Modeling method for simulation model of multi-component single-bubble motion and mass transfer coupling process

Abstract

Provided in the present invention is a modeling method for a simulation model of a multi-component single-bubble motion and mass transfer coupling process. The modeling method comprises the following steps: according to Newton's second law, establishing a bubble transient acceleration model on the basis of a viscous force dominant mechanism of spherical bubbles; according to a flow function in a spherical coordinate form, establishing a bubble transient non-equilibrium mass transfer model by means of a non-equilibrium mass transfer theory; establishing a bubble mass state equation on the basis of mass transfer kinetics and a mass state equation; and constructing a pollutant accumulation stagnation cap model on the basis of a stagnation cap model. In the present invention, multi-component expansion is performed on the basis of a single-component mass transfer model; the stagnation cap model is introduced; the mutual influence among motion, mass transfer and pollutant diffusion is solved by means of a mathematical model; and the simulation model is applied to the simulation of a multi-component single-bubble motion and mass transfer coupling process in a micro-interface scale range, and can predict, in view of bubble motion and mass transfer characteristics, the mutual influence between multi-component single-bubble motion and mass transfer, and the strengthening effect of bubble size on mass transfer.

Description

Modeling method for simulation model of multi-component single bubble motion and mass transfer coupling process Technical Field

[0001] The present invention relates to the technical field of chemical engineering mathematical modeling, and in particular to a modeling method for a simulation model of a multi-component single bubble motion and mass transfer coupling process. Background Art

[0002] Gas-liquid reaction is a common type of reaction in chemical industry. According to different mechanisms of action, it can be roughly divided into oxidation, hydrogenation, absorption, fermentation, etc.

[0003] However, at present, for most gas-liquid reaction processes, the mass transfer rate at the gas-liquid interface is usually the rate-limiting step of the entire reaction process. The fundamental reason is usually that the mass transfer area between the gas and liquid phases is too small, resulting in insufficient mass transfer flux and limited reaction.

[0004] In a conventional bubble column or stirred bubble reactor, the diameter of the bubbles is usually between 5 and 30 mm, and the gas-liquid interface area at normal pressure is 20 to 300 m 2 / m 3 Therefore, in order to provide the mass transfer flux required for the reaction, it is usually necessary to increase the gas volume or improve the stirring kinetic energy to enhance gas-liquid mixing, which inevitably leads to a decrease in gas utilization and energy utilization efficiency.

[0005] For many years, research on gas-liquid multiphase flow and bubble mass transfer enhancement has been a hot topic in the industry. In recent years, thanks to the development of gas-liquid mass transfer theory, the research and application of gas-liquid mass transfer enhancement technologies have also made significant progress. With in-depth research into bubble motion and factors influencing mass transfer, and the use of fluid simulation software such as CFD, the gas-liquid mass transfer process can be optimized, improving gas utilization efficiency.

[0006] However, at present, the basic theoretical research on gas-liquid mass transfer enhancement is still at the millimeter level, and there is a lack of suitable mathematical models, and the optimization of the gas-liquid mass transfer process lacks data support.

[0007] Summary of the Invention

[0008] In view of this, the purpose of the present invention is to base on the gas-liquid mass transfer theory and gas-liquid mass transfer enhancement technology, take multi-component single bubbles within the micro-interface scale range as the research object, realize the interaction of multiple components within the bubble through systematic experiments, construct a coupling model suitable for the motion mass transfer of multi-component microbubbles, deepen the research on micro-interface mass transfer enhancement, and provide basic theory and experimental data support for the technical optimization of multiple bubbles in the micro-interface system.

[0009] The mass transfer flux between the gas and liquid phases is roughly proportional to the specific surface area. Generally speaking, the smaller the bubble size in the reaction system, the faster the mass transfer rate between the gas and liquid. In addition, smaller bubbles also have a lower rising rate, so they stay in the liquid phase for a longer time, which can further promote the mass transfer between the two phases. The present invention is dedicated to the research and application of micro-interface mass transfer enhancement technology. Compared with the traditional industrial-grade large bubble reaction system, the micro-interface system is composed of bubbles with a diameter of 1-1000μm, which has many advantages in mass transfer.

[0010] The present invention provides a modeling method for a simulation model of a multi-component single bubble motion and mass transfer coupling process, comprising the following steps:

[0011] S1. According to Newton's second law and based on the viscosity-dominated mechanism of spherical bubbles, a bubble transient acceleration model is established;

[0012] Submillimeter bubbles with a diameter less than 1mm can be considered as rigid spheres during motion, with a linear upward trajectory. For single-component bubbles, the instantaneous acceleration model of the bubble can be obtained through force analysis. Considering that the bubble moves in a linear manner, the direction of the bubble's resultant force is vertical, and the external forces perpendicular to the bubble's motion direction are mutually balanced and can be ignored.

