Simulation method of turbulent flow field and suspended sediment concentration field under grid disturbance

Abstract

The application relates to a simulation method for a turbulent flow field and a suspended sediment concentration field under grid disturbance, which comprises the following steps: determining a turbulent flow model control equation based on a level set-based two-fluid space filtering large eddy simulation (LES) model; establishing a level set model; tracking the fluctuation of a free water surface by using a level set function method; setting the density and viscosity of the whole calculation domain as constant values; reconstructing the above formula into a single-fluid equation; solving the level set convection equation; integrating a viscous sediment model into a SCHISM simulation system; adopting a SCB model for a flocculation and sedimentation process of fine particle sediment; adopting an immersed boundary method to process a fluid-structure coupling problem; simultaneously adopting a split-step method to solve the fluid equation; improving the calculation efficiency by MPI parallelization; and finally solving and outputting the turbulent flow field and the suspended sediment concentration field under the grid disturbance. The application adds a fine particle sediment flocculation and sedimentation group model and a viscous sand model on the basis of the SCHISM model, and can effectively simulate the turbulent flow field and the suspended sediment concentration field under the grid disturbance.

Description

Technical Field

[0001] This application belongs to the field of experimental technology in water conservancy engineering, specifically a method for simulating turbulent flow field and suspended sediment concentration field under grid disturbance. Background Technology

[0002] Oscillating grid turbulence, generally referred to as approximately isotropic turbulence, is fundamental to the study of complex turbulence and related material transport. There are two methods for generating grid turbulence in the laboratory: the fixed grid method and the vibrating grid method. The fixed grid method is difficult to control and decays rapidly, resulting in a short observation period. The vibrating grid method involves vibrating one or more grid panels perpendicular to the grid plane within a water tank. Jet and wake flows are generated at the grid openings and junctions, respectively. These two flows mix and produce approximately isotropic turbulence at a certain distance from the grid, known as oscillating grid turbulence (OGT). The characteristics of OGT are easily controlled by changing the operating parameters of the grid, including the grid opening size, amplitude, and frequency, and can be maintained for a relatively long time without decay, making it convenient for measurement and widely used.

[0003] In nature, the initiation and suspension of sediment are sometimes caused by high-intensity turbulence rather than mean flow. Bar screen turbulence can effectively simulate sediment movement under such special flow conditions. Furthermore, bar screen turbulence can isolate the turbulent effects to study the turbulent diffusion of sediment and pollutants, and the adsorption and desorption of inorganic substances by sediment. Therefore, although the generation mechanism of indoor vibrating bar turbulence differs from that of natural turbulence, it is widely used to study the movement of sediment and pollutants. Using OGT, Rouse first studied sediment suspension characteristics and obtained the famous Rouse suspended mass vertical distribution formula. Other domestic and international scholars have studied key mechanisms of sediment transport, such as sediment initiation criteria, the relationship between sediment diffusion coefficient and momentum exchange coefficient. However, existing bar screen turbulence systems mostly use vertical vibrating bar screens, resulting in turbulence that differs from natural conditions. In addition, existing vibrating bar screens are relatively small, generally tens of centimeters in size, and are single or double-panel screens; multi-panel screens are rarely studied. Summary of the Invention

[0004] The purpose of this application is to provide a method for simulating the turbulent field and suspended sediment concentration field under grid disturbance, which can effectively simulate the turbulent field and suspended sediment concentration field under grid disturbance.

[0005] To achieve the above objectives, this application provides the following technical solution:

[0006] A method for simulating turbulent flow and suspended sediment concentration fields under grid disturbance includes the following specific steps:

[0007] S1. Establish the fluid control equations for a large eddy model of two-fluid spatial filtering based on the level set equation.

[0008] S2. Establish a level set model in the model and use the level set function method to track the fluctuations of the free water surface;

[0009] S3. The model describes the aggregation and splitting process of flocs based on the size classification of sediment particles;

[0010] S4. Apply the submerged boundary method to treat the solid and liquid phases in the model;

[0011] S5. Solve the model governing equations using the split-step method;

[0012] S6, Simulates the turbulent flow field and suspended sediment concentration field under grid disturbance.

