Modeling method, calculation method, device, storage medium and product

Abstract

The present invention discloses a modeling method, a calculation method, a device, a storage medium and a product. The modeling method includes dividing a gas storage tank into a liquid phase region, a gas phase region, a liquid phase side wall surface and a gas phase side wall surface according to the form of carbon dioxide in the gas storage tank; respectively constructing carbon dioxide mathematical models for the liquid phase region, the gas phase region, the liquid phase side wall surface and the gas phase side wall surface according to the principles of mass conservation and energy conservation. The carbon dioxide mathematical model constructed according to the present invention can well predict the changes of carbon dioxide supply parameters during the self-pressurizing supply process, has better prediction accuracy, and avoids the problem that for different test devices and different supply media, it is necessary to calibrate the coefficient k through experiments.

Description

Technical Field

[0001] The present invention belongs to the technical field of modeling and simulation, and particularly relates to a carbon dioxide self-pressurizing supply modeling method, calculation method, device, storage medium and product. Background Art

[0002] Carbon dioxide has the characteristics of stability, low cost, non-toxicity, pollution-free, etc., and is used as a cooling medium to cool high-temperature components, playing a crucial role in the thermal protection effect of high-temperature components. The supply pressure and physical properties such as temperature of carbon dioxide are affected by the carbon dioxide supply system. To predict the performance of the supply system, it is necessary to accurately model the supply process.

[0003] According to different driving methods, the carbon dioxide supply system can be divided into a pump-pressurized type and an extrusion type. The pump-pressurized carbon dioxide supply system relies on a pump to push carbon dioxide to flow, and requires a power source during operation, increasing the complexity of the system. According to whether the supply pressure is constant, the extrusion type carbon dioxide supply system can be further divided into a high-pressure gas extrusion supply system and a self-pressurizing supply system. The high-pressure gas extrusion supply system extrudes carbon dioxide through high-pressure gas to maintain a constant carbon dioxide pressure, but requires a high-pressure gas cylinder to be configured, resulting in an increase in system cost and weight. In the self-pressurizing supply system, the pressure of carbon dioxide will gradually decrease. Once the pressure is lower than the saturated vapor pressure, part of the liquid will vaporize, and the resulting vapor will compensate for the carbon dioxide pressure to keep its pressure relatively stable. The self-pressurizing supply system has a simple and reliable structure, but during the supply process, the physical parameters of carbon dioxide will change. Therefore, to master the performance of the self-pressurizing supply system, it is necessary to accurately model the self-pressurizing supply system.

[0004] The more widely used self-pressurizing supply model is the model established by Zilliac and Karabeyoglu (hereinafter briefly referred to as the ZK model). The ZK model divides carbon dioxide into three regions: a liquid phase region, a gas phase region, and a saturated thin layer region. The heat and mass transfer processes in the liquid phase region and the gas phase region are carried out through the thin layer, and it is assumed that the vapor mass is equal to the ratio of the net absorbed heat of the thin layer to the latent heat of vaporization of carbon dioxide. In order to make the calculated value of the ZK model coincide with the test result, the gas generation mass needs to be multiplied by a coefficient k. For different test devices and different supply media, the coefficient k needs to be calibrated through experiments.

[0005] Zimmerman et al. conducted self-pressurizing supply experiments and found that phase change not only occurs on the gas-liquid surface, but also during the self-pressurizing supply process, intense boiling occurs inside the liquid. The assumption of the vapor mass by Zilliac et al. is inconsistent with the experimental phenomenon of Zimmerman. For the self-pressurizing supply system, it is necessary to correctly simulate the mass transfer rate from the liquid phase region to the gas phase region in order to obtain a reasonable prediction of the supply pressure. Therefore, it is necessary to establish a new model to characterize the vapor mass. Summary of the Invention

[0006] The object of the present invention is to provide a modeling method, a calculation method, a device, a storage medium and a product, so as to solve the problem that in the traditional ZK model, for different test devices and different supply media, the coefficient k needs to be obtained through experimental calibration, and the complex calibration process leads to complex calculation of the ZK model.

[0007] The present invention solves the above technical problems through the following technical solutions: A carbon dioxide self-pressurizing supply modeling method, the modeling method includes:

[0008] Dividing the gas storage tank into a liquid phase region, a gas phase region, a liquid phase side wall surface and a gas phase side wall surface according to the state of carbon dioxide in the gas storage tank;

[0009] According to the principles of mass conservation and energy conservation, respectively constructing carbon dioxide mathematical models for the liquid phase region, the gas phase region, the liquid phase side wall surface and the gas phase side wall surface; wherein, the carbon dioxide mathematical model of the liquid phase region is:

[0010] ;

[0011] , ;

[0012] , ;

[0013] , ;

[0014] wherein, m l , ρ l , u l , P l and V l respectively represent the mass, density, specific internal energy, pressure and volume of liquid carbon dioxide, t represents the supply time, dt represents the supply time increment, d(m l u l ) represents the increment of the internal energy of liquid carbon dioxide within the supply time increment dt, m vap represents the vapor mass flow rate, m outlet represents the supply mass flow rate, h l represents the specific enthalpy of liquid carbon dioxide, h' g represents the specific enthalpy of saturated gas, Q wl represents the heat flow between the liquid phase side wall surface and the liquid phase region, Q lg represents the heat flow between the gas phase region and the liquid phase region, P g , V g respectively represent the pressure and volume of gaseous carbon dioxide, dV grepresents the volume increment of gaseous carbon dioxide within the supply time increment dt, f( ) represents the Span-Wagner equation of state, x represents the dryness of carbon dioxide, and A wl represents the contact area between the liquid-phase sidewall and liquid carbon dioxide, and b wl represents the heat transfer coefficient between the liquid-phase sidewall and liquid carbon dioxide, and T wl represents the temperature of the liquid-phase sidewall, and T l represents the temperature of the liquid-phase region, and A gl represents the contact area between gaseous carbon dioxide and liquid carbon dioxide, and b gl represents the heat transfer coefficient between gaseous carbon dioxide and liquid carbon dioxide, and T g represents the temperature of the gas-phase region;