[0013] The vertical force on the bubble mainly includes the buoyancy F V Gravity F G , viscous resistance F D , additional mass force F m and Basset Force F B According to Newton's second law, the rate of change of bubble momentum due to the combined contribution of the vertical forces is expressed as:

[0014] In formula (1), R is the bubble diameter; ρ G is the gas phase density; v b is the instantaneous velocity of the bubble; the force F on the right side of formula (1) V 、F G 、F D 、F m 、F B Respectively expressed as:

[0015] In formulas (2)-(6), ρ L is the liquid density, μ L is the liquid viscosity, C Drepresents the drag coefficient; according to the mechanism of the Tomiyama drag force model, the spherical bubbles studied in this paper belong to the viscosity-dominated mechanism. In this case, the surfactant on the bubble surface increases the viscous drag;

[0016] Based on the viscosity-dominated mechanism of spherical bubbles, in the range of -11≤log Mo≤0.63, 3.2×10 -9 Under the conditions of ≤Re≤720, 0.042≤Eo≤29, Re is the Reynolds number, and the drag coefficient of the clean bubble on the completely movable surface is calculated using formulas (7) and (8). The aspect ratio E of the spherical bubble is b is 1;

[0017] For multi-component gas systems commonly used in industry, the mole fraction of bubbles containing N gas components needs to be introduced; let the mole fraction, gas density, and molar mass of component i in the gas be y i ,ρ i and Mol i , the viscosity of liquid phase i component is μ L，i , then: Y=[y1 y2 ... y N ] μ L =[μ L，1 μ L，2 ... μ L，N ] / ρ=[ρ1 ρ2 ... ρ N ] M solute =[Mol1 Mol2 ... Mol N ]

[0018] For non-associating liquid mixtures, the viscosity of the mixture is calculated as: log μ L =Σx i log μ L，i (9)

[0019] In formula (9), μ L is the viscosity of the mixed liquid phase, μ L，i is the viscosity of component i in the liquid phase. During the bubble desorption process, the mole fraction of the component in the bubble changes in real time. The density of the mixed gas is calculated as follows: ρ G =ρ·Y T (10)

[0020] In formula (10), ρ is the gas phase density matrix, Y is the unit row vector, and T is the transposed sign. Substituting formulas (2) to (8) into formula (1), we obtain the transient acceleration model of multi-component bubbles;

[0021] S2. Based on the flow function in spherical coordinate form and the non-equilibrium mass transfer theory, a bubble transient non-equilibrium mass transfer model is established;

[0022] As mentioned above, microbubbles can maintain a stable spherical shape during movement without typical boundary layer separation. Therefore, the non-separated flow equation around the sphere can represent the peripheral flow field formed by the rising bubbles. Without considering the bubble wake phenomenon, the function expression of the flow function in spherical coordinate form is:

[0023] In formula (12), ψ is the stream function, r is the radial distance, and R is the radius. The mass transfer diffusion equation in the liquid phase is given in the form of spherical coordinates:

[0024] In formula (13), C is the dimensionless concentration;

[0025] According to the definition of stream function, the gas-liquid two-phase flow velocity is calculated as follows:

[0026] In formula (14), u r 、u θ are radial and tangential velocities respectively; the last term of equation (13) can be ignored, and the mass flow rate J is obtained by combining equations (12) to (14):

[0027] In formula (16), D AB is the diffusion coefficient, C A is the bulk concentration of the liquid phase, C I is the interfacial gas concentration; the mass transfer rate of the single-component bubble is obtained as follows:

[0028] In formula (17), m G is the bubble mass; accordingly, the total mass change in the bubble includes the mass change of each component, and the mass transfer rate of multi-component bubbles is as shown in Equation (18):

[0029] Formula (18) contains a key parameter C I : Gas concentration at the interface. For the models commonly used in the chemical industry (membrane model, permeation model, and surface renewal model, etc.), it is assumed that there is no resistance at the interface, that is, the interfacial thermodynamic equilibrium of the mass transfer process must satisfy Henry's law. However, when the internal concentration of microbubbles changes rapidly, the thermodynamic equilibrium at the interface cannot be achieved. Therefore, the relationship between the gas concentration in the bubble and the gas concentration at the phase interface does not conform to Henry's law. Therefore, C should be obtained through non-equilibrium mass transfer theory. I , C * represents the equilibrium concentration at the gas-liquid interface, as shown in Equation (19);

[0030] H=[H1 H2 ... H N ], H i refers to the solubility coefficient of gas component i; P atm is the atmospheric pressure, H is the solubility coefficient, and σ is the surface tension;

