Carbon dioxide underwater expansion acting numerical modeling method, calculation method, equipment and storage medium

Abstract

The invention discloses a carbon dioxide underwater expansion work doing numerical modeling method, a calculation method, equipment and a storage medium. The modeling method comprises the steps that the carbon dioxide phase change expansion work doing process is divided into a to-be-excited stage, a to-be-released stage, a release stage and a release ending stage; building a mathematical model of each stage according to the real physical property of carbon dioxide in each stage and a carbon dioxide phase change theory, and further obtaining a phase change tube excitation model; constructing a primary volume chamber pressure equalizing model according to a nozzle flow equation and a uniform gas theory; constructing a water tank extrusion model according to heat transfer theory, thermodynamic theory and Bernoulli equation; and the phase change pipe excitation model, the primary volume chamber pressure equalizing model and the water tank extrusion model form a carbon dioxide underwater expansion acting numerical model. According to the method, the numerical calculation precision of carbon dioxide underwater expansion acting is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical simulation, and particularly relates to a numerical modeling method, a calculation method, a device and a storage medium for carbon dioxide underwater expansion work. Background Art

[0002] When an underwater vehicle encounters a dangerous situation, it is necessary to use emergency drainage to increase the buoyancy of the vehicle, get out of danger and quickly return to the water surface. Accurately controlling the drainage process in the water tank, clarifying the navigation state of the underwater vehicle, and formulating an attitude control strategy are necessary technical means to ensure the underwater vehicle gets out of danger.

[0003] Currently, underwater vehicles generally use compressed air or gas for expansion drainage. However, at large depths, the capacity of compressed air is significantly insufficient, and there is a risk of secondary deflagration of gas. The liquid-gas phase change of carbon dioxide can achieve a large volume expansion. Therefore, using the phase change of carbon dioxide for expansion drainage can solve the deficiencies of compressed air or gas in the application of expansion drainage. However, when using the phase change of carbon dioxide instead of compressed air for expansion drainage, there is currently no numerical calculation method for the expansion work of carbon dioxide phase change, and it is impossible to determine whether it is suitable for the emergency drainage of underwater vehicles. Especially, there is a heat transfer effect during the phase change of carbon dioxide. At present, it has not been possible to accurately calculate the drainage process of carbon dioxide phase change expansion work. Therefore, it is necessary to establish an accurate numerical model for carbon dioxide underwater expansion work to accurately calculate the expansion drainage process. Summary of the Invention

[0004] The purpose of the present invention is to provide a numerical modeling method, a calculation method, a device and a storage medium for carbon dioxide underwater expansion work, so as to solve the problem that the drainage process of carbon dioxide phase change expansion work cannot be accurately calculated.

[0005] The present invention solves the above technical problems through the following technical solutions: A numerical modeling method for carbon dioxide underwater expansion work. The carbon dioxide underwater expansion work device includes a water tank and a drainage mechanism. The drainage mechanism includes an exhaust pipe, a plurality of carbon dioxide phase change pipes and an initial volume chamber; each carbon dioxide phase change pipe is connected to the initial volume chamber, and the initial volume chamber is connected to the water tank through the exhaust pipe; the water outlet of the water tank is connected to a drainage pipe, and each carbon dioxide phase change pipe contains liquid carbon dioxide and a reagent; the modeling method includes: Dividing the carbon dioxide phase change expansion work process into a stage to be excited, a stage to be released, a release stage and an end stage of release; Constructing a mathematical model for each stage according to the true physical properties of carbon dioxide in each stage and the carbon dioxide phase change theory, and then obtaining a phase change pipe excitation model; Constructing an initial volume chamber pressure equalization model according to the nozzle flow equation and the uniform gas theory; Construct a water tank extrusion model based on the theories of heat transfer, thermodynamics, and Bernoulli's equation; The carbon dioxide underwater expansion work numerical model is composed of the phase change tube excitation model, the initial volume chamber pressure equalization model, and the water tank extrusion model.

[0006] Furthermore, the phase change tube excitation model includes a mathematical model for the waiting-to-be-excited stage, a mathematical model for the waiting-to-be-released stage, a mathematical model for the release stage, and a mathematical model for the end-of-release stage; The mathematical model for the waiting-to-be-excited stage is: ; ; Among them, represents the pressure of carbon dioxide in the phase change tube during the waiting-to-be-excited stage, represents the specific internal energy of carbon dioxide in the phase change tube during the waiting-to-be-excited stage, represents the density of carbon dioxide in the phase change tube during the waiting-to-be-excited stage, represents the temperature of carbon dioxide in the phase change tube during the waiting-to-be-excited stage, represents the mass of carbon dioxide in the phase change tube during the waiting-to-be-excited stage, represents the volume of the phase change tube, represents the REFPROP function; The mathematical model for the waiting-to-be-released stage is: ; ; , , ; , ; Among them, represents the temperature of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the pressure of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the specific internal energy of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the density of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the internal energy of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the mass of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the proportionality coefficient of the agent converted into gas, represents the instantaneous mass of the gas product during combustion, represents the internal energy of carbon dioxide in the phase change tube during the waiting-to-be-excited stage, represents the proportion of the heat absorption value of the agent's exotherm, represents the instantaneous release heat in the phase change tube during combustion, represents the axial burning rate of the propellant, represents an empirical constant, n represents the burning rate pressure exponent, represents the mass of the propellant in the stage to be excited, represents the number of burning surfaces, represents the density of the propellant during combustion, represents the cross-sectional area or burning area of the propellant, represents time, represents the calorific value of the propellant during combustion; The mathematical model for the release stage is: ; ; ; , ; ; ; where, represents the energy discharged from the phase change tube during the release stage, represents the specific enthalpy of carbon dioxide in the phase change tube during the release stage, represents the temperature of carbon dioxide in the phase change tube during the release stage, represents the pressure of carbon dioxide in the phase change tube during the release stage, represents the specific internal energy of carbon dioxide in the tube during the release stage, represents the density of carbon dioxide in the phase change tube during the release stage, represents the internal energy of carbon dioxide in the phase change tube during the release stage, represents the mass of carbon dioxide in the phase change tube during the release stage, represents the injection mass flow rate of the phase change tube during the release stage, represents the flow correction coefficient, represents the effective discharge area of the diaphragm valve of the phase change tube, represents the gas constant, represents the specific heat ratio of carbon dioxide, represents the pressure in the initial volume chamber during the release stage, represents the constant related to ; The mathematical model for the end stage of release is: ; ; ; , ; , , ; ; Among them, represents the energy discharged from the phase change tube at the end of the release stage, represents the specific enthalpy of carbon dioxide in the phase change tube at the end of the release stage, represents the temperature of carbon dioxide in the phase change tube at the end of the release stage, represents the pressure of carbon dioxide in the phase change tube at the end of the release stage, represents the specific internal energy of carbon dioxide in the phase change tube at the end of the release stage, represents the internal energy of carbon dioxide in the phase change tube at the end of the release stage, represents the mass of carbon dioxide in the phase change tube at the end of the release stage, represents the density of carbon dioxide in the phase change tube at the end of the release stage, represents the injection mass flow rate of the phase change tube at the end of the release stage, represents the specific enthalpy of the mass flowing out of the high-pressure end, represents the pressure in the initial volume chamber at the end of the release stage, represents the specific enthalpy in the initial volume chamber at the end of the release stage, represents the pressure value at the high-pressure end of the valve between the phase change tube and the initial volume chamber, represents the pressure value at the low-pressure end of the valve between the phase change tube and the initial volume chamber, represents the temperature value at the high-pressure end of the valve between the phase change tube and the initial volume chamber, represents the temperature in the initial volume chamber at the end of the release stage.