[0015] The mathematical model of carbon dioxide in the gas-phase region is:

[0016] ;

[0017] , , ;

[0018] where m g , ρ g and u g respectively represent the mass, density, and specific internal energy of gaseous carbon dioxide, d(m g u g ) represents the increment of the internal energy of gaseous carbon dioxide within the supply time increment dt, Q wg represents the heat flux between the gas-phase sidewall and the gas-phase region, and A wg represents the contact area between the gas-phase sidewall and gaseous carbon dioxide, and b wg represents the heat transfer coefficient between the gas-phase sidewall and gaseous carbon dioxide, and T wg represents the temperature of the gas-phase sidewall;

[0019] The mathematical model of carbon dioxide on the liquid-phase sidewall is:

[0020] ;

[0021] where m sl represents the mass of the liquid-phase sidewall, c p represents the specific heat capacity of the solid wall, and dT wl represents the increment of the temperature of the liquid-phase sidewall within the supply time increment dt;

[0022] The mathematical model of carbon dioxide on the gas-phase sidewall is:

[0023] ;

[0024] where msg represents the mass of the gas-phase sidewall, dT wg represents the temperature increment of the gas-phase sidewall within the supply time increment dt.

[0025] Furthermore, the vapor mass flow rate m vap is calculated by the formula:

[0026] ;

[0027] wherein, dt represents the supply time increment.

[0028] Furthermore, the heat transfer coefficient b between the liquid-phase sidewall and liquid carbon dioxide, wl the heat transfer coefficient b between gaseous carbon dioxide and liquid carbon dioxide, gl and the heat transfer coefficient b between the gas-phase sidewall and gaseous carbon dioxide wg are solved according to the natural convection formula.

[0029] Based on the same concept, the present invention provides a method for calculating carbon dioxide self-pressurization supply parameters, including:

[0030] Step S1: Obtain the pressure P of liquid carbon dioxide when the carbon dioxide in the gas storage tank is all in liquid state l and the mass m l , the supply mass flow rate m outlet , the volume V of the gas storage tank, the height H of the gas storage tank, the inner diameter D of the gas storage tank, the mass m of the gas storage tank s and the specific heat capacity c of the solid wall p ;

[0031] Step S2: Calculate the temperature T of the liquid phase region l , the temperature T of the liquid-phase sidewall l , the density ρ of liquid carbon dioxide outlet , the specific internal energy u s and the specific enthalpy h p according to the pressure P of liquid carbon dioxide l , the mass m wl , the supply mass flow rate m l , the volume V of the gas storage tank, the height H of the gas storage tank, the inner diameter D of the gas storage tank, the mass m of the gas storage tank l and the specific heat capacity c of the solid wall l ;

[0032] Step S3: Calculate the pressure P of liquid carbon dioxide l , the temperature T of the liquid phase region l , the temperature T of the liquid-phase sidewall wl , the density ρ of liquid carbon dioxide l , the specific internal energy u land specific enthalpy h l 、carbon dioxide dryness x, and the heat flux Q between the liquid-phase side wall and the liquid phase region wl ;

[0033] Step S4: Determine whether the carbon dioxide dryness x is greater than 0 and less than 1. If not, increase the supply time t and transfer to Step S3; if so, transfer to Step S5;

[0034] Step S5: Calculate the heat flux Q between the liquid-phase side wall and the liquid phase region according to the carbon dioxide mathematical models of the liquid phase region, gas phase region, liquid-phase side wall, and gas-phase side wall in the carbon dioxide self-pressurization supply modeling method described above wl 、the heat flux Q between the gas-phase side wall and the gas phase region wg 、the heat flux Q between the gas phase region and the liquid phase region lg 、the liquid-phase side wall temperature T wl 、the gas-phase side wall temperature T wg ;

[0035] Step S6: Calculate the density ρ of the liquid carbon dioxide l 、specific internal energy u l 、pressure P l 、mass m l and volume V l 、the liquid phase region temperature T l 、vapor mass flow rate m vap 、specific enthalpy h' of the saturated gas g 、carbon dioxide dryness x, mass m of the gaseous carbon dioxide g 、density ρ g 、specific internal energy u g 、pressure P g and volume V g 、the gas phase region temperature T g 、height H of the liquid phase region l 、height H of the gas phase region g ;

[0036] Step S7: Determine whether the pressure P of the gaseous carbon dioxide g is less than or equal to the pressure P of the liquid carbon dioxide l , if not, increase the volume V of the gaseous carbon dioxide g and transfer to Step S8; if so, update the mass m of the liquid carbon dioxide l and transfer to Step S9;

[0037] Step S8: Calculate the density ρ of the liquid carbon dioxide l 、specific internal energy u l 、pressure P l and volume V l 、the liquid phase region temperature T l 、density ρg , specific internal energy u g , pressure P g and volume V g , temperature T in the gas phase region g , height H in the liquid phase region l , height H in the gas phase region g , and proceed to step S7;

[0038] Step S9: Determine whether the mass m of liquid carbon dioxide l is less than or equal to 0. If so, complete the calculation of the carbon dioxide self - pressurization supply parameters. If not, increase the supply time t and proceed to step S5.

