Gas-liquid phase change numerical simulation method and system considering CO2 non-condensable gas influence

Abstract

The invention provides a gas-liquid phase change numerical simulation method and system considering the influence of CO2 non-condensable gas, and the method comprises the steps: building a multi-component multi-phase fluid lattice Boltzmann pseudo-potential model, and simulating the flow of a multi-component multi-phase fluid; establishing a non-ideal gas state equation and an ideal gas state equation to obtain a relationship among density, temperature and pressure; establishing a temperature equation, and calculating the temperature of the multi-component multi-phase fluid; establishing a non-ideal gas potential function and an ideal gas potential function, and coupling the lattice Boltzmann pseudo-potential model and the temperature equation through potential functions; setting boundary conditions, and completing a numerical simulation process. The problems that the existing multi-component multi-phase fluid flow and heat transfer characterization difficulty is large, and the interface dynamic behavior in the gas-liquid phase change process is difficult to accurately obtain through experimental measurement are solved, and a scientific basis is provided for improving the CO2 and water vapor separation efficiency by regulating and controlling the supercooled wall surface temperature and the wall surface wettability. And algorithm reference is provided for phase change separation of other types of mixed gases.

Description

Technical Field

[0001] This invention relates to the fields of fluid mechanics and engineering thermophysics, and in particular to a numerical simulation method and system for gas-liquid phase change considering the influence of CO2 as a non-condensable gas. Background Technology

[0002] my country's resource endowment of "abundant coal, scarce oil, and limited gas" determines that coal will remain the country's primary energy source for a long time to come. Coal combustion releases large amounts of carbon dioxide (CO2), a major component of greenhouse gases. The global warming caused by CO2 has become a global concern, and CO2 capture and storage can reduce the greenhouse gas effect.

[0003] To meet the requirements for CO2 sequestration, captured CO2 needs to be separated and purified, a process involving the condensation of a mixed gas (CO2 and water vapor). Taking the most promising and widely used alkanolamine solution carbon capture technology as an example, this technology condenses the CO2 and water vapor released in the desorption tower, increasing the CO2 concentration and meeting the sequestration requirements. Studying the condensation characteristics of the CO2-water vapor mixture is of significant guiding importance for optimizing condenser heat exchanger design, improving CO2 separation efficiency, and achieving high-concentration CO2 sequestration.

[0004] During the condensation of CO2 and water vapor, CO2 exists as a non-condensable gas. This non-condensable gas significantly affects water vapor condensation, primarily by forming a non-condensable gas layer between the water vapor and the supercooled wall, hindering heat transfer during condensation. Current research mainly uses experimental setups to study the effects of mixed gas velocity, non-condensable gas content, and wall supercooling on the condensation form (bead condensation, film condensation) and condensation heat transfer coefficient of the mixed gas. While experimental methods can obtain the heat transfer characteristics of mixed gas condensation, the analytical process is cumbersome, and limitations in experimental conditions prevent precise observation of the flow and heat transfer details of non-condensable and condensable gases during the gas-liquid phase transition, resulting in an insufficient understanding of the underlying mechanism.

[0005] Numerical simulation, as a supplement to theoretical analysis and experimental testing, provides an efficient means to solve gas-liquid phase transition (GLP) problems. GLP processes are extremely complex, involving several dynamic processes such as nucleation, growth, and decoupling, making numerical simulation of GLP highly challenging. GLP falls under the domain of two-phase flow, and traditional two-phase flow numerical simulation methods have some shortcomings in studying GLP. For example, the Volume-of-Fluid (VOF) method and the Level Set Method (LSM) suffer from low accuracy in interface handling and non-conservation of volume. The Front-Tracking Method (FTM) and the Immersed Boundary Method (IBM) are unsuitable for simulating gas-liquid two-phase flows involving interfacial topological changes.

[0006] There is currently limited research on the condensation of CO2 and water vapor mixtures. Representative works include the following:

[0007] Ge et al. (Ge, MH; Wang, SX; Zhao, J.; Zhao, YL; Liu, LS. Condensation of steam with high CO2 concentration on a vertical plate. Exp. Therm. Fluid Sci. 2016, 75, 147-155.) conducted a study on the condensation of a mixture of CO2 and water vapor using a mixed steam circulation system, a cooling water system, and an experimental data measurement and acquisition system. They found that the higher the mass fraction of CO2, the greater the resistance to water vapor diffusion to the interface, which is less conducive to water vapor condensation.

