Numerical modeling method, calculation method, equipment and storage medium for underwater expansion work of carbon dioxide

Abstract

The present invention discloses a numerical modeling method, calculation method, device, and storage medium for the underwater expansion work of carbon dioxide. The modeling method includes dividing the carbon dioxide phase change expansion work process into a waiting stage, a waiting stage, a release stage, and a release completion stage; constructing mathematical models for each stage based on the actual physical properties of carbon dioxide in each stage and carbon dioxide phase change theory, thereby obtaining a phase change tube excitation model; constructing an initial volume chamber equalizing pressure model based on the nozzle flow equation and uniform gas theory; and constructing a water tank extrusion model based on heat transfer and thermodynamic theory and the Bernoulli equation. The phase change tube excitation model, the initial volume chamber equalizing pressure model, and the water tank extrusion model constitute a numerical model for the underwater expansion work of carbon dioxide. The present invention improves the accuracy of numerical calculations of the underwater expansion work of carbon dioxide.

Description

Technical Field

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

[0002] When an underwater vehicle encounters danger, emergency drainage is necessary to increase its buoyancy, escape danger, and quickly return to the surface. Accurately controlling the drainage process within the water tank, determining the vehicle's navigational state, and developing an attitude control strategy are essential technical measures to ensure the vehicle's escape from danger.

[0003] Currently, submersibles generally use compressed air or gas for expansion and drainage. However, at great depths, compressed air capacity is significantly insufficient, and gas presents the risk of secondary explosions. Carbon dioxide's liquid-gas phase transition allows for significant volume expansion, so utilizing carbon dioxide's phase transition for expansion and drainage can address the shortcomings of compressed air or gas in expansion and drainage applications. However, there is currently no numerical calculation method for the expansion work of carbon dioxide phase transition, replacing compressed air for expansion and drainage, making it impossible to determine its suitability for emergency drainage of underwater submersibles. In particular, the carbon dioxide phase transition process is affected by heat transfer, and it is currently not possible to accurately calculate the expansion work of carbon dioxide phase transition. Therefore, it is necessary to establish an accurate numerical model of the underwater expansion work of carbon dioxide phase transition to accurately calculate the expansion and drainage process. Summary of the Invention

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

[0005] The present invention solves the above-mentioned technical problems through the following technical solutions: a numerical modeling method for underwater expansion of carbon dioxide, wherein the underwater expansion device of carbon dioxide includes a water tank and a drainage mechanism, wherein the drainage mechanism includes an exhaust pipe, multiple carbon dioxide phase change tubes, and an initial volume chamber; each of the carbon dioxide phase change tubes 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 the drainage pipe, and each of the carbon dioxide phase change tubes is filled with liquid carbon dioxide and a reagent; the modeling method comprises:

[0006] The carbon dioxide phase change expansion process is divided into the waiting stage, the waiting stage, the release stage and the end of release stage.

[0007] According to the real physical properties of carbon dioxide in each stage and the carbon dioxide phase change theory, a mathematical model of each stage is constructed, and then a phase change tube excitation model is obtained;

[0008] The initial volume chamber pressure equalization model is constructed based on the nozzle flow equation and uniform gas theory;

[0009] Construct a water tank extrusion model based on heat transfer and thermodynamics theory and Bernoulli equation;

[0010] The phase change tube excitation model, the initial volume chamber pressure equalization model and the water tank extrusion model constitute a numerical model of underwater expansion work of carbon dioxide.

[0011] Furthermore, the phase change tube excitation model includes a mathematical model of the waiting-for-excitation stage, a mathematical model of the waiting-for-release stage, a mathematical model of the release stage, and a mathematical model of the release end stage;

[0012] The mathematical model of the waiting stage is:

[0013] ;

[0014] ;

[0015] in, represents the pressure of carbon dioxide in the phase change tube during the exciting stage, represents the specific internal energy of carbon dioxide in the phase change tube during the exciting stage, represents the density of carbon dioxide in the phase change tube during the exciting stage, represents the temperature of carbon dioxide in the phase change tube during the exciting stage, It represents the mass of carbon dioxide in the phase change tube during the exciting stage. represents the volume of the phase change tube, Represents the REFPROP function;

[0016] The mathematical model of the waiting-for-release stage is:

[0017] ;

[0018] ;

[0019] , , ;

[0020] , ;

[0021] in, Indicates the temperature of carbon dioxide in the phase change tube during the release stage, Indicates the pressure of carbon dioxide in the phase change tube during the release stage, represents the specific internal energy of carbon dioxide in the phase change tube during the release stage, Indicates the density of carbon dioxide in the phase change tube during the release phase. represents the internal energy of carbon dioxide in the phase change tube during the release phase, Indicates the mass of carbon dioxide in the phase change tube during the release phase, Indicates the proportional coefficient of the conversion of the agent into gas, Indicates the instantaneous mass of the gas products during combustion, represents the internal energy of carbon dioxide in the phase change tube during the exciting stage, Indicates the ratio of the exothermic absorption value of the agent, Indicates the instantaneous release of heat in the phase change tube during combustion. Indicates the axial burning velocity of the agent, represents the empirical constant, n represents the burning rate pressure index, Indicates the quality of the drug in the stage of waiting for excitation, Indicates the number of burning surfaces. Indicates the density of the agent during combustion. Indicates the cross-sectional area or combustion area of ​​the agent, Indicates time, Indicates the calorific value of the agent when burning;

[0022] The mathematical model of the release phase is:

[0023] ;

[0024] ;

[0025] ;

[0026] , ;

[0027] ;

[0028] ;

[0029] in, Indicates the energy discharged by the phase change tube during the release phase, represents the specific enthalpy of carbon dioxide in the tube during the phase change of the tube during the release phase, represents the temperature of carbon dioxide in the phase change tube during the release phase, represents the pressure of carbon dioxide in the phase change tube during the release phase, represents the specific internal energy of carbon dioxide in the tube during the release phase, represents the density of carbon dioxide in the phase change tube during the release phase, represents the internal energy of carbon dioxide in the phase change tube during the release phase, represents the mass of carbon dioxide in the phase change tube during the release phase, represents the injection mass flow rate of the phase change tube in the release stage, Indicates the flow correction coefficient, Indicates 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, Indicates the pressure in the initial chamber during the release phase. Represents Related constants;

[0030] The mathematical model of the release end stage is:

[0031] ;

[0032] ;

[0033] ;

[0034] , ;

[0035] , , ;

[0036] ;

[0037] in, Indicates the energy discharged by the phase change tube at the end of the release phase. represents the specific enthalpy of carbon dioxide in the phase change tube at the end of release, Indicates the temperature of carbon dioxide in the phase change tube at the end of release, Indicates the pressure of carbon dioxide in the phase change tube at the end of release, Indicates the specific internal energy of carbon dioxide in the phase change tube at the end of release, Indicates the internal energy of carbon dioxide in the phase change tube at the end of release, Indicates the mass of carbon dioxide in the phase change tube at the end of release, represents the density of carbon dioxide in the phase change tube at the end of release, represents the injection mass flow rate of the phase change tube at the end of the release stage, It represents the specific enthalpy of the mass flowing out of the high pressure end, Indicates the pressure in the initial chamber at the end of the release phase. represents the specific enthalpy in the initial chamber at the end of the release phase, Indicates the pressure value at the high-pressure end of the valve between the phase change tube and the initial volume chamber. Indicates the pressure value at the low-pressure end of the valve between the phase change tube and the initial volume chamber. Indicates the temperature value of the high pressure end of the valve between the phase change tube and the initial volume chamber, Indicates the temperature inside the initial chamber at the end of release.

