CN116822402A - Simulation method of turbulence field and suspended sediment concentration field under grid disturbance - Google Patents

Abstract

This application relates to a method for simulating the turbulence field and suspended sediment concentration field under grid disturbance, including determining the turbulence model control equations using a two-fluid spatial filtering large eddy simulation (LES) model based on level sets, and establishing a level set model. , use the level set function method to track the fluctuations of the free water surface, and set the density and viscosity of the entire calculation domain to constant values. Reconstruct the above equation into a single fluid equation, solve the level set convection equation, and integrate the viscous sediment model in SCHISM simulation system, the fine-grained sediment flocculation and settlement process adopts the SCB model, uses the immersed boundary method to deal with the fluid-solid coupling problem, and uses the split-step method to solve the fluid equation, and uses MPI parallelization to improve calculation efficiency, and finally solves it to simulate the output grid. Turbulence field and suspended sediment concentration field under grid disturbance. The present invention adds a fine-grained sediment flocculation settlement group model and a cohesive sand model on the basis of the SCHISM model, which can effectively simulate the turbulence field and suspended sediment concentration field under grid disturbance.

Description

Simulation method of turbulence field and suspended sediment concentration field under grid disturbance

Technical field

This application belongs to the field of water conservancy engineering experimental technology, specifically a simulation method of turbulence field and suspended sediment concentration field under grid disturbance.

Background technique

Grid turbulence is generally called approximately isotropic turbulence and is the basis for studying complex turbulence and related material transport. There are two ways to generate grid turbulence in the laboratory: fixed grid method and vibrating grid method. The fixed grid method is difficult to control and decays quickly, and the time available for observation is short. The vibrating grille method uses a single or multiple grilles to vibrate in the water tank perpendicular to the plane of the grille, generating jets and wakes at the openings and connections of the grilles. The two are mixed with each other and separated. The approximately isotropic turbulence produced at a certain distance from the grid is called Oscillating Grid Turbulence (OGT). The characteristics of OGT can be easily controlled by changing the operating parameters of the grid, including grid opening size, amplitude and frequency, etc., and can be maintained for a long time without attenuation, making it easy to implement measurements and widely used.

The starting and suspension of sediment in nature are sometimes caused by high-intensity turbulence rather than average flow. Grid turbulence can effectively simulate the movement of sediment under such special flow conditions. In addition, grid turbulence can separate the turbulence effect to study the turbulent diffusion of sediment and pollutants, the adsorption and desorption of inorganic substances by sediment, etc. Therefore, although the generation mechanisms of indoor vibrating grid turbulence and natural turbulence are different, they are widely used to study the movement of sediment and pollutants. Using OGT, Rouse studied the sediment suspension characteristics for the first time and obtained the famous Rouse suspended mass vertical distribution formula. Other domestic and foreign scholars have studied the sediment starting criterion, the relationship between sediment diffusion coefficient and momentum exchange coefficient, etc. The key mechanism of transport. However, existing grid turbulence systems mostly use vertical vibrating grids, and the turbulence generated is different from natural conditions. In addition, the size of the existing vibrating grids is small, generally tens of centimeters, and the grids are single-piece or double-piece, and there is little research on multi-piece ones.

Contents of the invention

The purpose of the embodiments of this application is to provide a simulation method for the turbulence field and suspended sediment concentration field under grid disturbance, which can effectively simulate the turbulence field and suspended sediment concentration field under grid disturbance.

In order to achieve the above purpose, this application provides the following technical solutions:

A method for simulating turbulence field and suspended sediment concentration field under grid disturbance, including the following specific steps:

S1. Establish the fluid control equations of the large eddy model of two-fluid space 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. Describe the aggregation and splitting process of flocs in the model based on the size classification of sediment particles;

S4. Apply the immersed boundary method in the model to process the solid and liquid phases;

S5. Use the split-step method to solve the model control equations;

S6. Simulate the turbulence field and suspended sediment concentration field under the disturbance of the output grid.

