A method of revealing the fouling process and evolution trends of an ultrafiltration system

Abstract

The application discloses a method for revealing the fouling process and evolution trend of an ultrafiltration system, relates to the technical field of data simulation, and comprises the following steps: constructing a numerical model of an ultrafiltration unit; iteratively solving a flow field and a concentration field to obtain the distribution of membrane surface shear force and solute concentration; calculating the net fouling growth rate by using a fouling dynamics model containing a deposition term and a detachment term to form a fouling rate distribution field; adaptively determining a dynamic time step based on the maximum net fouling rate, updating the thickness distribution of the fouling layer, and adjusting the geometric boundary of the fluid domain in real time through a dynamic mesh; repeating the above steps to perform time marching to obtain an evolution sequence of the thickness of the fouling layer; and performing space-time dimension reduction and feature extraction on the evolution sequence to generate a visual feature map. The method can continuously simulate the whole life cycle of the initiation, growth, peeling and redeposition of fouling, and output a process map which intuitively reflects the dynamic evolution of fouling.

Description

Technical Field

[0001] This invention relates to the field of data simulation technology, and specifically to a method for revealing the scaling process and evolution trend of an ultrafiltration system. Background Technology

[0002] Ultrafiltration (UF) is a pressure-driven membrane separation technology widely used in separation and concentration processes in water treatment, food processing, and biopharmaceuticals. During long-term operation, solutes in the feed solution accumulate on the membrane surface due to concentration polarization, gradually forming a fouling layer. This leads to decreased membrane flux and increased transmembrane pressure, ultimately necessitating shutdown for chemical cleaning or replacement of the membrane modules. Revealing the dynamic evolution of fouling in ultrafiltration systems provides direct guidance for optimizing operating parameters, developing cleaning strategies, and extending membrane lifespan. Computer simulation modeling, as a means of digitizing the physical filtration process and extrapolating it in a virtual environment, can efficiently acquire spatiotemporal distribution information of membrane fouling.

[0003] Existing technologies, such as patents related to the simulation of fouling processes in ultrafiltration systems (publication numbers CN110929426B and CN121096418B) and academic research papers on the dynamic numerical simulation of ultrafiltration membrane contaminant retention processes based on moving grids, demonstrate that most existing ultrafiltration fouling simulation methods rely on empirical resistance series models or simple cake filtration equations. Resistance series models treat the fouling layer as a uniformly growing additional resistance, only integrating flux decay over time, without solving for the membrane surface flow field and concentration field. While methods based on cake filtration equations introduce the relationship between local permeability and thickness, they lack a coupled solution for fluid shear force distribution and solute concentration distribution, typically directly using average shear force or feed concentration to calculate the growth rate across the entire membrane surface. These methods lack the ability to distinguish the spatial differences in fouling layer morphology and its non-monotonic behavior over time.

[0004] The existing solutions have significant technical flaws: First, the fouling kinetics model only considers the deposition process driven by concentration polarization, ignoring the local peeling effect driven by shear force. It cannot reproduce the non-monotonic evolution of the fouling layer on the membrane surface during actual operation, where it first thickens and then peels off due to a sudden increase in shear force caused by the narrowing of the flow channel. Second, the time progression often uses a fixed step size. If the step size is too small, the computation time becomes unacceptable. If the step size is too large, it will introduce significant discrete errors or even numerical instability during the rapid fouling stage. Third, the flow channel geometry continuously changes during the fouling layer growth process. The existing models fail to feed back the dynamic geometric boundary to the re-solution of the flow field and concentration field, severing the two-way coupling between fouling and flow field changes, causing the simulation to deviate from the actual physical process. Summary of the Invention

[0005] The purpose of this invention is to provide a method for revealing the scaling process and evolution trend of an ultrafiltration system, thereby solving the problems existing in the background art.

[0006] To solve the above technical problems, the present invention adopts the following technical solution: The present invention provides a method for revealing the scaling process and evolution trend of an ultrafiltration system, comprising: S1: obtaining the operating condition parameters of the ultrafiltration system, the geometric structural parameters of the ultrafiltration membrane module, and the physical property parameters of the fluid to be treated, and constructing a numerical model characterizing the fluid flow and solute transport within the ultrafiltration unit based on the operating condition parameters, geometric structural parameters, and physical property parameters.

[0007] S2: Perform coupled iterative solution of the flow field and solute concentration field of the numerical model to obtain the shear force distribution and solute concentration distribution on the membrane surface.

[0008] S3: Using a scaling kinetics model that characterizes the concentration polarization-driven deposition and shear force-driven stripping mechanisms, combined with the shear force distribution and solute concentration distribution on the membrane surface, the net scaling growth rate at each discrete location on the membrane surface is calculated to form a scaling rate distribution field. The scaling kinetics model includes a deposition rate term and a stripping rate term.

[0009] S4: Based on the fouling rate distribution field, determine the dynamic time step that matches the current fouling layer growth rate, and update the fouling layer thickness distribution on the membrane surface according to the dynamic time step. Then, adjust the fluid domain geometric boundary of the numerical model through the dynamic mesh method to adapt to the updated fouling layer thickness distribution.

[0010] S5: Use the adjusted numerical model as the new current numerical model, return to the steps of performing coupled iterative solution, and advance the time until the cumulative simulation time reaches the filtration cycle obtained based on the operating condition parameters, and obtain the spatial distribution sequence of the dirt layer thickness at different times as the evolution sequence.

[0011] S6: Perform spatiotemporal dimensionality reduction and feature extraction on the evolution sequence to generate a visual feature map characterizing the dynamic evolution of the scaling process.

[0012] The beneficial effects of this invention are as follows: (1) This invention regards the fouling layer as a dynamically evolving porous medium domain and embeds it into the fluid solution process, reproduces the physical nature of fouling where deposition and stripping compete with each other, improves the consistency between the simulation results of the spatial distribution evolution of the fouling layer on the membrane surface and the real filtration process, makes up for the shortcomings of traditional models that only consider unidirectional deposition and ignore the stripping mechanism, and provides an accurate digital reproduction capability of fouling behavior for ultrafiltration systems.

[0013] (2) This invention automatically adapts the dynamic time step by scaling rate distribution field and coordinates the constraints with the flow field characteristic time scale. It can solve the step size by itself during the stage of drastic scaling changes and relax the step size restriction during the stable stage. This reduces the simulation time while ensuring the stability of calculation and numerical accuracy, and improves the engineering applicability of the method.

