Simulation method for sludge floc distribution and gyration radius based on Langevin model

Abstract

The invention relates to a simulation method for sludge floc distribution and gyration radius based on a Langevin model, belongs to the technical field of molecular thermodynamic motion simulation, solves the problem that random motion of floc is difficult to accurately simulate in the prior art, and comprises the following steps: S1, obtaining parameters of silt particles in sludge floc, establishing a Langevin kinetic model of the sludge flocculation movement; s2, splitting the built Langevin kinetic model of the sludge flocculation movement into two subsystems; s3, dispersing the two subsystems to obtain numerical simulation values of the speed and the position of sediment particles in the floccules; step S4, obtaining numerical simulation of the sediment particle distribution density function of the floccules about time change, and taking the numerical simulation as long-time distribution density of the floccules; s5, obtaining the gyration radius of the floccules; and step S6, applying the obtained long-time distribution density and gyration radius of the floccules to a sewage treatment system and a water conservancy management system, and optimizing design and operation parameters of the system.

Description

Technical Field

[0001] The invention belongs to the technical field of molecular thermodynamic motion simulation, and in particular relates to a simulation method for sludge floc distribution and gyration radius based on a Langevin model. Background Art

[0002] Silt flocculation movement is an important process of sedimentation, transportation and distribution in water bodies, and has important applications in river dredging, water conservancy projects, sewage treatment and chemical production. During the silt flocculation movement, the floc distribution density and gyration radius are effectively simulated, which helps to deeply understand the movement law of flocs and calculate the sedimentation rate and distribution law of flocs. This provides a scientific basis and technical support for preventing and controlling water pollution, controlling soil erosion and controlling siltation. This plays an important role in optimizing engineering design, reducing construction costs and improving engineering efficiency.

[0003] During the movement, the sand particles collide with the liquid molecules randomly and are affected by the random noise of thermodynamics, so their movement is random. Due to the influence of complex factors such as friction, gravity, intermolecular attraction, thermal force and the organic force of the molecules themselves, the movement environment of the sand particles shows high nonlinearity. At present, the methods in this technical field are difficult to accurately simulate the random movement distribution law of flocs and predict the physical laws or physical quantities such as the gyration radius of flocs.

[0004] There are at least the following problems in the prior art:

[0005] (1) The existing numerical simulation method of floc gyration radius cannot handle the simulation problem of floc gyration radius of flocculation motion in highly nonlinear situations;

[0006] (2) The existing numerical simulation methods for evaluating the floc gyration radius have large errors or low computational efficiency on a long time scale, and cannot meet the needs of high-precision long-term numerical calculation of the floc gyration radius. In addition, the existing methods cannot achieve effective long-term numerical simulation of floc distribution density. Summary of the invention

[0007] In view of this, the present invention provides a new method for efficiently numerically simulating the floc distribution density and floc gyration radius of sludge flocculation movement, aiming at the highly nonlinear Langevin kinetic equation capable of simulating sludge flocculation movement.

[0008] According to an embodiment of the present invention, a simulation method for sludge floc distribution and gyration radius based on the Langevin model is provided, comprising the following steps:

[0009] Step S1, obtaining parameters of silt particles in sludge flocs, and establishing a Langevin kinetic model of sludge flocculation movement based on the parameters of the silt particles;

[0010] Step S2, splitting the established Langevin dynamic model of sludge flocculation movement into two subsystems;

[0011] Step S3, discretizing the two subsystems obtained by splitting to obtain numerical simulation values ​​of the velocity and position of the sediment particles in the flocs;

[0012] Step S4, obtaining a numerical simulation of the time variation of the distribution density function of the sediment particles in the flocs by using the numerical simulation value of the position of the sediment particles in the flocs obtained in S3, as the long-term distribution density of the flocs;

[0013] Step S5, obtaining the gyration radius of the floc through the numerical simulation value of the position of the sediment particles in the floc in S3;

[0014] Step S6, applying the obtained long-term distribution density and gyration radius of the flocs to the sewage treatment system and water management system, accurately predicting the movement trajectory and aggregation behavior of the flocs during the treatment process, and optimizing the design and operation parameters of the system.