[0031] S3. Based on mass transfer kinetics and mass state equation, establish the bubble mass state equation;

[0032] The gas mass transfer flux in the bubble is expressed as Through the pair Taking the derivative of both sides with respect to t, we get:

[0033] For a multicomponent bubble containing N components, there exists:

[0034] In formula (22), ρ G0 It is the various components in the bubble at a certain temperature and atmospheric pressure P atm The density vector under , the derivative of formula (22) with respect to t is:

[0035] Because -v b =dh / dt, and Equation (23) can be expressed as:

[0036] For multi-component bubbles, the multi-component mass in the multi-component bubble is defined as M G =[m G，1 m G，2 ... m G，N ], where m G，i represents the mass of gas component i in the bubble; the molar amount of all components is defined as N G =[n G，1 n G，2 ... n G，N ], where n i Expressed as the molar amount of gas component i;

[0037] The mole fraction of gas component i is expressed as The total mole fraction is expressed as Where I is the unit row vector, I=[1 1 ... 1]; M solute is the mass of the liquid phase, then the mass change in the bubble is expressed as:

[0038] Combining equation (20), we get:

[0039] S4. Based on the stagnation cap model, a pollutant accumulation stagnation cap model is constructed;

[0040] According to the Griffith stagnation cap model, if surface convection is faster than volume diffusion, adsorption and desorption are faster, and the adsorbed pollutants will accumulate at the tail, forming an immovable stagnation cap. Assuming that the pollutants are insoluble and controlled by diffusion, the diffusion rate of the pollutants from the bulk to the surface is Expressed as:

[0041] In formula (28), A is the bubble surface area, k s is the mass transfer coefficient of the pollutant, k s =k′(2R) -1 / 2 , determined by the number of moles of pollutants accumulated, n s and the area a occupied by each mole of pollutant s Calculate the stagnation cap area A cap , A cap =a s n s , let the coefficient k′, molar area a s , the main concentration of pollutants C ∞ The product is a constant, then: k=k′a s C ∞ (29)

[0042] In formula (29), k is the empirical fitting constant;

[0043] The rate of change of pollutant surface area over time is obtained:

[0044] The mass transfer flux of bubbles in unsaturated liquid is expressed as the liquid side mass transfer coefficient K L Expressed as:

[0045] The gas-liquid mass transfer flux is positively correlated with the mass transfer area, which involves the accumulation of pollutants on the bubble surface. Equation (18) can be rewritten as:

[0046] In formula (32) is the effective mass transfer area ratio, The stagnation angle θ is calculated by formula (33):

[0047] Construct a set of coupled model equations for multi-component single bubble motion and mass transfer:

[0048] Furthermore, the method for obtaining the transient acceleration model of the multi-component bubble in step S1 includes:

[0049] The drag coefficient C in equations (7) and (8) is D Substitute the calculation formula into formula (4), and replace F in formulas (2) to (6) V 、F G 、F D 、F m 、F B Substituting the calculation formula into formula (1), we can obtain the transient acceleration model of multi-component bubbles:

[0050] Industrial gas-liquid reactions are dominated by multi-bubble mass transfer. Compared to single-bubble mass transfer, multi-bubble systems are more complex to study due to the interactions between bubbles, including coalescence, breakup, and changes in the bubble flow field. To simplify the study of bubble mass transfer behavior, we can begin with a single bubble. By combining experimental studies with simulations, we can explore the influence of specific bubble-related parameters on the mass transfer behavior of a single bubble. Single-bubble research can lay the foundation for the development of multi-bubble mass transfer and related models. Using modified models, we can establish correlations between single-bubble and multi-bubble mass transfer.

[0051] Furthermore, the mass transfer rate of the single-component bubble in step S2 is expressed by a vector:

[0052] Formula (17) is derived for single-component bubbles. For multi-component bubbles containing N gases, we have To simplify the calculation, it is assumed that the mass transfer of multiple components in the boundary layer of Equation (17) will not affect each other, then Equation (17) can be expressed in vector form as follows:

[0053] Furthermore, the method for calculating the gas-liquid two-phase flow velocity in step S2 includes:

[0054] Due to the Peclet number (Pe m =2v b R / D AB ) is usually large, so the liquid far away from the bubble interface can be regarded as a constant concentration, and gas-liquid mass transfer dominates in the liquid boundary layer, as shown in Equation (15):

[0055] Furthermore, the method for establishing the bubble mass state equation in step S3 includes:

[0056] It is explained from the perspectives of mass transfer kinetics and mass state equation. The solutions of these two equations should be the same, so we can get Differentiation calculation of :

[0057] Furthermore, the method for constructing the pollutant accumulation stagnation cap model in step S4 includes:

[0058] The accumulation of pollutants not only affects mass transfer, but also significantly changes the drag coefficient of the bubble. The drag coefficient of some contaminated bubbles is calculated using the following expression:

[0059] In formula (34), C D，mobile , C D，rigid are the drag coefficients of bubbles in the clean and contaminated systems, respectively.