[0014] (3) This invention performs spatial statistical dimensionality reduction and time derivative analysis on the evolution sequence, automatically extracts characteristic nodes such as the start time of accelerated scaling, the peak rate time, and the time of local peeling, and divides the scaling process into the initiation period, growth period, peeling period, and redeposition period. It outputs the spatiotemporal evolution cloud map of the superimposed growth direction vector and the membrane thickness of the peeling area, as well as the time-series curve along the process, and transforms the simulation data into a process map that can be interpreted intuitively. This supports operators to quickly diagnose the stage of membrane fouling and trace the hydraulic conditions that induce local peeling. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the implementation steps of the method of the present invention.

[0017] Figure 2 This is a cloud map showing the spatiotemporal evolution of the dirt layer thickness on the membrane surface.

[0018] Figure 3 This is a time series and stage division diagram of the dirt thickness distribution along the process. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Reference Figure 1 As shown, the present invention provides a method for revealing the fouling process and evolution trend of an ultrafiltration system, comprising: S1: obtaining the operating condition parameters of the ultrafiltration system, the geometric structural parameters of the ultrafiltration membrane module, and the physical property parameters of the fluid to be treated, and constructing a numerical model characterizing the fluid flow and solute transport within the ultrafiltration unit based on the operating condition parameters, geometric structural parameters, and physical property parameters.

[0021] Specifically, operating parameters are collected online from the ultrafiltration system's monitoring instruments. These parameters include the feed volumetric flow rate, outlet pressure, and filtration duration determined based on the designed operating cycle. The feed volumetric flow rate, combined with the membrane module's flow cross-sectional area, can be converted into the average inlet flow velocity. The outlet pressure is the gauge pressure at the end of the flow channel. The geometric parameters of the ultrafiltration membrane module are obtained from the module design drawings or specification manuals, covering the flow channel length of the membrane channels. Flow channel height membrane area And the intrinsic cleaning resistance of the membrane. The height of the flow channel The vertical distance from the membrane surface to the opposite sidewall or plane of symmetry; cleaning membrane resistance. Measured experimentally from pure water, the unit is the reciprocal of length. The physical properties of the fluid to be treated include fluid density. Dynamic viscosity Molecular diffusion coefficient of solute And the linear correlation coefficient between osmotic pressure and solute concentration It can be found in the property handbook, measured with a rotational viscometer, or based on Van't Hoff's law. The data were obtained by fitting the experimental data, among which Osmotic pressure, This represents the mass concentration of the solute.

[0022] Based on the above three types of parameters, a numerical model characterizing fluid flow and solute transport within the ultrafiltration unit is constructed. For a flat-sheet membrane ultrafiltration unit, the rectangular cross-section flow channel above a single membrane is extracted as the representative computational domain, and a two-dimensional Cartesian coordinate system is established: The axis runs along the mainstream direction of the membrane surface, from the inlet to the outlet, with a coverage length of [missing information]. ; The axis is perpendicular to the membrane surface, from the membrane surface Pointing to the upper wall of the flow channel .

[0023] Within this region, the fluid is considered an incompressible Newtonian fluid, the flow is assumed to be laminar, and the fluid motion is described by the continuity equation and the Navier-Stokes equations:

[0024]

[0025] in, It is a velocity vector, which is decomposed into velocity vectors along the velocity vector in a two-dimensional domain. directional velocity components and along directional velocity components , For pressure, For time, and These represent the obtained fluid density and dynamic viscosity, respectively. Solute mass transfer is controlled by the solute convection-diffusion equation:

[0026] Here Indicates the mass concentration of the solute. is the solute diffusion coefficient.

[0027] On the membrane surface At this point, the osmotic flow through the membrane is measured by the osmotic velocity. The permeation rate is determined by Darcy's law relationship between the local transmembrane pressure difference and membrane resistance:

[0028] In the formula, It is the fluid-side pressure on the membrane surface. It is the osmotic pressure, which is preset as a known constant when constructing the model. It is the osmotic pressure at the membrane surface, caused by calculate, Membrane resistance for cleaning. Permeation rate. Perpendicular to the membrane surface, i.e. directional velocity components in Assignment The semi-permeable property of the membrane surface for solutes is expressed by the following boundary conditions: the normal solute diffusion flux at the membrane surface is in equilibrium with the net convective flux. For the ideal case of complete solute retention, the solute concentration on the permeate side is zero, and the boundary conditions simplify to:

[0029] The aforementioned governing equations, together with the membrane surface boundary conditions, constitute the mathematical framework of the numerical model.

[0030] The mesh required for spatial discretization is generated based on geometric parameters. Along The direction will affect the length of the flow channel. Divided into Each grid cell, along The direction will affect the height of the flow channel. Divided into Each grid cell is used to refine the grid near the membrane surface, reducing the thickness of the first-layer grid. Controlled The order of magnitude is sufficient to ensure the resolution of high shear gradients and concentration polarization layers. The grid node coordinates and element connections serve as the spatial discretization basis of the numerical model, thus completing the construction of a numerical model capable of iterative solutions under specific inlet and outlet conditions.

[0031] S2: Perform coupled iterative solution of the flow field and solute concentration field of the numerical model to obtain the shear force distribution and solute concentration distribution on the membrane surface.

[0032] In a specific embodiment of the present invention, the coupled iterative solution of the flow field and solute concentration field of the numerical model to obtain the shear force distribution and solute concentration distribution on the membrane surface includes: setting boundary conditions for the numerical model, wherein the boundary conditions include the inlet velocity and outlet pressure determined based on the operating condition parameters.

[0033] Specifically, based on the numerical model constructed in step S1, physical conditions need to be specified for all open boundaries of the computational domain. These boundary conditions include the inlet velocity and outlet pressure determined according to the operating parameters. The inlet boundary is located at the initial cross-section of the flow channel in a two-dimensional Cartesian coordinate system. At this point, the velocity inlet condition is set, and the velocity component along the main flow direction is... Assuming a uniform distribution, the value is equal to the average inlet velocity calculated from the feed volumetric flow rate. Velocity component perpendicular to the membrane surface Set to zero. The outlet boundary is located at the end section of the flow channel. At this location, the pressure outlet condition is set, and the pressure... The value is equal to the outlet relative pressure in the operating condition parameters. When the meter displays zero pressure, command Pascal. Upper wall of the flow channel. As a no-slip solid-wall treatment, all velocity components are zero, and no additional permeation or slip conditions are required. The membrane surface boundary has already been embedded in the governing equations in step S1 in the form of permeation rate and solute rejection conditions, so it will not be reset in this step. However, these implicit boundary conditions will dynamically affect the solution process as the flow field and concentration field are updated.