[0013] The specific steps for establishing the fluid control equations of the large eddy model based on the level set equations for two-fluid spatial filtering in step S1 are as follows:

[0014] Based on a large eddy simulation model with level set-based two-fluid spatial filtering, the governing equations for the turbulence model are constructed as follows:

[0015]

[0016]

[0017] In the formula, φ is the defined level set function; ξ i For grid coordinates, U is the transformation matrix; J is the Jacobian matrix of the transformation matrix; U i The flux of the control volume; u i ρ is the velocity component; μ is the density; p is the dynamic viscosity coefficient; τ is the pressure. li κ is the pressure lattice stress tensor; δ is the water surface curvature; ij Let be the Kronecker trigonometric function; h be the smooth Heaviside function; Re, Fr, and We be the dimensionless Reynolds number, Froude number, and Weber number, respectively, defined as follows:

[0018]

[0019] In the formula, U and L are the characteristic flow velocity and characteristic length, respectively; g is the acceleration due to gravity; ρ water and μ water σ represents the density and viscosity coefficient of water, respectively; σ is the surface tension.

[0020] The specific steps of step S2 are as follows:

[0021] S21. The level set function φ is a signed distance function, positive in the water phase and negative in the air phase. Density and viscosity are constant in both phases, and the transition is smooth near the interface, varying with distance 2ε. The level set function φ is used to calculate the density and viscosity in both the water and air phases.

[0022] ρ(φ)=ρ air +(ρ water -ρ air )h(φ)

[0023] μ(φ)=μ air +(μ water -μ air )h(φ)

[0024] h(φ) is a smooth heaviside function, defined as follows:

[0025]

[0026] S22. The free water surface is a set whose distance function φ is zero. Solving the level set equation yields:

[0027]

[0028] S23. After solving the convection equations of the level set, the distance function is no longer guaranteed to be a unit gradient. It is necessary to ensure the conservation of mass between the two phases. To compensate for the non-conservation problem, the model solves the mass conservation re-initialization equations.

[0029] The specific steps of step S3 are as follows:

[0030] S31. Divide the flocculation group into N discrete groups, using the fractal dimension n. f Describe the fractal properties of the i-th flocculation group:

[0031]

[0032]

[0033] In the formula, m i D i , ρ f,i Let D represent the mass, diameter, and density of the i-th flocculent group, respectively. p The main particle diameter;

[0034] S32. Each floc group corresponds to a representative size, and the group size is the main particle diameter D. p To the maximum floc size D max The logarithmic distribution between them, the number of floc groups depends on the set size range [D] min D max Automatic adjustment;

[0035] S33. The exchange of sediment particles between floc groups adopts a two-body interaction mode, controlled by the aggregation, shearing and collisional crushing of flocs, resulting in the capture and loss of sediment particles. The general equation is as follows:

[0036]

[0037] In the formula, n k G represents the number of sediment particles (m⁻³) in the kth group of flocs; aggr and L aggr These represent the number of sediment particles captured and lost (m⁻³) due to flocculation; G break-shear and L break-shear These represent the number of sediment particles captured and lost (m⁻³) due to shearing and fragmentation, respectively; G break-call and L break-call These represent the number of sediment particles captured and lost (m⁻³) due to collision and breakage of flocculated agglomerates.

[0038] 5. The method for simulating turbulent flow field and suspended sediment concentration field under grid disturbance, characterized in that the specific implementation steps of step S4 are as follows:

[0039] S41. In the intrusion boundary method, the grid is treated as a solid and the water in the tank is treated as a fluid; the porosity of the grid meets the conditions for generating approximately isotropic turbulence, and the locally refined grid can reflect the shape and spacing of the local grid holes.

[0040] S42. The LES method is applied to simulate the approximately isotropic turbulent field generated by grid oscillation, where the grid moves in a sinusoidal function in the transverse direction:

[0041] L = A·sin(f·2nt)

[0042] In the formula, A is the amplitude, f is the vibration frequency, t is the time, and L is the grid position;

[0043] S43. By adjusting the vibration frequency and amplitude of the grid, various working conditions of the physical model test can be generated to effectively simulate the turbulent field and suspended sediment concentration field under grid disturbance.