[0015] Optionally, the step S1 specifically includes:

[0016] Obtaining parameters of the silt particles in the silt flocs, including obtaining the damping force of the silt solution on the silt particles and the thermal external force on the silt particles;

[0017] The Langevin kinetic model of sludge flocculation movement is established and expressed as

[0018]

[0019] Where t represents the time, Q(t) represents the position of the sediment particles, P(t) represents the movement speed of the sediment particles, α is a positive integer, -(Q(t)) 2α+1 The term represents the force term carried by the sediment particles, v represents the damping force of the silt solution on the sediment particles and is obtained through actual measurement, 1 / v>0 is the Lagrangian time scale, {W(t), t≥0} represents the thermal external force on the sediment particles and is obtained through actual measurement, is a positive constant, c 0 is the Kolmogorov constant and ∈ is the dissipation rate.

[0020] Optionally, the step S2 specifically includes:

[0021] The Langevin kinetic model (1) of sludge flocculation motion is split into the following two subsystems: n ,

[0022]

[0023] and

[0024]

[0025] Where superscript D represents the deterministic subsystem, superscript S represents the random subsystem, given the time step τ∈(0,1), the interval [0,+∞) is uniformly partitioned: 0≤t 1 <t 2 <… <t n <…, and record the nth time point t n :=nτ, the nth time interval T n :=[t n ,t n+1 ),n∈N, N represents a natural number, represents the velocity of the deterministic subsystem at time t, represents the deterministic subsystem at time t n The speed at represents the velocity of the random subsystem at time t, Denotes the random subsystem at time t n The speed at represents the position of the deterministic subsystem at time t, represents the deterministic subsystem at time t n The location of represents the position of the random subsystem at time t, represents the random subsystem at time t n The location of the place.

[0026] Optionally, the step S3 specifically includes:

[0027] The calculation subsystems (2) and (3) are n+1 The numerical solution at the time is used as the numerical simulation value of the velocity and position of the sediment particles in the floc, as follows:

[0028]

[0029] Where n∈N,P O =P(0),Q O =Q(0), {P n ,Q n :n∈N} is the numerical simulation solution of the velocity and position of the floc particles, θ is a real number, representing the integral variable, here is the numerical solution of the deterministic subsystem, representing the numerical simulation value of the velocity of the sediment particles in the flocs. It is the numerical solution of the deterministic subsystem, representing the numerical simulation value of the position of the sediment particles in the floc.

[0030] Optionally, the step S4 specifically comprises: kSubstitute the mth sediment particle at time t into step S3 to obtain k The position of the mth sediment particle at time The position distribution of sediment particles in the state space is statistically calculated through Matlab built-in functions and normalized to obtain t k The numerical simulation of the sediment particle distribution density function of the floc at a certain moment is used as the long-term distribution density of the floc.

[0031] Optionally, the step S5 specifically includes:

[0032] The random sampling method is used to analyze the sediment particle content in the sample to determine the value of the floc sediment particle number M, and the Monte Carlo method is used to calculate the approximate value of the floc gyration radius:

[0033]

[0034] in, Indicates that t k Substitute the simulated value of the movement speed and position of the mth sediment particle driven by Brownian motion obtained in step S3 at the mth sediment particle at time instant, K is a positive integer and represents the maximum time node of the calculation, φ 1 (p,q) and φ 2 (p,q) is the test function, the initial position and initial velocity values ​​x = (P(0), Q(0)) T The approximate value of the floc gyration radius is taken as the floc gyration radius.