[0060] The bubble drag coefficient equation and its applicable conditions of the present invention are shown in Table 1:

[0061] Table 1 Bubble resistance coefficient equation and corresponding applicable conditions

[0062] The present invention uses Newton's second law to perform force analysis to obtain a bubble transient acceleration model. By solving the bubble motion around a sphere and the bubble state equation, a mass transfer model is obtained and expanded to multiple components. The stagnation cap model is introduced into the transient mass transfer model to obtain a multi-component single bubble motion and mass transfer coupling model suitable for contaminated conditions.

[0063] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process as described above.

[0064] The present invention also provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the program, the steps of the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process as described above are implemented.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The present invention expands the single-component mass transfer model into multiple components and introduces a stagnation cap model to expand the application scenarios of the model. The mutual influence among motion, mass transfer and pollutant diffusion is solved in the form of a mathematical model. A coupling model that can simulate the motion and mass transfer of multiple components single bubbles within the micro-interface scale is established. The coupled model is applied to simulate the coupled process of motion and mass transfer of multiple components single bubbles within the micro-interface scale. Combined with the bubble motion and mass transfer characteristics within the micro-interface scale, the mutual influence between motion and mass transfer of multiple components single bubbles and the enhancement effect of bubble size on mass transfer can be predicted. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Various other advantages and benefits will become apparent to those skilled in the art by reading the detailed description of the preferred embodiment below. The accompanying drawings are only for the purpose of illustrating the preferred embodiment and are not to be considered as limiting the present invention. In the accompanying drawings:

[0068] FIG1 is a flow chart of a modeling method for a simulation model of a multi-component single bubble motion and mass transfer coupling process according to the present invention;

[0069] FIG2 is a schematic diagram showing the structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0070] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, identical numerals in different figures represent identical or similar elements, unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible embodiments consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as detailed in the appended claims.

[0071] The terms used in this disclosure are for the purpose of describing specific embodiments only and are not intended to limit the disclosure. As used in this disclosure and the appended claims, the singular forms "a," "an," "the," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0072] It should be understood that although the terms first, second, and third may be used in the present disclosure to describe various signals, these signals should not be limited to these terms. These terms are only used to distinguish signals of the same type from each other. For example, without departing from the scope of the present disclosure, a first signal may also be referred to as a second signal, and similarly, a second signal may also be referred to as a first signal. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0073] The embodiments of the present invention are described in detail below with reference to the accompanying drawings:

[0074] The present invention provides a modeling method for a simulation model of a multi-component single bubble motion and mass transfer coupling process, as shown in FIG1 , comprising the following steps:

[0075] S1. According to Newton's second law and based on the viscosity-dominated mechanism of spherical bubbles, a bubble transient acceleration model is established;

[0076] Submillimeter bubbles with a diameter less than 1mm can be considered as rigid spheres during motion, with a linear upward trajectory. For single-component bubbles, the instantaneous acceleration model of the bubble can be obtained through force analysis. Considering that the bubble moves in a linear manner, the direction of the bubble's resultant force is vertical, and the external forces perpendicular to the bubble's motion direction are mutually balanced and can be ignored.

[0077] The vertical force on the bubble mainly includes the buoyancy F V Gravity F G , viscous resistance F D , additional mass force F m and Basset Force F B According to Newton's second law, the rate of change of bubble momentum due to the combined contribution of the vertical forces is expressed as:

[0078] In formula (1), R is the bubble diameter; ρ G is the gas phase density; v b is the instantaneous velocity of the bubble; the force F on the right side of formula (1) V 、F G 、F D 、F m 、F B Respectively expressed as:

[0079] In formulas (2)-(6), ρ L is the liquid density, μ L is the liquid viscosity, C D represents the drag coefficient; according to the mechanism of the Tomiyama drag force model, the spherical bubbles studied in this paper belong to the viscosity-dominated mechanism. In this case, the surfactant on the bubble surface increases the viscous drag;

[0080] Based on the viscosity-dominated mechanism of spherical bubbles, in the range of -11≤log Mo≤0.63, 3.2×10 -9 Under the conditions of ≤Re≤720, 0.042≤Eo≤29, Re is the Reynolds number, and the drag coefficient of the clean bubble on the completely movable surface is calculated using formulas (7) and (8). The aspect ratio E of the spherical bubble is b is 1;

