A method for constructing a numerical simulation model of hydrogen bubble growth process on electrode surface

Abstract

The present invention discloses a method for constructing a numerical simulation model of a hydrogen bubble growth process on an electrode surface, establishing a two-dimensional axisymmetric computational geometry model and performing mesh division and mesh encryption processing; deriving a mathematical physical model describing the gas-liquid two-phase mass transfer behavior and characteristics during the dynamic growth of a single hydrogen bubble on the electrode surface, considering the gas-liquid two-phase convection effect, the influence of the liquid convection induced by the growth of hydrogen bubbles, and the diffusion behavior of dissolved hydrogen components to establish a two-phase flow model; using the two-phase flow model to calculate the data of the growth process of a single hydrogen bubble on the electrode surface for hydrogen production by electrolysis of water, generating a hydrogen bubble growth curve on the electrode surface based on the obtained data, and completing the numerical simulation of the hydrogen bubble growth process on the electrode surface. This method accurately characterizes the complex gas-liquid two-phase flow process, as well as the dynamic process of mass transfer of hydrogen components from the gas-liquid interface or micro-liquid layer region to the bubble driven by the concentration gradient of the supersaturated dissolved hydrogen component, thereby promoting the growth of hydrogen bubbles.

Description

Technical Field

[0001] The invention relates to the field of numerical simulation of bubble dynamics, and in particular to a numerical simulation modeling and calculation method for a growth process of a single hydrogen bubble on the surface of an electrode for hydrogen production by electrolysis of water. Background Art

[0002] Among many clean energy sources, hydrogen is considered to be one of the most ideal clean and renewable energy carriers because of its high energy density and the fact that it does not produce air pollutants or greenhouse gases such as CO during combustion or reaction. Among the many methods of preparing hydrogen, water electrolysis is one of the mainstream technologies for hydrogen production. Due to its mature technology, abundant raw materials, clean energy, and low-carbon technology, water electrolysis has attracted more and more attention and research from scholars. The interaction between bubbles / bubble groups and electrolytes and electrodes in the actual water electrolysis hydrogen production system is very complex. It is a typical electrochemical gas evolution process with interactive effects of multiphase electrochemical reactions (electrolyte, hydrogen bubbles), multi-physical fields (flow field, electric field, temperature field, concentration field, etc.), multi-component diffusion, and heat and mass transfer. In-depth research on the complex kinetic behavior and heat and mass transfer process during the growth of hydrogen bubbles is of great significance for revealing the growth characteristics and mechanism of bubbles in the water electrolysis hydrogen production system.

[0003] At present, the relevant traditional experimental research methods still mainly stay in the methods of high-speed photography visualization, electrochemical measurement and theoretical analysis, etc., to explore the dynamic behaviors of bubble growth, adhesion and detachment on the surface of the electrolytic water hydrogen production electrode. However, the current measurement method is difficult to accurately measure the structural evolution law of the micro-liquid layer at the bottom of the bubble on the surface of the electrochemical gas evolution electrode, which makes it difficult to establish a micro-liquid layer mass transfer model. The related traditional simplified mathematical modeling method research often ignores the dynamic processes such as bubble growth and gas-liquid mass transfer. Steady-state calculations are performed by constructing multiple mathematical and physical model cases corresponding to different growth moments and different bubble sizes to approximately describe the actual process of non-steady-state bubble dynamic growth in the electrolytic water hydrogen production system. At the same time, most of the current numerical simulation studies only consider the diffusion mass transfer behavior of hydrogen components at the gas-liquid interface derived from Fick's law, and lack in-depth scientific quantitative description of the direct injection mass transfer behavior of the micro-liquid layer at the bottom of the bubble, as well as the influence of the coupling of the above two mass transfer behaviors on the dynamic growth process of hydrogen bubbles. Summary of the invention

[0004] In order to address the deficiencies in the prior art, the present application proposes a method for constructing a numerical simulation model of the hydrogen bubble growth process on the electrode surface. The method combines the structural characteristics of the micro-liquid layer and its mass transfer theory to make its calculation results more reasonable and accurate. It can accurately reveal the dynamic process law of the growth of a single hydrogen bubble on the electrode surface for hydrogen production by electrolysis of water, as well as the influence of the coupling of direct injection mass transfer of the micro-liquid layer and diffusion mass transfer of hydrogen components at the gas-liquid interface on the bubble growth behavior, which is conducive to scientifically guiding the design and application of actual hydrogen production equipment by electrolysis of water.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for constructing a numerical simulation model of a hydrogen bubble growth process on an electrode surface, the calculation method comprising the following steps:

[0007] Step 1: According to the geometric parameters of the electrodes and the hydrogen bubble growth process in the water electrolysis hydrogen production system, a two-dimensional axisymmetric computational geometry model is established, the geometric model is meshed, and the mesh encryption process is performed on the bubble growth area; the geometric parameters include cathode size, anode size, bubble detachment radius, bubble contact angle, and three-phase contact line;

[0008] Step 2: Derive a mathematical and physical model that describes the gas-liquid two-phase mass transfer behavior and characteristics during the dynamic growth of a single hydrogen bubble on the electrode surface in the water electrolysis hydrogen production system, wherein the mathematical and physical model includes the generation rate of dissolved hydrogen components on the electrode surface, the diffusion mass transfer rate of hydrogen components at the gas-liquid interface, and the direct injection mass transfer rate of the micro-liquid layer;

[0009] Step 3: Considering the gas-liquid two-phase flow effect, the influence of liquid phase flow induced by hydrogen bubble growth and the diffusion behavior of dissolved hydrogen components, a gas-liquid two-phase flow model describing the dynamic growth process of a single hydrogen bubble in the water electrolysis hydrogen production system is established based on the mathematical and physical model; the two-phase flow model is used to calculate the data of the growth process of a single hydrogen bubble on the surface of the water electrolysis hydrogen production electrode, and the hydrogen bubble growth curve on the electrode surface is generated based on the obtained data to complete the numerical simulation of the hydrogen bubble growth process on the electrode surface.

[0010] Further, the generation rate of dissolved hydrogen components on the electrode surface is expressed as:

[0011]

[0012] In the formula, is the generation rate of hydrogen components on the electrode surface (kg / m 2 s); is the molar mass of hydrogen molecule; I / A e is the current density flowing through the electrode surface, calculated by the potential equation in step 2; F is the Faraday constant.

[0013] Further, the gas-liquid interface hydrogen component diffusion mass transfer rate is expressed as:

[0014]

[0015] In the formula, is the saturation concentration of dissolved hydrogen component, It represents the concentration of dissolved hydrogen in the electrolyte (expressed in mass fraction kg / kg), is the mass transfer coefficient of dissolved hydrogen component in electrolyte convection diffusion, R b is the bubble equivalent radius, t is the hydrogen bubble growth time, ρ l is the electrolyte density.

[0016] Further, the micro-liquid layer direct injection mass transfer rate is expressed as:

[0017]

[0018] Where D micro is the diffusion coefficient of mass transfer directly injected into the micro-liquid layer, δ is the radial thickness of the micro-liquid layer, R e is the electrode radius.

[0019] Furthermore, the generation rate of dissolved hydrogen components on the electrode surface, the diffusion mass transfer rate of hydrogen components at the gas-liquid interface, and the direct injection mass transfer rate of the micro-liquid layer in step 2 are converted into volumetric mass transfer rates, respectively; they are expressed as:

[0020] The unit conversion of the generation rate of dissolved hydrogen components on the electrode surface is expressed as:

[0021]

[0022] In the formula, A e is the actual reactive active area of ​​the electrode surface; V e,c is the volume of the first layer of grid on the working electrode surface; L c is the height of the first grid layer on the electrode surface.

[0023] The unit conversion process is performed on the hydrogen component diffusion mass transfer rate at the gas-liquid interface, and the source term of the hydrogen component diffusion mass transfer at the gas-liquid interface of gas phase absorption is expressed as:

[0024]

[0025] Among them, A b is the gas-liquid interface area; V b,c is the volume of the grid contained by the gas-liquid interface, is the absolute value of the volume fraction gradient of the gas-liquid interface grid;

[0026] The micro-liquid layer direct injection mass transfer rate is converted into units, and the micro-liquid layer direct injection mass transfer source term is expressed as:

[0027]

[0028] Among them, A micro V is the gas-liquid interface area contained in the micro-liquid layer area; micro is the volume of the air-liquid interface grid contained in the micro-liquid layer area, is the absolute value of the volume fraction gradient of the gas-liquid interface grid.

[0029] Further, the two-phase flow model is established, and the two-phase flow model is expressed as:

[0030] (2) Establish a mathematical model of the evolution of the gas-liquid interface and the gas-liquid two-phase velocity field, expressed as:

[0031] Continuity equation:

[0032] α g +α l =1

[0033]

[0034]

[0035] In the formula, α g and α l are the volume fractions of the gas phase and the liquid phase, V g and V l are the velocity vectors of the gas phase and the liquid phase, S g,surface and S g,micro are the gas-liquid interface hydrogen component diffusion mass transfer source term of gas phase absorption and the micro-liquid layer direct injection mass transfer source term, is the hydrogen component source term generated by Faraday's law; S l,surface is the source term of hydrogen component consumed by the liquid phase during mass transfer; ρ g and ρ l are the densities of the gas phase and the liquid phase, respectively;

[0036] The momentum equation is expressed as:

[0037]

[0038] Wherein, μ and ρ are the volume average values ​​of each phase, F σ is the surface tension, is the relative pressure, V is the velocity vector;

[0039] (2) Establish a mathematical model of dissolved hydrogen component concentration field, expressed as:

[0040]

[0041] In the formula, is the hydrogen component source term generated by Faraday's law, is the saturation concentration of dissolved hydrogen component, is the diffusion coefficient of dissolved hydrogen component in the electrolyte.