[0038] Furthermore, the initial volume chamber pressure equalization model is:

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] , ;

[0044] ;

[0045] , , ;

[0046] ;

[0047] ;

[0048] in, It represents the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe. Indicates the diameter of the exhaust pipe, represents the resistance coefficient of the exhaust pipe, represents the gas constant, Indicates the temperature in the initial chamber. Indicates the equivalent length, Indicates the pressure in the initial volume chamber. Indicates the pressure in the water tank. It represents the energy discharged from the initial chamber through the exhaust pipe. represents the specific enthalpy in the initial chamber, Represents the REFPROP function, represents the specific internal energy of carbon dioxide in the initial volume, It represents the density of carbon dioxide in the initial volume chamber. Indicates the quality of carbon dioxide in the initial volume. represents the volume of the initial chamber, represents the internal energy of carbon dioxide in the initial volume, represents the initial mass of carbon dioxide in the initial volume chamber, It represents the total mass flow rate of multiple phase change tubes flowing into the initial volume chamber, represents the initial specific internal energy of carbon dioxide in the initial volume, It represents the total energy flowing into the initial volume chamber from multiple phase change tubes, Indicates the i The mass flow rate of a phase change tube in the release stage or the end of the release stage, Indicates the i The energy discharged by a phase change tube during the release stage or the end of the release stage is represents the Reynolds number, represents the average velocity of carbon dioxide in the exhaust pipe, Indicates the average density of carbon dioxide in the exhaust pipe, Represents the average viscosity of carbon dioxide in the exhaust pipe, Indicates the actual length of the exhaust pipe, Indicates inclusion Other drag coefficients, including represents the resistance coefficient of the elbow, t Indicates time.

[0049] Furthermore, the water tank extrusion model is:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] , , ;

[0055] , , , ;

[0056] in, Indicates the displacement of the water tank, represents the real-time drainage flow of the water tank, t represents time, Indicates the seawater flow rate in the drain pipe, Indicates the cross-sectional area of ​​the drain valve on the drain pipe. represents the density of seawater, Indicates the length of the drain pipe, Indicates the pressure in the water tank. Indicates the water outlet pressure of the water tank, represents the acceleration due to gravity, Indicates the water level in the tank. Indicates the height of the drain pipe outlet. represents the friction coefficient of the drainage pipe, Indicates the diameter of the drain pipe, represents the local resistance coefficient of the drainage pipe, Indicates the temperature of carbon dioxide in the water tank, Represents the REFPROP function, represents the specific internal energy of carbon dioxide in the water tank, represents the density of carbon dioxide in the water tank, Indicates the mass of carbon dioxide in the water tank, Indicates the volume of carbon dioxide in the water tank, represents the internal energy of carbon dioxide in the water tank, represents the heat loss coefficient, Indicates the total energy of carbon dioxide entering the water tank, Indicates the concentration of carbon dioxide in the water tank i Heat loss, is the pushing work done by the carbon dioxide in the water tank, represents the carbon dioxide energy at the water tank inlet, represents the mass flow rate of carbon dioxide at the water tank inlet, It represents the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe. It indicates the energy discharged from the primary chamber through the exhaust pipe.

[0057] Based on the same concept, the present invention also provides a method for numerically calculating the work done by underwater expansion of carbon dioxide, comprising:

[0058] Invoking a numerical model of the underwater expansion work of carbon dioxide, the numerical model comprising 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 comprising mathematical models for a waiting excitation stage, a waiting release stage, a release stage, and a release completion stage; wherein the numerical model of the underwater expansion work of carbon dioxide is constructed using the numerical modeling method for the underwater expansion work of carbon dioxide described above;

[0059] Obtain the carbon dioxide mass, volume and carbon dioxide temperature of each phase change tube;

[0060] The injection mass flow rate and discharged energy of the phase change tube are calculated based on the carbon dioxide mass, volume and carbon dioxide temperature of each phase change tube and the phase change tube excitation model;

[0061] Obtain the initial mass, volume and initial specific internal energy of carbon dioxide in the initial volume chamber;

[0062] Calculating the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe based on the injection mass flow rate and discharged energy of the phase change tube, the initial mass, volume and initial specific internal energy of carbon dioxide in the primary chamber, and the primary chamber pressure equalization model;

[0063] Obtain the initial carbon dioxide volume, initial pressure, and initial water outlet pressure of the water tank;

[0064] The real-time displacement of the water tank is calculated based on the mass flow and energy of carbon dioxide 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 water outlet pressure, and the water tank extrusion model.

[0065] Furthermore, the calculation of the injection mass flow rate and the discharged energy of the phase change tube specifically includes:

[0066] Step A1: For each phase change tube, determine whether the start time of the phase change tube has been reached. If so, the phase change tube enters the waiting release stage and proceeds to step A2. If not, the phase change tube is in the waiting excitation stage, and the injection mass flow rate and discharged energy of the phase change tube are both zero.

[0067] Step A2: calculating the carbon dioxide temperature and carbon dioxide pressure of the phase change tube according to the mathematical model of the waiting-for-release stage;

[0068] 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 stage, and the injection mass flow rate and discharged energy of the phase change tube are both 0.

[0069] Step A4: calculating the injection mass flow rate and discharged energy of the phase change tube according to the mathematical model of the release stage;

[0070] 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 release end stage and the process proceeds to step A6; if not, the phase change tube is in the release stage and the process proceeds to step A4;

[0071] Step A6: Calculating the injection mass flow rate and discharged energy of the phase change tube according to the mathematical model of the release end stage.

[0072] Furthermore, the calculation of the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe specifically includes:

[0073] Step B1: Calculate the mass and internal energy of carbon dioxide in the initial chamber based on the injection mass flow rate and exhaust energy of each phase change tube;

[0074] Step B2: determining the temperature and pressure in the primary chamber according to the mass and internal energy of carbon dioxide in the primary chamber;

[0075] Step B3: Determine whether the pressure in the primary 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 carbon dioxide discharged from the primary chamber through the exhaust pipe are both 0;

[0076] Step B4: Calculate the average velocity of carbon dioxide in the exhaust pipe of the primary chamber;

[0077] Step B5: judging whether the average velocity of carbon dioxide in the exhaust pipe of the primary chamber satisfies the iteration error, if so, proceeding to step B6; if not, proceeding to step B4;

[0078] Step B6: Calculate the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe.