[0008] Lu et al. (Lu, JH; Cao, HS; Li, JM Experimental study of condensation heat transfer of steam in the presence of non-condensable gas CO2 on ahorizontal tube at sub-atmospheric pressure. Exp. Therm. Fluid Sci. 2019, 105, 278-288.) experimentally studied the condensation of a mixture of CO2 and water vapor at temperatures ranging from 5 kPa to 101 kPa and with CO2 molar mass ranging from 0.05 to 0.2. They found that the condensation heat transfer coefficient decreased with increasing CO2 molar mass.

[0009] Takami et al. (Takami, KM; Mahmoudi, J.; Time, RW A simulated H2O / CO2 condenser design for oxy-fuel CO2 capture process. Energy Procedia 2009, 1, 1443-1450.) used COMSOL software to simulate the condensation of water vapor and CO2 in a condenser and designed a volumetric heat exchanger suitable for separating water vapor and CO2 in flue gas. They found that using the proposed design, the condenser could condense approximately 75% of the moisture in the flue gas, and after treatment by the condenser, the CO2 content in the flue gas exceeded 97%.

[0010] Lu et al. (Lu, JH; Ren, KX; Tang, JJ, Wang, SL Numericalsimulations of laminar film condensation of H2O / Air or H2O / CO2 on a verticalplate. Heat Transf. Eng. 2022, 44, 720-733.) used a volumetric fluid flow (VOF) model and a phase change model to study the effects of velocity, wall subcooling, and non-condensable gas content on the heat transfer of CO2 and water vapor mixtures. The results showed that the presence of non-condensable gases significantly reduced the mass flow rate and heat transfer coefficient of water vapor.

[0011] Existing numerical simulation methods for two-phase flow are mainly divided into interface tracking methods and interface capture methods. Interface tracking methods (immersed boundary method IBM, forward tracking method FTM) involve the addition, merging, and deletion of tracer points, which leads to cumbersome calculation processes, difficulty in handling interface topological changes, and low accuracy. Interface capture methods (level set method LSM, fluid volume method VOF, phase field method PFM) have problems such as complex interface reconstruction, failure to satisfy mass conservation, artificially increasing interface thickness, and difficulty in calculating physical quantities related to curvature. Summary of the Invention

[0012] To address the aforementioned technical problems, this invention provides a numerical simulation method for gas-liquid phase transition considering the influence of non-condensable CO2 gases, characterized by comprising the following steps:

[0013] S1: Establish a Boltzmann pseudopotential model for multi-component multiphase fluid lattice to simulate the flow of multi-component multiphase fluid;

[0014] S2: Establish the ideal gas law and the non-ideal gas law to obtain the relationship between density, temperature and pressure;

[0015] S3: Establish the temperature equation and calculate the temperature of multi-component multiphase fluid;

[0016] S4: Establish the potential functions for ideal and non-ideal gases, and couple the lattice Boltzmann pseudopotential model with the temperature equation through the potential functions;

[0017] S5: Set boundary conditions to complete the numerical simulation process.

[0018] Furthermore, step S1 includes the following sub-steps:

[0019] S11 defines the initial values ​​of each physical quantity and performs mesh generation;

[0020] S12 performs a collision process of different component distribution functions, and transfers the distribution functions after the collision to obtain the distribution functions of different components after transfer;

[0021] S13 computes the multi-relaxation time collision operator;

[0022] S14 calculates the equilibrium distribution function of different components;

[0023] S15 calculates the forces between identical components, the forces between different components, and the forces between fluid and solid.

[0024] S16 calculates the density and velocity of different components to obtain the flow field.

[0025] Furthermore, step S2 includes the following sub-steps:

[0026] S21 establishes the ideal gas law to describe non-condensable gases (CO2);

[0027] S22 establishes a non-ideal gas law to describe condensable gases (water vapor).

[0028] Furthermore, step S3 includes the following sub-steps:

[0029] S31 establishes the temperature equation based on the entropy balance law, thermodynamic relations, and the continuity equation;

[0030] S32 uses the fourth-order Runge-Kutta scheme to solve the temperature equation, calculate the fluid temperature, and obtain the temperature field.

[0031] Furthermore, step S4 includes the following sub-steps:

[0032] S41 establishes the ideal gas potential function;

[0033] S42 establishes the non-ideal gas potential function;

[0034] The temperature field and flow field of S43 are coupled through a potential function.

[0035] Furthermore, step S5 includes the following sub-steps:

[0036] The upper boundary of the S51 computational region is set to an open boundary;

[0037] The lower boundary of the S52 computational domain is set to a no-slip boundary.

[0038] The left and right boundaries of the S53 computational domain are set as periodic boundaries.