[0042] (3) Establish a mathematical model of electric field distribution, expressed as:

[0043]

[0044] Where φ is the electric potential, κ m is the volume average conductivity of the mixture.

[0045] Furthermore, the continuous surface force model is used to deal with the surface tension of the gas-liquid interface. σ It is expressed as:

[0046]

[0047] Where σ is the surface tension coefficient of the gas-liquid interface, κ g is the curvature of the gas phase interface, κ l is the curvature of the liquid interface.

[0048] Furthermore, multiple custom storage variables UDMI are defined, and the numerical values ​​at each time step in the numerical calculation process are assigned to the custom storage variables for storage.

[0049] Furthermore, the ANSYS MESH geometric model is used for meshing.

[0050] Furthermore, the Refine / Coarseness module in FLUENT software was used to perform mesh encryption on the bubble growth area.

[0051] Beneficial effects of the present invention:

[0052] (1) A more accurate multiphase flow VOF method is used to numerically simulate the growth process of a single hydrogen bubble on the surface of the electrode for hydrogen production by electrolysis of water. Compared with the traditional numerical simulation method of solid sphere single-phase flow with fixed bubble size, it can more accurately characterize the complex gas-liquid two-phase flow process, as well as the dynamic process of mass transfer of hydrogen components from the gas-liquid interface or micro-liquid layer region to the bubble driven by the concentration gradient of the supersaturated dissolved hydrogen component, thereby promoting the growth of hydrogen bubbles.

[0053] (2) The present invention applies the micro-liquid layer structure and mass transfer theory to the numerical simulation of the dynamic process of hydrogen bubble growth on the surface of the electrode for hydrogen production by electrolysis of water, which changes many traditional experiments and theories that only propose qualitative descriptions of the mass transfer characteristics of the micro-liquid layer at the bottom of the bubble, thereby being able to quantitatively describe the mass transfer characteristics of the micro-liquid layer and its influence on bubble growth, and the simulation calculation results are more consistent with the corresponding experimental results. By establishing a mass transfer model of direct injection of micro-liquid at the bottom of the bubble and coupling it to the entire calculation process using a user-defined function UDF, the calculation efficiency is significantly improved while ensuring the calculation accuracy.

[0054] (3) By combining user-defined functions (UDF) and custom storage (UDMI) and other code programs, the important process data in the numerical simulation modeling and calculation process of the growth process of a single hydrogen bubble on the surface of the electrode for hydrogen production by electrolysis of water are stored in real time, and the post-processing steps and procedures are simplified as much as possible.

[0055] (4) Compared with the relevant traditional experimental research methods, by establishing coupled numerical simulation and calculation methods such as multiphase flow, multi-physical field, multi-component diffusion and mass transfer, the dynamic process of single hydrogen bubble growth on the electrode surface in the electrolytic water hydrogen production system is obtained more clearly and accurately, and the laws of convective diffusion behavior of dissolved hydrogen components and the influence of the coupling of various mass transfer processes on bubble growth are scientifically and quantitatively studied. The research results of the present invention can directly and conveniently display the bubble morphology during the growth of hydrogen bubbles and the spatiotemporal evolution characteristics of the distribution of various physical fields, which helps technicians to deeply understand the laws and influences of the growth and evolution of hydrogen bubbles in the electrolytic water hydrogen production system, and provide strong theoretical guidance and technical reference for the development and application of high-efficiency and low-energy electrolytic water hydrogen production technology, which has important theoretical significance and engineering practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of the method of the present invention;

[0057] Figure 2 Schematic diagram of the physical geometric model and mesh division of the computational domain under a certain working condition.

[0058] Figure 3 Comparison between numerical simulation and experimental values ​​of hydrogen bubble growth curve under certain working conditions.

[0059] Figure 4 This is a spatiotemporal distribution cloud diagram of the gas phase volume fraction during the growth period of a single hydrogen bubble under certain working conditions.

[0060] Figure 5 This is a cloud diagram of the temporal and spatial distribution of dissolved hydrogen component concentration during the growth period of a single hydrogen bubble under certain working conditions.

[0061] Figure 6 This is the spatiotemporal distribution cloud diagram of the mass transfer source term at the gas-liquid interface during the growth period of a single hydrogen bubble under certain working conditions.