[0039] Furthermore, in step S3, when the carbon dioxide in the gas storage tank is all in liquid state, the mathematical model of carbon dioxide in the liquid phase region is:

[0040] ;

[0041] , , ;

[0042] The mathematical model of carbon dioxide on the side wall of the liquid phase is:

[0043] ;

[0044] where f( ) represents the Span - Wagner equation of state, dt represents the supply time increment, d(m l u l ) represents the internal energy increment of liquid carbon dioxide within the supply time increment dt, and dT wl represents the temperature increment of the side wall of the liquid phase within the supply time increment dt.

[0045] Furthermore, in step S8, the update formula for the mass m of liquid carbon dioxide l is:

[0046] ;

[0047] where m' l represents the updated mass of liquid carbon dioxide, and m l represents the mass of liquid carbon dioxide before update.

[0048] Based on the same concept, the present invention 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 carbon dioxide self - pressurization supply modeling method or the carbon dioxide self - pressurization supply parameter calculation method as described above.

[0049] Based on the same concept, the present invention further provides a computer-readable storage medium, on which a computer program / instructions are stored, and when the computer program / instructions are executed by a processor, the carbon dioxide self-pressurizing supply modeling method or the carbon dioxide self-pressurizing supply parameter calculation method as described above is implemented.

[0050] Based on the same concept, the present invention further provides a computer program product, including a computer program / instructions, and when the computer program / instructions are executed by a processor, the carbon dioxide self-pressurizing supply modeling method or the carbon dioxide self-pressurizing supply parameter calculation method as described above is implemented.

[0051] Compared with the prior art, the advantages of the present invention are as follows:

[0052] The carbon dioxide self-pressurizing supply modeling method provided by the present invention does not require experimental calibration of the coefficient k for different test devices and different supply media, avoiding the calibration of the coefficient k and simplifying the calculation of carbon dioxide self-pressurizing supply parameters; at the same time, the carbon dioxide mathematical model constructed according to the present invention can well predict the changes in carbon dioxide supply parameters during the self-pressurizing supply process, indicating that the carbon dioxide mathematical model constructed by the present invention has good prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] 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 without creative efforts based on these drawings.

[0054] Figure 1 is a schematic diagram of the division of the gas storage tank in the embodiment of the present invention;

[0055] Figure 2 is a schematic diagram of energy and mass transfer between different zones in the embodiment of the present invention;

[0056] Figure 3 is a schematic diagram of mass transfer between liquid carbon dioxide and gaseous carbon dioxide in the embodiment of the present invention;

[0057] Figure 4 is a schematic diagram of the principle of the carbon dioxide self-pressurizing supply test system in the embodiment of the present invention;

[0058] Figure 5 is a comparison diagram of the test results of test condition 1 in the embodiment of the present invention and the simulation results obtained by using the carbon dioxide mathematical model constructed by the present invention;

[0059] Figure 6It is a comparison diagram of the test results of test condition 2 in the embodiments of the present invention and the simulation results obtained by using the carbon dioxide mathematical model constructed by the present invention;

[0060] Figure 7 It is a comparison diagram of the test results of test condition 3 in the embodiments of the present invention and the simulation results obtained by using the carbon dioxide mathematical model constructed by the present invention;

[0061] Figure 8 It is a flowchart of the carbon dioxide self-pressurizing supply parameter calculation method in the embodiments of the present invention, where t' represents the updated supply time, and V' g represents the updated volume of gaseous carbon dioxide. Specific Embodiments

[0062] The following combines the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0063] The following uses specific embodiments to elaborate on the technical solutions of the present application in detail. These several specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.

[0064] Embodiment 1

[0065] A carbon dioxide self-pressurizing supply modeling method provided by an embodiment of the present invention includes the following steps:

[0066] Step A1: Divide the carbon dioxide storage tank into a liquid phase region, a gas phase region, a liquid phase side wall surface, and a gas phase side wall surface according to the state of carbon dioxide in the storage tank;

[0067] Step A2: Construct carbon dioxide mathematical models for the liquid phase region, the gas phase region, the liquid phase side wall surface, and the gas phase side wall surface respectively according to the principles of mass conservation and energy conservation.

[0068] As Figure 1 shown, the carbon dioxide storage tank is divided into a liquid phase region, a gas phase region, a liquid phase side wall surface, and a gas phase side wall surface, and each region is an independent control volume. The present invention considers the influence of side wall heat transfer on the carbon dioxide pressure, making the constructed carbon dioxide mathematical model more accurate.

[0069] For the convenience of calculation, it is assumed that the carbon dioxide fluid is evenly distributed, and the temperature at each point in the gas phase region or the liquid phase region is the same; only the heat transfer between different phases is considered, and the heat transfer within the phase is not considered. In addition, all heat transfer calculations in the storage tank are based on the natural convection mechanism.

[0070] Meanwhile, the outer layer of the gas storage tank is wound with heat insulation material. Therefore, heat exchange between the gas storage tank and the environment is not considered during the modeling process. In addition, the supplied carbon dioxide flow rate is low, so it can be considered that the pressure of the liquid carbon dioxide in the gas storage tank is the same as that of the gaseous carbon dioxide.