[0007] Furthermore, the pressure equalization model of the initial volume chamber is: ; ; ; ; , ; ; , , ; ; ; Among them, represents the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe, represents the diameter of the exhaust pipe, represents the resistance coefficient of the exhaust pipe, represents the gas constant, represents the temperature in the initial volume chamber, represents the equivalent length, represents the pressure in the initial volume chamber, represents the pressure in the water tank, represents the energy discharged from the initial volume chamber through the exhaust pipe, represents the specific enthalpy in the initial volume chamber, represents the REFPROP function, represents the specific internal energy of carbon dioxide in the initial volume chamber, represents the density of carbon dioxide in the initial volume chamber, represents the mass of carbon dioxide in the initial volume chamber, represents the volume of the initial volume chamber, represents the internal energy of carbon dioxide in the initial volume chamber, represents the initial mass of carbon dioxide in the initial volume chamber, represents the total mass flow rate of multiple phase change pipes flowing into the initial volume chamber, represents the initial specific internal energy of carbon dioxide in the initial volume chamber, represents the total energy of multiple phase change pipes flowing into the initial volume chamber, represents the i mass flow rate of the th phase change pipe at the release stage or at the end of the release stage, i represents the energy discharged by the th phase change pipe at the release stage or at the end of the release stage, represents the average velocity of carbon dioxide in the exhaust pipe, represents the average density of carbon dioxide in the exhaust pipe, represents the average viscosity of carbon dioxide in the exhaust pipe, represents the actual length of the exhaust pipe, represents including other resistance coefficients, represents the resistance coefficient of the elbow, t represents time.

[0008] Furthermore, the water tank extrusion model is: ; ; ; ; , , ; , , , ; Among them, represents the displacement of the water tank, represents the real-time drainage flow rate of the water tank, t represents time, represents the seawater flow velocity in the drain pipe, represents the cross-sectional area of the drain valve on the drain pipe, represents the seawater density, represents the length of the drain pipe, represents the pressure inside the water tank, represents the outlet pressure of the water tank, represents the acceleration due to gravity, represents the water surface height inside the water tank, represents the height of the drain pipe orifice, represents the friction coefficient of the drain pipe, represents the drain pipe diameter, represents the local resistance coefficient of the drain pipe, represents the temperature of carbon dioxide inside the water tank, represents the REFPROP function, represents the specific internal energy of carbon dioxide inside the water tank, represents the density of carbon dioxide inside the water tank, represents the mass of carbon dioxide inside the water tank, represents the volume occupied by carbon dioxide inside the water tank, represents the internal energy of carbon dioxide inside the water tank, represents the heat loss coefficient, represents the total energy of carbon dioxide entering the water tank, represents the i type of heat loss of carbon dioxide inside the water tank, represents the work done by carbon dioxide inside the water tank, represents the energy of carbon dioxide at the water tank inlet, represents the mass flow rate of carbon dioxide at the water tank inlet, represents the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe, represents the energy discharged from the initial volume chamber through the exhaust pipe.

[0009] Based on the same concept, the present invention also provides a numerical calculation method for the underwater expansion work of carbon dioxide, including: Call the numerical model of carbon dioxide underwater expansion work. The numerical model of carbon dioxide underwater expansion work includes a phase change tube excitation model, an initial volume chamber pressure equalization model, and a water tank extrusion model. The phase change tube excitation model includes a mathematical model in the stage to be excited, a mathematical model in the stage to be released, a mathematical model in the release stage, and a mathematical model at the end of the release stage. Among them, the numerical model of carbon dioxide underwater expansion work is constructed by using the above-mentioned numerical modeling method for carbon dioxide underwater expansion work; Obtain the carbon dioxide mass, volume, and carbon dioxide temperature of each phase change tube; According to the carbon dioxide mass, volume, and carbon dioxide temperature of each phase change tube and the phase change tube excitation model, calculate the injection mass flow rate and the discharged energy of the phase change tube; Obtain the initial carbon dioxide mass, volume, and initial specific internal energy of carbon dioxide in the initial volume chamber; According to the injection mass flow rate and the discharged energy of the phase change tube, the initial carbon dioxide mass, volume, and initial specific internal energy of carbon dioxide in the initial volume chamber, and the initial volume chamber pressure equalization model, calculate the carbon dioxide mass flow rate and energy discharged from the initial volume chamber through the exhaust pipe; Obtain the volume occupied by the initial carbon dioxide in the water tank, the initial pressure, and the initial outlet pressure; According to the carbon dioxide mass flow rate and energy discharged from the initial volume chamber through the exhaust pipe, the volume occupied by the initial carbon dioxide in the water tank, the initial pressure, and the initial outlet pressure, and the water tank extrusion model, calculate the real-time drainage volume of the water tank.

[0010] Furthermore, the calculation of the injection mass flow rate and the discharged energy of the phase change tube specifically includes: Step A1: For each phase change tube, determine whether the start time of the phase change tube is reached. If so, the phase change tube enters the stage to be released and proceeds to Step A2; if not, the phase change tube is in the stage to be excited, and the injection mass flow rate and the discharged energy of the phase change tube are both 0; Step A2: Calculate the carbon dioxide temperature and carbon dioxide pressure of the phase change tube according to the mathematical model in the stage to be released; Step A3: Determine whether the carbon dioxide pressure is greater than the release pressure threshold. If so, the phase change tube enters the release stage and proceeds to Step A4; if not, the phase change tube is in the stage to be released, and the injection mass flow rate and the discharged energy of the phase change tube are both 0; Step A4: Calculate the injection mass flow rate and the discharged energy of the phase change tube according to the mathematical model in the release stage; Step A5: Determine whether the carbon dioxide pressure of the phase change tube in the release stage is equal to the pressure of the initial volume chamber in the release stage. If so, the phase change tube enters the end of the release stage and proceeds to Step A6; if not, the phase change tube is in the release stage and proceeds to Step A4; Step A6: Calculate the injection mass flow rate and the discharged energy of the phase change tube according to the mathematical model of the end-of-release stage.

[0011] Furthermore, calculating the mass flow rate and energy of the carbon dioxide discharged from the initial volume chamber through the exhaust pipe specifically includes: Step B1: Calculate the mass of carbon dioxide and the internal energy of carbon dioxide in the initial volume chamber according to the injection mass flow rate and the discharged energy of each phase change tube. Step B2: Determine the temperature and pressure in the initial volume chamber according to the mass of carbon dioxide and the internal energy of carbon dioxide in the initial volume chamber. Step B3: Determine whether the pressure in the initial volume chamber is greater than the pressure in the water tank. If so, proceed to Step B4; if not, the mass flow rate and energy of the carbon dioxide discharged from the initial volume chamber through the exhaust pipe are both 0. Step B4: Calculate the average velocity of the carbon dioxide in the exhaust pipe of the initial volume chamber. Step B5: Determine whether the iteration error is satisfied according to the average velocity of the carbon dioxide in the exhaust pipe of the initial volume chamber. If so, proceed to Step B6; if not, return to Step B4. Step B6: Calculate the mass flow rate and energy of the carbon dioxide discharged from the initial volume chamber through the exhaust pipe.