[0062] Figure 7 This is a cloud diagram of the temporal and spatial distribution of current density and current lines during the growth period of a single hydrogen bubble under certain working conditions.

[0063] Figure 8 It shows the temporal variation trend of the mass transfer rate and mass transfer quality of hydrogen component diffusion mass transfer at the gas-liquid interface, direct injection mass transfer in the micro-liquid layer and total mass transfer during the growth period of hydrogen bubbles under certain working conditions. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0065] In this specific embodiment, the dynamic process of a single hydrogen bubble growing on the surface of a circular nickel electrode with a radius of 63.5 μm under a constant current of 5.2 μA is used as a specific example for research description.

[0066] like Figure 1 A method for constructing a numerical simulation model of a hydrogen bubble growth process on an electrode surface is shown, comprising the following steps:

[0067] Step 1: According to the relevant geometric parameters of the electrodes and hydrogen bubbles in the actual water electrolysis hydrogen production system, a two-dimensional axisymmetric computational geometry model is established, focusing on mesh encryption of the computational domain included in the evolution of the gas-liquid interface, specifically: Figure 2 As shown in (a), the computational domain is 4 mm long and 2 mm wide. The basic geometric parameters are: anode radius 4 mm, cathode radius 63.5 μm.

[0068] The pre-processing software ANSYS MESH is used to mesh the entire computational domain. Figure 2 (b) As shown. In the actual electrolysis process, gas-liquid two-phase mass transfer and other physical field changes are mainly concentrated in the gas-liquid interface and cathode surface area. In order to ensure the accuracy of the calculation results, the areas mainly involved in the evolution of the gas-liquid interface and other physical field changes need to be meshed to avoid the introduction of spatial convection and boundary conditions. Through the grid independence verification study, the square grid size data of the local encrypted area was finally selected. The Refine / Coarseness module in the FLUENT software was used for local encryption. After the local encrypted area was selected, the grid of the area was divided multiple times to finally achieve the mesh encryption effect.

[0069] Step 2: Derive a mathematical and physical model that can accurately describe the interphase mass transfer behavior and characteristics during the dynamic growth of a single hydrogen bubble on the electrode surface in the water electrolysis hydrogen production system. The specific process is as follows:

[0070] (1) Derivation of the generation rate of dissolved hydrogen components on the electrode surface:

[0071] In the constant current electrolysis experiment, the generation rate of hydrogen components in the electrochemical reaction follows Faraday's law and the Butler-Volmer equation, which is determined by the total amount of charge passing through the cathode surface. According to the law of conservation of charge and Faraday's law, the generation rate of hydrogen components can be directly calculated based on the current:

[0072]

[0073] In the formula, is the generation rate of hydrogen components on the electrode surface (kg / m 2 s); is the molar mass of hydrogen molecule; I / A e is the current density flowing through the electrode surface, calculated by the potential equation in step 2; F is the Faraday constant.

[0074] (2) Derivation of the diffusion and mass transfer rate of hydrogen components at the gas-liquid interface:

[0075] The supersaturated concentration difference at the gas-liquid interface is an important driving force for the diffusion mass transfer process. The growth of hydrogen bubbles depends on the molecular diffusion caused by the supersaturated hydrogen component concentration difference at the gas-liquid interface. According to Fick's second law, the gas-liquid interface diffusion mass transfer rate It can be calculated by the following formula:

[0076]

[0077] In the formula, is the saturation concentration of dissolved hydrogen component, It represents the concentration of dissolved hydrogen in the electrolyte (expressed in mass fraction kg / kg), is the diffusion coefficient of dissolved hydrogen in the electrolyte, R b is the bubble equivalent radius, t is the hydrogen bubble growth time, ρ l is the electrolyte density.

[0078] (3) Derivation of mass transfer rate of direct injection into micro-liquid layer:

[0079] Theoretically, as the bubble radius increases, the micro-layer direct injection mass transfer rate gradually increases. Therefore, the present invention introduces the relative size of the bubble equivalent radius and the electrode radius to correct the micro-liquid layer direct injection mass transfer rate equation. The calculation formula is as follows:

[0080]

[0081] Where D micro is the diffusion coefficient of mass transfer directly injected into the micro-liquid layer, δ is the radial thickness of the micro-liquid layer, R e is the electrode radius.

[0082] (4) The area and volume conversion method is used to convert the above three area mass transfer rates into volume mass transfer rates to match the nesting requirements of the grid volume mass transfer source term of the ANSYS FLUENT simulation computing platform. The specific process is as follows:

[0083] The production rate of dissolved hydrogen components on the electrode surface is regarded as the diffusion source of the electrode surface. In each iteration of the calculation process, the mass source term is loaded to the first layer of grid on the electrode surface through the program. The grid size of the bubble growth area is square unit, and the volume mass transfer rate of hydrogen components in the grid on the electrode surface is It can be calculated by the following formula:

[0084]

[0085] In the formula, A e is the actual reactive active area of ​​the electrode surface; V e,c is the volume of the first layer of grid on the working electrode surface; L c is the height of the first grid layer on the electrode surface.