[0071] Figure 2 Shows the energy and mass transfer processes between different zones, m vap Represents the vapor mass flow rate, m outlet Represents the supplied mass flow rate, Q wl Represents the heat flow rate between the liquid-phase side wall and the liquid-phase zone, Q lg Represents the heat flow rate between the gas-phase zone and the liquid-phase zone, Q wg Represents the heat flow rate between the gas-phase side wall and the gas-phase zone, T wl Represents the liquid-phase side wall temperature, T l Represents the liquid-phase zone temperature, T wg Represents the gas-phase side wall temperature, T g Represents the gas-phase zone temperature, H g 、H l Represent the height of the gas-phase side wall (or the height of the gas-phase zone) and the height of the liquid-phase side wall (or the height of the liquid-phase zone) respectively. The subscript g represents gas, and the subscript l represents liquid. According to the principles of mass conservation and energy conservation, the carbon dioxide mass and energy conservation equations for the liquid-phase zone can be obtained respectively (such as formulas (1) and (2)), that is, the carbon dioxide mathematical model for the liquid-phase zone is obtained:

[0072] (1)

[0073] (2)

[0074] (3)

[0075] (4)

[0076] (5)

[0077] (6)

[0078] (7)

[0079] (8)

[0080] Among them, m l 、ρ l 、u l 、P l and V lrespectively represent the mass, density, specific internal energy, pressure, and volume of liquid carbon dioxide, t represents the supply time, dt represents the supply time increment, d(m l u l ) represents the increment of the internal energy of liquid carbon dioxide within the supply time increment dt, h l represents the specific enthalpy of liquid carbon dioxide, h' g represents the specific enthalpy of saturated vapor, P g , V g respectively represent the pressure and volume of gaseous carbon dioxide, dV g represents the increment of the volume of gaseous carbon dioxide within the supply time increment dt, f( ) represents the Span - Wagner equation of state, x represents the carbon dioxide dryness, A wl represents the contact area between the liquid - phase side wall and liquid carbon dioxide, b wl represents the heat transfer coefficient between the liquid - phase side wall and liquid carbon dioxide, A gl represents the contact area between gaseous carbon dioxide and liquid carbon dioxide, b gl represents the heat transfer coefficient between gaseous carbon dioxide and liquid carbon dioxide.

[0081] Figure 3 shows the mass transfer process between liquid carbon dioxide and gaseous carbon dioxide. During the supply process, due to the continuous decrease in the carbon dioxide pressure, liquid carbon dioxide will boil due to the pressure reduction and generate saturated vapor; due to the low density of saturated vapor, it will float into the gas phase region. It is assumed that when liquid carbon dioxide boils, saturated vapor will quickly enter the gas phase region, and all the saturated vapor of the total mass will enter the gas phase region during the time period from t to t + dt. In the specific implementation manner of the present invention, the product of the mass m l of liquid carbon dioxide at the supply time t and the carbon dioxide dryness x is used to characterize the vapor mass entering the gas phase region from t to t + dt, that is, the vapor mass flow rate m vap is calculated by the formula:

[0082] (9)

[0083] where, dt represents the increment of the supply time.

[0084] At the initial moment (i.e., the supply time t = 0), the carbon dioxide in the gas storage tank is all in the liquid state, that is, there is no gas phase region and gas - phase side wall. At this time, the mass conservation equation of liquid carbon dioxide is:

[0085] (10)

[0086] The energy conservation equation of liquid carbon dioxide is:

[0087] (11)

[0088] When the carbon dioxide in the gas storage tank is in a fully liquid state, the volume of the liquid carbon dioxide is equal to the volume of the gas storage tank. Therefore, the specific enthalpy h of the liquid carbon dioxide l can be solved by formulas (12) and (13):

[0089] (12)

[0090] (13)

[0091] For the liquid-phase side wall, its mathematical model of carbon dioxide is as follows:

[0092] (14)

[0093] (15)

[0094] Among them, m sl represents the mass of the liquid-phase side wall, c p represents the specific heat capacity of the solid wall (i.e., the specific heat capacity of the gas storage tank), dT wl represents the temperature increment of the liquid-phase side wall within the supply time increment dt, and D represents the inner diameter of the gas storage tank.

[0095] At the initial moment (i.e., the supply time t = 0), the carbon dioxide in the gas storage tank is in a fully liquid state, that is, there is no gas phase region and gas-phase side wall. The energy conservation equation of the liquid-phase side wall is as follows:

[0096] (16)

[0097] Among them, m s represents the mass of the gas storage tank.

[0098] The dryness of carbon dioxide can be calculated using formula (5), and then it can be determined whether carbon dioxide vapor is generated based on the dryness of carbon dioxide. When 0 < x < 1, it indicates that carbon dioxide is in a saturated state, carbon dioxide vapor is generated, and the subcooled liquid supply stage ends.

[0099] According to the principles of mass conservation and energy conservation, the mass and energy conservation equations of carbon dioxide in the gas phase region (such as formulas (17) and (18)) can be obtained respectively, that is, the mathematical model of carbon dioxide in the gas phase region is obtained:

[0100] (17)

[0101] (18)

[0102] (19)

[0103] (20)

[0104] (21)

[0105] Among them, m g , ρ g and u g respectively represent the mass, density and specific internal energy of gaseous carbon dioxide, d(m g u g ) represents the increment of the internal energy of gaseous carbon dioxide within the supply time increment dt, Q wg represents the heat flux between the gas-phase side wall and the gas phase region, A wg represents the contact area between the gas-phase side wall and gaseous carbon dioxide, b wg represents the heat transfer coefficient between the gas-phase side wall and gaseous carbon dioxide, and T wg represents the temperature of the gas-phase side wall.

[0106] If the heat transfer processes in the supply system all satisfy the natural convection mechanism, then the natural convection formula is used to solve the heat transfer coefficient b wl between the liquid-phase side wall and liquid carbon dioxide, the heat transfer coefficient b gl between gaseous carbon dioxide and liquid carbon dioxide, and the heat transfer coefficient b wg between the gas-phase side wall and gaseous carbon dioxide.