[0081] For multi-component gas systems commonly used in industry, the mole fraction of bubbles containing N gas components needs to be introduced; let the mole fraction, gas density, and molar mass of component i in the gas be y i ,ρi and Mol i , the viscosity of liquid phase i component is μ L，i , then: Y=[y1 y2 ... y N ] μ L =[μ L，1 μ L，2 ... μ L，N ] / ρ=[ρ1 ρ2 ... ρ N ]

[0082] M solute =[Mol1 Mol2 ... Mol N ]

[0083] For non-associating liquid mixtures, the viscosity of the mixture is calculated as: log μ L =Σx i log μ L，i (9)

[0084] During the bubble desorption process, the mole fraction of the components in the bubble changes in real time. The density of the mixed gas is calculated as follows: ρ G =ρ·Y T (10)

[0085] The drag coefficient C in equations (7) and (8) is D Substitute the calculation formula into formula (4), and replace F in formulas (2) to (6) V 、F G 、F D 、F m 、F B Substituting the calculation formula into formula (1), we can obtain the transient acceleration model of multi-component bubbles:

[0086] Industrial gas-liquid reactions are dominated by multi-bubble mass transfer. Compared to single-bubble mass transfer, multi-bubble systems are more complex to study due to the interactions between bubbles, including coalescence, breakup, and changes in the bubble flow field. To simplify the study of bubble mass transfer behavior, we can begin with a single bubble. By combining experimental studies with simulations, we can explore the influence of specific bubble-related parameters on the mass transfer behavior of a single bubble. Single-bubble research can lay the foundation for the development of multi-bubble mass transfer and related models. Using modified models, we can establish correlations between single-bubble and multi-bubble mass transfer.

[0087] S2. Based on the flow function in spherical coordinate form and the non-equilibrium mass transfer theory, a bubble transient non-equilibrium mass transfer model is established;

[0088] As mentioned above, microbubbles can maintain a stable spherical shape during movement without typical boundary layer separation. Therefore, the non-separated flow equation around the sphere can represent the peripheral flow field formed by the rising bubbles. Without considering the bubble wake phenomenon, the function expression of the flow function in spherical coordinate form is:

[0089] The mass transfer diffusion equation in the liquid phase is given in the form of spherical coordinates:

[0090] According to the definition of stream function, the gas-liquid two-phase flow velocity is calculated as follows:

[0091] Due to the Peclet number (Pe m =2v b R / D AB ) is usually large, so the liquid far away from the bubble interface can be regarded as a constant concentration, and gas-liquid mass transfer dominates in the liquid boundary layer, as shown in Equation (15):

[0092] The last term of equation (13) can be ignored, and the mass flow rate J can be obtained by combining equations (12) to (14):

[0093] The mass transfer rate of single-component bubbles is obtained as follows:

[0094] Formula (17) is derived for single-component bubbles. For multi-component bubbles containing N gases, we have To simplify the calculation, it is assumed that the mass transfer of multiple components in the boundary layer of Equation (17) will not affect each other, then Equation (17) can be expressed in vector form as follows:

[0095] Accordingly, the total mass change in the bubble includes the mass change of each component, and the mass transfer rate of the multi-component bubble is as shown in Equation (18):

[0096] Formula (18) contains a key parameter C I : Gas concentration at the interface. For the models commonly used in the chemical industry (membrane model, permeation model, and surface renewal model, etc.), it is assumed that there is no resistance at the interface, that is, the interfacial thermodynamic equilibrium of the mass transfer process must satisfy Henry's law. However, when the internal concentration of microbubbles changes rapidly, the thermodynamic equilibrium at the interface cannot be achieved. Therefore, the relationship between the gas concentration in the bubble and the gas concentration at the phase interface does not conform to Henry's law. Therefore, C should be obtained through non-equilibrium mass transfer theory. I , C * represents the equilibrium concentration at the gas-liquid interface, as shown in Equation (19);

[0097] H=[H1 H2 ... H N ], H i refers to the solubility coefficient of gas component i;

[0098] S3. Based on mass transfer kinetics and mass state equation, establish the bubble mass state equation;

[0099] The gas mass transfer flux in the bubble is expressed as Through the pair Taking the derivative of both sides with respect to t, we get:

[0100] For a multicomponent bubble containing N components, there exists:

[0101] In formula (22), ρ0 (should it be ρ G0 ? ) is the various components in the bubble at a certain temperature and atmospheric pressure P atm The density vector under , the derivative of formula (22) with respect to t is:

[0102] Because -v b =dh / dt, and Equation (23) can be expressed as:

[0103] For multi-component bubbles, the multi-component mass in the multi-component bubble is defined as M G =[m G，1 M G，2 ... m G，N ], where m G，i represents the mass of gas component i in the bubble; the molar amount of all components is defined as N G =[n G，1 n G，2 ... n G，N ], where n i Expressed as the molar amount of gas component i;