[0044] The specific implementation steps of step S5 are as follows:

[0045] S51. Solve the fluid control equations using the split-step method. Discretize the space-time terms of the momentum equation using a second-order accurate central difference scheme, including viscosity, pressure gradient, and SGS terms. Discretize the convection terms using a third-order accurate WENO scheme or a second-order accurate central difference scheme. Use a second-order accurate Crank-Nicholson scheme for time advancement.

[0046]

[0047] In the formula, n represents the previous time step, Δt is the time step size, F is the right-hand side term of the second control equation in step S1 excluding the pressure term, and P is the pressure term.

[0048] S52. Using a 3-point central difference scheme, apply a continuity condition in the second stage of the splitting step and solve the following Poisson pressure equation:

[0049]

[0050] In the formula, Π is the pressure correction term, used to update the pressure and velocity fields calculated in the first step of the splitting step:

[0051] p n+1 =p n +Π

[0052]

[0053] The specific implementation steps of step S6 are as follows:

[0054] S61. Set the initial and boundary conditions of the mathematical model. Set the turbulent flow velocity and suspended sediment concentration as the initial conditions, and set the boundary conditions as periodic boundaries.

[0055] S62. Run the model and output the turbulent field and suspended sediment concentration field under simulated grid disturbance.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] This invention provides a method for simulating turbulent flow and suspended sediment concentration under grid disturbance. Based on the SCHISM model, a fine-particle sediment flocculation and sedimentation community model and a viscous sand model are added. The viscous sediment model is integrated into the SCHISM simulation system, and the submerged boundary method is used to simulate and solve the fluid-structure interaction problem. This method can effectively simulate turbulent flow and suspended sediment concentration under grid disturbance. Attached Figure Description

[0058] Figure 1 A schematic diagram of the method flow of the present invention.

[0059] Figure 2 A schematic diagram of the SCB model for the aggregation and splitting of flocs.

[0060] Figure 3 A schematic diagram of the discrete grid of the water in the water tank and the vibration grid.

[0061] Figure 4 A partial mesh diagram of a transverse vibration grid.

[0062] Figure 5 Schematic diagram of vibration frequency and amplitude settings for a transverse vibration grid.

[0063] Figure 6 A graph showing the time-averaged flow velocity at measuring point A in the water tank.

[0064] Figure 7 A diagram showing the change in suspended sediment concentration at measuring point A in the water tank.

[0065] Figure 8 Vector diagram of flow velocity in a grid turbulent flow field.

[0066] Figure 9 Contour map of longitudinal flow velocity U.

[0067] Figure 10 Isosurface distribution of longitudinal flow velocity U.

[0068] Figure 11 Instantaneous field of suspended sediment concentration (T = 30 s). Detailed Implementation

[0069] 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.

[0070] A method for simulating turbulent flow and suspended sediment concentration fields under grid disturbance includes the following specific steps:

[0071] S1. Large eddy simulation (LES) model based on level set equations for two-fluid spatial filtering, constructing fluid control equations:

[0072]

[0073]

[0074] In the formula, φ is the defined level set function; ξ i For grid coordinates, U is the transformation matrix; J is the Jacobian matrix of the transformation matrix; U i The flux of the control volume; u i ρ is the velocity component; μ is the density; p is the dynamic viscosity coefficient; τ is the pressure. li κ is the stress lattice (SGS) tensor; δ is the water surface curvature; ijLet be the Kronecker trigonometric function; h be the smooth Heaviside function; Re, Fr, and We be the dimensionless Reynolds number, Froude number, and Weber number, respectively, defined as follows:

[0075]

[0076] In the formula, U and L are the characteristic flow velocity and characteristic length, respectively; g is the acceleration due to gravity; ρ water and μ water σ represents the density and viscosity coefficient of water, respectively; σ is the surface tension.

[0077] S2. Establish a level set model, use the level set function method to track the fluctuations of the free water surface, and use the level set function φ to calculate the density and viscosity in the water and air phases.