[0034] Solve the fluid flow control equations to obtain the velocity and pressure distributions in the flow field.

[0035] After setting the boundary conditions, the numerical solution of the fluid flow governing equations is performed to obtain the velocity and pressure distributions of the flow field. The fluid flow governing equations are the continuity equations describing incompressible viscous flow. and Navier-Stokes equations

[0036] In the formula As a velocity vector, decompose into Directional components and Directional components , For pressure, and The fluid density and dynamic viscosity are obtained from step S1. Considering that the current solution objective is a steady-state coupled field, the time derivative terms in the equations are retained as pseudo-transient terms to enhance iterative stability, or directly set to steady-state form. The above equations are discretized on the discrete grid generated in step S1 using the finite volume method. The convection term uses a second-order upwind scheme to suppress numerical dissipation, and the diffusion term uses a central difference scheme. The coupling relationship between pressure and velocity is handled by the SIMPLE algorithm. That is, for each flow iteration, the momentum discrete equation based on the predicted velocity and pressure correction is solved first, then the pressure correction equation is constructed and solved, and then the velocity and pressure fields are updated using the pressure correction until the mass flow residual is reduced to a certain inner iteration tolerance. The discretized linear algebraic equations are solved using the algebraic multigrid method to accelerate convergence to the solution of the flow field in that step. Finally, the velocity components at each grid node in the entire computational domain are obtained. , and pressure These together constitute the velocity and pressure distribution of the flow field.

[0037] The solute convection-diffusion equation is solved based on the flow field velocity distribution to obtain the solute concentration field. The shear force distribution and solute concentration distribution at the membrane surface are extracted by iterating alternately until the relative changes in the flow field velocity distribution and the solute concentration field are lower than the convergence threshold. These are then used as the membrane surface shear force distribution and membrane surface solute concentration distribution.

[0038] Specifically, after obtaining the latest flow field velocity distribution, the process then proceeds to solving the solute convection-diffusion equation to obtain the solute concentration field. The solute convection-diffusion equation in steady-state form can be written as:

[0039] In the formula This refers to the mass concentration of the solute. The solute diffusion coefficients are derived from the physical properties in step S1. The convection term in the equation employs a second-order upwind scheme with flux constraints to prevent non-physical concentration overflows or oscillations, while the diffusion term retains the central difference scheme. The discrete linear equations for solving this equation are obtained using the pre-conditional conjugate gradient method to determine the concentration distribution under the current velocity field. In this step, the permeation rate at the membrane surface... Recalculated based on the updated pressure and concentration fields, the formula is as follows:

[0040] in For the fluid side pressure of the membrane surface, The osmotic pressure is constant. The osmotic pressure coefficient is... For cleaning membrane resistance, these parameters have all been determined in step S1. The newly calculated... It also serves as the normal velocity component of the membrane surface. The boundary value of the flow field has a reverse effect on the flow field, forming a strong two-way coupling between the flow field and the solute concentration field.

[0041] To reliably obtain solutions consistent with this bidirectional coupling, an alternating iteration strategy is employed until convergence. An external iteration counter is set, and each external iteration includes one complete flow field solution and one complete concentration field solution. After one external iteration, the relative changes in the flow velocity distribution and solute concentration field are calculated and compared with a convergence threshold. The relative changes in the flow velocity distribution and solute concentration field are defined as follows:

[0042] superscript and These represent the current and previous outer iterations, respectively. Denotes the L2 norm of the scalar field on all grid nodes. It is a preset minimum constant. To avoid the denominator being zero. Convergence threshold. Set as .when When the flow field and concentration field reach a stable state, the external iteration cycle is terminated. Otherwise, the updated permeation velocity is used as the membrane condition, and the process returns to the solution steps of the fluid flow control equations to begin a new round of external iteration.

[0043] After convergence is successful, the shear force distribution and solute concentration distribution on the membrane surface are extracted from the stabilized physical field. Membrane surface shear force... Defined as fluid acting on the membrane surface The viscous shear stress at a given point, for a Newtonian fluid, is given by the following equation:

[0044] In the formula This is the gradient of the velocity component parallel to the membrane surface along the normal direction of the membrane surface. On a discrete mesh, this gradient is calculated using the velocity values ​​of multiple mesh layers adjacent to the membrane surface, employing a three-node or four-node one-sided difference formula. For example, for a non-uniform mesh, if the center of the first mesh layer is at a distance from the membrane surface... The center of the second layer of mesh is at a distance from the membrane surface. The second-order precision expression can be derived as follows:

[0045] Subscript 1 represents a membrane surface node, 2 represents a first-layer internal node, and 3 represents a second-layer internal node. Discretize each location along the path. place The shear force distribution on the membrane surface is obtained by sequentially calculating and storing the results in a one-dimensional array. The solute concentration distribution on the membrane surface is directly extracted from the converged concentration field. Concentration values ​​at nodes Composition sequence, which reflects the solute enrichment along the membrane surface from inlet to outlet.

[0046] S3: Using a scaling kinetics model that characterizes the concentration polarization-driven deposition and shear force-driven stripping mechanisms, combined with the shear force distribution and solute concentration distribution on the membrane surface, the net scaling growth rate at each discrete location on the membrane surface is calculated to form a scaling rate distribution field. The scaling kinetics model includes a deposition rate term and a stripping rate term.

[0047] In a specific embodiment of the present invention, the scaling kinetics model that characterizes the concentration polarization-driven deposition and shear force-driven stripping mechanisms, combined with the shear force distribution and solute concentration distribution on the membrane surface, calculates the net scaling growth rate at each discrete location on the membrane surface to form a scaling rate distribution field, including: obtaining the concentration polarization at each discrete location on the membrane surface based on the solute concentration distribution on the membrane surface.

[0048] Specifically, based on the membrane surface shear force distribution and membrane surface solute concentration distribution obtained in step S2, a fouling kinetic model characterizing the concentration polarization-driven deposition and shear force-driven stripping mechanisms is activated. The membrane surface solute concentration distribution is the sum of the solute concentrations at discrete locations along the membrane surface flow direction. solute mass concentration sequence The coupled solution in step S2 has been stored as a one-dimensional array at the end. First, the concentration polarization at each discrete location on the membrane surface is obtained based on the solute concentration distribution on the membrane surface. Concentration polarization is defined as the ratio of the solute concentration on the membrane surface to the solute concentration in the bulk feed, used to measure the degree of solute accumulation on the membrane surface. The calculation formula is:

[0049] in For position The local bulk concentration at the flow channel cross-section is defined as the concentration from the surface of the dirt layer. to the upper wall of the flow channel The cross-sectional average of solute concentration between them. It is a dimensionless quantity.