[0104] The mole fraction of gas component i is expressed as The total mole fraction is expressed as Where I is the unit row vector, I=[1 1 ... 1]; The mass change in the bubble is then expressed as:

[0105] Combining equation (20), we get:

[0106] It is explained from the perspectives of mass transfer kinetics and mass state equation. The solutions of these two equations should be the same, so we can get Differentiation calculation of :

[0107] S4. Based on the stagnation cap model, a pollutant accumulation stagnation cap model is constructed;

[0108] According to the Griffith stagnation cap model, if surface convection is faster than volume diffusion, adsorption and desorption are faster, and the adsorbed pollutants will accumulate at the tail, forming an immovable stagnation cap. Assuming that the pollutants are insoluble and controlled by diffusion, the diffusion rate of the pollutants from the bulk to the surface is Expressed as:

[0109] In formula (28), k s is the mass transfer coefficient of the pollutant, k s =k′(2R) -1 / 2 , determined by the number of moles of pollutants accumulated, n s and the area a occupied by each mole of pollutant s Calculate the stagnation cap area A cap , A cap =a s n s , let the coefficient k′, molar area a s , the main concentration of pollutants C ∞ The product is a constant, then: k=k′a s C ∞ (29)

[0110] The rate of change of pollutant surface area over time is obtained:

[0111] The mass transfer flux of bubbles in unsaturated liquid is expressed as the liquid side mass transfer coefficient K L Expressed as:

[0112] The gas-liquid mass transfer flux is positively correlated with the mass transfer area, which involves the accumulation of pollutants on the bubble surface. Equation (18) can be rewritten as:

[0113] In formula (32) is the effective mass transfer area ratio, The stagnation angle θ is calculated by formula (33):

[0114] Furthermore, the method for constructing the pollutant accumulation stagnation cap model in step S4 includes:

[0115] The accumulation of pollutants not only affects mass transfer, but also significantly changes the drag coefficient of the bubble. The drag coefficient of some polluted bubbles is calculated as follows:

[0116] In formula (34), C D，mobile , C D，rigid are the drag coefficients of bubbles in the clean and contaminated systems, respectively.

[0117] The bubble drag coefficient equation and its applicable conditions of the embodiment of the present invention are shown in Table 1:

[0118] Table 1 Bubble resistance coefficient equation and corresponding applicable conditions

[0119] Construct a set of coupled model equations for multi-component single bubble motion and mass transfer:

[0120] In this embodiment, force analysis is performed with the help of Newton's second law to obtain a bubble transient acceleration model. The mass transfer model is obtained by solving the bubble motion around the sphere and the bubble state equation and is expanded to multiple components. The stagnation cap model is introduced into the transient mass transfer model to obtain a multi-component single bubble motion and mass transfer coupling model suitable for contaminated conditions.

[0121] The embodiment of the present invention expands the single-component mass transfer model to multiple components, introduces a stagnation cap model, expands the application scenarios of the model, and explains the mutual influence between motion, mass transfer and pollutant diffusion in the form of a mathematical model. A set of coupling models that can simulate the motion and mass transfer of multiple components single bubbles within the micro-interface scale is established, which is applied to the simulation of the coupling process of the motion and mass transfer of multiple components single bubbles within the micro-interface scale. Combined with the bubble motion and mass transfer characteristics within the micro-interface scale, it can predict the mutual influence between the motion and mass transfer of multiple components single bubbles and the enhancement effect of bubble size on mass transfer.

[0122] An embodiment of the present invention also provides a computer device. Figure 2 is a structural schematic diagram of a computer device provided by an embodiment of the present invention. Referring to Figure 2 of the accompanying drawings, the computer device includes: an input device 23, an output device 24, a memory 22 and a processor 21; the memory 22 is used to store one or more programs; when the one or more programs are executed by the one or more processors 21, the one or more processors 21 implement the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process provided by the above embodiment; wherein the input device 23, the output device 24, the memory 22 and the processor 21 can be connected via a bus or other means, and Figure 2 takes the connection via a bus as an example.

[0123] The memory 22 is a readable and writable storage medium of a computing device and can be used to store software programs and computer executable programs, such as program instructions corresponding to the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupled process described in the embodiment of the present invention; the memory 22 can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system and at least one application required for a function; the data storage area can store data created according to the use of the device, etc.; In addition, the memory 22 can include a high-speed random access memory and can also include a non-volatile memory, such as at least one disk storage device, a flash memory device, or other non-volatile solid-state storage device; In some examples, the memory 22 can further include a memory remotely located relative to the processor 21, and these remote memories can be connected to the device via a network. Examples of the above-mentioned network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0124] The input device 23 may be used to receive input digital or character information, and generate key signal input related to user settings and function control of the device; the output device 24 may include a display device such as a display screen.