[0086] For the diffusion mass transfer of dissolved hydrogen components at the gas-liquid interface and the direct injection mass transfer process of the micro-liquid layer at the bottom of the bubble, it is necessary to solve the absolute value of the volume fraction gradient of the gas-liquid interface grid The area mass transfer rate of hydrogen components at the bubble interface Converted to volumetric mass transfer rate S i As shown below:

[0087]

[0088]

[0089] In the formula, S g,surface and S g,micro A is the gas-liquid interface hydrogen component diffusion mass transfer source term of gas phase absorption and the micro-liquid layer direct injection mass transfer source term; b is the gas-liquid interface area; V b,c is the volume of the grid contained in the gas-liquid interface; A micro V is the gas-liquid interface area contained in the micro-liquid layer area; micro is the volume of the air-liquid interface grid contained in the micro-liquid layer area, is the absolute value of the volume fraction gradient of the gas-liquid interface grid.

[0090] Step 3: In order to fully consider the gas-liquid convection effect, the influence of liquid convection induced by hydrogen bubble growth and the diffusion effect of dissolved hydrogen components, a two-phase flow model that accurately describes the dynamic process of single hydrogen bubble growth in the water electrolysis hydrogen production system is established based on the ANSYS FLUENT simulation computing platform and the mathematical and physical model derived and converted in step 2. The two-phase flow model is used to calculate the data of the growth process of a single hydrogen bubble on the surface of the water electrolysis hydrogen production electrode. Based on the obtained data, the electrode surface hydrogen bubble growth curve is generated to complete the numerical simulation of the hydrogen bubble growth process on the electrode surface.

[0091] The two-phase flow model established in this embodiment can couple multiphase flow, multi-physical field action, interphase mass transfer and other processes. The specific process of establishing the two-phase flow model is:

[0092] (1) Establishment and solution of mathematical model of gas-liquid interface evolution and gas-liquid two-phase velocity field:

[0093] On the FLUENT computing platform, the two-phase flow model volume fraction method (VOF) was used to simulate the dynamic process of the growth of a single hydrogen bubble on the electrode surface. The electrolyte (liquid phase) was set as the main phase, and the hydrogen bubble (gas phase) attached to the electrode surface was set as the secondary phase. Both satisfy the continuity equation:

[0094] α g +α l =1

[0095]

[0096]

[0097] In the formula, α g and α l are the volume fractions of the gas phase and the liquid phase, V g and V l are the velocity vectors of the gas phase and the liquid phase, S g,surface and S g,micro are the gas-liquid interface hydrogen component diffusion mass transfer source term of gas phase absorption and the micro-liquid layer direct injection mass transfer source term, is the hydrogen component source term generated by Faraday’s law. S l,surface is the source term of hydrogen component consumed by the liquid phase during mass transfer. g and μ l are the viscosities of the gas phase and the liquid phase, respectively, g and ρ l are the densities of the gas phase and the liquid phase respectively. In the process of solving the VOF model, the gas and liquid phases share a set of momentum equations:

[0098]

[0099] The values ​​of μ and ρ are the volume averages of each phase, and F σ is the surface tension, which is added to the momentum equation as a volume force source term. The continuous surface force model (CSF) is used to treat the surface tension of the gas-liquid interface. σ The calculation formula is as follows:

[0100]

[0101] Where σ is the surface tension coefficient of the gas-liquid interface, and κ is the curvature of the phase interface.

[0102] (2) Establishment and solution of the mathematical model of dissolved hydrogen component concentration field:

[0103] Due to the complexity of the electrochemical reaction process, there are multiple ions and reaction product components in the electrolyte. In order to simplify the mathematical calculation model, the present invention ignores other product components and only considers the evolution of dissolved hydrogen concentration. The component transport equation calculation formula is:

[0104]

[0105] In the formula is the hydrogen component source term generated by Faraday's law.

[0106] (3) Establishment and solution of the mathematical model of electric field distribution:

[0107] The potential distribution in the electrolyte during the simulation follows the Laplace potential equation:

[0108]

[0109] where φ is the electric potential, κ m is the volume average conductivity of the mixture, calculated as: m =α g κ g +α l κ l .

[0110] The electric field distribution during electrolysis is calculated by the scalar equation:

[0111]

[0112] Where Γ k is the diffusion coefficient, the convection term of the scalar equation is zero, and the diffusion coefficient Γ k is the conductivity of each phase of gas and liquid κ, the source term of the scalar equation S φk is the cathode current density I / A e .