[0012] Furthermore, calculating the real-time drainage volume of the water tank specifically includes: Step C1: Calculate the mass of carbon dioxide, the internal energy of carbon dioxide, and the heat loss coefficient in the water tank according to the mass flow rate and energy of the carbon dioxide discharged from the initial volume chamber through the exhaust pipe. Step C2: Calculate the seawater velocity in the drain pipe according to the mass of carbon dioxide, the internal energy of carbon dioxide, and the heat loss coefficient in the water tank. Step C3: Determine whether the iteration error is satisfied according to the seawater velocity in the drain pipe. If so, proceed to Step C4; if not, return to Step C2. Step C4: Calculate the real-time drainage volume of the water tank.

[0013] Based on the same concept, the present application also provides an electronic device, including a memory, a processor, and a computer program / instructions stored on the memory. The processor executes the computer program / instructions to implement the above-mentioned numerical modeling method or numerical calculation method for carbon dioxide underwater expansion work.

[0014] Based on the same concept, the present application also provides a computer-readable storage medium, on which a computer program / instructions is stored. When the computer program / instructions is executed by a processor, it implements the above-mentioned numerical modeling method or numerical calculation method for carbon dioxide underwater expansion work.

[0015] Compared with the prior art, the advantages of the present invention are as follows: Compared with the traditional drainage calculation technology that uses the ideal gas model, the present invention adopts the physical property model of real gases in the NIST (National Institute of Standards and Technology) database to characterize the thermodynamic properties of CO2, which has higher accuracy in the high-pressure and large-temperature range; the present invention establishes a full-process model of phase-change drainage starting from the excitation of the phase-change tube, which helps to quickly calculate and predict the phase-change drainage process after environmental changes, phase-change tube parameter changes, and phase-change tube excitation timing strategy changes in the actual application scenario of the phase-change drainage technology, and improves the drainage calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only one embodiment of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0017] Figure 1 It is a schematic structural diagram of a carbon dioxide underwater expansion work device in an embodiment of the present invention; Figure 2 It is a flow chart of a numerical modeling method for carbon dioxide underwater expansion work in an embodiment of the present invention; Figure 3 It is a CFD simulation model of a CO2 underwater expansion work device in an embodiment of the present invention; Figure 4 It is a process cloud map within 10s of a certain phase-change drainage CFD simulation in an embodiment of the present invention; Figure 5 It is a heat loss coefficient surface in an embodiment of the present invention; Figure 6 It is a flow chart of a numerical calculation method for carbon dioxide underwater expansion work in an embodiment of the present invention.

[0018] Description of the reference numerals: 1 - water tank, 11 - drain pipe, 2 - drainage mechanism, 21 - exhaust pipe, 22 - phase-change tube, 23 - carbon dioxide, 24 - agent, 25 - valve between the phase-change tube and the initial volume chamber, 26 - initial volume chamber. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] The following clearly and completely describes the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts fall within the protection scope of the present invention.

[0020] The following specifically describes the technical solutions of the present application with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0021] Embodiment 1 As Figure 1 shown, the carbon dioxide underwater expansion work device includes a water tank 1 and a drainage mechanism 2. The drainage mechanism 2 includes an exhaust pipe 21, a plurality of carbon dioxide phase change pipes 22, and an initial volume chamber 26; each carbon dioxide phase change pipe 22 is connected to the initial volume chamber 26 through a valve 25, and the initial volume chamber 26 is connected to the water tank 1 through the exhaust pipe 21; the water outlet of the water tank 1 is connected to the drain pipe 11, and each carbon dioxide phase change pipe 22 contains liquid carbon dioxide 23 and a medicament 24. The specific working process of the work device is as follows: The medicament 24 in the phase change pipe 22 burns and releases heat under the excitation of an external power supply. This heat is absorbed by the liquid carbon dioxide 23, and the liquid carbon dioxide 23 undergoes a phase change and is released through the valve 25 into the initial volume chamber 26 for pressure equalization and pressure reduction. The high-pressure carbon dioxide mixture in the initial volume chamber 26 after pressure equalization and pressure reduction enters the water tank 1 through the exhaust pipe 21, squeezing the water in the water tank 1 to be discharged through the drain pipe 11.

[0022] As Figure 1 shown, a carbon dioxide underwater expansion work numerical modeling method provided by an embodiment of the present invention includes the following steps: Step S11: Divide the carbon dioxide phase change expansion work process into a stage to be excited, a stage to be released, a release stage, and a release end stage.

[0023] There are a plurality of phase change pipes, and the energy released by the combustion of the medicament in the phase change pipes needs to be accurately determined. In order to accurately calculate the changes in the thermal parameters of the drainage mechanism of the carbon dioxide underwater expansion work device and the change in the drainage volume of the water tank, the carbon dioxide underwater expansion work device is simplified into a carbon dioxide underwater expansion work numerical model through numerical analysis methods, specifically including a phase change pipe excitation model, an initial volume chamber pressure equalization model, and a water tank extrusion model.

[0024] The low-temperature and low-pressure liquid carbon dioxide stored in the phase change tube is phase-changed into high-temperature and high-pressure supercritical carbon dioxide, and then injected into the initial volume chamber through a valve to become supercritical or gaseous. To accurately calculate the real-time curves of the mass flow rate and energy in the phase change tube during the excitation process, the phase change and expansion work process of carbon dioxide in the phase change tube is divided into a stage to be excited (i.e., the stage where the agent and liquid carbon dioxide are stored in the phase change tube), a stage to be released (i.e., the stage where the agent burns and carbon dioxide is to be released), a release stage (i.e., the stage where the excitation agent burns carbon dioxide), and an end stage of release, and mathematical models for each stage are constructed.

[0025] Step S12: Construct mathematical models for each stage based on the real physical properties of carbon dioxide in each stage and the carbon dioxide phase change theory, and then obtain the phase change tube excitation model.

[0026] The real physical properties of carbon dioxide can be obtained by referring to the real physical property database of the National Institute of Standards and Technology (NIST) of the United States, and the real physical property data is obtained through the REFPROP software (or function) developed by it as an interface, that is, through two intensive quantities (i.e., quantities independent of the amount of substance, such as pressure, temperature, specific internal energy, specific enthalpy, density, etc.) and the specified substance symbol, and other intensive quantities corresponding to the REFPROP query are used, that is: (1) Among them, 、 respectively represent the known thermodynamic physical property intensive quantities, represents the other thermodynamic physical property intensive quantity to be obtained, represents the REFPROP function, represents the substance symbol.

[0027] In the stage to be excited, carbon dioxide is stored in the phase change tube in the form of normal temperature and high density. According to the relevant parameters of the phase change tube in this stage and based on formula (1) for query, the pressure and specific internal energy of carbon dioxide in the phase change tube can be obtained. Therefore, the mathematical model for the stage to be excited is: (2) (3) Among them, represents the pressure of carbon dioxide in the phase change tube in the stage to be excited, represents the specific internal energy of carbon dioxide in the phase change tube in the stage to be excited, represents the density of carbon dioxide in the phase change tube in the stage to be excited, represents the temperature of carbon dioxide in the phase change tube in the stage to be excited, represents the mass of carbon dioxide in the phase change tube in the stage to be excited, represents the volume of the phase change tube.