[0039] In addition, the present invention also provides a numerical simulation system for gas-liquid phase change considering the influence of CO2, a non-condensable gas, characterized in that it includes the following modules:

[0040] The model building module is used to build a Boltzmann pseudopotential model for multi-component multiphase fluid lattice to simulate the flow of multi-component multiphase fluid.

[0041] The gas state equation module is used to establish ideal gas state equations and non-ideal gas state equations to obtain the relationship between density, temperature and pressure; wherein non-condensable gases are described by establishing ideal gas state equations, and condensable gases are described by establishing non-ideal gas state equations.

[0042] Temperature equation module, which is used to establish temperature equations and calculate the temperature of multi-component multiphase fluids;

[0043] The gas potential function module is used to establish ideal gas potential functions and non-ideal gas potential functions. The lattice Boltzmann pseudopotential model is coupled with the temperature equation through the potential function.

[0044] Boundary module, which is used to set boundary conditions to complete the numerical simulation process.

[0045] The embodiments of the present invention have the following technical effects:

[0046] (1) A lattice Boltzmann pseudo-potential model, ideal gas equation of state, non-ideal gas equation of state, temperature equation, ideal gas potential function, and non-ideal gas potential function were established and cleverly coupled. A numerical simulation method and system for gas-liquid phase change considering the influence of CO2 non-condensable gas was proposed. This method can accurately simulate the condensation phase change process of condensable gas when non-condensable gas is present. In addition, this method can be easily extended to solve the condensation phase change problem of mixed gas when more types of non-condensable and condensable gases coexist. (2) This method compensates for the inability of experimental means to accurately observe the changes in density field, velocity field, and temperature field of each component during the phase change process of multi-component gas. The flow and heat transfer laws of multi-component multiphase fluids were obtained in real time and accurately. (3) This method provides a scientific basis for improving the separation efficiency of CO2 and water vapor by controlling the temperature of the supercooled wall and the wettability (contact angle). It also provides an algorithm reference for the phase change separation of other types of mixed gases (non-condensable gas + condensable gas). Attached Figure Description

[0047] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0048] Figure 1 This is a flowchart of a numerical simulation method for gas-liquid phase change considering the influence of non-condensable CO2 gas, provided in an embodiment of the present invention.

[0049] Figure 2 This is a diagram showing the interface changes during the droplet evaporation process provided in an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram illustrating the relationship between the square of the dimensionless diameter of the droplet and the dimensionless time during the evaporation process, provided in an embodiment of the present invention.

[0051] Figure 4 This is a schematic diagram of a droplet placed on a solid wall surface at the initial moment, provided by an embodiment of the present invention;

[0052] Figure 5 This is a schematic diagram of the contact angle formed between the droplet and the solid wall in a stable state, provided by an embodiment of the present invention.

[0053] Figure 6 This is a schematic diagram of the open boundary provided in an embodiment of the present invention;

[0054] Figure 7 This is a schematic diagram of a slip-free boundary provided in an embodiment of the present invention;

[0055] Figure 8 This is a schematic diagram of a periodic boundary provided in an embodiment of the present invention;

[0056] Figure 9 The non-condensable gas (CO2) content provided in the embodiments of the present invention is respectively and During the condensation process, the density of condensable gas (water vapor) changes with time. A schematic diagram illustrating the changes;

[0057] Figure 10 The non-condensable gas (CO2) content provided in the embodiments of the present invention is respectively and During the condensation process, the density of the non-condensable gas (CO2) changes with time. A diagram illustrating the changes. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are part of this invention.

[0059] The calculation flow of the numerical simulation method for gas-liquid phase change considering the influence of non-condensable CO2 gas in this invention is as follows: Figure 1 As shown.

[0060] A Boltzmann pseudopotential model for a multi-component, multi-phase lattice is established, and a collision process involving different component distribution functions is performed: ;

[0061] in, Components In position Location and Time Density distribution function at time, For time step, This is an external force term.

[0062] The multi-relaxation time (MRT) collision operator is defined by the following formula: ;

[0063] in Let be the transformation matrix. For a relaxed diagonal matrix, , … For multiple relaxation parameters.

[0064] For discrete velocities, the expression is:

[0065] ;

[0066] Subscript It represents 9 discrete velocity directions.

[0067] The equilibrium distribution function is expressed as:

[0068] ;

[0069] in, Components density, Components speed, For the speed of sound in a grid, For grid speed, For grid step size, For time step.

[0070] For the weights, the expression is:

[0071] .