[0079] Furthermore, the calculation of the real-time displacement of the water tank specifically includes:

[0080] Step C1: Calculate the mass of carbon dioxide, internal energy of carbon dioxide, and heat loss coefficient in the water tank based on the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe;

[0081] Step C2: Calculating the seawater flow rate in the drain pipe based on the mass of carbon dioxide in the water tank, the internal energy of carbon dioxide, and the heat loss coefficient;

[0082] Step C3: judging whether the iterative error is satisfied based on the seawater flow rate in the drainage pipe; if so, proceeding to step C4; if not, proceeding to step C2;

[0083] Step C4: Calculate the real-time displacement of the water tank.

[0084] 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, wherein the processor executes the computer program / instructions to implement the numerical modeling method of underwater expansion work of carbon dioxide or the numerical calculation method of underwater expansion work of carbon dioxide as described above.

[0085] Based on the same concept, the present application also provides a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the numerical modeling method for underwater expansion work of carbon dioxide or the numerical calculation method for underwater expansion work of carbon dioxide as described above is implemented.

[0086] Compared with the prior art, the advantages of the present invention are:

[0087] Compared with the traditional drainage calculation technology that uses the ideal gas model, the present invention uses the physical property model of real gas in the NIST (National Institute of Standards and Technology) database to characterize the thermodynamic properties of CO2, which has higher accuracy under high pressure and large temperature range; the present invention establishes a phase change drainage process model starting from the phase change tube excitation, which helps to realize the phase change drainage process of phase change drainage technology in actual application scenarios due to environmental changes, phase change tube parameter changes, and phase change tube excitation timing strategy changes. Rapid calculation and prediction, thereby improving the accuracy of drainage calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only one embodiment of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0089] Figure 1 2. It is a schematic structural diagram of a carbon dioxide underwater expansion device according to an embodiment of the present invention;

[0090] Figure 2 This is a flow chart of a numerical modeling method for the underwater expansion work of carbon dioxide in an embodiment of the present invention;

[0091] Figure 3 This is a CFD simulation model of the CO2 underwater expansion device in an embodiment of the present invention;

[0092] Figure 4 This is a cloud diagram of a phase change drainage CFD simulation process within 10 seconds in an embodiment of the present invention;

[0093] Figure 5 is the heat loss coefficient surface in the embodiment of the present invention;

[0094] Figure 6 This is a flow chart of a method for numerically calculating the work done by underwater expansion of carbon dioxide in an embodiment of the present invention.

[0095] Explanation of the reference numerals: 1-water tank, 11-drain pipe, 2-drain 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

[0096] The following is a clear and complete description of the technical solutions of the present invention in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0097] The following specific embodiments are used to describe the technical solution of the present application in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0098] Example 1

[0099] like Figure 1 As shown, the CO2 underwater expansion device includes a water tank 1 and a drainage mechanism 2. The drainage mechanism 2 includes an exhaust pipe 21, multiple CO2 phase change tubes 22, and an initial volume chamber 26. Each CO2 phase change tube 22 is connected to the initial volume chamber 26 via a valve 25, and the initial volume chamber 26 is connected to the water tank 1 via the exhaust pipe 21. The water outlet of the water tank 1 is connected to the drainage pipe 11. Each CO2 phase change tube 22 contains liquid CO2 23 and a reagent 24. The specific working process of the device is as follows: the reagent 24 in the phase change tube 22 burns under external electrical excitation and releases heat. This heat is absorbed by the liquid CO2 23, which undergoes a phase change and is released through the valve 25 into the initial volume chamber 26 for equalization and decompression. The high-pressure CO2 mixture in the initial volume chamber 26, after equalization and decompression, enters the water tank 1 through the exhaust pipe 21, displacing the water in the water tank 1 and being discharged through the drainage pipe 11.

[0100] like Figure 1 As shown, a numerical modeling method for underwater expansion work of carbon dioxide provided by an embodiment of the present invention includes the following steps:

[0101] Step S11: dividing the carbon dioxide phase change expansion work process into a waiting-for-excitation stage, a waiting-for-release stage, a release stage, and a release completion stage.

[0102] There are multiple phase change tubes, and the energy released by the combustion of the reagent in the phase change tubes needs to be accurately determined. In order to accurately calculate the changes in the thermodynamic parameters of the drainage mechanism and the displacement of the water tank of the carbon dioxide underwater expansion device, the carbon dioxide underwater expansion device is simplified into a carbon dioxide underwater expansion numerical model through numerical analysis methods, which specifically includes a phase change tube excitation model, an initial volume chamber equalization model, and a water tank extrusion model.

[0103] The low-temperature, low-pressure liquid carbon dioxide stored in the phase-change tube transforms into high-temperature, high-pressure supercritical carbon dioxide, which is then injected into the initial chamber through a valve to become supercritical or gaseous. To accurately calculate the real-time mass flow rate and energy curves within the phase-change tube during its activation, the process of carbon dioxide's phase change expansion and work within the tube is divided into the waiting phase (i.e., the stage where the reagent and liquid carbon dioxide are stored in the tube), the waiting phase (i.e., the stage where the reagent burns and the carbon dioxide is ready for release), the release phase (i.e., the stage where the reagent is activated to burn the carbon dioxide), and the end of release. Mathematical models for each phase are constructed.

[0104] Step S12: constructing a mathematical model for each stage based on the actual physical properties of carbon dioxide at each stage and the carbon dioxide phase change theory, thereby obtaining a phase change tube excitation model.

[0105] The real physical properties of carbon dioxide can be obtained by referencing the real physical property database of the National Institute of Standards and Technology (NIST) of the United States. The real physical property data can be obtained using the REFPROP software (or function) developed by NIST as an interface. That is, by using two intensity quantities (i.e., quantities whose properties are independent of the amount of substance, such as pressure, temperature, specific internal energy, specific enthalpy, density, etc.) and a specified substance symbol, REFPROP is used to query the corresponding other intensity quantities, namely:

[0106] (1)

[0107] in, 、 Represent the known thermodynamic physical property strength quantities, represents the intensity of other thermodynamic properties to be determined, Represents the REFPROP function, Indicates the symbol of matter.

[0108] In the waiting stage, carbon dioxide is stored in the phase change tube at room temperature and high density. According to the relevant parameters of the phase change tube at this stage, the pressure and specific internal energy of carbon dioxide in the phase change tube can be obtained by querying based on formula (1). Therefore, the mathematical model of the waiting stage is:

[0109] (2)

[0110] (3)

[0111] in, represents the pressure of carbon dioxide in the phase change tube during the exciting stage, represents the specific internal energy of carbon dioxide in the phase change tube during the exciting stage, represents the density of carbon dioxide in the phase change tube during the exciting stage, represents the temperature of carbon dioxide in the phase change tube during the exciting stage, It represents the mass of carbon dioxide in the phase change tube during the exciting stage. Indicates the volume of the phase change tube.