[0028] The agent in the phase change tube is ignited by an externally supplied ignition current and starts to burn, releasing heat and combustion gas products into the phase change tube, entering the stage of waiting to be released. Among them, the calculation formulas for the instantaneous mass and instantaneous heat release of the gas products during combustion are as follows: (4) (5) Among them, represents the instantaneous mass of the gas products during combustion, represents the instantaneous heat release in the phase change tube during combustion, represents the axial burning rate of the agent, represents the number of burning surfaces, represents the density of the agent during combustion (unit: kg / m 3 ) represents the cross-sectional area or burning area of the agent (unit: m 2 ) represents time, represents the calorific value of the agent during combustion (unit: kJ / m 3 ). After the agent is ignited, it burns along the axis, and the surface where the combustion progresses after ignition is the burning surface. For example, if the agent starts burning from the middle, it will spread from the middle point to both sides, and there are 2 burning surfaces.

[0029] The calculation formulas for the mass and internal energy in the phase change tube during the waiting-to-be-released stage are as follows: (6) (7) Among them, represents the mass of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the proportionality coefficient of the agent converted into gas (usually 0.6 - 0.7), represents the internal energy of carbon dioxide in the phase change tube during the waiting-to-be-released stage, represents the internal energy of carbon dioxide in the phase change tube during the waiting-to-be-excited stage, represents the proportional value of the heat release absorption of the agent (usually 0.6 - 0.95, which can be accurately calibrated through combustion tests ).

[0030] The axial burning rate of the agent adopts the Vieille burning rate law with a relatively wide pressure application range, and the specific calculation formula is as follows: (8) Among them, represents the empirical constant, n represents the burning rate pressure exponent, represents the pressure of carbon dioxide in the phase change tube during the stage to be released represents the mass of the agent during the stage to be excited. Empirical constant , burning rate pressure exponent n can all be accurately calibrated through combustion tests. During the stage to be released, the density , specific internal energy increase, and the temperature and pressure continue to rise. The calculation formulas for density and specific internal energy are: (9) Taking density , specific internal energy as intensive quantities and substituting them into formula (10), query the temperature and pressure in the phase change tube at this time through REFPROP: (10) The phase change tube is equipped with a diaphragm valve, which automatically opens when the release pressure threshold is reached. When the pressure in the phase change tube reaches the release pressure threshold, the high-pressure carbon dioxide mixture is released from the phase change tube and enters the release stage. The opening time of the diaphragm valve is measured to be less than 1 ms through experiments, and the opening process of the diaphragm valve is completed instantaneously. The effective discharge area of the diaphragm valve opening is set as , and the calculation formula for the injection mass flow rate of the phase change tube is: (11) (12) Among them, represents the injection mass flow rate of the phase change tube during the release stage, represents the flow correction coefficient, represents the pressure of carbon dioxide in the phase change tube during the release stage, represents the temperature of carbon dioxide in the phase change tube during the release stage, represents the gas constant, represents the specific heat ratio of carbon dioxide, represents the pressure in the initial volume chamber during the release stage (or the pressure at the tail of the phase change tube), represents the constant related to . The flow correction coefficient is the ratio of the actual flow rate to the theoretical flow rate, and its value can be selected within 0.85 - 0.95 according to experimental results or experience. The mass in the phase change tube during the release stage is: (13) Among them, Represents the mass of carbon dioxide in the phase change tube during the release stage. Assuming the injection of carbon dioxide is an isentropic flow, the internal energy of the phase change tube during the release stage is equal to the initial internal energy plus the heat released by the combustion of the agent, minus the energy flowing out of the nozzle: (14) Among them, Represents the internal energy of carbon dioxide in the phase change tube during the release stage, Represents the specific enthalpy of carbon dioxide in the phase change tube during the release stage (unit: kJ / kg, which can be queried through the REFPROP function). The pressure and temperature in the phase change tube during the release stage can be queried through the REFPROP function in combination with intensive quantities: (15) (16) Among them, Represents the specific internal energy of carbon dioxide in the tube during the release stage, Represents the density of carbon dioxide in the phase change tube during the release stage. According to the specific enthalpy and the injection mass flow rate Calculate the energy discharged from the phase change tube during the release stage: (17) At the end of the release stage, the pressure of carbon dioxide in the phase change tube and the pressure of the initial volume chamber reach a basic balance, the flow rate approaches 0, and the pressure of the initial volume chamber increases due to the excitation of other phase change tubes, resulting in the phenomenon of carbon dioxide reflux. Therefore, the mathematical model for the end of the release stage is: (18) (19) (20) (21) (22) (23) Among them, Represents the energy discharged from the phase change tube at the end of the release stage, Represents the specific enthalpy of carbon dioxide in the phase change tube at the end of the release stage, Represents the temperature of carbon dioxide in the phase change tube at the end of the release stage, Represents the pressure of carbon dioxide in the phase change tube at the end of the release stage, Represents the specific internal energy of carbon dioxide in the phase change tube at the end of the release stage, Represents the internal energy of carbon dioxide in the phase change tube at the end of the release stage, represents the mass of carbon dioxide in the phase change tube at the end of the release stage, represents the density of carbon dioxide in the phase change tube at the end of the release stage, represents the injection mass flow rate of the phase change tube at the end of the release stage, represents the specific enthalpy of the mass flowing out of the high-pressure end, represents the pressure in the initial volume chamber at the end of the release stage, represents the specific enthalpy in the initial volume chamber at the end of the release stage, represents the pressure value at the high-pressure end of the valve between the phase change tube and the initial volume chamber, represents the pressure value at the low-pressure end of the valve between the phase change tube and the initial volume chamber, represents the temperature value at the high-pressure end of the valve between the phase change tube and the initial volume chamber, represents the temperature in the initial volume chamber at the end of the release stage.

[0031] Step S13: Construct an equalizing pressure model for the initial volume chamber according to the nozzle flow equation and the uniform gas theory.

[0032] The equalizing pressure model for the initial volume chamber is realized through the carbon dioxide inflow equation into the initial volume chamber and the thermodynamic and fluid equations in the initial volume chamber. The injection mass flow rate of the carbon dioxide phase change expansion of a single phase change tube is calculated through the phase change tube excitation model. During the phase change drainage process, there are multiple phase change tubes injecting mass flow rate into the initial volume chamber, and each phase change tube starts to release the high-pressure carbon dioxide mixture at a certain time interval. Therefore, the inflow mass flow rate in the initial volume chamber is the sum of the injection mass flow rates of multiple phase change tubes, and the instantaneous energy flowing into the initial volume chamber is the sum of the energies discharged by multiple phase change tubes: (24) Among them, represents the total mass flow rate of multiple phase change tubes flowing into the initial volume chamber, represents the total energy of multiple phase change tubes flowing into the initial volume chamber, represents the i th phase change tube's mass flow rate during the release stage or at the end of the release stage, represents the i th phase change tube's discharged energy during the release stage or at the end of the release stage.

[0033] There is a certain amount of air initially stored in the initial volume chamber. An exhaust pipe is provided between the initial volume chamber and the water tank, and a one-way valve is installed. If the initial air pressure stored in the initial volume chamber is small, the gas in the initial volume chamber can be approximately simplified as carbon dioxide. According to the initial pressure of the initial volume chamber, the temperature of the initial volume chamber, and the volume , specific internal energy of the initial volume chamber and the initial mass . From this, the mass and internal energy of the initial volume chamber can be calculated: (25) wherein, represents the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe, represents the energy discharged from the initial volume chamber through the exhaust pipe, represents the initial mass of carbon dioxide in the initial volume chamber, represents the total mass flow rate of multiple phase change pipes flowing into the initial volume chamber, represents the initial specific internal energy of carbon dioxide in the initial volume chamber, represents the total energy of multiple phase change pipes flowing into the initial volume chamber.