[0050] Substitute the concentration polarization into the deposition rate term to calculate the local deposition rate.

[0051] Substituting concentration polarization into the deposition rate term allows for the calculation of local deposition rates. The deposition rate term represents the rate at which high-concentration solutes, caused by concentration polarization at the film surface, deposit and adhere to the film surface to form a fouling layer. The model expresses this as a linear response driven by the concentration polarization exceeding 1.

[0052] In the formula, It is the local deposition rate, measured in meters per second. It is the deposition rate coefficient, measured in meters per second. Its value is calibrated based on the scaling thickness growth data from multiple sets of flat-plate membrane cross-flow filtration experiments. For example, it is fitted to scaling experimental data of 12 sets of dextran solutions at different flow rates and uniformly calibrated as follows: Maximum value function It can ensure that only when A value greater than 1 indicates that deposition-driven deposition occurs only when the film concentration exceeds the feed concentration.

[0053] The local peeling rate is calculated by substituting the shear force distribution on the membrane surface and the current dirt layer thickness distribution into the peeling rate term.

[0054] Specifically, the stripping rate term describes the ability of fluid shearing to remove the formed fouling layer, and its magnitude is proportional to the wall shear force and the thickness of the locally accumulated fouling layer:

[0055] in, It is the local peeling rate, measured in meters per second. This is the shear force distribution on the membrane surface extracted in step S2, in Pascals. This represents the current fouling layer thickness distribution, indicating the accumulated fouling layer thickness at each discrete location, in meters. When this step is called for the first time, the simulation is in the initial filtration stage, and the membrane surface is still clean. It is assumed to be a zero distribution. It is the stripping coefficient, with dimensions of square meters per Newton-second, equivalent to per Pascal-second. The values ​​were also identified from the peeling process data of the scaling experiments. For example, parameters were estimated for the local scaling thinning sections in 12 sets of experiments, and calibrated as follows: .

[0056] The difference between the local deposition rate and the local stripping rate is calculated to obtain the net scale growth rate, and the net scale growth rates at all discrete locations are combined to form a scale rate distribution field.

[0057] Specifically, the difference between the local deposition rate and the local stripping rate is calculated to obtain the net scale growth rate at that discrete location:

[0058] Net fouling growth rate characterizes the instantaneous rate of change in fouling layer thickness at various points on the membrane surface. A positive value indicates increased fouling accumulation and thickening, while a negative value represents net stripping thinning. Discrete all locations on the membrane surface... Net scale growth rate at the site The scale is arranged in a spatial order to form a one-dimensional array, which forms a scale rate distribution field, giving a complete spatial distribution of scale growth from the inlet to the outlet.

[0059] S4: Based on the fouling rate distribution field, determine the dynamic time step that matches the current fouling layer growth rate, and update the fouling layer thickness distribution on the membrane surface according to the dynamic time step. Then, adjust the fluid domain geometric boundary of the numerical model through the dynamic mesh method to adapt to the updated fouling layer thickness distribution.

[0060] Specifically, step S3 has already output the scaling rate distribution field, which is composed of discrete locations on the membrane surface. Net scale growth rate Composition, measured in meters per second. To convert the scaling rate into actual fouling layer geometry, a time step that matches the current scaling intensity needs to be determined first, to avoid excessive thickness increments within a single step that could lead to mesh distortion or calculation divergence.

[0061] In a specific embodiment of the present invention, determining the dynamic time step adapted to the current fouling growth rate based on the fouling rate distribution field includes: obtaining the maximum net fouling growth rate in the fouling rate distribution field.

[0062] Specifically, it traverses all discrete locations along the flow direction. The net scaling growth rate values ​​are taken, and the maximum value is denoted as . ,Right now:

[0063] The physical meaning of the maximum net fouling growth rate is the fastest local rate of fouling growth across the entire membrane surface, measured in meters per second. This value changes continuously as the simulation time step progresses because it depends on the constantly updated concentration field and shear force field.

[0064] The allowable time step is calculated based on the maximum net fouling growth rate and the preset limit for fouling layer thickness growth.

[0065] Specifically, the preset limit for the increase in dirt layer thickness is denoted as... The unit is meters, and it is defined as the maximum allowable increase in the thickness of the fouling layer on the membrane surface within a single time step. This limit is based on the thickness of the first layer of the mesh on the membrane surface in spatial discretization. If the fouling layer grows too rapidly within a time step, the membrane boundary displacement will significantly exceed the scale of the first-layer mesh, leading to severe mesh distortion, decreased computational accuracy, and even iteration failure. Therefore, It is taken as one-tenth of the smallest grid size on the membrane surface, that is... This ensures that the displacement can be effectively absorbed by the elastic smoothness. Allowable time step. Calculate using the following formula:

[0066] The dimension of this formula is meters divided by meters per second, and the result is seconds.

[0067] The allowed time step is compared with the upper limit time step determined based on the flow field characteristic time scale, and the smaller one is selected as the dynamic time step.

[0068] Specifically, to ensure the stability of the flow calculation, an upper limit time step determined based on the characteristic time scale of the flow field needs to be introduced. Here, the characteristic time scale of the flow field is taken as the average residence time of the bulk fluid within the membrane channel, i.e., the channel length. With average inlet velocity The ratio of the two values, that is, the estimated time taken for the fluid element to move from the inlet to the outlet:

[0069] The residence time is determined by the inlet average velocity in the operating condition parameters of step S1 and the channel length in the geometric parameters. It is the basic time scale for the flow response and concentration boundary layer development. Limiting the time step to no more than this scale can prevent excessive numerical dissipation or non-physical oscillations in the convective numerical scheme.

[0070] Allow time step With upper limit time step Compare the two values ​​and select the smaller one as the dynamic time step. This selection mechanism allows the process to automatically adapt to the severity of scaling at different stages: in the early stages of scaling or during periods of low growth, Smaller Larger step sizes are often limited by While maintaining high propulsion efficiency; during the rapid scaling phase... Increase By reducing the step size, the step size will automatically shorten to prevent the dirt layer from displacing beyond the limit, thereby maintaining computational efficiency while ensuring accuracy.