[0035] Compared with the prior art, the simulation method of sludge floc distribution and gyration radius based on the Langevin model provided in accordance with an embodiment of the present invention proposes an efficient numerical simulation method of floc distribution density and gyration radius, which can effectively simulate the physical quantities when the steady state is reached; in addition, the method has long-term numerical calculation stability and convergence, can improve the accuracy of long-term floc physical quantity simulation, can provide reliable simulation for the efficient prediction of floc distribution density and gyration radius of the Langevin kinetic model of sludge flocculation movement, realizes long-term stable and efficient numerical simulation of the floc distribution law of sludge flocculation movement in a highly nonlinear complex environment, and is used for efficient simulation of the floc gyration radius, thereby providing effective treatment decision-making solutions when used in river dredging, water conservancy projects, sewage treatment, chemical production and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments will be briefly introduced below. The features and advantages of the present invention can be more clearly understood by referring to the drawings. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0037] Figure 1 The present invention is a flowchart of a method for simulating the distribution and gyration radius of sludge flocs based on the Langevin model according to an embodiment of the present invention.

[0038] Figure 2 It is a convergence order diagram of the simulation method of sludge floc distribution and gyration radius based on the Langevin model provided according to an embodiment of the present invention.

[0039] Figure 3 This is a diagram of the simulation accuracy of the floc gyration radius obtained in accordance with an example of a simulation method for sludge floc distribution and gyration radius based on the Langevin model provided in accordance with an embodiment of the present invention.

[0040] Figure 4 A comparison chart of the long-term evolution of the calculation error between the floc gyration radius obtained by an embodiment of the simulation method for sludge floc distribution and gyration radius based on the Langevin model provided in accordance with an embodiment of the present invention and the floc gyration radius obtained by the prior art method.

[0041] Figures 5 to 8 This is a long-term evolution diagram of floc distribution density obtained by an example of a simulation method for sludge floc distribution and gyration radius based on the Langevin model provided in accordance with an embodiment of the present invention.

[0042] Fig. 9 This is a long-term evolution diagram of the floc gyration radius obtained in an example of a simulation method for sludge floc distribution and gyration radius based on the Langevin model provided in accordance with an embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0044] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0045] The following is a detailed description of the simulation method of sludge floc distribution and gyration radius based on the Langevin model provided according to an embodiment of the present invention.

[0046] Explanation of symbols:

[0047] Q(t) is the position of the sediment particle;

[0048] P(t) is the velocity of sediment particles;

[0049] v The damping force of the silt solution on the sediment particles is obtained through actual measurement;

[0050] W(t) is the thermal force on sediment particles, obtained through actual measurement;

[0051] σ is a positive constant;

[0052] α is a positive integer;

[0053] c O Kolmogorov constant (Kolmogorov constant);

[0054] ∈ dissipation rate;

[0055] E-expectation;

[0056] Test function;

[0057] x 1 Initial velocity;

[0058] x 2 Initial position;

[0059] x=(x 1 ,x 2 ) an initial vector with initial velocity and initial position as components;

[0060] (P x (t),Q x (t)) T The exact solution at time t with x as the initial vector;

[0061] T: termination time;

[0062] π stationary distribution;

[0063] τ time step;

[0064] t moment;

[0065] t n The nth time point, n∈N, N represents a natural number;

[0066] T n The nth time interval, n∈N, N represents a natural number;

[0067] D. Determine the subsystem tag;

[0068] S random subsystem tag;

[0069] The velocity of the deterministic subsystem at time t The deterministic subsystem at time t n The speed at which

[0070] The velocity of the random subsystem at time t;

[0071] The random subsystem at time t n The speed at which

[0072] The position of the deterministic subsystem at time t;

[0073] The deterministic subsystem at time t n location;

[0074] The position of the random subsystem at time t;

[0075] The random subsystem at time t n location;

[0076] P n Numerical simulation solution representing the velocity of floc particles;

[0077] Q n Numerical simulation solution representing the location of floc particles;

[0078] θ is a real number, representing the integral variable;