[0034] From this, the pressure and temperature of the initial volume chamber can be calculated: (26) (27) wherein, represents the temperature in the initial volume chamber, represents the pressure in the initial volume chamber, represents the specific enthalpy in the initial volume chamber, represents the REFPROP function, represents the specific internal energy of carbon dioxide in the initial volume chamber, represents the density of carbon dioxide in the initial volume chamber, represents the mass of carbon dioxide in the initial volume chamber, represents the volume of the initial volume chamber, represents the internal energy of carbon dioxide in the initial volume chamber.

[0035] The carbon dioxide in the initial volume chamber flows out through the exhaust pipe, following the flow equation of a compressible fluid pipeline, to obtain the mass flow rate of carbon dioxide discharged from the exhaust pipe and the energy discharged from the exhaust pipe: (28) (29) (30) (31) (32) wherein, represents the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe, represents the diameter of the exhaust pipe, represents the resistance coefficient of the exhaust pipe, represents the gas constant, represents the temperature in the initial volume chamber, represents the equivalent length, represents the pressure in the initial volume chamber, represents the pressure in the water tank, represents the energy discharged from the initial volume chamber through the exhaust pipe, represents the specific enthalpy in the initial volume chamber, represents the Reynolds number, represents the average velocity of carbon dioxide in the exhaust pipe (i.e., the average fluid velocity in the exhaust pipe), represents the average density of carbon dioxide in the exhaust pipe, represents the average viscosity of carbon dioxide in the exhaust pipe, represents the actual length of the exhaust pipe, represents including other resistance coefficients, represents the resistance coefficient of the elbow.

[0036] and are both parameters related to the Reynolds number Re, and the Reynolds number is related to the flow velocity, and the flow velocity is related to the mass flow rate. Therefore, in Equation (28), in fact, cannot be directly calculated, but instead, it is necessary to substitute a preset initial for calculation to obtain a new iterative value until the deviation between the result of this iteration and the result of the previous iteration meets the iterative error, and then it can be considered as the calculation result. The equivalent length of the pipeline is the sum of the equivalent length after converting the resistance coefficient of the elbow in the pipeline, the resistance coefficient of the valve, etc. to the equivalent length and the initial pipeline length. The resistance coefficient of the valve is obtained based on experience or tests, and the resistance coefficient of the elbow is calculated according to Equation (32).

[0037] Step S14: Construct a water tank extrusion model based on heat transfer and thermodynamics theories and the Bernoulli equation.

[0038] The water tank extrusion simulation calculation is determined by the thermodynamic equation in the water tank and the drainage flow rate calculation equation. Assuming there is no energy loss in the exhaust pipe, the mass flow rate and energy of carbon dioxide entering the water tank are equal to the mass flow rate and energy discharged from the initial volume chamber. That is: (33) The mass of carbon dioxide entering the water tank is: (34) The total energy of carbon dioxide entering the water tank is: (35) Since the temperature of carbon dioxide is relatively high, heat will be transferred in the water tank, resulting in a loss of the volume of carbon dioxide. The direction of heat transfer is: heat is transferred to the seawater, and to the water tank wall and other equipment in the water tank. The remaining energy constitutes the internal energy of carbon dioxide and the pushing work that drives the seawater movement (i.e., the pushing work done by carbon dioxide in the water tank), that is: (36) Among them, the pushing work of draining water is: (37) To facilitate the description of the heat loss in the water tank, the heat loss coefficient is defined as the ratio of the current heat loss to the total energy entering the water tank: (38) Then the internal energy in the water tank system is: (39) At the same time, define the ratio of the change in effective energy to the change in total energy per unit time in the water tank as the instantaneous heat loss ratio : (40) Therefore, the current pressure in the water tank and temperature can be queried through formula (41): (41) (42) In formula (42), the volume occupied by carbon dioxide in the water tank is a real-time variable, consistent with the current drainage volume . The drainage volume needs to be calculated through the drainage flow equation (43) and substituted into formula (42). Therefore, the above calculation is an iterative process. The seawater in the water tank is pushed by the incoming carbon dioxide and flows out from the drain pipe at the bottom. Its flow rate follows the transient form based on Bernoulli's equation: (43) Among them, represents the seawater flow velocity in the drain pipe, represents the seawater density, represents the length of the drain pipe, represents the pressure inside the water tank, represents the outlet pressure of the water tank, represents the acceleration due to gravity, represents the water surface height inside the water tank, represents the height of the drain pipe orifice, represents the friction coefficient of the drain pipe (which can be obtained by referring to a manual or through experiments), represents the drain pipe diameter, represents the local resistance coefficient of the drain pipe (which can be determined by referring to a hydraulic manual).

[0039] It can be seen from formula (43) that it must be solved by an iterative method. Therefore, in actual calculations, an initial value needs to be preset and substituted into the calculation to obtain a new iterative value until the deviation between the current iterative result and the previous iterative result meets the iterative error, and then it can be regarded as the calculation result.

[0040] Through the flow velocity and the cross-sectional area of the drain valve on the drain pipe the flow rate is calculated, and the real-time drainage flow rate is: (44) Since water can be basically regarded as an incompressible fluid, the drainage volume is equal to the volume occupied by carbon dioxide inside the water tank : (45) Step S15: A numerical model for carbon dioxide underwater expansion work is constructed from a phase change tube excitation model, an initial volume chamber pressure equalization model, and a water tank extrusion model.

[0041] The calibration of the heat loss coefficient can be carried out through CFD (Computational Fluid Dynamics) or experimental mechanical energy. When using CFD for simulation calibration, the CFD simulation model constructed is as Figure 3 shown. The CFD simulation model describes the system accurately, has an appropriate calculation scale, and reasonable parameter settings. Considering that the carbon dioxide underwater expansion work device generally has a large size and a long duration (usually exceeding 10 s), a 2D axisymmetric model is used for calculation. The determination process of several main dimension parameters in the 2D axisymmetric model is as follows: The equivalent diameter D1 of the water tank: Generally, the water tank is not cylindrical. In the model, the equivalent diameter of the water tank should be equivalently converted with reference to the cross-sectional area of the real water tank; Water tank height L1: The water tank height is the same as the distance from the top to the bottom outlet of the submersible's water tank; CO2 nozzle diameter d1: It is consistent with the design of the carbon dioxide underwater expansion work device. If flow guidance is increased, the diameter should be set as the equivalent diameter after flow guidance; CO2 nozzle positioning l1: It is consistent with the design of the carbon dioxide underwater expansion work device; Water tank outlet diameter d2: It is the same as the size of the vent opening designed for the carbon dioxide underwater expansion work device; Water tank outlet length l2: The calculated resistance should be consistent with the sum of the frictional resistance and local resistance of the carbon dioxide underwater expansion work device along the way.

[0042] After verification and analysis, the 2D axisymmetric model should be established and set according to the following requirements. The values in Table 1 can all be determined by the above formulas.

[0043] Table 1 Requirements for the CFD simulation model of the CO2 underwater expansion work device

[0044] In Table 1, the calculation should cover the depth range required for the operation of the submersible, and calculate one working condition every 50 - 100 meters. Figure 4 The process cloud diagram within 10s of a certain phase change drainage CFD simulation is shown, where the color band represents the temperature distribution of carbon dioxide in the water tank. From Figure 4 the simulation results, all unit pressure, temperature, volume, and volume fraction data at equally spaced moments are extracted as calibration basic parameters, and the effective heat Q of the carbon dioxide underwater expansion work device at this moment is calculated according to the following formula e Calculation: (46) (47) Among them, represents the CO2 volume fraction of the i-th CFD model grid cell, represents the volume of the i-th CFD model grid cell, represents the density of the i-th CFD model grid cell, represents the specific internal energy of the i-th CFD model grid cell, represents the water surface pressure, and the average pressure can be taken, represents the drainage volume.