[0113] In this embodiment, the specific process of using the custom program UDF to perform the coupling calculation of the above two mass transfer processes is as follows:

[0114] (1) Using the data variable transfer macro DEFINE_ADJUST, the hydrogen bubble volume and equivalent radius are solved through the gas phase grid volume, and the storage call is updated in real time; (2) Using the boundary condition macro DEFINE_PROFILE, the bubble contact angle wall condition is adjusted through the bubble equivalent radius; (3) Using the data variable transfer macro DEFINE_ADJUST, the hydrogen bubble contact radius and electrode activation reaction area are solved through the cathode surface gas phase grid, and the storage call is updated in real time; (4) The current density flowing through the electrode surface and the source term of the electric field equation are solved through the electrode activation reaction area; (5) The source term of the dissolved hydrogen component produced on the electrode surface is solved through the current density; (6) Using the data variable transfer macro DEFINE_ADJUST, the volume fraction gradient is obtained by solving the continuity equation; (7) Using the custom source term macro DEFINE_SOURCE, the gas-liquid interface hydrogen component diffusion mass transfer source term and the micro-liquid layer direct injection mass transfer source term are solved through the solved hydrogen bubble equivalent radius, grid dissolved hydrogen component concentration and volume fraction gradient.

[0115] In this embodiment, multiple custom storage variables UDMI can be defined, such as udm-0, udm-1 and udm-2, respectively. The user-defined function UDF is used to assign the values ​​of the production rate source term of the dissolved hydrogen component on the electrode surface, the diffusion mass transfer source term of the hydrogen component at the gas-liquid interface and the direct injection mass transfer source term of the micro-liquid layer to the custom storage variables udm-0, udm-1 and udm-2, respectively, at each time step in the numerical calculation process. The custom report macro DEFINE_REPORT_DEFINITION is used to store the important result data required for post-processing, such as the bubble equivalent radius, bubble contact radius, bubble contact angle, etc. at each time step in the calculation process. The Report Definitions module in the FLUENT software is used to export the above-mentioned important result data stored in the form of an OUT file to facilitate subsequent data processing. Among them, the three mass transfer source item storage macros udm-0, udm-1 and udm-2... Before outputting in the OUT file, it is necessary to perform volume integration to change the unit from the mass equation source item unit kg / m 3 s was converted into the mass transfer rate unit kg / s to facilitate subsequent in-depth quantitative discussion and analysis.

[0116] In this embodiment, the calculation process of simulating the dynamic process of growth of a single hydrogen bubble on the electrode surface is described in detail in combination with specific electrode parameters, as follows:

[0117] The specific objects and parameter settings used in this embodiment are: the constant current is 5.2μA, the radius of the disc nickel electrode is 63.5μm, and the calculation process and settings for simulating the dynamic process of the growth of a single hydrogen bubble on the electrode surface under these conditions are:

[0118] The numerical simulation is carried out in two steps: first, before the bubble nucleation, there is only liquid phase in the calculation domain, which is a unidirectional flow. As the electrolysis reaction proceeds, the dissolved hydrogen component gradually enriches in the electrolyte near the electrode surface and reaches supersaturation conditions. Under the conditions of a constant current of 5.2μA and a disk nickel electrode radius of 63.5μm, the electrode current density is 410A / m 2 According to the literature, the concentration conditions of dissolved hydrogen components for the nucleation of hydrogen bubbles on the electrode surface under this current density condition were searched. When the concentration of dissolved hydrogen components in the electrolyte monitored during the simulation reached this condition, the computational grid on the center surface of the electrode was set to the gas phase in the form of a patch, and a seed bubble with an initial radius of 5 μm was placed on the electrode surface. On the basis of obtaining the initial nucleation concentration, the gas-liquid interface hydrogen component diffusion mass transfer source term and the micro-liquid layer direct injection mass transfer source term were added to the continuity equation and the component equation, and the unsteady-state solution of the dynamic process of the growth of a single hydrogen bubble on the electrode surface was performed until the hydrogen bubble detached from the electrode surface. In order to ensure the convergence of the calculation and reduce the calculation time, the continuity equation, momentum equation, and UDS equation in the calculation process all adopted the second-order upwind format, the PRESTO! method was used to discretize the pressure equation, the PISO method (Gradient format is Green-Gauss Node-Based format) was used to solve the coupled equations of pressure and velocity, and the geometry reconstruction method (Geo-Reconstruct) was used to discretize the volume fraction model. The relaxation factors of all calculation equations were set by default. The variable time step method is used for calculation. A small time step is selected first, and then the time step is controlled to 1e by limiting the Courant number to less than 0.25. -5 To 1e -6 between.