[0107] For the gas-phase side wall, its mathematical model of carbon dioxide is:

[0108] (22)

[0109] (23)

[0110] Among them, m sg represents the mass of the gas-phase side wall, dT wg represents the increment of the temperature of the gas-phase side wall within the supply time increment dt, H represents the height of the gas storage tank, and H g represents the height of the gas-phase side wall or the gas phase region.

[0111] To achieve a higher heat exchange effect between carbon dioxide and high-temperature components, the phase of the supplied carbon dioxide needs to be liquid. Therefore, the present invention focuses on the supply process of liquid carbon dioxide. When all the carbon dioxide in the gas storage tank is in the gaseous state, the calculation ends.

[0112] To verify the accuracy and reliability of the model of the present invention, a Figure 4The shown carbon dioxide self-pressurizing supply test system mainly includes multiple control valves (such as the inflation valve G1, the solenoid valve G2, and the deflation valve G3), an orifice plate, and a carbon dioxide storage tank. The inflation valve G1, the solenoid valve G2, and the deflation valve G3 are respectively used to control the filling, supply, and exhaust of carbon dioxide, and the orifice plate is used to control the supply flow rate of carbon dioxide. The carbon dioxide storage tank is made of a titanium alloy inner liner and a composite material woven fabric and is used to store carbon dioxide.

[0113] The system also includes pressure sensors P1 / P2, a mass flow meter F, and an electronic scale. The pressure sensors P1 / P2 are used to measure the carbon dioxide supply pressure P, and the mass flow meter is used to measure the mass flow rate m of the supplied carbon dioxide outlet , and the electronic scale is used to measure the weight of the filled carbon dioxide.

[0114] Three groups of carbon dioxide self-pressurizing supply tests are carried out, and the test conditions are shown in Table 1.

[0115] Table 1 Carbon dioxide self-pressurizing supply test conditions

[0116]

[0117] As the supply time increases, the test results under the three test conditions and the simulation results obtained by using the carbon dioxide mathematical model constructed by the present invention are as Figures 5 to 7 shown. It can be Figures 5 to 7 seen that the simulation results of the present invention have good prediction accuracy for the supply pressure, indicating that the carbon dioxide mathematical model constructed by the present invention can well predict the change of the carbon dioxide supply pressure with time during the self-pressurizing supply process.

[0118] Example 2

[0119] As Figure 8 shown, a carbon dioxide self-pressurizing supply parameter calculation method provided by an embodiment of the present invention includes the following steps:

[0120] Step S1: Obtain the pressure P l and mass m l of liquid carbon dioxide when the carbon dioxide in the storage tank is in a fully liquid state, the supply mass flow rate m outlet , the volume V of the storage tank, the height H of the storage tank, the inner diameter D of the storage tank, the mass m s of the storage tank, and the specific heat capacity c p of the solid wall surface.

[0121] At the initial moment of supply, that is, when the supply time t = 0, the carbon dioxide in the storage tank is in a fully liquid state, and the pressure P l and mass m l of liquid carbon dioxide, and the supply mass flow rate m outlet, the volume V of the gas storage tank, the height H of the gas storage tank, the inner diameter D of the gas storage tank, the mass m of the gas storage tank s and the specific heat capacity c of the solid wall p .

[0122] Step S2: According to the pressure P of the liquid carbon dioxide l and the mass m l , the supply mass flow rate m outlet , the volume V of the gas storage tank, the height H of the gas storage tank, the inner diameter D of the gas storage tank, the mass m of the gas storage tank s and the specific heat capacity c of the solid wall p calculate the temperature T of the liquid phase region l , the temperature T of the liquid phase side wall wl , the density ρ of the liquid carbon dioxide l , the specific internal energy u l and the specific enthalpy h l .

[0123] As Figure 1 shown, according to the state of carbon dioxide in the gas storage tank, the gas storage tank is divided into a gas phase region, a liquid phase region, a gas phase side wall and a liquid phase side wall. When the carbon dioxide in the gas storage tank is all liquid, there is no gas phase region and gas phase side wall. At the initial moment (i.e., the supply time t = 0), the carbon dioxide in the gas storage tank is all liquid, that is, there is no gas phase region and gas phase side wall. Therefore, according to formula (11), calculate the specific internal energy u of the liquid carbon dioxide l , according to formula (12), calculate the density ρ of the liquid carbon dioxide l , according to formula (13), calculate the specific enthalpy h of the liquid carbon dioxide l .

[0124] The calculation of the temperature T of the liquid phase region l and the temperature T of the liquid phase side wall wl is the prior art. For reference, see the literature: Wang Zhengkai, Research on the Self-Pressurization Scheme Based on Regenerative Cooling[D]. National University of Defense Technology, 2015.

[0125] Step S3: According to the mathematical model of carbon dioxide in the liquid phase region and the liquid phase side wall when the carbon dioxide in the gas storage tank is all liquid, calculate the pressure P of the liquid carbon dioxide l , the temperature T of the liquid phase region l , the temperature T of the liquid phase side wall wl , the density ρ of the liquid carbon dioxide l , the specific internal energy u l and the specific enthalpy h l , the dryness x of carbon dioxide and the heat flux Q between the liquid phase side wall and the liquid phase region wl .