[0045] Taking the drainage depth - drainage volume as variables and the heat loss coefficient as the dependent variable, a surface relationship formula is established, so that the heat loss coefficient surface database can be obtained, as Figure 5 shown. The heat loss coefficient Combine the curve with the established numerical model of carbon dioxide underwater expansion work. That is, in the water tank extrusion model, by taking the value of the water tank pressure as a parameter and the value of the drained volume of the water tank as a parameter to query the heat loss coefficient , that is , the expansion drainage process can be calculated quickly and accurately.

[0046] The present invention proposes to use the CFD simulation method to calculate the heat loss coefficient in the numerical model of carbon dioxide underwater expansion work, realizing the accurate calculation of the heat loss coefficient under the condition of uneven heat distribution in the water tank. After introducing the numerical model of carbon dioxide underwater expansion work, the drainage prediction accuracy can be greatly corrected, and the accurate control of drainage can be realized.

[0047] Embodiment 2 As Figure 6 shown, a numerical calculation method for carbon dioxide underwater expansion work provided by an embodiment of the present invention includes the following steps: Step S21: Invoke the numerical model of carbon dioxide underwater expansion work. The numerical model of carbon dioxide underwater expansion work includes a phase change tube excitation model, an initial volume chamber pressure equalization model, and a water tank extrusion model. The phase change tube excitation model includes a mathematical model in the to-be-excited stage, a mathematical model in the to-be-released stage, a mathematical model in the release stage, and a mathematical model in the end-of-release stage. Among them, the numerical model of carbon dioxide underwater expansion work is constructed by using the numerical modeling method of carbon dioxide underwater expansion work in Embodiment 1 of the present application; Step S22: Obtain the carbon dioxide mass, volume, and carbon dioxide temperature of each phase change tube; Step S23: Calculate the injection mass flow rate and the discharged energy of the phase change tube according to the carbon dioxide mass, volume, and carbon dioxide temperature of each phase change tube and the phase change tube excitation model; Step S24: Obtain the initial carbon dioxide mass, volume, and initial specific internal energy of the initial volume chamber; Step S25: Calculate the carbon dioxide mass flow rate and energy discharged from the initial volume chamber through the exhaust pipe according to the injection mass flow rate and discharged energy of the phase change tube, the initial carbon dioxide mass, volume, and initial specific internal energy of the initial volume chamber, and the initial volume chamber pressure equalization model; Step S26: Obtain the initial volume occupied by carbon dioxide, the initial pressure, and the initial outlet pressure of the water tank; Step S27: Calculate the real-time drainage volume of the water tank according to the carbon dioxide mass flow rate and energy discharged from the initial volume chamber through the exhaust pipe, the initial volume occupied by carbon dioxide, the initial pressure, and the initial outlet pressure of the water tank, and the water tank extrusion model.

[0048] In a specific embodiment of the present invention, calculating the injection mass flow rate and the discharged energy of the phase change tube specifically includes: Step A1: For each phase change tube i, determine whether the start time of the phase change tube is reached. If so, the phase change tube enters the waiting-for-release stage and proceeds to Step A2; if not, the phase change tube is in the waiting-for-excitation stage, and the injection mass flow rate and the discharged energy are both 0; Step A2: Calculate the carbon dioxide temperature and the carbon dioxide pressure of the phase change tube according to Formulas (4) to (10) in Embodiment 1 of the present application; Step A3: Determine whether the carbon dioxide pressure is greater than the release pressure threshold. If so, the phase change tube enters the release stage and proceeds to Step A4; if not, the phase change tube is in the waiting-for-release stage, and the injection mass flow rate and the discharged energy are both 0; Step A4: Calculate the injection mass flow rate ( ) and the discharged energy ( ) of the phase change tube according to Formulas (11) to (17) in Embodiment 1 of the present application; Step A5: Determine whether the carbon dioxide pressure of the phase change tube in the release stage is equal to the pressure of the initial chamber in the release stage. If so, the phase change tube enters the end-of-release stage and proceeds to Step A6; if not, the phase change tube is in the release stage and proceeds to Step A4; Step A6: Calculate the injection mass flow rate ( ) and the discharged energy ( ) of the phase change tube according to Formulas (18) to (23) in Embodiment 1 of the present application.

[0049] In a specific embodiment of the present invention, calculating the carbon dioxide mass flow rate and energy discharged from the initial chamber through the exhaust pipe specifically includes: Step B1: Based on Formulas (24) to (25) in Embodiment 1 of the present application, according to the injection mass flow rate and the discharged energy of each phase change tube, calculate the carbon dioxide mass and the carbon dioxide internal energy of the initial chamber; Step B2: Based on Formulas (26) to (27) in Embodiment 1 of the present application, according to the carbon dioxide mass and the carbon dioxide internal energy Determine the temperature in the initial volume chamber and pressure ; Step B3: Determine whether the pressure in the initial volume chamber is greater than the pressure in the water tank , if so, proceed to Step B4; if not, the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe and energy are both 0; Step B4: Calculate the average velocity of carbon dioxide in the exhaust pipe of the initial volume chamber ; Step B5: Determine whether the iteration error is satisfied based on the average velocity of carbon dioxide in the exhaust pipe of the initial volume chamber , if so, proceed to Step B6; if not, proceed to Step B4; Step B6: Based on Formulas (28) to (32) in Embodiment 1 of the present application, calculate the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe and energy .

[0050] In this embodiment, the iteration error is set to 1%.

[0051] In the specific implementation manner of the present invention, calculating the real-time drainage volume of the water tank specifically includes: Step C1: Based on Formulas (33) to (39) in Embodiment 1 of the present application, according to the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe and energy , calculate the mass of carbon dioxide in the water tank , the internal energy of carbon dioxide and the heat loss coefficient ; Step C2: Based on Formulas (41) to (43) in Embodiment 1 of the present application, according to the mass of carbon dioxide in the water tank, the internal energy of carbon dioxide and the heat loss coefficient , calculate the seawater velocity in the drain pipe ; Step C3: Determine whether the iteration error is satisfied based on the seawater velocity in the drain pipe , if so, proceed to Step C4; if not, proceed to Step C2; Step C4: Based on Formulas (44) to (45) in Embodiment 1 of the present application, calculate the real-time drainage volume of the water tank .

[0052] Embodiment 3 An embodiment of the present application further provides an electronic device, which includes: a memory, a processor, and a computer program / instruction stored in the memory. The processor executes the computer program / instruction to implement the carbon dioxide underwater expansion work numerical modeling method or the carbon dioxide underwater expansion work numerical calculation method in the embodiments of the present application.

[0053] Although not shown, the electronic device includes a processor, which can perform various appropriate operations and processes according to the programs and / or data stored in the read-only memory (ROM) or the programs and / or data loaded from the storage section into the random access memory (RAM). The processor can be a multi-core processor or can include multiple processors. In some embodiments, the processor can include a general main processor and one or more special coprocessors, such as a central processing unit, a graphics processing unit (GPU), a neural network processing unit (NPU), a digital signal processing unit (DSP), and so on. In the RAM, various programs and data required for device operation are also stored. The processor, the ROM, and the RAM are connected to each other through a bus. The input / output (I / O) interface is also connected to the bus.