[0112] The agent in the phase change tube is ignited by the ignition current provided by the outside and begins to burn, releasing heat and combustion gas products into the phase change tube, entering the waiting release stage. Among them, the calculation formula for the instantaneous mass of the gas products and the instantaneous heat released during combustion is:

[0113] (4)

[0114] (5)

[0115] in, Indicates the instantaneous mass of the gas products during combustion, Indicates the instantaneous release of heat in the phase change tube during combustion. Indicates the axial burning velocity of the agent, Indicates the number of burning surfaces. Indicates the density of the agent during combustion (unit: kg / m 3 ), Indicates the cross-sectional area or combustion area of ​​the agent (unit: m 2 ), Indicates time, Indicates the calorific value of the agent during combustion (unit: kJ / m 3 After the agent is ignited, it burns along the axis. The surface where the burning moves after being ignited is the burning surface. For example, if the agent starts to burn from the middle, it will move from the middle point to both sides, and there will be two burning surfaces.

[0116] The calculation formula for the mass and internal energy in the phase change tube during the release phase is:

[0117] (6)

[0118] (7)

[0119] in, Indicates the mass of carbon dioxide in the phase change tube during the release phase, Indicates the ratio coefficient of the drug to gas (usually 0.6~0.7), represents the internal energy of carbon dioxide in the phase change tube during the release phase, represents the internal energy of carbon dioxide in the phase change tube during the exciting stage, Indicates the ratio of the exothermic absorption value of the agent (usually 0.6~0.95, which can be accurately calibrated through combustion tests ).

[0120] Axial burning velocity of the agent The Vieille burning rate law with a wide pressure application range is used, and the specific calculation formula is:

[0121] (8)

[0122] in, represents the empirical constant, n represents the burning rate pressure index, Indicates the pressure of carbon dioxide in the phase change tube during the release stage, Indicates the mass of the drug in the stage of waiting for excitation. , burning rate pressure index n All can be accurately calibrated through combustion tests. In the release stage, the density in the phase change tube , specific internal energy Increase, temperature and pressure Continuously improve, the calculation formula of density and specific internal energy is:

[0123] (9)

[0124] The density , specific internal energy As the intensity quantity, substitute it into formula (10) and query the temperature inside the phase change tube at this time through REFPROP and pressure :

[0125] (10)

[0126] The phase change tube is equipped with a diaphragm valve, which automatically opens when the pressure reaches the release pressure threshold. When the pressure inside 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 diaphragm valve opening time is less than 1 ms after experimental measurement, and the diaphragm valve opening process is completed instantaneously. The effective discharge area of ​​the diaphragm valve opening is set to , the calculation formula of the injection mass flow rate of the phase change tube is:

[0127] (11)

[0128] (12)

[0129] in, represents the injection mass flow rate of the phase change tube in the release stage, Indicates the flow correction coefficient, represents the pressure of carbon dioxide in the phase change tube during the release phase, represents the temperature of carbon dioxide in the phase change tube during the release phase, represents the gas constant, represents the specific heat ratio of carbon dioxide, Indicates the pressure in the initial chamber during the release phase (or the pressure at the end of the phase change tube). Represents Related constants. Flow correction factor The ratio of actual flow rate to theoretical flow rate can be selected within the range of 0.85 to 0.95 based on test results or experience. The mass in the phase change tube during the release phase is:

[0130] (13)

[0131] in, represents the mass of carbon dioxide in the phase change tube during the release phase. Assuming that the carbon dioxide injection is an isentropic flow, the internal energy of the phase change tube during the release phase 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:

[0132] (14)

[0133] in, represents the internal energy of carbon dioxide in the phase change tube during the release phase, Indicates the specific enthalpy of carbon dioxide in the phase change tube during the release phase (unit: kJ / kg, which can be queried using the REFPROP function). ,temperature You can query it by combining the REFPROP function with the intensity quantity:

[0134] (15)

[0135] (16)

[0136] in, represents the specific internal energy of carbon dioxide in the tube during the release phase, Indicates the density of carbon dioxide in the phase change tube during the release phase. and injection mass flow rate Calculate the energy discharged by the phase change tube during the release phase:

[0137] (17)

[0138] At the end of the release phase, the carbon dioxide pressure in the phase change tube and the pressure in the initial chamber reach a basic balance, and the flow rate approaches 0. The pressure in the initial chamber increases due to the stimulation of other phase change tubes, and carbon dioxide backflow occurs. Therefore, the mathematical model of the end of the release phase is:

[0139] (18)

[0140] (19)

[0141] (20)

[0142] (twenty one)

[0143] (twenty two)

[0144] (twenty three)

[0145] in, Indicates the energy discharged by the phase change tube at the end of the release phase. represents the specific enthalpy of carbon dioxide in the phase change tube at the end of release, Indicates the temperature of carbon dioxide in the phase change tube at the end of release, Indicates the pressure of carbon dioxide in the phase change tube at the end of release, Indicates the specific internal energy of carbon dioxide in the phase change tube at the end of release, Indicates the internal energy of carbon dioxide in the phase change tube at the end of release, Indicates the mass of carbon dioxide in the phase change tube at the end of release, represents the density of carbon dioxide in the phase change tube at the end of release, represents the injection mass flow rate of the phase change tube at the end of the release stage, It represents the specific enthalpy of the mass flowing out of the high pressure end, Indicates the pressure in the initial chamber at the end of the release phase. represents the specific enthalpy in the initial chamber at the end of the release phase, Indicates the pressure value at the high-pressure end of the valve between the phase change tube and the initial volume chamber. Indicates the pressure value at the low-pressure end of the valve between the phase change tube and the initial volume chamber. Indicates the temperature value of the high pressure end of the valve between the phase change tube and the initial volume chamber, Indicates the temperature inside the initial chamber at the end of release.

[0146] Step S13: constructing an initial volume chamber pressure equalization model according to the nozzle flow equation and uniform gas theory.

[0147] The primary chamber pressure equalization model is realized by the equation of carbon dioxide flowing into the primary chamber and the thermodynamic and fluid equations of the process in the primary chamber. The injection mass flow rate of carbon dioxide phase change expansion of a single phase change tube is calculated by the phase change tube excitation model. During the phase change drainage process, there are multiple phase change tubes injecting mass flow into the primary chamber, and each phase change tube starts phase change at a certain time interval to release carbon dioxide high-pressure mixed gas. Therefore, the inflow mass flow rate in the primary chamber is 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 energy discharged by multiple phase change tubes:

[0148] (twenty four)

[0149] in, It represents the total mass flow rate of multiple phase change tubes flowing into the initial volume chamber, It represents the total energy flowing into the initial volume chamber from multiple phase change tubes, Indicates the i The mass flow rate of a phase change tube in the release stage or the end of the release stage, Indicates the i The energy discharged by a phase change tube during the release stage or the end of the release stage.