[0126] Judge whether carbon dioxide vapor is generated according to the carbon dioxide dryness x. When the carbon dioxide dryness x ≤ 0, it indicates that the carbon dioxide in the gas storage tank is in a fully liquid state. When the carbon dioxide dryness x ≥ 1, it indicates that the carbon dioxide in the gas storage tank is in a fully gaseous state, and the calculation ends. When 0 < carbon dioxide dryness x < 1, it indicates that carbon dioxide vapor is generated, and the carbon dioxide in the gas storage tank is partially gaseous and partially liquid, with a gas phase region and a gas-phase side wall surface.

[0127] Calculate the carbon dioxide dryness x according to formula (5), and calculate the heat flux Q between the liquid-phase side wall surface and the liquid-phase region according to formula (7). wl Calculate the pressure P of the liquid carbon dioxide according to formula (3). l , the temperature T of the liquid-phase region l , the temperature T of the liquid-phase side wall surface wl , the density ρ of the liquid carbon dioxide l , the specific internal energy u l and the specific enthalpy h l are calculated in the same way as the calculation in step S2.

[0128] Step S4: Judge whether the carbon dioxide dryness x is greater than 0 and less than 1. If not, the supply time t is increased (the increment is dt), and it is transferred to step S3; if so, it is transferred to step S5.

[0129] When the carbon dioxide dryness x ≤ 0, repeat step S3; when 0 < carbon dioxide dryness x < 1, it indicates that there is a gas phase region and a gas-phase side wall surface, and it is transferred to step S5.

[0130] Step S5: Calculate the heat flux Q between the liquid-phase side wall surface and the liquid-phase region according to the carbon dioxide mathematical models of the liquid-phase region, gas-phase region, liquid-phase side wall surface and gas-phase side wall surface in the carbon dioxide self-pressurizing supply modeling method described in Embodiment 1. wl , the heat flux Q between the gas-phase side wall surface and the gas-phase region wg , the heat flux Q between the gas-phase region and the liquid-phase region lg , the temperature T of the liquid-phase side wall surface wl , the temperature T of the gas-phase side wall surface wg .

[0131] Calculate the heat flux Q between the liquid-phase side wall surface and the liquid-phase region, the heat flux Q between the gas-phase side wall surface and the gas-phase region, and the heat flux Q between the gas-phase region and the liquid-phase region respectively according to formula (7), formula (21) and formula (8). wl , the heat flux Q between the gas-phase side wall surface and the gas-phase region wg , the heat flux Q between the gas-phase region and the liquid-phase region lg , the calculation of the temperature T of the gas-phase side wall surface wg is the prior art, and the literature can be referred to: Wang Zhengkai, Research on Self-Pressurizing Scheme Based on Regenerative Cooling [D]. National University of Defense Technology, 2015.

[0132] Step S6: Calculate the density ρ of liquid carbon dioxide l , specific internal energy u l , pressure P l , mass m l and volume V l , temperature T in the liquid phase region l , vapor mass flow rate m vap , specific enthalpy h' of the saturated gas g , carbon dioxide dryness x, mass m of gaseous carbon dioxide g , density ρ g , specific internal energy u g , pressure P g and volume V g , temperature T in the gas phase region g , height H of the liquid phase region l , height H of the gas phase region g .

[0133] The density ρ of liquid carbon dioxide l , specific internal energy u l and pressure P l , temperature T in the liquid phase region l . The calculation of the carbon dioxide dryness x and the specific enthalpy h' of the saturated gas are the same as those in step S3, and are calculated according to formula (4) g .

[0134] Calculate the carbon dioxide dryness x according to formula (5), and then obtain the vapor mass flow rate m according to formula (9) vap . Since the vapor enters the gas phase region, P g is greater than P l , therefore, the gas phase region will expand. Assume that the increment of the volume V g of gaseous carbon dioxide is dv, then the volume of liquid carbon dioxide in the liquid phase region is updated to V' l = V l - dv; the volume of gaseous carbon dioxide in the gas phase region is updated to V' g = V g + dv. Then, according to the geometric relationship, the height H l of the liquid phase region and the height H g of the gas phase region can be obtained

[0135] The mass of carbon dioxide in the liquid phase region is updated to m' l = m l - m vap ×dt; the mass of carbon dioxide in the gas phase region is updated to m' g = m g + m vap ×dt; the density of carbon dioxide in the liquid phase region is ρ l = m' l / V' l; the density of carbon dioxide in the gas phase is ρ g = m' g / V' g ; u and u are calculated respectively according to the energy conservation equation (2) in the liquid phase region and the energy conservation equation (18) in the gas phase region l and u g .

[0136] According to the Span-Wagner equation of state, the pressures P and P in the liquid phase region and the gas phase region can be obtained respectively l 、P g , and similarly, the temperatures T and T in the liquid phase region and the gas phase region can be obtained respectively l 、T g .

[0137] Step S7: Determine whether the pressure P of gaseous carbon dioxide g is less than or equal to the pressure P of liquid carbon dioxide l . If not, the volume V of gaseous carbon dioxide g increases (the increment is dv), and go to step S8; if so, update the mass m of liquid carbon dioxide l , and go to step S9

[0138] In this embodiment, the update formula for the mass m of liquid carbon dioxide l is:

[0139] m' l = m l - m outlet × dt (24)

[0140] where m' l represents the updated mass of liquid carbon dioxide, and m l represents the mass of liquid carbon dioxide before update

[0141] Step S8: Calculate the density ρ of liquid carbon dioxide l 、specific internal energy u l 、pressure P l and volume V l 、liquid phase region temperature T l 、density ρ g 、specific internal energy u g 、pressure P g and volume V g 、gas phase region temperature T g 、liquid phase region height H l 、gas phase region height H g , and go to step S7

[0142] Step S9: Determine the mass m of liquid carbon dioxide lIs it less than or equal to 0? If so, the calculation of the carbon dioxide self-pressurization supply parameters is completed. If not, the supply time t is increased (the increment is dt), and the process proceeds to step S5.