[0119] Based on post-processing platforms such as TECPLOT and ORIGIN, the numerical simulation results of the growth process of a single hydrogen bubble on the surface of the electrode for hydrogen production by electrolysis of water obtained by this method were analyzed.

[0120] Figure 3 The comparison result of the hydrogen bubble growth curve on the electrode surface obtained by numerical simulation of the present invention and the experimental value under the condition of constant current of 5.2μA and disk nickel electrode radius of 63.5μm. The bubble growth rate curve obtained by numerical simulation is consistent with the experimental value well, and the maximum error is only 3.9%.

[0121] Figure 4 The cloud diagram of the temporal and spatial distribution of the gas phase volume fraction during the growth cycle of a single hydrogen bubble. During the electrolysis reaction, due to the combined effect of diffusion-controlled mass transfer at the gas-liquid interface and direct injection mass transfer at the microlayer, a single hydrogen bubble continues to grow and the bubble size increases. The bubble contact angle and the area of ​​the three-phase contact region will also change. Once the upward force that promotes bubble detachment exceeds the downward force that inhibits bubble detachment, the bubble detaches from the electrode surface.

[0122] Figure 5 This is a cloud diagram of the spatial and temporal distribution of dissolved hydrogen component concentration during the growth cycle of a single hydrogen bubble. Near the gas-liquid interface, there is an obvious hydrogen component concentration gradient from the electrode surface to the bulk electrolyte area. The hydrogen component concentration near the gas-liquid interface, especially in the wedge-shaped area at the bottom of the bubble, is significantly higher than the hydrogen component concentration in most other electrolytes.

[0123] Figure 6 This is a spatiotemporal distribution cloud diagram of the gas-liquid interface mass transfer source term during the growth cycle of a single hydrogen bubble. In areas with high concentrations of dissolved hydrogen components, especially the wedge-shaped area at the bottom of the bubble, the gas-liquid interface diffusion-controlled mass transfer source term has a large value. This is because the concentration of supersaturated hydrogen components is closely related to the gas-liquid interface diffusion-controlled mass transfer.

[0124] Figure 7 This is a cloud diagram of the current density and the time-space distribution of current lines during the growth cycle of a single hydrogen bubble. All current lines start from the anode surface and converge on the cathode surface. When the current lines pass through the gas-liquid interface with lower conductivity, they will be significantly distorted.

[0125] Figure 8 It shows the temporal variation trend of the mass transfer rate and mass transfer quality of hydrogen component diffusion mass transfer at the gas-liquid interface, direct injection mass transfer in the micro-liquid layer and total mass transfer during the growth period of hydrogen bubbles. Figure 8 In (a), the diffusion mass transfer rate at the gas-liquid interface rapidly increases to a stable value at the beginning of bubble growth, and then fluctuates around this stable value during most of the bubble growth period. The mass transfer rate of direct injection into the micro-liquid layer shows a continuous growth trend throughout the bubble growth period. Figure 8 The mass transfer qualities in (b) are obtained by integrating the OUT file data of the three mass transfer source storage macros udm-0, udm-1 and udm-2 over time. During the entire bubble growth cycle, the gas-liquid interface diffusion mass transfer quality exceeds the micro-liquid layer direct injection mass transfer quality. As the bubble grows, the micro-liquid layer direct injection mass transfer quality gradually increases. Before the bubble detaches from the electrode surface, the micro-liquid layer direct injection mass transfer quality accounts for 35% of the total mass of the hydrogen component during the bubble growth process.