[0150] There is a certain amount of air in the initial chamber. There is an exhaust pipe between the initial chamber and the water tank, and a one-way valve is installed. If the initial air pressure in the initial chamber is small, the gas in the initial chamber can be simplified to carbon dioxide. , initial chamber temperature and volume , through the REFPROP function query, the initial density of the initial volume chamber can be obtained , initial chamber specific energy and initial mass From this we can calculate the mass of the initial volume chamber and internal energy :

[0151] (25)

[0152] in, It represents the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe. It represents the energy discharged from the initial chamber through the exhaust pipe. represents the initial mass of carbon dioxide in the initial volume chamber, It represents the total mass flow rate of multiple phase change tubes flowing into the initial volume chamber, represents the initial specific internal energy of carbon dioxide in the initial volume, Represents the total energy flowing into the initial chamber from multiple phase change tubes.

[0153] From this, the pressure and temperature of the initial chamber can be calculated:

[0154] (26)

[0155] (27)

[0156] in, Indicates the temperature in the initial chamber. Indicates the pressure in the initial volume chamber. represents the specific enthalpy in the initial chamber, Represents the REFPROP function, represents the specific internal energy of carbon dioxide in the initial volume, It represents the density of carbon dioxide in the initial volume chamber. Indicates the quality of carbon dioxide in the initial volume. represents the initial chamber volume, It represents the internal energy of carbon dioxide in the initial chamber.

[0157] The carbon dioxide in the initial chamber flows out through the exhaust pipe. Following the flow equation of compressible fluid pipeline, the mass flow rate of carbon dioxide discharged from the exhaust pipe and the energy discharged from the exhaust pipe are obtained:

[0158] (28)

[0159] (29)

[0160] (30)

[0161] (31)

[0162] (32)

[0163] in, It represents the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe. Indicates the diameter of the exhaust pipe, represents the resistance coefficient of the exhaust pipe, represents the gas constant, Indicates the temperature in the initial chamber. Indicates the equivalent length, Indicates the pressure in the initial volume chamber. Indicates the pressure in the water tank. It represents the energy discharged from the initial chamber through the exhaust pipe. represents the specific enthalpy in the initial 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), Indicates the average density of carbon dioxide in the exhaust pipe, Represents the average viscosity of carbon dioxide in the exhaust pipe, Indicates the actual length of the exhaust pipe, Indicates inclusion Other drag coefficients, including It represents the resistance coefficient of the elbow.

[0164] and are all parameters related to the Reynolds number Re, which is related to the flow velocity, and the flow velocity is related to the mass flow rate. Therefore, in formula (28), it is actually impossible to directly calculate , but need to preset an initial Substitute it into the calculation to get a new iteration value, until the deviation between the current iteration result and the previous iteration result meets the iteration error, it can be considered as the calculation result. The resistance coefficient of the elbow in the pipe , valve resistance coefficient The sum of the converted equivalent length and the initial pipe length. Valve resistance coefficient According to experience or test, the resistance coefficient of the elbow is Calculate according to formula (32).

[0165] Step S14: Construct a water tank extrusion model based on heat transfer and thermodynamics theory and Bernoulli equation.

[0166] The water tank squeeze simulation is determined by the thermodynamic equations in the water tank and the drainage flow calculation equation. Assuming there is no energy loss in the exhaust pipe, the mass flow rate of carbon dioxide entering the water tank is ,energy The mass flow rate discharged from the initial volume chamber ,energy Equal. That is:

[0167] (33)

[0168] Mass of carbon dioxide entering the water tank for:

[0169] (34)

[0170] Total energy of carbon dioxide entering the water tank for:

[0171] (35)

[0172] Since the temperature of carbon dioxide is high, it will transfer heat in the water tank, causing the loss of carbon dioxide volume. The direction of heat transfer is: heat transfer to the seawater, and heat transfer to the water tank wall and other equipment in the water tank. The remaining energy constitutes the internal energy of carbon dioxide. and the propulsion power that drives the movement of seawater (i.e. the pushing work done by the carbon dioxide in the water tank), namely:

[0173] (36)

[0174] The driving force of drainage for:

[0175] (37)

[0176] In order to describe the heat loss in the water tank, the heat loss coefficient is defined as is the ratio of the current heat loss to the total energy entering the water tank:

[0177] (38)

[0178] The internal energy in the water tank system is for:

[0179] (39)

[0180] At the same time, the ratio of the effective energy change and the total energy change of the water tank per unit time is defined as the instantaneous heat loss ratio :

[0181] (40)

[0182] Therefore, the current pressure in the water tank is and temperature This can be queried using formula (41):

[0183] (41)

[0184] (42)

[0185] In formula (42), the volume of carbon dioxide in the water tank is is the real-time change, which is different from the current discharge volume The displacement needs to be calculated by the drainage flow equation (43) and substituted into formula (42), so 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 follows the transient form based on the Bernoulli equation:

[0186] (43)

[0187] in, Indicates the seawater flow rate in the drain pipe, represents the density of seawater, Indicates the length of the drain pipe, Indicates the pressure in the water tank. Indicates the water outlet pressure of the water tank, represents the acceleration due to gravity, Indicates the water level in the tank. Indicates the height of the drain pipe outlet. Indicates the friction coefficient of the drainage pipe (can be found in the manual or measured by experiment), Indicates the diameter of the drain pipe, Represents the local resistance coefficient of the drainage pipe (can be determined by consulting a hydraulic manual).

[0188] From formula (43), we can see that The solution must be obtained through iteration, so in actual calculation, an initial Substitute it into the calculation to get a new iteration value, until the deviation between the current iteration result and the previous iteration result meets the iteration error, it can be considered as the calculation result.

[0189] Through flow rate 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 for:

[0190] (44)

[0191] Since water can be considered as an incompressible fluid, the displacement The volume of carbon dioxide in the water tank equal:

[0192] (45)

[0193] Step S15: A numerical model of the underwater expansion work of carbon dioxide is constructed by the phase change tube excitation model, the initial volume chamber equalization model and the water tank extrusion model.

[0194] The heat loss coefficient can be calibrated by CFD (Computational Fluid Dynamics) or experimental mechanical energy. The CFD simulation model constructed when CFD is used for simulation calibration is as follows: Figure 3As shown in the figure, the CFD simulation model accurately describes the system, has an appropriate calculation scale, and uses reasonable parameter settings. Considering that CO2 underwater expansion devices are generally large in size and have a long duration (generally exceeding 10 seconds), a 2D rotational axisymmetric model is used for calculations. The process for determining several key dimensional parameters in the 2D rotational axisymmetric model is as follows:

[0195] Water tank equivalent diameter D1: Generally, water tanks are not cylindrical. In the model, the equivalent diameter of the water tank should be converted based on the actual water tank cross-sectional area.

[0196] Water tank height L1: The water tank height is the same as the distance from the top to the bottom outlet of the submersible water tank;

[0197] CO2 nozzle diameter d1: consistent with the design of the CO2 underwater expansion device. If a diversion is added, the diameter should be set to the equivalent diameter after the diversion;

[0198] CO2 nozzle positioning l1: consistent with the design of the CO2 underwater expansion device;

[0199] Water tank outlet diameter d2: consistent with the sea outlet size designed for the CO2 underwater expansion device;

[0200] Water tank outlet length l2: The calculated resistance should be consistent with the sum of the extended resistance and local resistance of the carbon dioxide underwater expansion device.