[0079] The intermediate value of the velocity simulation value of the sediment particles in the flocs was initially obtained; The intermediate value of the simulated position of the sediment particles in the flocs is preliminarily obtained; p represents the variable of the particle velocity;

[0080] q is the variable representing the particle position;

[0081] υ is the variable of the damping force of the silt solution on the sediment particles;

[0082] C H A positive constant related to the energy function H;

[0083] H energy function;

[0084] L 2 (R 2;π)R 2 On the space of functions that are square-integrable with respect to measure π;

[0085] R real number space;

[0086] k sequence of positive integers;

[0087] K is the maximum time node of the calculation;

[0088] C is a positive constant;

[0089] t with x as the initial vector k The velocity of sediment particles at any moment;

[0090] t with x as the initial vector k The position of sediment particles at any moment;

[0091] ρ(q) long-term distribution density of flocs;

[0092] φ 1 Test function;

[0093] φ 2 Test function;

[0094] P n Numerical simulation solution of the velocity of floc particles;

[0095] Q n Numerical simulation solution for the location of floc particles;

[0096] M is the number of sediment particles in the floccules;

[0097] R f (P,Q) Approximate value of floc gyration radius;

[0098] Simulated values ​​of the velocity and position of the mth sediment particle driven by Brownian motion.

[0099] According to an embodiment of the present invention, a simulation method for sludge floc distribution and gyration radius based on the Langevin model is provided, comprising the following steps:

[0100] Step S1, obtaining parameters of the silt particles in the sludge flocs, and establishing a Langevin dynamic model of sludge flocculation motion based on the parameters of the silt particles. The parameters of the silt particles obtained may include the damping force of the silt solution on the silt particles, the thermal external force on the silt particles, etc. The above parameters can be obtained by actual measurement of the sludge flocs.

[0101] The Langevin kinetic model of sludge flocculation movement is established and expressed as

[0102]

[0103] Among them, the equation satisfies the deterministic initial value (the value of the initial position and the initial velocity) condition, and the value of the initial position and the initial velocity is x = (P(0), Q(0)) T Here, t represents the time, Q(t) represents the position of the sediment particles, P(t) represents the movement speed of the sediment particles, α is a positive integer, -(Q(t)) 2α+1 The term represents the force term carried by the sediment particles, v represents the damping force of the silt solution on the sediment particles and is obtained through actual measurement, 1 / v>0 is the Lagrangian time scale, {W(t), t≥0} is the one-dimensional standard Brownian motion, represents the thermal external force on the sediment particles and is obtained through actual measurement, is a positive constant, c 0 is the Kolmogorov constant and ∈ is the dissipation rate.

[0104] The solution distribution of the Langevin kinetic model (1) of sludge flocculation motion tends to a stable distribution over a long period of time, which is also called the ergodicity of the Langevin kinetic model of sludge flocculation motion, that is, in the square integrable function space L 2 (R 2 ;π) the following convergence holds:

[0105]

[0106] In order to emphasize the dependence of the solution on the values ​​of the initial position and initial velocity, the exact solution at time t with x as the initial position and initial velocity is denoted as (P x (t),Q x (t)) T , E represents expectation, represents the test function, R represents the real number space, T represents the termination time, and π represents the stable distribution. That is to say, in the sludge flocculation process, the movement of floc particles will reach a steady state after a long time, which is manifested as the distribution density of flocs tending to a Gibbs probability distribution, that is, π. At this time, the gyration radius of the flocs will tend to a stable constant value, which can be obtained from the above convergence limit.