[0126] The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. A method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface, characterized in that: The method comprises the following steps: Step 1: According to the geometric parameters of the electrodes and the hydrogen bubble growth process in the water electrolysis hydrogen production system, a two-dimensional axisymmetric computational geometry model is established, the geometric model is meshed, and the mesh encryption process is performed on the bubble growth area; the geometric parameters include cathode size, anode size, bubble detachment radius, bubble contact angle, and three-phase contact line; Step 2: Derive a mathematical and physical model that describes the gas-liquid two-phase mass transfer behavior and characteristics during the dynamic growth of a single hydrogen bubble on the electrode surface in the water electrolysis hydrogen production system, wherein the mathematical and physical model includes the generation rate of dissolved hydrogen components on the electrode surface, the diffusion mass transfer rate of hydrogen components at the gas-liquid interface, and the direct injection mass transfer rate of the micro-liquid layer; Step 3: Considering the gas-liquid two-phase convection effect, the influence of the liquid convection induced by the growth of hydrogen bubbles, and the diffusion behavior of dissolved hydrogen components, a gas-liquid two-phase flow model describing the dynamic growth process of a single hydrogen bubble in the water electrolysis hydrogen production system is established based on the mathematical physics model; the data of the growth process of a single hydrogen bubble on the surface of the water electrolysis hydrogen production electrode is calculated using the two-phase flow model, and the hydrogen bubble growth curve on the electrode surface is generated based on the obtained data to complete the numerical simulation of the hydrogen bubble growth process on the electrode surface; The two-phase flow model is established, and the two-phase flow model is expressed as: (1) The mathematical model of gas-liquid interface evolution and gas-liquid two-phase velocity field is established, which can be expressed as: Continuity equation: α g +α l ＝1 In the formula, α g and α l are the volume fractions of the gas phase and the liquid phase, V g and V l are the velocity vectors of the gas phase and the liquid phase, S g,surface and S g,micro are the gas-liquid interface hydrogen component diffusion mass transfer source term of gas phase absorption and the micro-liquid layer direct injection mass transfer source term, is the hydrogen component source term generated by Faraday's law; S l,surface is the source term of hydrogen component consumed by the liquid phase during mass transfer; ρ g and ρ l are the densities of the gas phase and the liquid phase, respectively; The momentum equation is expressed as: Wherein, μ and ρ are the volume average values ​​of each phase, F σ is the surface tension, is the relative pressure, V is the velocity vector; (2) Establish a mathematical model of dissolved hydrogen component concentration field, expressed as: In the formula, is the hydrogen component source term generated by Faraday's law, is the saturation concentration of dissolved hydrogen component, is the diffusion coefficient of dissolved hydrogen component in the electrolyte; (3) Establish a mathematical model of electric field distribution, expressed as: Where φ is the electric potential, κ m is the volume average conductivity of the mixture.

2. The method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to claim 1, characterized in that: The generation rate of dissolved hydrogen components on the electrode surface is expressed as: In the formula, is the generation rate of hydrogen components on the electrode surface, in kg / m 2 s; is the molar mass of hydrogen molecule; I / A e is the current density flowing through the electrode surface, calculated by the potential equation in step 2; F is the Faraday constant.

3. The method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to claim 2, characterized in that: The gas-liquid interface hydrogen component diffusion mass transfer rate is expressed as: In the formula, is the saturation concentration of dissolved hydrogen component, It indicates the concentration of dissolved hydrogen component in the electrolyte, expressed as mass fraction kg / kg; is the diffusion coefficient of convective mass transfer of dissolved hydrogen components in the electrolyte, R b is the bubble equivalent radius, t is the hydrogen bubble growth time, ρ l is the electrolyte density.

4. The method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to claim 3, characterized in that: The micro-liquid layer direct injection mass transfer rate is expressed as: Where D micro is the diffusion coefficient of mass transfer directly injected into the micro-liquid layer, δ is the radial thickness of the micro-liquid layer, R e is the electrode radius.

5. The method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to claim 4, characterized in that: The area mass transfer rates of step 2, such as the generation rate of dissolved hydrogen components on the electrode surface, the diffusion mass transfer rate of hydrogen components at the gas-liquid interface, and the direct injection mass transfer rate of the micro-liquid layer, are converted into volumetric mass transfer rates; they are expressed as: The unit conversion of the generation rate of dissolved hydrogen components on the electrode surface is expressed as: In the formula, A e is the actual reactive active area of ​​the electrode surface; V e,c is the volume of the first layer of grid on the working electrode surface; L c is the height of the first layer of grid on the electrode surface; The unit conversion process is performed on the hydrogen component diffusion mass transfer rate at the gas-liquid interface, and the source term of the hydrogen component diffusion mass transfer at the gas-liquid interface of gas phase absorption is expressed as: Among them, A b is the gas-liquid interface area; V b,c is the volume of the grid contained by the gas-liquid interface, is the absolute value of the volume fraction gradient of the gas-liquid interface grid; The micro-liquid layer direct injection mass transfer rate is converted into units, and the micro-liquid layer direct injection mass transfer source term is expressed as: Among them, A micro V is the gas-liquid interface area contained in the micro-liquid layer area; micro is the volume of the air-liquid interface grid contained in the micro-liquid layer area, is the absolute value of the volume fraction gradient of the gas-liquid interface grid.

6. The method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to claim 1, characterized in that: The continuous surface force model is used to deal with the surface tension of the gas-liquid interface. The surface tension F σ It is expressed as: Where σ is the surface tension coefficient of the gas-liquid interface, κ g is the curvature of the gas phase interface, κ l is the curvature of the liquid interface.

7. A method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to any one of claims 1 to 6, characterized in that: Define multiple custom storage variables UDMI, and assign the values ​​at each time step in the numerical calculation process to the custom storage variables for storage.

8. The method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to claim 7, characterized in that: ANSYS MESH geometric model is used for meshing.

9. The method for constructing a numerical simulation model of hydrogen bubble growth process on an electrode surface according to claim 7, characterized in that: The Refine / Coarseness module in FLUENT software is used to encrypt the grid in the bubble growth area.

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