[0201] After verification and analysis, the 2D rotational axisymmetric model should be established and set up according to the following requirements. The values ​​in Table 1 can all be determined by the above formula.

[0202] Table 1 Requirements for the CFD simulation model of the CO2 underwater expansion device

[0203]

[0204] In Table 1, the calculation The depth range in which the submersible needs to work should be covered, and one working condition should be calculated every 50 to 100 meters. Figure 4 The following figure shows a 10s process cloud diagram of a phase change drainage CFD simulation, where the color band represents the temperature distribution of carbon dioxide in the water tank. Figure 4 The simulation results of all the unit pressure, temperature, volume, and volume fraction data at equal intervals are extracted as calibration basic parameters, and the effective heat Q of the carbon dioxide underwater expansion device at that moment is calculated according to the following formula: e calculate:

[0205] (46)

[0206] (47)

[0207] in, 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, Indicates the water surface pressure, which can be taken as the average pressure. Indicates the drainage volume.

[0208] With drainage depth-discharge volume as variables, the heat loss coefficient As the dependent variable, the surface relationship formula is established to obtain the heat loss coefficient Surface databases, such as Figure 5 As shown. The curve is combined with the established numerical model of carbon dioxide underwater expansion work, that is, in the water tank squeeze model, the water tank pressure is The value as a parameter , water tank displacement volume The value as a parameter Query the heat loss coefficient ,Right now , the expansion and drainage process can be calculated quickly and accurately.

[0209] The present invention proposes to use CFD simulation method to calculate the heat loss coefficient in the numerical model of carbon dioxide underwater expansion work The calculation can realize 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 the underwater expansion of carbon dioxide, the drainage prediction accuracy can be greatly corrected, and the precise control of drainage can be achieved.

[0210] Example 2

[0211] like Figure 6 As shown, a method for numerically calculating the work done by underwater expansion of carbon dioxide provided by an embodiment of the present invention includes the following steps:

[0212] Step S21: calling a numerical model of the underwater expansion work of carbon dioxide, which 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 for a waiting excitation stage, a mathematical model for a waiting release stage, a mathematical model for a release stage, and a mathematical model for a release completion stage. The numerical model of the underwater expansion work of carbon dioxide is constructed using the numerical modeling method for the underwater expansion work of carbon dioxide in Example 1 of the present application.

[0213] Step S22: Obtaining the carbon dioxide mass, volume, and carbon dioxide temperature of each phase change tube;

[0214] Step S23: Calculating the injection mass flow rate and discharged energy of the phase change tube according to the mass, volume, and temperature of carbon dioxide in each phase change tube and the phase change tube excitation model;

[0215] Step S24: Obtaining the initial mass, volume, and initial specific internal energy of carbon dioxide in the initial volume chamber;

[0216] Step S25: Calculating the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe based on the injection mass flow rate and discharged energy of the phase change tube, the initial mass and volume of carbon dioxide in the primary chamber, and the initial specific internal energy of carbon dioxide, as well as the primary chamber pressure equalization model;

[0217] Step S26: Obtaining the initial carbon dioxide volume, initial pressure, and initial water outlet pressure of the water tank;

[0218] Step S27: Calculate the real-time displacement of the water tank based on the mass flow and energy of carbon dioxide discharged from the initial volume chamber through the exhaust pipe, the initial carbon dioxide volume, initial pressure and initial outlet pressure of the water tank, and the water tank extrusion model.

[0219] In a specific embodiment of the present invention, the calculation of the injection mass flow rate and the discharged energy of the phase change tube specifically includes:

[0220] Step A1: For each phase change tube i, determine whether the start time of the phase change tube has been reached. If so, the phase change tube enters the waiting release stage and proceeds to step A2; if not, the phase change tube is in the waiting excitation stage, and the injection mass flow rate of the phase change tube is and the energy discharged All are 0;

[0221] Step A2: Calculate the carbon dioxide temperature of the phase change tube according to formula (4) to formula (10) in Example 1 of this application and carbon dioxide pressure ;

[0222] Step A3: Determine the carbon dioxide pressure Is it greater than the release pressure threshold? If so, the phase change tube enters the release stage and goes to step A4; if not, the phase change tube is in the waiting release stage, and the injection mass flow rate of the phase change tube is and the energy discharged All are 0;

[0223] Step A4: Calculate the injection mass flow rate of the phase change tube according to formula (11) to formula (17) in Example 1 of the present application ( ) and the energy discharged ( );

[0224] Step A5: Determine the carbon dioxide pressure of the phase change tube during the release phase Is it equal to the pressure of the initial chamber during the release phase? If yes, the phase change tube enters the release end stage and goes to step A6; if no, the phase change tube is in the release stage and goes to step A4;

[0225] Step A6: Calculate the injection mass flow rate of the phase change tube according to formula (18) to formula (23) in Example 1 of the present application ( ) and the energy discharged ( ).

[0226] In a specific embodiment of the present invention, calculating the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe specifically includes:

[0227] Step B1: Based on formula (24) to formula (25) in Example 1 of the present application, according to the injection mass flow rate of each phase change tube and the energy discharged , calculate the mass of carbon dioxide in the initial chamber and carbon dioxide internal energy ;

[0228] Step B2: Based on formula (26) to formula (27) in Example 1 of this application, according to the mass of carbon dioxide in the initial chamber and carbon dioxide internal energy Determine the temperature in the initial chamber and pressure ;

[0229] Step B3: Determine the pressure in the initial volume chamber Is it greater than the pressure in the water tank? If yes, go to step B4; if no, the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe is and energy All are 0;

[0230] Step B4: Calculate the average velocity of carbon dioxide in the exhaust pipe of the primary chamber ;

[0231] Step B5: Based on the average velocity of carbon dioxide in the exhaust pipe of the primary chamber Determine whether the iteration error is satisfied. If so, proceed to step B6; if not, proceed to step B4;

[0232] Step B6: Based on formula (28) to formula (32) in Example 1 of the present application, calculate the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe and energy .

[0233] In this embodiment, the iteration error is set to 1%.

[0234] In a specific embodiment of the present invention, calculating the real-time displacement of the water tank specifically includes:

[0235] Step C1: Based on formula (33) to formula (39) in Example 1 of the present application, according to the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe and energy , calculate the mass of carbon dioxide in the water tank 、CO2 internal energy and heat loss coefficient ;

[0236] Step C2: Based on formula (41) to formula (43) in Example 1 of this application, according to the carbon dioxide mass and carbon dioxide internal energy in the water tank and heat loss coefficient , calculate the seawater flow rate in the drain pipe ;

[0237] Step C3: Based on the flow rate of seawater in the drain pipe Determine whether the iteration error is satisfied. If so, proceed to step C4; if not, proceed to step C2;

[0238] Step C4: Calculate the real-time displacement of the water tank based on formula (44) to formula (45) in Example 1 of this application .