[0071] Once the dynamic time step is determined, the fouling layer thickness distribution on the membrane surface is updated immediately. Let the current fouling layer thickness distribution at any given time be denoted as... The updated formula is:

[0072] This formula applies to each discrete position. Execute separately. Physically, This is the thickness increment generated within that time step, measured in meters. If net peeling occurs at a certain location, i.e. The value is negative, and the increment is also negative. To ensure physical rationality, when the updated thickness value is less than zero, it is forcibly set to zero, which indicates that the dirt layer has been completely removed and the membrane surface has returned to a clean boundary.

[0073] In a specific embodiment of the present invention, adjusting the fluid domain geometric boundary of the numerical model using the dynamic mesh method to adapt to the updated fouling layer thickness distribution includes: generating new membrane boundary node displacements based on the updated membrane fouling layer thickness distribution.

[0074] A method combining elastic smoothing and local mesh reconstruction is adopted to update the mesh node positions within the fluid domain in order to maintain mesh quality and meet computational stability requirements.

[0075] Specifically, the updated fouling layer thickness distribution alters the flow space in the simulation domain, necessitating adjustments to the fluid domain geometry of the numerical model using a dynamic meshing method to accommodate the newly formed membrane profile. First, new membrane boundary node displacements are generated based on the updated fouling layer thickness distribution. For nodes located on the membrane surface… Each grid node on the grid originally had the following coordinates: After thickness accumulation, the actual physical position of the membrane surface should rise towards the interior of the fluid domain; the amount of rise is the change in fouling layer thickness between the two time points. Therefore, the nodal displacement component in The direction is zero, in The direction is:

[0076] This refers to the displacement of the membrane boundary nodes. All membrane nodes move to their new coordinate positions according to this displacement. At the first time step of the simulation startup, The displacement is The initial dirt layer profile was directly established.

[0077] After the membrane boundary moves, the positions of the mesh nodes inside the fluid domain must be adjusted accordingly to maintain mesh quality and meet computational stability requirements. This embodiment employs a combination of elastic smoothing and local mesh reconstruction. Elastic smoothing treats mesh edges as spring connections, and node displacements are transferred to internal nodes by solving the following equilibrium equations:

[0078] In the formula It is the displacement vector of the internal nodes. This is the diffusion coefficient, often taken as a value proportional to the reciprocal of the mesh volume or side length, making small mesh regions less prone to deformation. After solving this equation, all internal nodes receive smoothed displacements, and the original mesh topology remains unchanged. Local mesh reconstruction is triggered when the local mesh skew exceeds a preset skew threshold, such as 0.85, or when the minimum mesh size is lower than a preset minimum size threshold. The principle of local mesh reconstruction is to delete the original low-quality cells in the local region where the mesh quality has deteriorated, regenerate the mesh based on the current boundary node positions, and transfer the field variables between the old and new meshes in the neighboring region through interpolation, thereby restoring the entire computational domain to a higher mesh quality. The synergistic effect of elastic smoothing and local reconstruction ensures that even under conditions of non-uniform variation in fouling layer thickness along the flow direction and continuous evolution of membrane shape, numerical calculations are always performed in a stable and divergent state.

[0079] Thus, step S4 completes the entire closed loop from determining the scaling rate distribution field to the dynamic time step, and then to updating the film thickness and adapting the fluid domain geometric boundary, laying the geometric and mesh foundation for the coupled solution in step S5.

[0080] S5: Use the adjusted numerical model as the new current numerical model, return to the steps of performing coupled iterative solution, and advance the time until the cumulative simulation time reaches the filtration cycle obtained based on the operating condition parameters, and obtain the spatial distribution sequence of the dirt layer thickness at different times as the evolution sequence.

[0081] In a specific embodiment of the present invention, the filtration cycle is determined based on the time when the membrane flux decline rate in the operating condition parameters reaches a preset threshold, or based on the time when the transmembrane pressure difference growth rate reaches a preset threshold.

[0082] Specifically, after adjusting the dynamic mesh of the fluid domain geometry in step S4, the adjusted numerical model is used as the new current numerical model, and a time-progression loop is started to track the continuous cumulative evolution of the fouling layer. Before the loop is executed, the filtration cycle, i.e., the cumulative simulation time at the simulation endpoint, needs to be determined. The filtration cycle is determined based on operating parameters: one method is based on the time it takes for the membrane flux decline rate to reach a preset threshold, and the other is based on the time it takes for the transmembrane pressure difference growth rate to reach a preset threshold. Membrane flux decline rate Defined as the current global membrane flux relative to the initial membrane flux The relative decrease percentage is calculated as follows:

[0083] Transmembrane pressure differential growth rate Defined as the current transmembrane pressure difference Relative to the initial transmembrane pressure difference The relative growth rate is calculated as follows:

[0084] when Reaching the preset threshold ,or Reaching the preset threshold The corresponding cumulative simulation time is the filtering period. Preset threshold According to industrial membrane cleaning standards, the threshold value can be set to 0.30. It can be set to 0.50. During the simulation, the condition is calculated and checked after each complete time step, and the loop terminates once the condition is met.

[0085] This invention automatically adapts the scaling rate distribution field to the dynamic time step and coordinates the constraints with the flow field characteristic time scale. It can automatically solve the step size during the stage of drastic scaling changes and relax the step size restriction during the stable stage. This reduces the simulation time while ensuring computational stability and numerical accuracy, and improves the engineering applicability of the method.

[0086] In a specific embodiment of the present invention, in the step of returning to perform coupled iterative solution by taking the adjusted numerical model as the new current numerical model, the coupled iterative solution includes: transforming the updated fouling layer thickness distribution into a porous media domain with position-dependent permeability.

[0087] Specifically, the fouling layer, composed of deposits, can be viewed as a porous framework with high flow resistance. As the thickness increases, the underlying fouling layer is compressed, reducing its porosity and causing permeability to decrease along the thickness direction. To express this location dependence in a two-dimensional model, an equivalent permeability model homogenized along the normal direction is used, representing it as a local thickness. Exponential decay function:

[0088] in, For corresponding discrete positions Permeability of porous media at a given location, per square meter; It is the reference permeability of the dirt layer under zero pressure, in square meters, and is obtained by reverse calculation from pure filter cake permeation experiments using Darcy's law; The compaction attenuation coefficient is dimensionless and obtained by fitting experimental data of multi-layer filter cake compaction. For reference thickness, in meters, the characteristic thickness of significant filter cake compaction during the experiment is typically taken. Areas with lower permeability exhibit greater flow resistance, quantitatively reflecting the more significant suppressive effect of thicker fouling layers on permeation flux.