[0143] The carbon dioxide self-pressurization supply parameter calculation method of the present invention can predict various parameters in the carbon dioxide self-pressurization supply process in real time until all the carbon dioxide in the gas storage tank is in a gaseous state. The simulation results in Example 1 show that the carbon dioxide self-pressurization supply parameter calculation method of the present invention has good supply parameter prediction accuracy.

[0144] Example 3

[0145] An embodiment of the present invention further provides an electronic device, which includes: a memory, a processor, and a computer program / instructions stored on the memory. The processor executes the computer program / instructions to implement the carbon dioxide self-pressurization supply modeling method or the carbon dioxide self-pressurization supply parameter calculation method in the embodiments of the present application.

[0146] 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) and / or the programs and / or data loaded from the storage part 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, ROM, and RAM are connected to each other through a bus. The input / output (I / O) interface is also connected to the bus.

[0147] The above-mentioned processor and memory are jointly used to execute the programs / instructions stored in the memory, and when the programs / instructions are executed by a computer, they can implement the methods, steps, or functions described in the above embodiments.

[0148] Although not shown, an embodiment of the present invention further provides a computer-readable storage medium, on which computer programs / instructions are stored, and when the computer programs / instructions are executed by a processor, they implement the carbon dioxide self-pressurization supply modeling method or the carbon dioxide self-pressurization supply parameter calculation method in the embodiments of the present application.

[0149] A readable storage medium includes permanent and non-permanent, removable and non-removable media and can implement information storage 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 do not include transitory media such as modulated data signals and carrier waves.

[0150] Although not shown, an embodiment of the present invention also provides a computer program product, including: a computer program / instructions, which, when executed by a processor, implement the carbon dioxide self-pressurizing supply modeling method or the carbon dioxide self-pressurizing supply parameter calculation method in the embodiments of the present application.

[0151] The specific embodiments disclosed above are only specific implementation manners of the present invention, but the protection scope 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 think of changes or variations, which should all be covered within the protection scope of the present invention.

Claims

1. A modeling method for self-pressurizing supply of carbon dioxide, characterized in that, The modeling method includes: Dividing the gas storage tank into a liquid phase region, a gas phase region, a liquid phase side wall surface, and a gas phase side wall surface according to the form of carbon dioxide in the gas storage tank; Constructing carbon dioxide mathematical models for the liquid phase region, the gas phase region, the liquid phase side wall surface, and the gas phase side wall surface respectively according to the principles of mass conservation and energy conservation; wherein, the carbon dioxide mathematical model for the liquid phase region is: ； ， ； ， ； ， ； where, m l , ρ l , u l , P l and V l respectively represent the mass, density, specific internal energy, pressure and volume of liquid carbon dioxide, t represents the supply time, dt represents the supply time increment, d(m l u l ) represents the increment of the internal energy of liquid carbon dioxide within the supply time increment dt, m vap represents the vapor mass flow rate, m outlet represents the supply mass flow rate, h l represents the specific enthalpy of liquid carbon dioxide, h' g represents the specific enthalpy of saturated gas, Q wl represents the heat flux between the liquid-phase side wall and the liquid phase region, Q lg represents the heat flux between the gas phase region and the liquid phase region, P g , V g respectively represent the pressure and volume of gaseous carbon dioxide, dV g represents the volume increment of gaseous carbon dioxide within the supply time increment dt, f( ) represents the Span-Wagner equation of state, x represents the carbon dioxide dryness, A wl represents the contact area between the liquid-phase side wall and liquid carbon dioxide, b wl represents the heat transfer coefficient between the liquid-phase side wall and liquid carbon dioxide, T wl represents the liquid-phase side wall temperature, T l represents the liquid phase region temperature, A gl represents the contact area between gaseous carbon dioxide and liquid carbon dioxide, b gl represents the heat transfer coefficient between gaseous carbon dioxide and liquid carbon dioxide, T g represents the gas phase region temperature; The carbon dioxide mathematical model for the gas phase region is: ； ， ， ； where m g , ρ g and u g represent the mass, density and specific internal energy of gaseous carbon dioxide respectively, d(m g u g ) represents the increment of the internal energy of gaseous carbon dioxide within the supply time increment dt, Q wg represents the heat flux between the gas-phase sidewall and the gas phase region, A wg represents the contact area between the gas-phase sidewall and gaseous carbon dioxide, b wg represents the heat transfer coefficient between the gas-phase sidewall and gaseous carbon dioxide, T wg represents the gas-phase sidewall temperature; The carbon dioxide mathematical model for the liquid phase side wall surface is: ； Among them, m sl represents the mass of the liquid-phase side wall, c p represents the specific heat capacity of the solid wall, dT wl represents the temperature increment of the liquid-phase side wall within the supply time increment dt; The carbon dioxide mathematical model for the gas phase side wall surface is: ； Among them, m sg represents the mass of the gas-phase sidewall, and dT wg represents the temperature increment of the gas-phase sidewall within the supply time increment dt.

2. The carbon dioxide self-pressurizing supply modeling method according to claim 1, wherein The vapor mass flow rate m vap is calculated by the following formula: ； wherein, dt represents the supply time increment.

3. The carbon dioxide self-pressurizing supply modeling method according to claim 1 or 2, characterized in that Solve for the heat transfer coefficient b between the liquid-phase side wall and liquid carbon dioxide according to the natural convection formula wl and the heat transfer coefficient b between gaseous carbon dioxide and liquid carbon dioxide gl and the heat transfer coefficient b between the gas-phase side wall and gaseous carbon dioxide wg .