[0078] ρ(φ)=ρ air +(ρ water -ρ air )h(φ)

[0079] μ(φ)=μ air +(μ water -μ air )h(φ)

[0080] In the formula, φ is a signed distance function, positive in the water phase and negative in the air phase, with constant density and viscosity. It smoothly transitions near the interface and varies with distance 2ε. h(φ) is the smooth Heaviside function, defined as follows:

[0081]

[0082] S3, the free water surface is a set whose distance function φ is zero. Solving the level set equation proposed by Osher and Sethian yields:

[0083]

[0084] Solve the mass conservation reinitialization equations proposed by Sussman and Fatemi. The level set equations are discretized using an efficient matrix-free Newton-Krylov solver, and the Poisson stress equations are solved using the GMRES method with multigrid preprocessing. The level set equations are discretized spatially using a 3rd-order WENO scheme and temporally using a 2nd-order Runge-Kutta scheme. The reinitialization step is computed using a 2nd-order ENO scheme.

[0085] S4. Integrated model of fine-particle sediment flocculation based on sediment particle group equation. The flocculation group is divided into N discrete subgroups, and the fractal dimension n is used. f Describe the fractal properties of the i-th flocculation group:

[0086]

[0087]

[0088] In the formula, m i D i , ρ f,i Let D represent the mass, diameter, and density of the i-th flocculent group, respectively. p The main particle diameter is defined as D. Each floc group corresponds to a representative size, and the group size is the main particle diameter D. p To the maximum floc size D max The logarithmic distribution between them, the number of floc groups depends on the set size range [D] min D max Automatic adjustment.

[0089] The exchange of sediment particles between floc groups adopts a two-body interaction mode, controlled by the aggregation, shearing, and collisional fragmentation of the flocs, leading to the capture and loss of sediment particles. The general equation is as follows:

[0090]

[0091] In the formula, n k G represents the number of sediment particles (m⁻³) in the kth group of flocs; aggr and L aggr These represent the number of sediment particles captured and lost (m⁻³) due to flocculation; G break-shear and L break-shear These represent the number of sediment particles captured and lost (m⁻³) due to shearing and fragmentation, respectively; G break-call and L break-call These represent the number of sediment particles captured and lost (m⁻³) due to collision and breakage of flocculated agglomerates.

[0092] S5. Applying the submerged boundary method to handle boundary conditions. In the submerged boundary method, the grid is treated as a solid, and the water in the tank is treated as a fluid; the porosity of the grid meets the conditions for generating approximately isotropic turbulence, and locally refined meshing can reflect the shape and spacing of local grid openings. The LES method is applied to simulate the approximately isotropic turbulent field generated by grid oscillation, with the grid moving in a sinusoidal function in the transverse direction:

[0093] L = A·sin(f·2πt)

[0094] In the formula, A is the amplitude (cm), f is the vibration frequency (Hz), t is the time (s), and L is the grid position (cm).

[0095] S6. Solve the fluid control equations using the split-step method. Discretize the space-time terms of the momentum equation using a second-order accurate central difference scheme, including viscosity, pressure gradient, and SGS terms. Discretize the convection terms using a third-order accurate WENO scheme or a second-order accurate central difference scheme. Use a second-order accurate Crank-Nicholson scheme for time advancement.

[0096]

[0097] In the formula, n represents the previous time step, Δt is the time step size, F is the right-hand side term of the second control equation in step S1 excluding the pressure term, and P is the pressure term.

[0098] S6. Apply a continuity condition in the second stage of the splitting step using a 3-point central difference scheme to solve the following Poisson pressure equation:

[0099]

[0100] In the formula, Π is the pressure correction term, used to update the pressure and velocity fields calculated in the first step of the splitting step:

[0101] p n+1 =p n +∏

[0102]

[0103] S7. Set the initial and boundary conditions for the mathematical model. The initial conditions should set the turbulent flow velocity and suspended sediment concentration. The boundary conditions should be set to periodic boundaries. Run the model and output the turbulent field and suspended sediment concentration field under simulated grid disturbance.