[0089] The porous medium domain is embedded into the fluid domain of the numerical model.

[0090] Specifically, in step S4, the fluid domain height has changed with the fouling layer, and the membrane boundary has moved to... Delineate the self-film surface to The region is a porous medium domain, within which the aforementioned permeability is imparted. and the porosity of the dirt layer . This can be determined by mass conservation experiments, and a value of 0.4 can be taken for typical dextran filter cakes. Porosity will be used to correct the effective diffusion coefficient of the solute in the porous medium. The pure fluid region will remain... In some cases, the penetration rate is considered infinite, and the source term is closed.

[0091] Solve for the flow field and solute concentration field coupled in porous media flow to update the shear force distribution and solute concentration distribution on the membrane surface.

[0092] Specifically, the governing equations for fluid motion are uniformly adopted throughout the region using the Navier-Stokes equations with an additional Darcy drag term:

[0093] This equation is related to the continuity equation. Together, they form the flow control equations. In the equations... It is a velocity vector. For pressure, and For the fluid density and dynamic viscosity in step S1, Set as the maximum value in the pure fluid region, and take as the actual value in the calculation. The magnitude of the molecular diffusion coefficient makes the drag term almost zero. The solute convection-diffusion equation takes the same form as in step S2, but in the porous medium domain, the molecular diffusion coefficient... Effective diffusion coefficient required Alternatives, to account for the effects of porosity and tortuosity:

[0094] In the formula Tortuosity is dimensionless and can be estimated based on porosity. The interface between the dirt layer and the pure fluid. Infiltration rate at the location Driven by the Darcy pressure drop of the fluid within the fouling layer, it can be expressed as:

[0095] The intrinsic resistance of the cleaning membrane is measured by a pure water permeation experiment, characterizing the membrane's ability to impede water flow. For the surface of the dirt layer, y= Local static pressure on the fluid side, solute retention boundary conditions on the membrane surface permeability. Apply as The entry and exit boundaries remain unchanged. and There is no slippage on the upper wall of the flow channel.

[0096] The solution process employs the same alternating iterative strategy as step S2: first, the pressure-velocity coupling is solved using the current velocity field; then, the concentration field is updated, and the permeation velocity is recalculated. This reacts on the flow boundary. External iteration continues until the relative changes in the flow field velocity distribution and solute concentration field are observed. Below the convergence threshold After convergence, the interface is extracted. Calculate the fluid velocity gradient at the membrane surface and the shear force distribution on the membrane surface:

[0097] Simultaneously extract the solute concentration at the interface. As an updated solute concentration distribution on the membrane surface.

[0098] After obtaining the updated distribution, proceed to step S3 to calculate the net fouling growth rate under the current physical field using the fouling kinetics model, thereby forming a fouling rate distribution field. Subsequently, following the process of step S4, determine the appropriate dynamic time step based on this rate field, update the fouling layer thickness distribution on the membrane surface, and readjust the fluid domain geometry boundary using the dynamic mesh method to prepare the model for the next time step. Simultaneously, the current cumulative simulation time is... Spatial distribution of dirt layer thickness at that moment Stored in a serialized data structure. After completing one full loop, the cumulative simulation time increases. And determine whether the filtration cycle has been reached. If the target is not met, return to the beginning of this step, take the current adjusted model as the new current numerical model, and execute the entire process of coupled iterative solution and fouling update again. When the cumulative simulation time meets the stopping criterion, the end time is advanced, and the spatial distribution sequence of the recorded fouling layer thickness at different times, i.e., the evolution sequence, is output.

[0099] This invention treats the fouling layer as a dynamically evolving porous media domain and embeds it into the fluid solution process, reproducing the physical nature of fouling where deposition and stripping compete with each other. This improves the consistency between the simulation results of the spatial distribution evolution of the fouling layer on the membrane surface and the actual filtration process, and makes up for the shortcomings of traditional models that only consider unidirectional deposition and ignore the stripping mechanism. This provides an accurate digital reproduction capability of fouling behavior for ultrafiltration systems.

[0100] S6: Perform spatiotemporal dimensionality reduction and feature extraction on the evolution sequence to generate a visual feature map characterizing the dynamic evolution of the scaling process.

[0101] In a specific embodiment of the present invention, the step of performing spatiotemporal dimensionality reduction and feature extraction on the evolution sequence to generate a visual feature map characterizing the dynamic evolution of the fouling process includes: performing spatial statistical dimensionality reduction on the evolution sequence along the flow direction of the membrane surface to generate a time series of fouling thickness distribution along the process.

[0102] Specifically, after the simulation in step S5 is completed, an evolution sequence is generated. This sequence contains the spatial distribution of the membrane fouling layer thickness at each recorded moment from the initial clean state to the end of the filtration cycle. The data structure of the evolution sequence can be viewed as a two-dimensional matrix. ,in The coordinates of discrete positions on the membrane surface along the flow direction are given by the subscript. Mark each discrete node, This is a series of simulation moments accumulated according to a dynamic time step. For time indexing, when faced with high-dimensional spatiotemporal data, spatial statistical dimensionality reduction is first performed along the flow direction of the membrane surface to generate a time series of fouling thickness distribution along the process.

[0103] The process of spatial statistical dimensionality reduction is as follows: the membrane surface is reduced from the inlet... To the exit All discrete nodes are divided into equal intervals according to the flow direction coordinates. Each segment contains several consecutive nodes. For the... Section At the current moment The representative thickness is taken as the arithmetic mean of the dirt layer thickness of all nodes within this section:

[0104] In the formula For section The number of discrete nodes on the membrane surface and the location of the center point of each segment. Take the average value of the node coordinates for that section. The time series of dirt thickness distribution along the pipeline is obtained by analyzing the curve of the average thickness of each section over time. Composed of, Traverse all partitioned segments, Iterate through all recorded moments. The amount of data after dimensionality reduction is reduced from the original... Reduced to It preserves the macroscopic thickness evolution trend along the flow direction while suppressing high-frequency fluctuations at the local grid level.

[0105] Time derivative analysis was performed on the time series of fouling thickness distribution along the process to extract the onset time of accelerated fouling, the peak time of fouling rate, and the time of local flaking, thus forming a characteristic time set of fouling.