[0107] Step S2, split the established Langevin dynamic model (1) of sludge flocculation into two subsystems. Given a time step τ∈(0,1), make a consistent partition on the interval [0,+∞): 0≤t 1 <t 2 <… <t n <…, and record t n :=nτ,T n :=[t n ,t n+1), n∈N, N represents a natural number. The Langevin kinetic model (1) of sludge flocculation motion is split into the following two subsystems: for t∈T n ,

[0108]

[0109] and

[0110]

[0111] The superscript D represents the deterministic subsystem, and the superscript S represents the stochastic subsystem. represents the velocity of the deterministic subsystem at time t, represents the deterministic subsystem at time t n The speed at represents the velocity of the random subsystem at time t, represents the random subsystem at time t n The speed at represents the position of the deterministic subsystem at time t, represents the deterministic subsystem at time t n The location of represents the position of the random subsystem at time t, represents the random subsystem at time t n The location of the place.

[0112] Step S3, discretize the two subsystems obtained by splitting, and obtain the numerical simulation values ​​of the velocity and position of the sediment particles in the floc {P n ,Q n :n∈N}, referred to as numerical solution, where P n The numerical simulation solution representing the velocity of floc particles, Q n The numerical simulation solution represents the position of the floc particles. Specifically, the subsystems (2) and (3) are calculated at t n+1 The numerical solution at time is as follows:

[0113]

[0114] Where n∈N,P O =P(0),Q O =Q(0), θ is a real number representing the integral variable. It represents the numerical solution of the deterministic subsystem, that is, the intermediate value of the velocity and position simulation values ​​of the sediment particles in the flocs.

[0115] Property 1: The above numerical solutions tend to be stable over a long period of time, so the distribution density and gyration radius of floc movement can be obtained from the stable distribution and numerical solution. The numerical solution satisfies: This shows that the energy of the discrete system has a uniform dissipation over time, so the numerical solution will reach a steady state after a long time: that is, at L 2 (R 2 ; π τ ) holds the following convergence Among them, p represents the variable of particle velocity, q represents the variable of particle position, H represents the energy function, C H represents a positive constant related to the energy function H. Therefore, the simulation method of sludge floc distribution and gyration radius based on the Langevin model provided in accordance with an embodiment of the present invention has the ability to simulate floc distribution density and gyration radius for a long time.

[0116] Property 2: The simulation method for sludge floc distribution and gyration radius based on the Langevin model provided in accordance with an embodiment of the present invention has a calculation accuracy of order 1. The polynomial moment of the method has long-term stability, and the exponential moment has an exponential growth law: The obtained method has a first-order calculation accuracy, that is: in, represents t with initial vector x k The speed of the sediment particles at any moment, represents t with initial vector x k The position of the sediment particles at the moment, C is a positive constant. This shows that the simulation method has the ability to numerically simulate physical quantities with high precision and for a long time.

[0117] Step S4, obtain the numerical simulation of the sediment particle distribution density function of the floc as the long-term distribution density of the floc. Calculate the approximate value of the sediment particle distribution density function of the floc: Use the calculation method of the above step S3 to obtain t k The position of the mth sediment particle at time The position distribution of sediment particles in the state space is statistically calculated using Matlab built-in functions and normalized to obtain t k Numerical simulation of the floc sediment particle distribution density function at the moment.

[0118] A certain initial position and initial velocity are generated by initial random distribution. As time goes by, the distribution of floc particles gradually becomes stable. The theoretical distribution density of the stable state can be expressed as

[0119]

[0120] Among them, q represents the variable of the particle position, υ represents the variable of the damping force of the silt solution on the sediment particles, and R represents the real number space.

[0121] Step S5, calculate the radius of gyration of the floc. Set a certain initial position and initial velocity x, and test the function φ 1 (x 1 ,x 2 )=x 2 2 and φ 2 (x 1 ,x 2 )=x 2 The radius of gyration of the flocs reaching equilibrium is in Where x=(x 1 ,x 2 ), x 1 represents the speed variable, x 2 Represents a position variable.