4. A method for obtaining carbon dioxide self-pressurizing supply parameters, characterized in that, The obtaining method includes: Step S1: Obtain the pressure P of the liquid carbon dioxide when the carbon dioxide in the gas storage tank is in a fully liquid state l and the mass m l , the supply mass flow rate m outlet , the volume V of the gas storage tank, the height H of the gas storage tank, the inner diameter D of the gas storage tank, the mass m of the gas storage tank s and the specific heat capacity c of the solid wall p ; Step S2: According to the pressure P of liquid carbon dioxide l and the mass m l , supply mass flow rate m outlet , the volume V of the gas storage tank, the height H of the gas storage tank, the inner diameter D of the gas storage tank, the mass m of the gas storage tank s and the specific heat capacity c of the solid wall p , calculate the temperature T of the liquid phase region l , the temperature T of the liquid phase side wall wl , the density ρ of liquid carbon dioxide l , the specific internal energy u l and the specific enthalpy h l ; Step S3: Calculate the pressure P of the liquid carbon dioxide according to the mathematical models of the liquid phase region and the liquid-phase side wall surface of the carbon dioxide in the gas storage tank when the carbon dioxide is in a fully liquid state l , the temperature T of the liquid phase region l , the temperature T of the liquid-phase side wall surface wl , the density ρ of the liquid carbon dioxide l , the specific internal energy u l , the specific enthalpy h l , the dryness x of the carbon dioxide and the heat flux Q between the liquid-phase side wall surface and the liquid phase region wl ; Step S4: Judging whether the carbon dioxide dryness x is greater than 0 and less than 1. If not, the supply time t is increased, and it goes to step S3; if so, it goes to step S5; Step S5: Calculate the heat flux Q between the liquid-phase sidewall and the liquid phase region, the heat flux Q between the gas-phase sidewall and the gas phase region, the heat flux Q between the gas phase region and the liquid phase region, the liquid-phase sidewall temperature T, and the gas-phase sidewall temperature T according to the carbon dioxide mathematical models of the liquid phase region, the gas phase region, the liquid-phase sidewall, and the gas-phase sidewall in the carbon dioxide self-pressurizing supply modeling method according to any one of claims 1 to 3 wl , the heat flux Q between the gas-phase sidewall and the gas phase region wg , the heat flux Q between the gas phase region and the liquid phase region lg , the liquid-phase sidewall temperature T wl , the gas-phase sidewall temperature T wg ; Step S6: Calculate the density ρ of liquid carbon dioxide l , specific internal energy u l , pressure P l , mass m l and volume V l , temperature T in the liquid phase region l , vapor mass flow rate m vap , specific enthalpy h' of the saturated gas g , dryness x of carbon dioxide, mass m of gaseous carbon dioxide g , density ρ g , specific internal energy u g , pressure P g and volume V g , temperature T in the gas phase region g , height H in the liquid phase region l , height H in the gas phase region g ; Step S7: Determine the pressure P of gaseous carbon dioxide g Is it less than or equal to the pressure P of liquid carbon dioxide l , if not, then the volume V of gaseous carbon dioxide g Increases, and proceed to step S8; if so, then update the mass m of liquid carbon dioxide l , and proceed to step S9; Step S8: Calculate the density ρ of liquid carbon dioxide l , specific internal energy u l , pressure P l and volume V l , temperature T in the liquid phase region l , density ρ g , specific internal energy u g , pressure P g and volume V g , temperature T in the gas phase region g , height H in the liquid phase region l , height H in the gas phase region g , and transfer to Step S7; Step S9: Determine whether the mass m of the liquid carbon dioxide l is less than or equal to 0. If so, complete the calculation of the self-pressurizing supply parameters of carbon dioxide. If not, increase the supply time t and transfer to step S5; wherein, in the step S3, when the carbon dioxide in the gas storage tank is in a fully liquid state, the carbon dioxide mathematical model for the liquid phase region is: ； ， ， ； The carbon dioxide mathematical model for the liquid phase side wall surface is: ； Among them, f( ) represents the Span-Wagner equation of state, dt represents the supply time increment, d(m l u l ) represents the increment of the internal energy of liquid carbon dioxide within the supply time increment dt, dT wl represents the increment of the temperature of the liquid-phase side wall within the supply time increment dt.

5. The method for obtaining carbon dioxide self-pressurizing supply parameters according to claim 4, wherein In the step S8, the mass m of the liquid carbon dioxide l is updated by the following formula: ； where m' l represents the mass of the updated liquid carbon dioxide, and m l represents the mass of the liquid carbon dioxide before the update.

6. An electronic device, including a memory, a processor, and a computer program / instructions stored on the memory, the processor executing the computer program / instructions to implement the carbon dioxide self-pressurizing supply modeling method as described in any one of claims 1 to 3 or the carbon dioxide self-pressurizing supply parameter obtaining method as described in claim 4 or 5.

7. A computer-readable storage medium, having a computer program / instructions stored thereon, the computer program / instructions, when executed by a processor, implementing the carbon dioxide self-pressurizing supply modeling method as described in any one of claims 1 to 3 or the carbon dioxide self-pressurizing supply parameter obtaining method as described in claim 4 or 5.

8. A computer program product, including a computer program / instructions, the computer program / instructions, when executed by a processor, implementing the carbon dioxide self-pressurizing supply modeling method as described in any one of claims 1 to 3 or the carbon dioxide self-pressurizing supply parameter obtaining method as described in claim 4 or 5.

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