[0106] Specifically, after dimensionality reduction, the time derivative is numerically approximated using a central difference scheme. The first time derivative represents the local rate of fouling layer growth or stripping, while the second time derivative reflects the rate of change of this rate. For segment (j) at time... The first and second derivatives are defined as follows:

[0107]

[0108] Forward or backward differencing is used at the end of the sequence to ensure temporal integrity. The criterion for identifying the start time of accelerated scaling is: the first derivative is consistently positive and the second derivative transitions from negative to positive and crosses a preset positive threshold, indicating that the thickness growth of this section has shifted from a slowing or stable state to an accelerated state. The peak scaling rate time is the moment when the first derivative reaches its maximum value, obtained by scanning the first derivative values ​​at each moment and extracting the maximum point. The identification of the local spalling occurrence time relies on the detection of non-monotonic thickness decrease: when the first derivative of a certain section changes from positive to negative and remains negative for several consecutive recording moments, and the magnitude of this negative value exceeds the threshold determined by numerical noise, the moment when the derivative first crosses zero downwards is marked as the local spalling occurrence time. The above characteristic times extracted from all sections are merged and redundant terms are removed to form a scaling characteristic time set. .

[0109] Based on the scale formation characteristic time set, the scale formation process is divided into the initiation stage, growth stage, peeling stage and redeposition stage, and the formation stage is marked.

[0110] Specifically, the division rules are as follows: The period from the simulation start time to the earliest acceleration of scaling among the characteristic times is the germination period, during which the scaling rate is relatively slow. From the earliest acceleration of scaling until the moment corresponding to the global maximum peak value among the peak scaling rate times is considered the growth period, during which scaling accumulates rapidly. From the first detected local peeling until the time when a certain section subsequently enters a stable growth phase, it is classified as the peeling period, during which the scale layer in some areas is significantly sheared and detached. If accelerated growth occurs again after the peeling period without new peeling, it is considered the redeposition period. The start and end times corresponding to each stage are recorded using integer identifiers to generate stage division labels, for example, 1 represents the germination period, 2 represents the growth period, 3 represents the peeling period, and 4 represents the redeposition period, and the identifier is bound to the corresponding time interval.

[0111] By overlaying the stage division identifiers with the original evolution sequence, a visual feature map characterizing the dynamic evolution of the scaling process is generated.

[0112] Specifically, the visualized feature map consists of two main parts. The first is a cloud map overlaid with the fouling growth direction vector and the spatiotemporal evolution of the film thickness in localized peeling areas. The horizontal axis represents the simulation time. The vertical axis represents the position of the membrane surface flow direction. Color mapping represents the thickness of the dirt layer. This creates a thickness color block map that unfolds over time. The scaling growth direction vector is calculated as a unit vector of the thickness temporal gradient at each pixel location and represented on the cloud map as a short arrow or directional texture, with the arrow pointing in the direction of increasing thickness. Localized peeling areas are identified as spatiotemporal blocks with continuously decreasing local thickness over a certain time period and displayed with a specific outline or semi-transparent highlight overlay.

[0113] Reference Figure 2 As shown, Figure 2 This is a spatiotemporal evolution cloud map of the fouling layer thickness on the membrane surface generated according to an embodiment of the present invention. The horizontal axis represents simulation time, and the vertical axis represents the dimensionless position of the membrane surface along the flow direction. The grayscale depth maps the fouling layer thickness: darker grayscale indicates a thicker fouling layer. The distribution map is overlaid with a fouling growth direction vector, represented by short black arrows: arrows pointing upwards indicate increasing thickness, meaning the spatiotemporal location is in the deposition-dominant stage; arrows pointing downwards indicate the peeling and thinning stage. Local peeling areas are marked with dashed closed outlines, corresponding to the spatiotemporal location where non-monotonic peeling of the fouling layer occurs due to a sudden increase in shear force caused by channel narrowing. This cloud map condenses the fouling evolution information across the entire membrane surface and time dimension into a single map, providing an intuitive and visual representation of the entire process of fouling initiation, growth, peeling, and redeposition. This facilitates operators in quickly locating fouling hotspots and tracing the hydraulic conditions corresponding to peeling events.

[0114] Secondly, there is the time-series curve diagram corresponding to the time series of fouling thickness distribution along the process. This is a combination of multiple curves showing the change of the average thickness of each segment over time after spatial statistical dimensionality reduction. The horizontal axis represents time, and the vertical axis represents the fouling layer thickness. Each curve corresponds to a segment, supplemented by color bands or vertical dividing lines to indicate the stage division, making the stage attributes intuitively displayed. The time-series curve diagram can explicitly mark characteristic points with concentrated fouling time, such as using hollow circles to mark the start time of accelerated fouling, using solid triangles to mark the peak time of fouling rate, and using solid diamonds to mark the time of local peeling.

[0115] Reference Figure 3 As shown, Figure 3 This is a time series and stage division diagram of the fouling thickness distribution along the membrane surface generated according to an embodiment of the present invention. The diagram shows five sections along the membrane surface drawn with different line types, with the center of each section located at... to The time-series curves showing the average fouling thickness change over simulation time are presented. The curves exhibit a non-monotonic trend of first increasing, then decreasing, and then rising again. Segments 3 and 4, located in the middle of the membrane surface, show a significant thickness drop around 80 minutes, corresponding to localized detachment events. The graph uses different grayscale background bands to divide the fouling process into four characteristic stages: the initiation stage (curve rises gently, with a low fouling rate); the growth stage (curve slope increases continuously, with rapid thickness accumulation); the detachment stage (curve declines, with localized fouling being sheared off); and the redeposition stage (curve rises again, with fouling re-accumulating on the detached membrane surface). Hollow dots indicate the start time of accelerated fouling, solid triangles indicate the peak fouling rate, and solid rhombuses indicate the time of localized detachment, collectively forming a characteristic time set of fouling. This graph reduces the high-dimensional spatiotemporal data output from the simulation into a visually readable multi-curve comparison chart. Combined with stage divisions and feature annotations, it provides operators with a quantitative basis for quickly determining the stage of membrane fouling and the corresponding chemical cleaning decision window.

[0116] Thus, through spatial statistical dimensionality reduction, temporal derivative analysis, feature time extraction and stage division, and multi-map overlay, the calculated evolution sequence is transformed into a visual feature map that intuitively presents the dynamics of the entire scaling process.