[0125] The processor 21 executes various functional applications and data processing of the device by running the software programs, instructions and modules stored in the memory 22, that is, realizes the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process mentioned above.

[0126] The computer device provided above can be used to execute the modeling method of the simulation model of the multi-component single bubble movement and mass transfer coupling process provided in the above embodiment, and has corresponding functions and beneficial effects.

[0127] The present invention also provides a storage medium containing computer executable instructions, which, when executed by a computer processor, is used to perform the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupled process provided in the above embodiment. The storage medium is any of various types of memory devices or storage devices, including: installation media, such as CD-ROM, floppy disk or tape device; computer system memory or random access memory, such as DRAM, DDR RAM, SRAM, EDO RAM, Rambus RAM, etc.; non-volatile memory, such as flash memory, magnetic media (such as hard disk or optical storage); registers or other similar types of memory elements; the storage medium may also include other types of memory or a combination thereof; in addition, the storage medium may be located in the first computer system in which the program is executed, or may be located in a different second computer system, the second computer system being connected to the first computer system via a network (such as the Internet); the second computer system may provide program instructions to the first computer for execution. The storage medium includes two or more storage media that can reside in different locations (e.g., in different computer systems connected via a network). The storage medium can store program instructions (e.g., embodied as a computer program) that can be executed by one or more processors.

[0128] Of course, the storage medium containing computer-executable instructions provided in an embodiment of the present invention is not limited to the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process as described in the above embodiment, and can also execute the relevant operations in the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process provided in any embodiment of the present invention.

[0129] Thus far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art may make various modifications or substitutions to the relevant technical features, and the technical solutions after such modifications or substitutions will fall within the scope of protection of the present invention.