[0054] The above-mentioned processor and the memory are jointly used to execute the program / instruction stored in the memory. When the program / instruction is executed by a computer, it can implement the methods, steps, or functions described in the above embodiments.

[0055] Although not shown, an embodiment of the present application further provides a computer-readable storage medium, on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, it implements the carbon dioxide underwater expansion work numerical modeling method or the carbon dioxide underwater expansion work numerical calculation method in the embodiments of the present application.

[0056] The readable storage medium includes permanent and non-permanent, removable and non-removable media, and information storage can be achieved by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, disk storage, or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media, such as modulated data signals and carrier waves.

[0057] The specific embodiments of the present invention disclosed above are only illustrative, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily conceive of changes or modifications, which should all be covered within the scope of protection of the present invention.

Claims

1. A numerical modeling method for carbon dioxide underwater expansion work. The carbon dioxide underwater expansion work device includes a water tank and a drainage mechanism. The drainage mechanism includes an exhaust pipe, a plurality of carbon dioxide phase change pipes, and an initial volume chamber; each carbon dioxide phase change pipe is connected to the initial volume chamber, and the initial volume chamber is connected to the water tank through the exhaust pipe; the water outlet of the water tank is connected to a drainage pipe, and each carbon dioxide phase change pipe contains liquid carbon dioxide and a chemical agent; characterized in that, The described modeling method includes: Dividing the carbon dioxide phase change expansion work process into a to-be-excited stage, a to-be-released stage, a release stage, and a release end stage; Constructing mathematical models for each stage based on the true physical properties of carbon dioxide in each stage and the carbon dioxide phase change theory, and then obtaining a phase change tube excitation model; Constructing an initial volume chamber pressure equalization model according to the nozzle flow equation and the uniform gas theory; Constructing a water tank extrusion model according to the heat transfer and thermodynamics theories and the Bernoulli equation; Forming a carbon dioxide underwater expansion work numerical model from the phase change tube excitation model, the initial volume chamber pressure equalization model, and the water tank extrusion model.

2. The numerical modeling method for carbon dioxide underwater expansion work according to claim 1, characterized in that The phase change tube excitation model includes a mathematical model for the to-be-excited stage, a mathematical model for the to-be-released stage, a mathematical model for the release stage, and a mathematical model for the release end stage; The mathematical model for the to-be-excited stage is: ； ； Among them, represents the pressure of carbon dioxide in the phase change tube during the stage to be excited, represents the specific internal energy of carbon dioxide in the phase change tube during the stage to be excited, represents the density of carbon dioxide in the phase change tube during the stage to be excited, represents the temperature of carbon dioxide in the phase change tube during the stage to be excited, represents the mass of carbon dioxide in the phase change tube during the stage to be excited, represents the volume of the phase change tube, represents the REFPROP function; The mathematical model for the to-be-released stage is: ； ； ， ， ； ， ； Among them, represents the temperature of carbon dioxide in the phase change tube during the stage of waiting for release, represents the pressure of carbon dioxide in the phase change tube during the stage of waiting for release, represents the specific internal energy of carbon dioxide in the phase change tube during the stage of waiting for release, represents the density of carbon dioxide in the phase change tube during the stage of waiting for release, represents the internal energy of carbon dioxide in the phase change tube during the stage of waiting for release, represents the mass of carbon dioxide in the phase change tube during the stage of waiting for release, represents the proportionality coefficient of the agent converted into gas, represents the instantaneous mass of the gas product during combustion, represents the internal energy of carbon dioxide in the phase change tube during the stage of waiting for excitation, represents the ratio of the heat absorption value of the agent, represents the instantaneous heat release in the phase change tube during combustion, represents the axial burning rate of the agent, represents the empirical constant, n represents the burning rate pressure exponent, represents the mass of the agent during the stage of waiting for excitation, represents the number of burning surfaces, represents the density of the agent during combustion, represents the cross-sectional area or burning area of the agent, represents time, represents the calorific value of the agent during combustion; The mathematical model for the release stage is: ； ； ； ， ； ； ； Among them, represents the energy discharged by the phase change tube during the release stage, represents the specific enthalpy of carbon dioxide in the phase change tube during the release stage, represents the temperature of carbon dioxide in the phase change tube during the release stage, represents the pressure of carbon dioxide in the phase change tube during the release stage, represents the specific internal energy of carbon dioxide in the tube during the release stage, represents the density of carbon dioxide in the phase change tube during the release stage, represents the internal energy of carbon dioxide in the phase change tube during the release stage, represents the mass of carbon dioxide in the phase change tube during the release stage, represents the injection mass flow rate of the phase change tube during the release stage, represents the flow correction coefficient, represents the effective discharge area of the diaphragm valve of the phase change tube, represents the gas constant, represents the specific heat ratio of carbon dioxide, represents the pressure in the initial volume chamber during the release stage, represents related to related constant; The mathematical model for the release end stage is: ； ； ； ， ； ， ， ； ； Among them, represents the energy discharged by the phase change tube during the end stage of release, represents the specific enthalpy of carbon dioxide in the phase change tube during the end stage of release, represents the temperature of carbon dioxide in the phase change tube during the end stage of release, represents the pressure of carbon dioxide in the phase change tube during the end stage of release, represents the specific internal energy of carbon dioxide in the phase change tube during the end stage of release, represents the internal energy of carbon dioxide in the phase change tube during the end stage of release, represents the mass of carbon dioxide in the phase change tube during the end stage of release, represents the density of carbon dioxide in the phase change tube during the end stage of release, represents the injection mass flow rate of the phase change tube during the end stage of release, represents the specific enthalpy of the mass flowing out of the high-pressure end, represents the pressure in the initial volume chamber during the end stage of release, represents the specific enthalpy in the initial volume chamber during the end stage of release, represents the pressure value at the high-pressure end of the valve between the phase change tube and the initial volume chamber, represents the pressure value at the low-pressure end of the valve between the phase change tube and the initial volume chamber, represents the temperature value at the high-pressure end of the valve between the phase change tube and the initial volume chamber, represents the temperature in the initial volume chamber during the end stage of release.

3. The numerical modeling method for carbon dioxide underwater expansion work according to claim 1, characterized in that The initial volume chamber pressure equalization model is: ； ； ； ； ， ； ； ， ， ； ； ； Among them, represents the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe, represents the diameter of the exhaust pipe, represents the resistance coefficient of the exhaust pipe, represents the gas constant, represents the temperature in the initial volume chamber, represents the equivalent length, represents the pressure in the initial volume chamber, represents the pressure in the water tank, represents the energy discharged from the initial volume chamber through the exhaust pipe, represents the specific enthalpy in the initial volume chamber, represents the REFPROP function, represents the specific internal energy of carbon dioxide in the initial volume chamber, represents the density of carbon dioxide in the initial volume chamber, represents the mass of carbon dioxide in the initial volume chamber, represents the volume of the initial volume chamber, represents the internal energy of carbon dioxide in the initial volume chamber, represents the initial mass of carbon dioxide in the initial volume chamber, represents the total mass flow rate of multiple phase change pipes flowing into the initial volume chamber, represents the initial specific internal energy of carbon dioxide in the initial volume chamber, represents the total energy of multiple phase change pipes flowing into the initial volume chamber, represents the i mass flow rate of the th phase change pipe in the release stage or at the end of the release stage, i represents the energy discharged by the th phase change pipe in the release stage or at the end of the release stage, represents the average velocity of carbon dioxide in the exhaust pipe, represents the average density of carbon dioxide in the exhaust pipe, represents the average viscosity of carbon dioxide in the exhaust pipe, represents the actual length of the exhaust pipe, represents including and other resistance coefficients, represents the resistance coefficient of the elbow, t represents time.