[0117] This invention performs spatial statistical dimensionality reduction and temporal derivative analysis on the evolution sequence, automatically extracting characteristic nodes such as the onset time of accelerated scaling, the peak rate time, and the time of local spalling. It also divides the scaling process into the initiation stage, growth stage, spalling stage, and redeposition stage, outputting a spatiotemporal evolution cloud map of the superimposed growth direction vector and the membrane thickness of the spalling area, as well as a time-series curve along the process. This transforms simulation data into an intuitively interpretable process map, enabling operators to quickly diagnose the stage of membrane fouling and trace the hydraulic conditions that induce local spalling.

[0118] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0119] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0120] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of protection of the claims.

[0121] The above content is merely an example and illustration of the concept of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the concept of the invention or exceed the scope defined by the present invention, and all such modifications and additions should fall within the protection scope of the present invention.

Claims

1. A method for revealing the scaling process and evolution trend of an ultrafiltration system, characterized in that, include: S1: Obtain the operating condition parameters of the ultrafiltration system, the geometric parameters of the ultrafiltration membrane module, and the physical property parameters of the fluid to be treated, and construct a numerical model characterizing the fluid flow and solute transport within the ultrafiltration unit based on the operating condition parameters, geometric parameters, and physical property parameters. S2: Perform coupled iterative solution of the flow field and solute concentration field of the numerical model to obtain the shear force distribution and solute concentration distribution on the membrane surface; S3: Using a scaling kinetics model that characterizes the concentration polarization-driven deposition and shear force-driven stripping mechanisms, combined with the shear force distribution and solute concentration distribution on the membrane surface, the net scaling growth rate at each discrete location on the membrane surface is calculated to form a scaling rate distribution field. The scaling kinetics model includes a deposition rate term and a stripping rate term. S4: Based on the fouling rate distribution field, determine the dynamic time step that is adapted to the current fouling layer growth rate, and update the fouling layer thickness distribution on the membrane surface according to the dynamic time step. Then, adjust the fluid domain geometric boundary of the numerical model through the dynamic mesh method to adapt to the updated fouling layer thickness distribution. S5: Use the adjusted numerical model as the new current numerical model, return to the steps of performing coupled iterative solution, and advance the time until the cumulative simulation time reaches the filtration cycle based on the operating condition parameters, and obtain the spatial distribution sequence of the dirt layer thickness at different times as the evolution sequence. S6: Perform spatiotemporal dimensionality reduction and feature extraction on the evolution sequence to generate a visual feature map characterizing the dynamic evolution of the scaling process.

2. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 1, characterized in that, The numerical model is coupled with the flow field and solute concentration field for iterative solution to obtain the shear force distribution and solute concentration distribution on the membrane surface, including: Set boundary conditions for the numerical model, the boundary conditions including the inlet flow velocity and outlet pressure determined based on the operating condition parameters; Solve the governing equations of fluid flow to obtain the velocity and pressure distributions in the flow field; The solute convection-diffusion equation is solved based on the flow field velocity distribution to obtain the solute concentration field. The shear force distribution and solute concentration distribution at the membrane surface are extracted by iterating alternately until the relative changes in the flow field velocity distribution and the solute concentration field are lower than the convergence threshold. These are then used as the membrane surface shear force distribution and membrane surface solute concentration distribution.

3. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 1, characterized in that, The fouling kinetics model, which characterizes the concentration polarization-driven deposition and shear force-driven stripping mechanisms, combines the shear force distribution and solute concentration distribution on the membrane surface to calculate the net fouling growth rate at discrete locations on the membrane surface, forming a fouling rate distribution field, including: The concentration polarization at discrete locations on the membrane surface is obtained based on the solute concentration distribution on the membrane surface. Substitute the concentration polarization into the deposition rate term to calculate the local deposition rate; The local peeling rate is calculated by substituting the shear force distribution on the membrane surface and the current dirt layer thickness distribution into the peeling rate term. The difference between the local deposition rate and the local stripping rate is calculated to obtain the net scale growth rate, and the net scale growth rates at all discrete locations are combined to form a scale rate distribution field.

4. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 1, characterized in that, The determination of the dynamic time step adapted to the current fouling layer growth rate based on the fouling rate distribution field includes: Obtain the maximum net scale growth rate in the scale rate distribution field; The allowable time step is calculated based on the maximum net fouling growth rate and the preset limit for fouling layer thickness growth. The allowed time step is compared with the upper limit time step determined based on the flow field characteristic time scale, and the smaller one is selected as the dynamic time step.

5. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 1, characterized in that, The filtration cycle is determined based on the time it takes for the membrane flux decline rate in the operating condition parameters to reach a preset threshold, or based on the time it takes for the transmembrane pressure difference growth rate to reach a preset threshold.

6. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 1, characterized in that, In the step of returning to perform coupled iterative solution by using the adjusted numerical model as the new current numerical model, the coupled iterative solution includes: The updated fouling layer thickness distribution is transformed into a porous media domain with position-dependent permeability; Embed the porous medium domain into the fluid domain of the numerical model; Solve for the flow field and solute concentration field coupled in porous media flow to update the shear force distribution and solute concentration distribution on the membrane surface.

7. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 1, characterized in that, The process of performing spatiotemporal dimensionality reduction and feature extraction on the evolution sequence to generate a visual feature map characterizing the dynamic evolution of the scaling process includes: Spatial statistical dimensionality reduction of the evolution sequence is performed along the membrane flow direction to generate a time series of fouling thickness distribution along the membrane. Time derivative analysis was performed on the time series of fouling thickness distribution along the process to extract the onset time of accelerated fouling, the peak time of fouling rate, and the time of local flaking, which constituted a set of fouling characteristic time sets. Based on the scale formation characteristic time set, the scaling process is divided into the initiation stage, growth stage, peeling stage and redeposition stage, with the formation stage being identified; By overlaying the stage division markers with the evolution sequence, a visual feature map is generated.

8. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 7, characterized in that, The visualized feature map includes a cloud map of the spatiotemporal evolution of membrane thickness superimposed with the fouling growth direction vector and the local peeling area, as well as a time series curve corresponding to the time series of fouling thickness distribution along the process.

9. The method for revealing the scaling process and evolution trend of an ultrafiltration system according to claim 1, characterized in that, The method of adjusting the fluid domain geometry boundary of the numerical model using a dynamic mesh method to adapt to the updated fouling layer thickness distribution includes: New membrane boundary node displacements are generated based on the updated membrane fouling layer thickness distribution. The positions of mesh nodes within the fluid domain are updated using a combination of elastic smoothing and local mesh reconstruction.

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