[0122] The value of the number of floc sediment particles M is obtained by random sampling method, and the approximate value of the floc gyration radius is calculated by Monte Carlo method:

[0123]

[0124] in, m represents the mth sediment particle, represents the simulated value of the velocity and position of the mth sediment particle driven by Brownian motion, K is a positive integer and represents the maximum time node of the calculation, φ 1 (p,q)=q 2 and φ 2 (p,q)=q is the test function. The approximate value of the gyration radius of the floc is obtained as the gyration radius of the floc.

[0125] Step S6, applying the obtained long-term distribution density and gyration radius of flocs to sewage treatment systems, water management systems, etc., can not only accurately predict the movement trajectory and aggregation behavior of flocs during the treatment process, but also optimize the design and operation parameters of the system to improve the pollutant removal efficiency. In addition, it can also be used to improve the flocculant delivery strategy, improve the effect of sewage purification, help monitor and control the distribution of suspended matter and sediments in water bodies in water management, and ensure the sustainable management and ecological balance of the water environment.

[0126] The following is a detailed description of an embodiment of a method for simulating the distribution and gyration radius of sludge flocs based on the Langevin model provided according to an embodiment of the present invention.

[0127] Example 1

[0128] Step S1: Establish the Langevin kinetic equation for sludge flocculation motion affected by nonlinear potential energy. The potential energy of the silt particles is So let α=1, and the equation has an external force F=-(Q(t)) 3 Assume the Lagrangian time scale is 0.1, that is, v = 10, and the influence intensity of the random force is The following nonlinear Langevin equation for the motion of sediment particles is obtained:

[0129]

[0130] Assume that the values ​​of the initial position and initial velocity are P 0 =1,Q 0 =1, end time: T=1.

[0131] Step S2: The consistent segmentation step length is: τ = 2- 12 , the Langevin kinetic model (1) of sludge flocculation is split into the following two systems: for t∈T n ,n=1,...,2 12 ,

[0132]

[0133] and

[0134]

[0135] Step S3: Discretize the system (2) to obtain the numerical simulation values ​​of sediment particle velocity and position as follows:

[0136]

[0137] Figure 1 A flowchart for implementing the method (4) of the present invention, according to Figure 1 The velocity and position of the sediment particles in the floccules at different times can be obtained by processing the process. n ,Q n :n=0,...,2 12}.

[0138] The following numerical calculations and comparative analyses are respectively performed on the convergence order, the calculation accuracy of the floc distribution density and the gyration radius, and the time evolution of the calculation error in the examples of the method provided by the embodiments of the present invention.

[0139] Analysis 1: The exact solution of system (1) can be obtained by using the above equation (4) with a step size of τ = 2 -1 The solution obtained is denoted as {P n ,Q n :n=0,...,2 15}. Assume that there are 3000 sediment particles in the floc, calculate the error: Here, different values ​​of superscript i (i.e. (P i,Q i ) T and Represents the movement speed and position of different sediment particles. Take the consistent step size as 2 -9 ,2 -10 ,2 -1 Generate simulated values ​​of sediment particle velocity and position and their strong errors, and draw loglog curves to obtain Figure 2 , which numerically verifies that the velocity and position of the sediment particles obtained by the method of the present invention can have an optimal convergence order of 1. Figure 2 Here, SAVF stands for the splitting average vector field method.

[0140] Analysis 2: Further, the approximate error between the numerical simulation value and the true value of the floc gyration radius is calculated: We can draw a loglog curve to get Figure 3 , which numerically verifies that the accuracy of the floc gyration radius calculated by the method described in the present invention is 1.

[0141] Analysis 3: In order to compare the long-term evolution of the error in the calculation of the floc gyration radius, the other method considered for comparison with the method provided by the embodiment of the present invention is the following splitting algorithm:

[0142]

[0143] This method has a strong convergence order of 1, but it is not ergodic and cannot calculate the gyration radius of the flocs in a stable state for a long time. The end time is T = 1000, and the step size of the exact solution is 1.25×2 -6 , the step size of the numerical solution is 2 -5 , the number of sediment particles is taken as 50000. According to the above method, the strong error is numerically calculated, and the comparison chart obtained is Figure 4 , wherein the legend SAVF is a floc gyration radius error curve obtained by a method provided in an embodiment of the present invention; SAVF1 represents a floc gyration radius error curve calculated by other existing methods. Figure 4 It is shown that the algorithm of the present invention not only has the characteristics of long-term calculation stability, but also significantly improves the calculation accuracy.