[0130] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A modeling method for a simulation model of a multi-component single bubble motion and mass transfer coupling process, characterized in that: The following steps are involved: S1. According to Newton's second law and based on the viscosity-dominated mechanism of spherical bubbles, a bubble transient acceleration model is established; The vertical forces acting on the bubble include the buoyancy F V , gravity F G , viscous resistance F D , additional mass force F m and Basset F B According to Newton's second law, the rate of change of bubble momentum is expressed by the combined contribution of the vertical forces: In formula (1), R is the bubble diameter; ρ G is the gas phase density; v b is the instantaneous velocity of the bubble; the force F on the right side of equation (1) V 、F G 、F D 、F m 、F B Respectively expressed as: In formulas (2)-(6), ρ L is the liquid density, μ L is the liquid viscosity, C D represents the drag coefficient; Based on the viscosity-dominated mechanism of spherical bubbles, Under the condition, Re is the Reynolds number, and the drag coefficient of the clean bubble on the completely movable surface is calculated using equations (7) and (8). The aspect ratio of the spherical bubble E b is 1; Assume that the molar fraction, gas density, and molar mass of component i in the gas are y i ,ρ i and Mol i , the viscosity of liquid phase i is μ L，i , then: Y=[y1 y2 ... y N ] m L =[μ L，1 m L，2 ... m L，N ] / p=[p1 p2 ... p N ] Msolute=[Mole1 Mol2 ... Mole N ] For non-associating liquid mixtures, the viscosity of the mixed liquid is calculated as: logμ L =∑x i logμ L，i (9) In formula (9), μ L is the viscosity of the mixed liquid phase, μ L，i is the viscosity of component i in the liquid phase. During the bubble desorption process, the mole fraction of the component in the bubble changes in real time. The density calculation formula of the mixed gas is: r G =ρ·Y T (10) In formula (10), ρ is the gas phase density matrix, Y is the unit row vector, and T is the transposition sign. Substituting formulas (2) to (8) into formula (1), the transient acceleration model of multi-component bubbles is obtained; S2. According to the flow function in spherical coordinate form and the non-equilibrium mass transfer theory, a bubble transient non-equilibrium mass transfer model is established; The functional expression of the flow function in spherical coordinate form is: In formula (12), ψ is the stream function, r is the radial distance, and R is the radius. The mass transfer diffusion equation in the liquid phase is given in the form of spherical coordinates: In formula (13), C is the dimensionless concentration; According to the definition of stream function, the gas-liquid two-phase flow velocity is calculated, and the calculation expression is: In formula (14), u r 、u θ are radial and tangential velocities respectively; the latter term of equation (13) is ignored, and the mass flow rate J is obtained by combining equations (12) to (14): In formula (16), D AB is the diffusion coefficient, C A is the bulk concentration of the liquid phase, C I is the interfacial gas concentration; the mass transfer rate of the single-component bubble is obtained as follows: In formula (17), m G is the bubble mass; accordingly, the total mass change in the bubble includes the mass change of each component, and the mass transfer rate of multi-component bubbles is as shown in formula (18): Formula (18) contains a key parameter C I : Gas concentration at the interface, obtained by nonequilibrium mass transfer theory C I , C * represents the equilibrium concentration at the gas-liquid interface, as shown in formula (19): H=[H1 H2 ... H N ], H i refers to the solubility coefficient of gas component i; P atm is the atmospheric pressure, H is the solubility coefficient, and σ is the surface tension; S3. Based on mass transfer kinetics and mass state equation, a bubble mass state equation is established; The gas mass transfer flux in the bubble is expressed as Through the pair Taking the derivative of both sides with respect to t, we get: For a multi-component bubble containing N components, there exists: In formula (22), ρ G0 It is the various components in the bubble at a certain temperature and atmospheric pressure P atm The density vector under , the derivative of equation (22) with respect to t is: Because -v b =dh / dt, and equation (23) can be expressed as: The multi-component mass in the multi-component bubble is defined as M G =[m G，1 m G，2 ... m G，N ], where m G，i represents the mass of gas component i in the bubble; the molar amount of all components is defined as N G =[n G，1 n G，2 ... n G，N ], where n i Expressed as the molar amount of gas component i; The mole fraction of gas component i is expressed as The total mole fraction is expressed as Where I is the unit row vector, I = [1 1 ... 1]; M solute is the mass of the liquid phase, then the mass change in the bubble is expressed as: Combining equation (20), we get: S4. Based on the stagnation cap model, a pollutant accumulation stagnation cap model is constructed; According to the stagnation cap model, if surface convection is faster than volume diffusion, adsorption and desorption are both faster, and the adsorbed pollutants will accumulate at the tail, forming an immovable stagnation cap. Assuming that the pollutants are insoluble and controlled by diffusion, the diffusion rate of the pollutants from the bulk to the surface is It is expressed as: In formula (28), A is the bubble surface area, k s is the mass transfer coefficient of the pollutant, k s = k′(2R) -1 / 2 , given by the number of moles of pollutants accumulated n s and the area a occupied by each mole of pollutant s Calculate the stagnation cap area A cap , A cap =a s n s , let coefficient k′, molar area a s , the main concentration of pollutants C ∞ The product is a constant, then: k=k′a s C ∞ (29) In formula (29), k is the empirical fitting constant; The rate of change of pollutant surface area over time is obtained: The mass transfer flux of bubbles in unsaturated liquid is expressed as the liquid side mass transfer coefficient K L It is expressed as: The gas-liquid mass transfer flux is positively correlated with the mass transfer area, which involves the accumulation of pollutants on the bubble surface. Equation (18) can be rewritten as: In formula (32), is the effective mass transfer area ratio, The stagnation angle θ is calculated by formula (33): Construct a set of equations for the multi-component single bubble motion and mass transfer coupling model:

2. The modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process according to claim 1 is characterized in that: The method for obtaining the transient acceleration model of the multi-component bubble in step S1 includes: The drag coefficient C in equations (7) and (8) is D Substitute the calculation formula into formula (4) and convert the F in formulas (2) to (6) V 、F G 、F D 、F m 、F B Substituting the calculation formula into formula (1), we can obtain the transient acceleration model of multi-component bubbles:

3. The modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process according to claim 1 is characterized in that: The mass transfer rate of the single-component bubble in step S2 is expressed by vectorization: For a multi-component bubble containing N gases, we have Assuming that the mass transfer of multiple components in the boundary layer of equation (17) does not affect each other, equation (17) can be expressed in vector form as follows:

4. The modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process according to claim 1 is characterized in that: The method for calculating the gas-liquid two-phase flow velocity in step S2 includes: The liquid far from the bubble interface is regarded as a constant concentration, and the gas-liquid mass transfer dominates in the liquid boundary layer, as shown in Equation (15):

5. The modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process according to claim 1 is characterized in that: The method for establishing the bubble mass state equation in step S3 includes: By combining equations (18) and (26), we can obtain Differentiation calculation of :

6. The modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process according to claim 1 is characterized in that: The method for constructing the pollutant accumulation stagnation cap model in step S4 includes: Calculate the drag coefficient of some contaminated bubbles, the calculation expression is: In formula (34), C D，mobile , C D，rigid are the drag coefficients of bubbles in the clean and contaminated systems, respectively.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process described in any one of claims 1 to 6 are implemented.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the modeling method of the simulation model of the multi-component single bubble motion and mass transfer coupling process as described in any one of claims 1-6 are implemented.

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