[0072] Acting on components The total force on ( This includes: forces between the same components ( ), the forces between different components ( ), fluid-solid interaction forces ( The specific expression is:

[0073] , , ;

[0074] in, The strength of the interaction between the same components. The strength of the interaction between different components, The strength of the interaction between the component and the solid wall. For weighting coefficients, Let be the potential function. For indicator functions, To adjust the parameters of the wall contact angle.

[0075] Summing the distribution function yields the density and velocity of different components:

[0076] , ;

[0077] in, Components density, Components The speed.

[0078] Establish the ideal gas law:

[0079] ;

[0080] in, For ideal gas pressure, The density is that of an ideal gas (non-condensable gas CO2). The gas constant is For temperature.

[0081] Establish the equation of state for a nonideal gas:

[0082] ;

[0083] in, For non-ideal gas pressure, For non-ideal gases (condensable gases like water vapor), the density is... , , , , The gas constant is For temperature, The critical temperature. This is the critical pressure.

[0084] Local entropy balance law:

[0085] ;

[0086] in, For entropy, Thermal conductivity, .

[0087] Thermodynamic relation:

[0088] ;

[0089] in, It is a constant volume heat capacity.

[0090] Establish the temperature equation based on the local entropy balance law and thermodynamic relations:

[0091] The time was discretized using a fourth-order Runge-Kutta scheme to obtain:

[0092] ;

[0093] in, , , , .

[0094] Calculate the temperature of a multi-component mixed system:

[0095] .

[0096] Establish the ideal gas potential function:

[0097] ;

[0098] in, This refers to the density of the non-condensable gas CO2.

[0099] Establish the nonideal gas potential function:

[0100] ;

[0101] in, The density of condensable gas water vapor. This is a non-ideal gas pressure.

[0102] Flow field and temperature field through potential function and To couple.

[0103] Example 1:

[0104] use The law verifies the correctness of the multi-component phase transition model established in this invention. The law can be described as follows:

[0105] ;

[0106] in: Where is the droplet diameter, The initial droplet diameter, For parameters related to the thermal conductivity of fluids, For time.

[0107] Initially, a temperature of The droplets were placed at a temperature of In an environment where the thermal conductivity is The four boundaries are set as periodic boundary conditions. The interface changes during droplet evaporation are as follows: Figure 2 As shown. Figure 2 middle , This represents time, or the number of iterations.

[0108] During the evaporation of a droplet, the square of the dimensionless diameter of the droplet ( ) and dimensionless time ( The relationship is as follows: Figure 3 As shown. Discovery and A linear relationship exists, which conforms to The law verified the correctness of the model.

[0109] Example 2:

[0110] The correctness of the multi-component phase transition model established in this invention is further verified by the contact angle formed by the solid-liquid-gas three phases. Initially, the system is filled with gas (blue), and a circular liquid droplet (red) is placed on the solid wall (dark gray). The upper boundary of the computational domain is set as an open boundary, the lower boundary as a no-slip boundary, and both left and right boundaries as periodic boundaries, as shown below. Figure 4 As shown.

[0111] The contact angle between a droplet and a solid wall is influenced by the strength of the solid-liquid interaction. The influence of different interaction strengths. This causes the droplets to spread or contract on the solid wall surface, eventually reaching a stable state. Figure 5 The contact angle formed between the droplet and the solid wall when a stable state is achieved.

[0112] Table 1 shows the interaction strength between the components and the solid wall. When different values ​​are taken, the theoretical value and numerical simulation results of the contact angle formed when the droplet reaches a stable state on the solid wall are compared. The results show that the two values ​​are in good agreement, which verifies the correctness of the model.

[0113] Table 1 Different interaction strengths Comparison of theoretical and calculated values ​​of lower contact angle

[0114]

[0115] Example 3:

[0116] This study investigates the effect of the non-condensable gas CO2 content on the condensation of condensable gases. Initially, the system is filled with a mixture of non-condensable gas (CO2) and condensable gas (water vapor), and the temperature of the mixture is... The solid wall temperature is The content of non-condensable gases is defined as:

[0117] ;

[0118] in: The density of a non-condensable gas. This refers to the density of condensable gases.

[0119] The upper boundary of the computational domain is set as an open boundary, where physical quantities such as velocity, density, and pressure remain unchanged in the mainstream direction. Figure 6 As shown. The expression for open boundary is:

[0120] .

[0121] The lower boundary of the computational domain is set to a no-slip boundary, such as... Figure 7 As shown. The expression for a no-slip boundary is:

[0122] , , ;

[0123] in, , … These are distribution functions in different directions.