[0239] Example 3

[0240] An embodiment of the present application also provides an electronic device, which includes: a memory, a processor, and a computer program / instructions stored on the memory, and the processor executes the computer program / instructions to implement the numerical modeling method or the numerical calculation method of the underwater expansion work of carbon dioxide in the embodiment of the present application.

[0241] Although not shown, the electronic device includes a processor that can perform various appropriate operations and processes based on programs and / or data stored in a read-only memory (ROM) or programs and / or data loaded from a storage portion into a 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-purpose main processor and one or more special coprocessors, such as a central processing unit, a graphics processing unit (GPU), a neural network processor (NPU), a digital signal processor (DSP), etc. Various programs and data required for device operation are also stored in the RAM. The processor, ROM, and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0242] The processor and memory are used together to execute the program / instructions stored in the memory. When the program / instructions are executed by the computer, the methods, steps or functions described in the above embodiments can be implemented.

[0243] Although not shown, an embodiment of the present application also provides a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the numerical modeling method for the underwater expansion work of carbon dioxide or the numerical calculation method for the underwater expansion work of carbon dioxide in the embodiment of the present application is implemented.

[0244] Computer-readable storage media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. 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 technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0245] The above disclosure is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of changes or modifications within the technical scope disclosed in the present invention, and they should all be covered by the scope of protection of the present invention.

Claims

1. A numerical modeling method for underwater expansion of carbon dioxide, wherein the underwater expansion device of carbon dioxide includes a water tank and a drainage mechanism, wherein the drainage mechanism includes an exhaust pipe, a plurality of carbon dioxide phase change tubes and an initial volume chamber; each of the carbon dioxide phase change tubes 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 the drainage pipe, and each of the carbon dioxide phase change tubes is filled with liquid carbon dioxide and a reagent; characterized in that The modeling method comprises: The carbon dioxide phase change expansion process is divided into the waiting stage, the waiting stage, the release stage and the end of release stage. According to the real physical properties of carbon dioxide in each stage and the carbon dioxide phase change theory, a mathematical model of each stage is constructed, and then a phase change tube excitation model is obtained; The initial volume chamber pressure equalization model is constructed based on the nozzle flow equation and uniform gas theory; Construct a water tank extrusion model based on heat transfer and thermodynamics theory and Bernoulli equation; The phase change tube excitation model, the initial volume chamber pressure equalization model and the water tank extrusion model constitute a numerical model of the underwater expansion work of carbon dioxide; Wherein, the water tank extrusion model is: ； ； ； ； ， ， ； ， ， ， ； in, Indicates the displacement of the water tank, represents the real-time drainage flow of the water tank, t represents time, Indicates the seawater flow rate in the drain pipe, Indicates the cross-sectional area of ​​the drain valve on the drain pipe. represents the density of seawater, Indicates the length of the drain pipe, Indicates the pressure in the water tank. Indicates the water outlet pressure of the water tank, represents the acceleration due to gravity, Indicates the water level in the tank. Indicates the height of the drain pipe outlet. represents the friction coefficient of the drainage pipe, Indicates the diameter of the drain pipe, represents the local resistance coefficient of the drainage pipe, Indicates the temperature of carbon dioxide in the water tank, Represents the REFPROP function, represents the specific internal energy of carbon dioxide in the water tank, represents the density of carbon dioxide in the water tank, Indicates the mass of carbon dioxide in the water tank, Indicates the volume of carbon dioxide in the water tank, represents the internal energy of carbon dioxide in the water tank, represents the heat loss coefficient, Indicates the total energy of carbon dioxide entering the water tank, Indicates the concentration of carbon dioxide in the water tank i Heat loss, is the pushing work done by the carbon dioxide in the water tank, represents the carbon dioxide energy at the water tank inlet, represents the mass flow rate of carbon dioxide at the water tank inlet, It represents the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe. It indicates the energy discharged from the primary chamber through the exhaust pipe.

2. The numerical modeling method for underwater expansion of carbon dioxide according to claim 1, characterized in that: The phase change tube excitation model includes a mathematical model of the waiting-for-excitation stage, a mathematical model of the waiting-for-release stage, a mathematical model of the release stage, and a mathematical model of the release end stage; The mathematical model of the waiting stage is: ； ； in, represents the pressure of carbon dioxide in the phase change tube during the exciting stage, represents the specific internal energy of carbon dioxide in the phase change tube during the exciting stage, represents the density of carbon dioxide in the phase change tube during the exciting stage, represents the temperature of carbon dioxide in the phase change tube during the exciting stage, It represents the mass of carbon dioxide in the phase change tube during the exciting stage. represents the volume of the phase change tube, Represents the REFPROP function; The mathematical model of the waiting-for-release stage is: ； ； ， ， ； ， ； in, Indicates the temperature of carbon dioxide in the phase change tube during the release stage, Indicates the pressure of carbon dioxide in the phase change tube during the release stage, represents the specific internal energy of carbon dioxide in the phase change tube during the release stage, Indicates the density of carbon dioxide in the phase change tube during the release phase. represents the internal energy of carbon dioxide in the phase change tube during the release phase, Indicates the mass of carbon dioxide in the phase change tube during the release phase, Indicates the proportional coefficient of the conversion of the agent into gas, Indicates the instantaneous mass of the gas products during combustion, represents the internal energy of carbon dioxide in the phase change tube during the exciting stage, Indicates the ratio of the exothermic absorption value of the agent, Indicates the instantaneous release of heat in the phase change tube during combustion. Indicates the axial burning velocity of the agent, represents the empirical constant, n represents the burning rate pressure index, Indicates the quality of the drug in the stage of waiting for excitation, Indicates the number of burning surfaces. Indicates the density of the agent during combustion. Indicates the cross-sectional area or combustion area of ​​the agent, Indicates time, Indicates the calorific value of the agent when burning; The mathematical model of the release phase is: ； ； ； ， ； ； ； in, Indicates the energy discharged by the phase change tube during the release phase, represents the specific enthalpy of carbon dioxide in the tube during the phase change of the tube during the release phase, represents the temperature of carbon dioxide in the phase change tube during the release phase, represents the pressure of carbon dioxide in the phase change tube during the release phase, represents the specific internal energy of carbon dioxide in the tube during the release phase, represents the density of carbon dioxide in the phase change tube during the release phase, represents the internal energy of carbon dioxide in the phase change tube during the release phase, represents the mass of carbon dioxide in the phase change tube during the release phase, represents the injection mass flow rate of the phase change tube in the release stage, Indicates the flow correction coefficient, Indicates 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, Indicates the pressure in the initial chamber during the release phase. Represents Related constants; The mathematical model of the release end stage is: ； ； ； ， ； ， ， ； ； in, Indicates the energy discharged by the phase change tube at the end of the release phase. represents the specific enthalpy of carbon dioxide in the phase change tube at the end of release, Indicates the temperature of carbon dioxide in the phase change tube at the end of release, Indicates the pressure of carbon dioxide in the phase change tube at the end of release, Indicates the specific internal energy of carbon dioxide in the phase change tube at the end of release, Indicates the internal energy of carbon dioxide in the phase change tube at the end of release, Indicates the mass of carbon dioxide in the phase change tube at the end of release, represents the density of carbon dioxide in the phase change tube at the end of release, represents the injection mass flow rate of the phase change tube at the end of the release stage, It represents the specific enthalpy of the mass flowing out of the high pressure end, Indicates the pressure in the initial chamber at the end of the release phase. represents the specific enthalpy in the initial chamber at the end of the release phase, Indicates the pressure value at the high-pressure end of the valve between the phase change tube and the initial volume chamber. Indicates the pressure value at the low-pressure end of the valve between the phase change tube and the initial volume chamber. Indicates the temperature value of the high pressure end of the valve between the phase change tube and the initial volume chamber, Indicates the temperature inside the initial chamber at the end of release.

