer, and gas heat transfer methods, and determine the physical parameters of the spacer material, reflective material, and vacuum level of the liquid hydrogen storage tank. Step 3: Calculate the net heat flow rate between different insulation layers under actual operating conditions of different vehicle speeds, ambient temperatures, and ambient wind speeds; Step 4: Calculate the temperature changes between different insulation layers based on the net flow rate, insulation layer volume, and heat exchange surface area, and update the temperature accordingly. Step 5: Calculate the heat leakage from the operating environment to the liquid hydrogen storage tank. Calculate the mass of liquid hydrogen vaporization based on the properties of liquid hydrogen and the heat leakage. Obtain the liquid hydrogen mass flow rate, liquid hydrogen filling flow rate, and gaseous hydrogen emission flow rate during actual vehicle operation. Use the Kalman filter algorithm to process the noise in the sensor observations. Finally, calculate the total mass of liquid hydrogen vaporization and the pressure and volume of the gas phase space after liquid hydrogen vaporization. Step 6: Calculate the mass of gaseous hydrogen emitted to the outside and the actual mass of liquid hydrogen used. Finally, obtain the mass of remaining liquid hydrogen inside the liquid hydrogen storage tank and the mass of hydrogen in the gas phase space. The effective hydrogen balance is the sum of the mass of remaining liquid hydrogen and the mass of hydrogen in the gas phase space.

2. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 1, characterized in that, The specific details of step one are as follows: A vacuum multilayer insulation numerical simulation model was established based on the finite volume method. The vacuum multilayer insulation liquid hydrogen storage tank is mainly composed of an inner liner, spacer material, reflective material, and outer liner. The spacer material and reflective material are combined in multiple layers and then evacuated to form an insulation barrier. The vacuum multilayer insulation numerical simulation model mainly calculates the volume and heat transfer surface area of ​​the spacer material and reflective material between different layers. In the model calculation, one layer of spacer material and one layer of reflective material are treated as a whole for calculation. The storage tank is simplified as a cylinder for calculation. The volume calculation formulas for different insulation layers are as follows: (1) The formulas for calculating the surface area of ​​different insulation layers are as follows: (2) in The number of different insulation layers; This corresponds to the thickness of the insulation layer spacer material; This corresponds to the thickness of the reflective material in the insulation layer; This refers to the length of the inner liner of the liquid hydrogen storage tank. Let be the radius of the inner liner of the liquid hydrogen storage tank.

3. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 1, characterized in that, Step two, specifically, is as follows: Set the physical property parameters of the reflective material and the spacer material, as well as the vacuum degree simulation parameters, and establish a heat exchange module. The heat exchange mainly includes radiation heat transfer, convection heat transfer, gas heat transfer and solid heat transfer. The main influencing factors of convection heat transfer are the vehicle speed, ambient wind speed and ambient temperature of the vehicle equipped with the on-board liquid hydrogen system. The formulas for calculating the heat flow rate of different heat exchange methods are as follows: Radiative heat transfer: (3) in Boltzmann's constant; and These are the temperatures of the corresponding insulation layers; and These represent the emissivity of the reflective materials of adjacent insulation layers at the corresponding temperatures; Convection heat transfer: (4) in Temperature of the outer liner of the storage tank; The ambient temperature; The convective heat transfer coefficient is calculated using the following formula: (5) (6) (7) (8) in The thermal conductivity of a fluid at a given temperature; For Nusselt numbers; The characteristic length of the fluid in the flow direction; It is the Reynolds number; For flow rate; The kinematic viscosity of the fluid; For fluid density; The dynamic viscosity of the fluid; It is a Prandtl number; The specific heat capacity at constant pressure of the fluid; Heat transfer in rarefied gases under vacuum conditions: (9) in These are empirical constants; Vacuum pressure; This refers to the gas adaptability coefficient; Solid heat transfer: (10) in These are empirical constants; The thickness of the spacer material between adjacent insulation layers and the vacuum pressure; The degree of looseness of the spacer material; It represents the thermal conductivity of the material separating adjacent insulation layers.

4. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 1, characterized in that, Step three, the specific content of which is as follows: Calculation of heat flux of different insulation layers; The outer liner of the liquid hydrogen storage tank is separated from the multi-layer insulation material by a high-vacuum gap. The heat exchange occurs through radiation and rarefied gas transfer in a vacuum environment. The heat exchange with the environment is through convection and radiation. The formula for calculating the net heat flow rate of heat exchange to the outer liner is as follows: (11) in Heat transferred from the environment to the outer shell; This refers to the heat transferred from the outer liner to the outermost insulation material. The formula for calculating the net heat flow rate for the outermost insulation material is as follows: (12) The innermost layer of insulation material is in direct contact with the inner liner of the storage tank. The heat transfer to the inner liner is the final heat loss, which directly causes changes in the temperature of liquid hydrogen and vaporization. The formula for calculating the net heat flow rate of heat loss from the external environment to the storage tank is: (13) in The temperature of the inner liner of the storage tank can be simplified to the temperature of the liquid hydrogen inside the storage tank. The emissivity of the material inside the storage tank; For insulation materials in other locations, the formula for calculating the net heat flow rate is: (14)。 5. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 1, characterized in that, Step four, specifically, is as follows: Temperature update calculation between different insulation layers: The calculation process uses one layer of spacer material and one layer of reflective material as a calculation unit; The formula for updating the interlayer temperature of different insulation layers is as follows: (15) in The temperature of the corresponding calculation unit; This corresponds to the heat flux rate of the calculation unit; For heat exchange surface area; Total volume; This refers to the composite specific heat capacity at the corresponding temperature. Composite density; For materials with specific heat capacity, such as common spacer and reflective materials, the specific heat capacity varies with temperature. The specific heat capacity of the two materials is fitted with a polynomial, and the composite specific heat capacity is calculated based on the mass fraction in the calculation unit. (16) in This refers to the specific heat capacity of the corresponding spacer material or reflective material; These are the fitting coefficients; The current calculated temperature; (17) in For composite specific heat capacity; For the quality of the corresponding material; Density of the spacer material; For the volume of the spacer material; Density of the reflective material; The volume of the reflective material; This refers to the specific heat capacity of the material at a given temperature. (18) in Composite density; This represents the density of the corresponding material.

6. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 1, characterized in that, Step five, specifically, is as follows: Liquid hydrogen vaporization and evaporation and gas pressure calculation: Mass of liquid hydrogen vaporization: (19) in The mass of liquid hydrogen vaporized due to heat leakage; The net heat flow rate from the external environment to the storage tank; For heat exchange area; This represents the latent heat of vaporization of liquid hydrogen under the corresponding conditions. Calculation of gas pressure inside the liquid hydrogen storage tank after vaporization: (20) in The mass of gaseous hydrogen in the original gas phase space; where is the molar mass of hydrogen; is Gas phase space volume; It is the ideal gas constant; The current calculation temperature is assumed to be the same as the liquid hydrogen temperature. (21) in This represents the remaining mass of liquid hydrogen. This represents the density of liquid hydrogen under the corresponding conditions. This refers to the water volume of the liquid hydrogen storage tank.

7. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 1, characterized in that, Step six, specifically, is as follows: Calculation of changes in liquid hydrogen reserves; There are three main ways for hydrogen to be sourced and consumed in vehicle-mounted liquid hydrogen systems: liquid discharge from the outlet, liquid filling from the inlet, and overpressure relief of gaseous hydrogen. The formula for calculating the mass of liquid hydrogen in a liquid hydrogen storage tank is: (22) in The mass of liquid hydrogen in its initial state; This refers to the mass flow rate of liquid hydrogen during the refueling process; The mass flow rate at the liquid outlet during operation is positively correlated with vehicle speed and fuel cell system operating power. The formula for calculating gaseous hydrogen reserves is: (23) in This refers to the mass of gaseous hydrogen inside the storage tank. This represents the initial mass of gaseous hydrogen. The mass of liquid hydrogen vaporization caused by heat leakage; The mass of gaseous hydrogen discharged by the safety valve after overpressure; The calculation formulas are as follows: (24) in The initial pressure inside the tank. and These represent the mass and density of liquid hydrogen in its initial state; This represents the initial temperature inside the storage tank. (25) in The pressure difference before and after the safety valve opens and closes; and These represent the mass and density of liquid hydrogen in the liquid hydrogen storage tank, respectively. The temperature inside the storage tank during the release; The final formula for calculating the remaining effective hydrogen balance in the onboard liquid hydrogen system is as follows: (26) In practical application, the above process , , The values ​​are the observations from the relevant sensors. To ensure accuracy, they are processed by the Kalman filter algorithm to remove observation noise and then input into equations (20) to (26) for calculation.

8. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 7, characterized in that, The main steps of the Kalman filter algorithm are as follows: Initialize state variables and covariance (27) (28) State prediction (29) Observation and prediction (30) Covariance matrix prediction (31) Kalman gain calculation (32) Status update (33) Covariance Update (34) In the above steps, the subscript Represented as the state parameters at the corresponding time; subscript " "and" "" represents the state parameters before and after the update at the corresponding time point; the meanings of each parameter are as follows: This is the state vector at the initial moment; These are the state variables at the initial moment; Let k be the state vector before the update. Let be the updated state vector at time k; The mathematical expectation of the relevant computation matrix; This is the state transition matrix; This is the transpose of the state transition matrix; The state control input matrix is ​​used to describe the transformation relationship between the states at different times and the state at the next time. The system process noise vector corresponding to time k; This is the observation noise vector corresponding to time k; Let be the observation matrix at time k, representing the linear transformation relationship from the system state to the observed values; This is the transpose of the observation matrix at time k; and These are process noise and observation noise, respectively. Process noise represents the dynamic error introduced by the model, while observation noise is the error introduced by sensor observation, which varies depending on the sensor accuracy. The estimated covariance under the initial conditions; The calculation relationship between system state observation noise; The prediction of the system state at time k is calculated based on the state at the previous time step. is the Kalman gain at time k, used to evaluate the reliability of prediction and observation data.

9. The method for calculating the remaining effective hydrogen storage capacity of an on-board liquid hydrogen system according to claim 8, characterized in that: The calculation uses the effective hydrogen mass, liquid hydrogen mass, and gaseous mass in the storage tank as state variables, and the mass flow rates at the liquid hydrogen storage tank outlet, inlet, and gaseous emission flow rate sensors as inputs. The corresponding matrices in the Kalman filter algorithm are as follows: ， ， ， ， ； in The sampling interval is denoted as .

10. The evaluation model established by the method for calculating the remaining effective hydrogen storage of an on-board liquid hydrogen system according to any one of claims 1 to 9, characterized in that the model include: The module for calculating key parameters is used to establish a finite volume simulation model of a liquid hydrogen storage tank and calculate the key parameters of heat transfer area and volume for different insulation layers. The vacuum degree determination module is used to establish a heat transfer simulation model using convective heat transfer, radiative heat transfer, solid heat transfer, and gas heat transfer methods, and to determine the physical parameters of the spacer material, reflective material, and vacuum degree of the liquid hydrogen storage tank. The net heat flow rate calculation module is used to calculate the net heat flow rate between different insulation layers under actual operating conditions of different vehicle speeds, ambient temperatures, and ambient wind speeds. The temperature update module is used to calculate the temperature change between different insulation layers based on the net flow rate, insulation layer volume, and heat exchange surface area, and to update the temperature accordingly. The module calculates the conversion amount of gaseous hydrogen after heat absorption and the pressure of the gas phase space. It is used to calculate the heat leakage from the operating environment to the liquid hydrogen storage tank. Based on the properties of liquid hydrogen and the heat leakage, it calculates the mass of liquid hydrogen vaporization. It obtains the liquid hydrogen mass flow rate, liquid hydrogen filling flow rate and gaseous hydrogen emission flow rate during actual vehicle operation. The sensor observation values ​​are noise-processed by Kalman filtering algorithm. Finally, it calculates the total mass of liquid hydrogen vaporization and the pressure and volume of the gas phase space after liquid hydrogen vaporization. The module for calculating the effective hydrogen reserve is used to calculate the mass of gaseous hydrogen emitted to the outside and the actual mass of liquid hydrogen used, and finally obtains the mass of liquid hydrogen remaining inside the liquid hydrogen storage tank and the mass of hydrogen in the gas phase space. The effective hydrogen reserve is the sum of the mass of the remaining liquid hydrogen and the mass of hydrogen in the gas phase space.

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