[0104] The following example, along with accompanying drawings, will provide a detailed explanation of the specific implementation methods and simulation results of the present invention.

[0105] Case Study: Simulation of Turbulent Flow Field and Suspended Sediment Concentration Field under Grid Disturbance

[0106] Case Summary: The experimental conditions for physical model experiment 1 are as follows: concentration of 15 kg / m³ 3 The grid amplitude was 5 cm and the vibration frequency was 5 Hz. Ultimately, the average concentration was measured to be 14.921 kg / m³. 3 The initial conditions for the turbulence and suspended sediment concentration fields in the numerical simulation were set to 0 m / s and 15.0 kg / m³, respectively. 3 This can accelerate the convergence of turbulence and suspended sediment concentration to a fully developed state. Since the experiment uses a cubic water tank and a transverse vibrating grid, the boundary conditions are set according to periodic boundaries.

[0107] The steps for simulating the turbulent flow field and suspended sediment concentration field under grid disturbance using this invention are as follows:

[0108] After at least one minute of numerical simulation, the working conditions of turbulent flow and suspended sediment concentration field tending towards a stochastic process will be generated.

[0109] Based on the implementation of the physical model test, one observation point A was selected, and the time series processes of the mean flow velocity and the mean suspended sediment concentration were extracted, as follows: Figure 6 and Figure 7 .

[0110] Simulations were performed on the contour lines and isosurface distribution of the mean velocity vector and longitudinal velocity in the water tank, such as... Figure 8 , Figure 9 and Figure 10 .

[0111] Simulations were performed on the concentration field distribution of suspended sediment, such as... Figure 11 .

[0112] Because suspended sediment particles are relatively fine, approximately 10–15 μm, they exhibit strong following properties with the fluid. Furthermore, fine sediment particles undergo flocculation and sedimentation. The interaction between the flocs and fluid turbulence leads to the aggregation and breakup of these flocs, ultimately forming a turbulent field with randomly varying suspended sediment concentrations. Figure 11 The magnitude of suspended sediment concentration varies with the spatiotemporal distribution of turbulence, resulting in phenomena such as... Figure 11 The distribution pattern shown is alternating between large and small sizes, with an average value of approximately 14.9 kg / m³. 3 The results are consistent with the average values ​​measured in the physical model experiments.

[0113] The above embodiments are merely illustrative examples of the technical solution of the present invention. The method for constructing time-varying forms of hydrological model parameters involved in the present invention is not limited to the content described in the above embodiments, but is subject to the scope defined by the claims. Any modifications, additions, or equivalent substitutions made by those skilled in the art based on these embodiments are within the scope of protection claimed by the present invention.

Claims

1. A method for simulating turbulent flow field and suspended sediment concentration field under grid disturbance, characterized in that, The specific steps include the following: S1. Establish the fluid control equations for a large eddy model of two-fluid spatial filtering based on the level set equation. S2. Establish a level set model in the model and use the level set function method to track the fluctuations of the free water surface; S3. The model describes the aggregation and splitting process of flocs based on the size classification of sediment particles; S4. Apply the submerged boundary method to treat the solid and liquid phases in the model; S5. Solve the model governing equations using the split-step method; S6. Simulate the turbulent flow field and suspended sediment concentration field under grid disturbance; The specific steps for establishing the fluid control equations of the large eddy model based on the level set equations for two-fluid spatial filtering in step S1 are as follows: Based on a large eddy simulation model with level set-based two-fluid spatial filtering, the governing equations for the turbulence model are constructed as follows: , ， In the formula, The level set function is defined; For grid coordinates, This is the transformation matrix; The Jacobian matrix of the transformation matrix; For the flux of the control volume; For the velocity component; Density; The coefficient of dynamic viscosity; For pressure, For the compressive lattice stress tensor; The curvature of the water surface; These are Kronecker trigonometric functions; For smooth Heaviside functions; , and Let Reynolds number, Froude number, and Weber number be dimensionless numbers, respectively, and defined as follows: ， In the formula, and These are characteristic flow velocity and characteristic length, respectively; It is the acceleration due to gravity; and These are the density and viscosity coefficient of water, respectively. Surface tension; The specific implementation steps of step S4 are as follows: S41. In the intrusion boundary method, the grid is treated as a solid and the water in the tank is treated as a fluid; the porosity of the grid meets the conditions for generating approximately isotropic turbulence, and the locally refined grid can reflect the shape and spacing of the local grid holes. S42. The LES method is applied to simulate the approximately isotropic turbulent field generated by grid oscillation, where the grid moves in a sinusoidal function in the transverse direction: ， In the formula, A is the amplitude, f is the vibration frequency, t is the time, and L is the grid position; S43. By adjusting the vibration frequency and amplitude of the grid, various working conditions of the physical model test are generated to achieve effective simulation of the turbulent field and suspended sediment concentration field under grid disturbance.