[0144] Step S4: simulating the long-term distribution density of flocs in the sludge flocculation process.

[0145] The density maps of floc position distribution at t = 0, t = 2, t = 256, and t = 512 are calculated respectively, and the sediment particle content in the uniformly divided interval is counted and normalized to obtain the distribution histogram, and the empirical density function of sediment particles in space is approximately obtained, and the obtained Figure 5-Figure 8 .from Figure 5-Figure 8 It can be seen that with the increase of time, the empirical density function of the floc particles tends to a density function of the Gibbs measure, which reflects that the method provided according to the embodiment of the present invention has the ability to calculate the distribution density of floc particles for a long time.

[0146] Step S5: Calculate the floc gyration radius.

[0147] Given 5 initial positions and initial velocities, they are x=

[0148] (1,1) T ,(2,2) T ,(3,3) T ,(4,4) T ,(5,5) T , the end time is T = 500, the step size of the numerical solution is 0.005, the number of sediment particles is M = 50000, K = 10 5 The approximate value of the floc gyration radius is

[0149]

[0150] Fig. 9 is the floc gyration radius obtained with time t for the above five different initial positions and initial velocities n , evolution diagram for n≤K.

[0151] Step S6, applying the simulation method of the distribution density and gyration radius of the silt particle flocs to the sewage treatment system and the water management system. Calculating the spatial distribution density of flocs in the sewage treatment tank or river water body can show which areas have sedimentation or blockage problems, thereby optimizing the flow path of the fluid in the reaction tank and the distribution area of ​​the flocs, adjusting the size and shape of the reaction tank or regularly cleaning the river to improve the sewage treatment efficiency and prevent river siltation. In addition, the size of the floc gyration radius determines the rotation and migration behavior of the flocs in the flow field, which can be used to predict the behavior of suspended matter in different treatment stages, thereby determining the optimal placement and amount of flocculants, ensuring that the flocs can quickly aggregate and effectively settle, and achieving reasonable regulation of water quality.

[0152] The above steps can be summarized to show that the present invention can efficiently and accurately simulate the long-term distribution density of flocs in the sludge flocculation process based on the Langevin kinetic model and calculate the size of the floc gyration radius. It also provides a methodological basis for the long-term high-precision numerical simulation needs of nonlinear Langevin equations in other practical applications in the fields of physics, biology, etc.

[0153] All the above optional technical solutions can be arbitrarily combined to form optional embodiments of the present application, which will not be described one by one here.

[0154] It should be understood that the order of execution of the steps in the above embodiment does not necessarily mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0155] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A simulation method for sludge floc distribution and gyration radius based on the Langevin model, characterized in that: The following steps are involved: Step S1, obtaining parameters of silt particles in sludge flocs, and establishing a Langevin kinetic model of sludge flocculation movement based on the parameters of the silt particles; Step S2, splitting the established Langevin dynamic model of sludge flocculation movement into two subsystems; Step S3, discretizing the two subsystems obtained by splitting to obtain numerical simulation values ​​of the velocity and position of the sediment particles in the flocs; Step S4, obtaining a numerical simulation of the time variation of the distribution density function of the sediment particles in the flocs by using the numerical simulation value of the position of the sediment particles in the flocs obtained in S3, as the long-term distribution density of the flocs; Step S5, obtaining the gyration radius of the floc through the numerical simulation value of the position of the sediment particles in the floc in S3; Step S6, applying the obtained long-term distribution density and gyration radius of the flocs to the sewage treatment system and water management system, accurately predicting the movement trajectory and aggregation behavior of the flocs during the treatment process, and optimizing the design and operation parameters of the system.