3. The numerical modeling method for underwater expansion of carbon dioxide according to claim 1, characterized in that: The initial volume chamber pressure equalization model is: ； ； ； ； ， ； ； ， ， ； ； ； in, It represents the mass flow rate of carbon dioxide discharged from the initial chamber through the exhaust pipe. Indicates the diameter of the exhaust pipe, represents the resistance coefficient of the exhaust pipe, represents the gas constant, Indicates the temperature in the initial chamber. Indicates the equivalent length, Indicates the pressure in the initial volume chamber. Indicates the pressure in the water tank. It represents the energy discharged from the initial chamber through the exhaust pipe. represents the specific enthalpy in the initial chamber, Represents the REFPROP function, represents the specific internal energy of carbon dioxide in the initial volume, It represents the density of carbon dioxide in the initial volume chamber. Indicates the quality of carbon dioxide in the initial volume. represents the volume of the initial chamber, represents the internal energy of carbon dioxide in the initial volume, represents the initial mass of carbon dioxide in the initial volume chamber, It represents the total mass flow rate of multiple phase change tubes flowing into the initial volume chamber, represents the initial specific internal energy of carbon dioxide in the initial volume, It represents the total energy flowing into the initial volume chamber from multiple phase change tubes, Indicates the i The mass flow rate of a phase change tube in the release stage or the end of the release stage, Indicates the i The energy discharged by a phase change tube during the release stage or the end of the release stage is represents the Reynolds number, represents the average velocity of carbon dioxide in the exhaust pipe, Indicates the average density of carbon dioxide in the exhaust pipe, Represents the average viscosity of carbon dioxide in the exhaust pipe, Indicates the actual length of the exhaust pipe, Indicates inclusion Other drag coefficients, including represents the resistance coefficient of the elbow, t Indicates time.

4. A numerical calculation method for the work done by underwater expansion of carbon dioxide, characterized in that: The calculation method includes: Invoking a numerical model of the underwater expansion work of carbon dioxide, the numerical model comprising 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 comprising a mathematical model for a waiting excitation stage, a mathematical model for a waiting release stage, a mathematical model for a release stage, and a mathematical model for a release completion stage; wherein the numerical model of the underwater expansion work of carbon dioxide is constructed using the numerical modeling method for the underwater expansion work of carbon dioxide according to any one of claims 1 to 3; Obtain the carbon dioxide mass, volume and carbon dioxide temperature of each phase change tube; The injection mass flow rate and discharged energy of the phase change tube are calculated based on the carbon dioxide mass, volume and carbon dioxide temperature of each phase change tube and the phase change tube excitation model; Obtain the initial mass, volume and initial specific internal energy of carbon dioxide in the initial volume chamber; Calculating the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe based on the injection mass flow rate and discharged energy of the phase change tube, the initial mass, volume and initial specific internal energy of carbon dioxide in the primary chamber, and the primary chamber pressure equalization model; Obtain the initial carbon dioxide volume, initial pressure, and initial water outlet pressure of the water tank; The real-time displacement of the water tank is calculated based on the mass flow and energy of carbon dioxide 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 water outlet pressure, and the water tank extrusion model.

5. The numerical calculation method for the underwater expansion work of carbon dioxide according to claim 4 is characterized in that: 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 has been reached. If so, the phase change tube enters the waiting release stage and proceeds to step A2. If not, the phase change tube is in the waiting excitation stage, and the injection mass flow rate and discharged energy of the phase change tube are both zero. Step A2: calculating the carbon dioxide temperature and carbon dioxide pressure of the phase change tube according to the mathematical model of the waiting-for-release 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 stage, and the injection mass flow rate and discharged energy of the phase change tube are both 0. Step A4: calculating the injection mass flow rate and discharged energy of the phase change tube according to the mathematical model of 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 chamber in the release stage. If so, the phase change tube enters the release end stage and the process proceeds to step A6; if not, the phase change tube is in the release stage and the process proceeds to step A4; Step A6: Calculating the injection mass flow rate and discharged energy of the phase change tube according to the mathematical model of the release end stage.

6. The numerical calculation method for the underwater expansion work of carbon dioxide according to claim 4, characterized in that: The calculation of the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe specifically includes: Step B1: Calculate the mass and internal energy of carbon dioxide in the initial chamber based on the injection mass flow rate and exhaust energy of each phase change tube; Step B2: determining the temperature and pressure in the primary chamber according to the mass and internal energy of carbon dioxide in the primary chamber; Step B3: Determine whether the pressure in the primary 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 carbon dioxide discharged from the primary chamber through the exhaust pipe are both 0; Step B4: Calculate the average velocity of carbon dioxide in the exhaust pipe of the primary chamber; Step B5: judging whether the average velocity of carbon dioxide in the exhaust pipe of the primary chamber satisfies the iteration error, if so, proceeding to step B6; if not, proceeding to step B4; Step B6: Calculate the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe.

7. The method for numerically calculating the work done by underwater expansion of carbon dioxide according to claim 4, characterized in that: The calculation of the real-time displacement of the water tank specifically includes: Step C1: Calculate the mass of carbon dioxide, internal energy of carbon dioxide, and heat loss coefficient in the water tank based on the mass flow rate and energy of carbon dioxide discharged from the primary chamber through the exhaust pipe; Step C2: Calculating the seawater flow rate in the drain pipe based on the mass of carbon dioxide in the water tank, the internal energy of carbon dioxide, and the heat loss coefficient; Step C3: judging whether the iterative error is satisfied based on the seawater flow rate in the drainage pipe; if so, proceeding to step C4; if not, proceeding to step C2; Step C4: Calculate the real-time displacement of the water tank.

8. An electronic device comprising a memory, a processor, and a computer program / instruction stored in the memory, characterized in that: The processor executes the computer program / instruction to implement the numerical modeling method for underwater expansion work of carbon dioxide according to any one of claims 1 to 3 or the numerical calculation method for underwater expansion work of carbon dioxide according to any one of claims 4 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the method for numerical modeling of the underwater expansion work of carbon dioxide according to any one of claims 1 to 3 or the method for numerical calculation of the underwater expansion work of carbon dioxide according to any one of claims 4 to 7 is implemented.

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