The specific steps of step S1 to establish the fluid control equation of the large eddy model of two-fluid space filtering based on the level set equation are:

Based on the large eddy simulation model of two-fluid spatial filtering based on level set, the turbulence model control equation is constructed:

In the formula, φ is the defined level set function; ξ ⁱ is the grid coordinate, is the transformation matrix; J is the Jacobian matrix of the transformation matrix; U ⁱ is the flux of the control body; u _i is the flow velocity component; ρ is the density; μ is the dynamic viscosity coefficient; p is the pressure, τ _li is the compressive grid stress tension quantity; κ is the curvature of the water surface; δ _ij is the Kronecker trigonometric function; h is the smooth Heaviside function; Re, Fr and We are the dimensionless Reynolds number, Froude number and Weber number respectively, which are defined as follows:

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

The specific steps of step S2 are:

S21. The level set function φ is a signed distance function. It has a positive value in the water phase and a negative value in the air phase. The density and viscosity in each phase are constant values. It transitions smoothly near the interface and changes with the distance 2ε Change, use the level set function φ to calculate the density and viscosity in the water phase and air phase,

ρ(φ)＝ρ _air +(ρ _water -ρ _air )h(φ)

μ(φ)＝μ _air +(μ _water -μ _air )h(φ)

h(φ) is a smooth Heaviside function, defined as follows:

S22. The free water surface is a set where the distance function φ is zero. Solve the level set equation to obtain:

S23. After solving the level set convection equation, the distance function is no longer guaranteed to be unit gradient, and mass conservation between the two phases needs to be ensured. To compensate for the non-conservation problem, the model solves the mass conservation reinitialization equation.

The specific steps of step S3 are:

S31. Divide the flocculation group into N discrete groups, and use the fractal dimension n _f to describe the fractal characteristics of the i-th flocculation group:

In the formula, m _i , D _i , ρ _f,i respectively represent the mass, diameter and density of the i-th flocculation group, and D _p is the main particle diameter;

S32. Each flocculation group group corresponds to a representative size. The grouping size is the logarithmic distribution between the main particle diameter D _p and the maximum flocculation group size D _max . The number of flocculation group groupings is based on the set size range [D _min , D _max ]auto-adjust;

S33. The exchange of sediment particles between flocculation groups adopts a two-body interaction mode and is controlled by the aggregation, shearing and collision of flocculation groups, resulting in the capture and loss of sediment particles. The general equation is as follows:

In the formula, n _k is the number of sediment particles in the k-th group of flocculation groups (m-3); G _aggr and L _aggr are the number of sediment particles captured and lost due to the aggregation of flocculation groups (m-3) respectively; G _{break -shear} and L _break-shear are respectively the number of sediment particles captured and lost due to shear breakage (m-3); G _break-call and L _break-call are respectively the capture and loss of sediment particles caused by collision and breakage of flocculation groups. Number (m-3).

5. The turbulence field and suspended sediment concentration field simulation method under grid disturbance according to claim 1, characterized in that the specific implementation steps of step S4 are:

S41. In the intrusive boundary method, the grid is treated as a solid and the water in the water tank is treated as a fluid; the void ratio of the grid meets the conditions for generating approximately isotropic turbulence, and the locally dense grid can reflect the shape and spacing of the local grid holes. ;

S42. Apply the LES method to simulate the approximately isotropic turbulence field generated by grid oscillation. The grid moves in the transverse direction in the form of a sinusoidal function:

L＝A·sin(f·2nt)

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 can be generated to achieve effective simulation of the turbulence field and suspended sediment concentration field under grid disturbance.

The specific implementation steps of step S5 are:

S51. Use the split-step method to solve the fluid control equation. The momentum equation uses the second-order precision central difference scheme to discretize the space-time terms, including viscosity, pressure gradient and SGS terms. The third-order accuracy WENO scheme or the second-order central difference scheme is used to discretize the convection terms. Use the second-order precision Crank-Nicholson format for time advancement:

In the formula, n represents the previous time step, Δt is the time step, F is the right-hand term in the second control equation in step S1 except the pressure term, and P is the pressure term.

S52. Use the 3-point central difference format to impose continuity conditions in the second stage of the splitting step and solve the following Poisson pressure equation:

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

pn ⁺¹ = ^pn +Π

The specific implementation steps of step S6 are:

S61. Set the initial conditions and boundary conditions of the mathematical model. The initial conditions are set to turbulent flow velocity and suspended sediment concentration, and the boundary conditions are set to periodic boundaries.

S62. Run the model and output the turbulence field and suspended sediment concentration field under the simulated grid disturbance.

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

The invention provides a method for simulating the turbulence field and suspended sediment concentration field under grid disturbance. On the basis of the SCHISM model, a fine-grained sediment flocculation settlement group model and a sticky sand model are added to integrate the sticky sand model. In the SCHISM simulation system, the immersed boundary method is used to simulate the solution of fluid-solid coupling problems, which can effectively simulate the turbulence field and suspended sediment concentration field under grid disturbance.

Description of the drawings

Figure 1 is a schematic flow chart of the method of the present invention.