2. The method for simulating turbulent flow field and suspended sediment concentration field under grid disturbance according to claim 1, characterized in that, The specific steps of step S2 are as follows: S21, Level Set Function It is a signed distance function, positive in the water phase and negative in the air phase. Density and viscosity are constant in all phases. It exhibits a smooth transition near the interface, increasing with distance. Changes, using level set functions Calculate the density and viscosity in the water and air phases. ， ， A smooth heaviside function is defined as follows: ， S22, Free water surface is a distance function The set of zeros is obtained by solving the level set equation: ， S23. After solving the convection equations of the level set, the distance function is no longer guaranteed to be a unit gradient. It is necessary to ensure the conservation of mass between the two phases. To compensate for the non-conservation problem, the model solves the mass conservation re-initialization equations.

3. The method for simulating turbulent flow field and suspended sediment concentration field under grid disturbance according to claim 1, characterized in that, The specific steps of step S3 are as follows: S31. Divide the flocculation group into N discrete groups and use the fractal dimension. Describe the fractal properties of the i-th flocculation group: ， ， In the formula, , , Let these represent the mass, diameter, and density of the i-th flocculent group, respectively. The main particle diameter; S32. Each floc group corresponds to a representative size, and the group size is the main particle diameter. To the maximum floc size The logarithmic distribution between them, the number of floc groups depends on the set size range [ , Automatic adjustment; S33. The exchange of sediment particles between floc groups adopts a two-body interaction mode, controlled by the aggregation, shearing and collisional crushing of flocs, resulting in the capture and loss of sediment particles. The general equation is as follows: ， In the formula, For the first Number of mud and sand particles (m) in the flocculent group -3 ; and The number of sediment particles captured and lost (m) due to flocculation are respectively. -3 ; and The number of sediment particles captured and lost (m) due to shearing and fracturing are respectively. -3 ; and The number of sediment particles captured and lost (m) due to collision and floc fragmentation are respectively. -3 .

4. The method for simulating turbulent flow field and suspended sediment concentration field under grid disturbance according to claim 1, wherein the specific implementation steps of step S5 are as follows: S51. Solve the fluid control equations using the split-step method. Discretize the space-time terms of the momentum equation using a second-order accurate central difference scheme, including viscosity, pressure gradient, and SGS terms. Discretize the convection terms using a third-order accurate WENO scheme or a second-order accurate central difference scheme. Use a second-order accurate Crank-Nicholson scheme for time advancement. ， In the formula, Indicates the previous time step, For time step, This refers to the right-hand side term of the second governing equation in step S1, excluding the pressure term. For stress terms; S52. Using a 3-point central difference scheme, apply a continuity condition in the second stage of the splitting step and solve the following Poisson pressure equation: ， In the formula, This is a pressure correction term used to update the pressure and velocity fields calculated in the first step of the splitting step: ， 5. The method for simulating turbulent flow field and suspended sediment concentration field under grid disturbance according to claim 1, wherein the specific implementation steps of step S6 are as follows: S61. Set the initial and boundary conditions of the mathematical model. Set the turbulent flow velocity and suspended sediment concentration as the initial conditions, and set the boundary conditions as periodic boundaries. S62. Run the model and output the turbulent field and suspended sediment concentration field under simulated grid disturbance.

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