4. The numerical modeling method for carbon dioxide underwater expansion work according to claim 1, characterized in that The water tank extrusion model is: ； ； ； ； ， ， ； ， ， ， ； Wherein, represents the displacement of the water tank, represents the real-time drainage flow rate of the water tank, t represents time, represents the seawater flow velocity in the drain pipe, represents the cross-sectional area of the drain valve on the drain pipe, represents the seawater density, represents the length of the drain pipe, represents the pressure inside the water tank, represents the outlet pressure of the water tank, represents the acceleration due to gravity, represents the water surface height inside the water tank, represents the height of the drain pipe orifice, represents the friction coefficient of the drain pipe, represents the drain pipe diameter, represents the local resistance coefficient of the drain pipe, represents the temperature of carbon dioxide inside the water tank, represents the REFPROP function, represents the specific internal energy of carbon dioxide inside the water tank, represents the density of carbon dioxide inside the water tank, represents the mass of carbon dioxide inside the water tank, represents the volume occupied by carbon dioxide inside the water tank, represents the internal energy of carbon dioxide inside the water tank, represents the heat loss coefficient, represents the total energy of carbon dioxide entering the water tank, represents the i type of heat loss of carbon dioxide in the water tank, represents the pushing work done by carbon dioxide inside the water tank, represents the energy of carbon dioxide at the water tank inlet, represents the mass flow rate of carbon dioxide at the water tank inlet, represents the mass flow rate of carbon dioxide discharged from the initial volume chamber through the exhaust pipe, represents the energy discharged from the initial volume chamber through the exhaust pipe.

5. A numerical calculation method for the underwater expansion work of carbon dioxide, characterized in that, The described calculation method includes: Invoking a carbon dioxide underwater expansion work numerical model, the carbon dioxide underwater expansion work numerical model includes a phase change tube excitation model, an initial volume chamber pressure equalization model, and a water tank extrusion model, and the phase change tube excitation model includes a mathematical model for the to-be-excited stage, a mathematical model for the to-be-released stage, a mathematical model for the release stage, and a mathematical model for the release end stage; wherein, the carbon dioxide underwater expansion work numerical model is constructed by using the carbon dioxide underwater expansion work numerical modeling method described in any one of claims 1 to 4; Obtaining the carbon dioxide mass, volume, and carbon dioxide temperature of each phase change tube; Calculating the injection mass flow rate and the discharged energy of the phase change tube according to the carbon dioxide mass, volume, and carbon dioxide temperature of each phase change tube and the phase change tube excitation model; Obtaining the initial carbon dioxide mass, volume, and initial specific internal energy of the initial volume chamber; Calculating the carbon dioxide mass flow rate and energy discharged from the initial volume chamber through the exhaust pipe according to the injection mass flow rate and the discharged energy of the phase change tube, the initial carbon dioxide mass, volume, and initial specific internal energy of the initial volume chamber, and the initial volume chamber pressure equalization model; Obtaining the initial volume occupied by carbon dioxide in the water tank, the initial pressure, and the initial outlet pressure; Calculating the real-time drainage volume of the water tank according to the carbon dioxide mass flow rate and energy discharged from the initial volume chamber through the exhaust pipe, the initial volume occupied by carbon dioxide in the water tank, the initial pressure, and the initial outlet pressure, and the water tank extrusion model.

6. The numerical calculation method for the work done by the underwater expansion of carbon dioxide according to claim 5, characterized in that The specific calculation of the injection mass flow rate and the discharged energy of the phase change tube includes: Step A1: For each phase change tube, determine whether the start time of the phase change tube is reached. If so, the phase change tube enters the to-be-released stage and proceeds to step A2; if not, the phase change tube is in the to-be-excited stage, and both the injection mass flow rate and the discharged energy of the phase change tube are 0; Step A2: Calculate the carbon dioxide temperature and carbon dioxide pressure of the phase change tube according to the mathematical model for the to-be-released stage. Step A3: Determine whether the carbon dioxide pressure is greater than the release pressure threshold. If so, the phase change tube enters the release stage and proceeds to Step A4; if not, the phase change tube is in the waiting-to-release stage, and both the injection mass flow rate and the discharged energy of the phase change tube are 0; Step A4: Calculate the injection mass flow rate and the discharged energy of the phase change tube according to the mathematical model in the release stage; Step A5: Determine whether the carbon dioxide pressure in the phase change tube in the release stage is equal to the pressure in the initial volume chamber at the beginning of the release stage. If so, the phase change tube enters the end-of-release stage and proceeds to Step A6; if not, the phase change tube is in the release stage and proceeds to Step A4; Step A6: Calculate the injection mass flow rate and the discharged energy of the phase change tube according to the mathematical model in the end-of-release stage.

7. The numerical calculation method for the work done by underwater expansion of carbon dioxide according to claim 5, characterized in that, The calculation of the carbon dioxide mass flow rate and energy discharged from the initial volume chamber through the exhaust pipe specifically includes: Step B1: Calculate the carbon dioxide mass and carbon dioxide internal energy of the initial volume chamber according to the injection mass flow rate and the discharged energy of each phase change tube; Step B2: Determine the temperature and pressure inside the initial volume chamber based on the carbon dioxide mass and carbon dioxide internal energy of the initial volume chamber; Step B3: Determine whether the pressure inside the initial volume chamber is greater than the pressure inside the water tank. If so, proceed to Step B4; if not, both the carbon dioxide mass flow rate and the energy discharged from the initial volume chamber through the exhaust pipe are 0; Step B4: Calculate the average velocity of the carbon dioxide in the exhaust pipe of the initial volume chamber; Step B5: Determine whether the iteration error is satisfied based on the average velocity of the carbon dioxide in the exhaust pipe of the initial volume chamber. If so, proceed to Step B6; if not, proceed to Step B4; Step B6: Calculate the carbon dioxide mass flow rate and the energy discharged from the initial volume chamber through the exhaust pipe.

8. The numerical calculation method for the underwater expansion work of carbon dioxide according to claim 5, characterized in that The calculation of the real-time drainage volume of the water tank specifically includes: Step C1: Calculate the carbon dioxide mass, carbon dioxide internal energy, and heat loss coefficient of the water tank according to the carbon dioxide mass flow rate and the energy discharged from the initial volume chamber through the exhaust pipe; Step C2: Calculate the seawater velocity in the drainage pipe based on the carbon dioxide mass, carbon dioxide internal energy, and heat loss coefficient of the water tank; Step C3: Determine whether the iteration error is satisfied based on the seawater velocity in the drainage pipe. If so, proceed to Step C4; if not, proceed to Step C2; Step C4: Calculate the real-time drainage volume of the water tank.

9. An electronic device, comprising a memory, a processor, and a computer program / instructions stored on the memory, characterized in that The processor executes the computer program / instructions to implement the numerical modeling method for underwater expansion work of carbon dioxide as described in any one of claims 1 to 4 or the numerical calculation method for underwater expansion work of carbon dioxide as described in any one of claims 5 to 8.

10. A computer-readable storage medium having computer programs / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the numerical modeling method for underwater expansion work of carbon dioxide as described in any one of claims 1 to 4 or the numerical calculation method for underwater expansion work of carbon dioxide as described in any one of claims 5 to 8.

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