Figure 2 Schematic diagram of the SCB model of flocculation aggregation and splitting.

Figure 3 Schematic diagram of the discrete mesh of the water tank and vibrating grid.

Figure 4 is a partial grid diagram of the transverse vibration grid.

Figure 5 Schematic diagram of the vibration frequency and amplitude settings of the transverse vibration grid.

Figure 6. Time variation process diagram of the time average flow velocity at measuring point A of the water tank.

Figure 7. The change process of suspended sediment concentration at measuring point A of the water tank.

Figure 8 Flow velocity vector diagram in the grid turbulence field.

Figure 9 Contour filled plot of longitudinal flow velocity U.

Figure 10 Isosurface distribution diagram of longitudinal flow velocity U.

Figure 11 Instantaneous field of suspended sediment concentration (T=30s).

Detailed ways

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

A method for simulating turbulence field and suspended sediment concentration field under grid disturbance, including the following specific steps:

S1. Large eddy simulation (LES) model of two-fluid space filtering based on level set equations to construct the fluid control equation:

In the formula, φ is the defined level set function; ξ ⁱ is the grid coordinate, is the conversion matrix; J is the Jacobian matrix of the conversion matrix; U ⁱ is the flux of the control body; u _i is the flow velocity component; ρ is the density; μ is the dynamic viscosity coefficient; p is the pressure, and τ _li is the compressive grid stress ( SGS) tensor; κ is the curvature of the water surface; δ _ij is the Kronecker trigonometric function; h is the smooth Heaviside function; Re, Fr and We are the dimensionless Reynolds number, Froude number and Weber number respectively, defined as follows:

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

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 phase and air phase.

ρ(φ)＝ρ _air +(ρ _water -ρ _air )h(φ)

μ(φ)＝μ _air +(μ _water -μ _air )h(φ)

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

S3. The free water surface is a set where the distance function φ is zero. Solve the level set equation suggested by Osher and Sethian to obtain:

Solve the mass conservation reinitialization equation suggested by Sussman and Fatemi. An efficient matrix-free Newton-Krylov solver is used to discretize the level set equation, and the multigrid preconditioned GMRES method is used to solve the Poisson pressure equation. The level set equation is discretized using the third-order WENO scheme in space and the second-order Runge-Kutta scheme in time. The re-initialization step is calculated using the 2nd order ENO format.

S4. Integrate the fine-grained sediment floc model based on the sediment particle group equation. Divide the flocculation group into N discrete groups, and use the fractal dimension n _f to describe the fractal characteristics of the i-th flocculation group:

In the formula, m _i , D _i , ρ _f,i respectively represent the mass, diameter and density of the i-th flocculation group, and D _p is the main particle diameter. Each flocculation group group corresponds to a representative size. The grouping size is the logarithmic distribution between the main particle diameter D _p and the maximum flocculation group size D _max . The number of flocculation group groupings is automatically based on the set size range [D _min , D _max ]. Adjustment.

The exchange of sediment particles between flocculation groups adopts a two-body interaction mode and is controlled by the aggregation, shearing and collision crushing of flocculation groups, resulting in the capture and loss of sediment particles. The general equation is as follows:

In the formula, n _k is the number of sediment particles in the k-th group of flocculation groups (m-3); G _aggr and L _aggr are the number of sediment particles captured and lost due to the aggregation of flocculation groups (m-3) respectively; G _{break -shear} and L _break-shear are respectively the number of sediment particles captured and lost due to shear breakage (m-3); G _break-call and L _break-call are respectively the capture and loss of sediment particles caused by collision and breakage of flocculation groups. Number (m-3).

S5. Use the immersed boundary method to handle boundary conditions. In the intrusive boundary method, the grid is treated as a solid and the water in the water tank is treated as a fluid; the void ratio of the grid meets the conditions for generating approximately isotropic turbulence, and the locally dense grid can reflect the shape and spacing of the local grid holes. Application The LES method simulates the approximately isotropic turbulence field generated by grid oscillation, and the grid moves in the transverse direction in the form of a sinusoidal function:

L＝A·sin(f·2πt)

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).

S6. Use the split-step method to solve the fluid control equations. The momentum equation uses the second-order precision central difference scheme to discretize the space-time terms, including viscosity, pressure gradient and SGS terms. The third-order accuracy WENO scheme or the second-order central difference scheme is used to discretize the convection terms. Use the Crank-Nicholson format with second-order precision for time advancement:

In the formula, n represents the previous time step, Δt is the time step, F is the right-hand term in the second control equation in step S1 except the pressure term, and P is the pressure term.