[0124] The left and right boundaries of the computational domain are both set as periodic boundaries. When a fluid particle leaves the flow field from one boundary, it will enter the flow field from the other boundary in the next time step, such as... Figure 8 As shown. The expression for the periodic boundary is:

[0125] , .

[0126] Figure 9 The contents of non-condensable gases (CO2) are respectively and The density change of condensable gas (water vapor) during condensation. It was found that condensable gas at hydrophilic walls ( The droplets condense and nucleate on the surface, gradually growing larger. When the content of non-condensable gases is low, the droplet growth rate is faster.

[0127] Figure 10 The contents of non-condensable gases (CO2) are respectively and The density change of non-condensable gases during condensation was observed. It was found that a higher content of non-condensable gases resulted in longer droplet condensation time and slower growth rate, indicating that the presence of non-condensable gases weakened heat transfer during droplet condensation. During droplet growth, condensable gases continuously condensed near the solid-liquid-gas three-phase contact line, causing non-condensable gases to gradually accumulate from above the droplet near the solid-liquid-gas three-phase contact line.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A numerical simulation method of gas-liquid phase change considering the effect of CO2 non-condensable gas, characterized in that, It comprises the following steps: S1: establishing a multi-component multi-phase fluid lattice Boltzmann pseudo-potential model to simulate the flow of the multi-component multi-phase fluid; S2: establishing an ideal gas state equation and a non-ideal gas state equation to obtain the relationship between density, temperature and pressure; S3: establishing a temperature equation to calculate the temperature of the multi-component multi-phase fluid; S4: establishing an ideal gas potential function and a non-ideal gas potential function, and the lattice Boltzmann pseudo-potential model and the temperature equation are coupled through the potential function; S5: setting boundary conditions to complete the numerical simulation process.

2. The gas-liquid phase transition numerical simulation method considering the influence of CO2 non-condensable gas according to claim 1, characterized in that, The step S1 comprises the following sub-steps: S11: defining initial values of physical quantities and performing grid division; S12: performing collision processes of different component distribution functions, and migrating the distribution functions after collision to obtain the distribution functions of different components after migration; S13: calculating a multi-relaxation time collision operator; S14: calculating equilibrium state distribution functions of different components; S15: calculating the forces between the same components, the forces between different components, and the forces between the fluid and the solid; S16: calculating the density and velocity of different components to obtain the flow field.

3. The gas-liquid phase transition numerical simulation method considering the effect of CO2 non-condensable gas according to claim 1, characterized in that, The step S2 comprises the following sub-steps: S21: establishing an ideal gas state equation to describe the non-condensable gas; S22: establishing a non-ideal gas state equation to describe the condensable gas.

4. The gas-liquid phase transition numerical simulation method considering the influence of CO2 non-condensable gas according to claim 1, characterized in that, The step S3 comprises the following sub-steps: S31: establishing a temperature equation according to the entropy balance law, thermodynamic relations and continuity equations; S32: solving the temperature equation by using a fourth-order Runge-Kutta format to calculate the fluid temperature and obtain the temperature field.

5. The method for gas-liquid phase change numerical simulation considering the effect of CO2 non-condensable gas according to claim 1, characterized in that, The step S4 comprises the following sub-steps: S41: establishing an ideal gas potential function; S42: establishing a non-ideal gas potential function; S43: coupling the temperature field and the flow field through the potential function.

6. The gas-liquid phase transition numerical simulation method considering the influence of CO2 non-condensable gas according to claim 1, characterized in that, The step S5 comprises the following sub-steps: S51: calculating the upper boundary of the region to be set as an open boundary; S52: calculating the lower boundary of the region to be set as a no-slip boundary; S53: calculating the left and right boundaries of the region to be set as periodic boundaries.

7. A gas-liquid phase change numerical simulation system considering the effect of CO2 non-condensable gas, characterized in that, It comprises the following modules: A model establishing module, which is used to establish a multi-component multi-phase fluid lattice Boltzmann pseudo-potential model to simulate the flow of the multi-component multi-phase fluid; A gas state equation module, which is used to establish an ideal gas state equation and a non-ideal gas state equation to obtain the relationship between density, temperature and pressure; wherein the ideal gas state equation is used to describe the non-condensable gas, and the non-ideal gas state equation is used to describe the condensable gas; A temperature equation module, which is used to establish a temperature equation to calculate the temperature of the multi-component multi-phase fluid; A gas potential function module, which is used to establish an ideal gas potential function and a non-ideal gas potential function, and the lattice Boltzmann pseudo-potential model and the temperature equation are coupled through the potential function; A boundary module, which is used to set boundary conditions to complete the numerical simulation process.

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