2. The simulation method for sludge floc distribution and gyration radius based on the Langevin model according to claim 1, characterized in that: The step S1 specifically includes: Obtaining parameters of the silt particles in the silt flocs, including obtaining the damping force of the silt solution on the silt particles and the thermal external force on the silt particles; The Langevin kinetic model of sludge flocculation movement is established and expressed as Where t represents the time, Q(t) represents the position of the sediment particles, P(t) represents the movement speed of the sediment particles, α is a positive integer, -(Q(t)) 2α+1 The term represents the force term carried by the sediment particles, v represents the damping force of the silt solution on the sediment particles and is obtained through actual measurement, 1 / v>0 is the Lagrangian time scale, {W(t), t≥0} represents the thermal external force on the sediment particles and is obtained through actual measurement is a positive constant, c0 is the Kolmogorov constant, and ∈ is the dissipation rate.

3. The simulation method for sludge floc distribution and gyration radius based on the Langevin model according to claim 2, characterized in that: The step S2 specifically includes: The Langevin kinetic model (1) of sludge flocculation motion is split into the following two subsystems: n , and Where superscript D represents the deterministic subsystem, superscript S represents the random subsystem, given the time step τ∈(0,1), the interval [0,+∞) is uniformly partitioned: 0≤t1 <t2<…<t n <…, and record the nth time point t n :=nτ, the nth time interval T n :=[t n ,t n+1 ),n∈N, N represents a natural number, Denotes the deterministic subsystem at time t∈T n The speed at represents the deterministic subsystem at time t n The speed at represents the velocity of the random subsystem at time t, represents the random subsystem at time t n The speed at represents the position of the deterministic subsystem at time t, represents the deterministic subsystem at time t n The location of represents the position of the random subsystem at time t, Denotes the random subsystem at time t n The location of the place.

4. The simulation method for sludge floc distribution and gyration radius based on the Langevin model according to claim 3, characterized in that: The step S3 specifically includes: The calculation subsystems (2) and (3) are n+1 The numerical solution at the time is used as the numerical simulation value of the velocity and position of the sediment particles in the floc, as follows: Where n∈N, P0=P(0), Q0=Q(0), {P n ,Q n :n∈N} is the numerical simulation solution of the velocity and position of the floc particles, θ is a real number, representing the integral variable, here is the numerical solution of the deterministic subsystem, representing the numerical simulation value of the velocity of the sediment particles in the flocs. It is the numerical solution of the deterministic subsystem, representing the numerical simulation value of the position of the sediment particles in the floc.

5. The simulation method for sludge floc distribution and gyration radius based on the Langevin model according to claim 4, characterized in that: The step S4 specifically includes: t k Substitute the mth sediment particle at time t into step S3 to obtain k The position of the mth sediment particle at time The position distribution of sediment particles in the state space is statistically calculated through Matlab built-in functions and normalized to obtain t k The numerical simulation of the sediment particle distribution density function of the floc at a certain moment is used as the long-term distribution density of the floc.

6. The simulation method for sludge floc distribution and gyration radius based on the Langevin model according to claim 5, characterized in that: The step S5 specifically includes: The random sampling method is used to analyze the sediment particle content in the sample to determine the value of the floc sediment particle number M, and the Monte Carlo method is used to calculate the approximate value of the floc gyration radius: in, Indicates that t k Substitute the mth sediment particle at time instant into the simulation value of the movement speed and position of the mth sediment particle driven by Brownian motion obtained in step S3, K is a positive integer and represents the maximum time node of the calculation, φ1(p,q) and φ2(p,q) are test functions, the values ​​of the initial position and initial velocity x=(P(0),Q(0))T, and the approximate value of the gyration radius of the floc is obtained as the gyration radius of the floc.

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