S6. Use the 3-point central difference format to impose continuity conditions in the second stage of the splitting step and solve the following Poisson pressure equation:

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

pn ⁺¹ ＝ ^pn +∏

S7. Set the initial conditions and boundary conditions of the mathematical model. The initial conditions are set to turbulent flow velocity and suspended sediment concentration, and the boundary conditions are set to periodic boundaries. Run the model and output the turbulence field and suspended sediment concentration field under simulated grid disturbance.

The specific implementation manner and simulation results of the present invention will be described in detail below through a case and in conjunction with the accompanying drawings.

Case: Simulation of turbulence field and suspended sediment concentration field under grid disturbance

Case introduction: The test conditions of physical model test 1 are: the configuration concentration is 15kg/m ³ , the grid amplitude is 5cm, and the vibration frequency is 5Hz. Finally, the average value of the measured concentration was 14.921kg/m ³ . The initial conditions of the numerically simulated turbulent flow and suspended sediment concentration fields are set to 0m/s and 15.0kg/m ³ respectively, which can accelerate the convergence of the turbulent flow and suspended sediment concentration to a fully developed state. Since it is a test of a cube water tank and a transverse vibrating grid, the boundary conditions are set according to the periodic boundary.

The practical steps for using this invention to simulate the turbulence field and suspended sediment concentration field under grid disturbance are as follows:

After at least 1 minute of numerical simulation, the working conditions of turbulence and suspended sediment concentration field that tend to be random processes will be generated.

According to the implementation of the physical model test, select the location of one of the observation points A, and extract the time series process of the time mean value of the flow velocity and the time mean value of the suspended sediment concentration, as shown in Figures 6 and 7.

Simulate the isoline filling and isosurface distribution of the flow velocity vector in the water tank, the longitudinal flow velocity mean, as shown in Figure 8, Figure 9 and Figure 10.

Simulate the distribution of suspended sediment concentration field, as shown in Figure 11.

Since the suspended sediment particles are very fine, about 10-15 μm, the sediment particles have a strong ability to follow the fluid, and the fine-grained sediment will flocculate and settle. There is an interaction between the flocculation group and the fluid turbulence, leading to flocculation. The aggregation and fragmentation of clusters will eventually form a randomly varying turbulence field of suspended sediment concentration, as shown in Figure 11. The changes in suspended sediment concentration are related to the spatiotemporal distribution of turbulence, resulting in a turbulence field as shown in Figure 11 The distribution pattern of alternating sizes has an average value of about 14.9kg/m ³ , which is consistent with the measured average value of the physical model test.

The above embodiments are only illustrative of the technical solutions of the present invention. The method for constructing the time-varying form of hydrological model parameters involved in the present invention is not limited to what is 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 this embodiment are within the scope of protection claimed by the present invention.

Claims (7)

1. A method for simulating a turbulence field and a suspended sediment concentration field under grid disturbance is characterized by comprising the following specific steps:

s1, establishing a fluid control equation of a large vortex model of double-fluid space filtration based on a level set equation;

s2, establishing a level set model in the model, and tracking the fluctuation of the free water surface by using a level set function method;

s3, classifying and describing flocculation polymerization and splitting processes based on the size of sediment particles in a model;

s4, treating the solid-liquid two phases in the model by using an immersed boundary method;

s5, solving a model control equation by adopting a split step method;

s6, simulating a turbulent flow field and a suspended mass sediment concentration field under the disturbance of the output grid.

2. The method for simulating a turbulent flow field and a suspended sediment concentration field under grid disturbance according to claim 1, wherein the step S1 of establishing a fluid control equation of a large vortex model of double fluid space filtration based on a level set equation comprises the following specific steps:

and constructing a turbulence model control equation by using a large vortex simulation model of double-fluid space filtration based on a level set:

wherein phi is a defined level set function; zeta type toy ⁱ In the form of a grid of coordinates,is a conversion matrix; j is the Jacobian matrix of the conversion matrix; u (U) ⁱ To control the flux of the body; u (u) _i Is the flow rate component; ρ is the density; μ is the dynamic viscosity coefficient; p is the pressure, τ _li Is the compressive lattice stress tensor; kappa is the surface curvature; delta _ij Is a Kronecker trigonometric function; h is a smooth Heaviside function; re, fr and We are the dimensionless Reynolds number, froude number and Weber number, respectively, defined as follows:

wherein U and L are respectively a characteristic flow rate and a characteristic length; g is gravity acceleration; ρ _water Sum mu _water The density and viscosity coefficient of water respectively; σ is the surface tension.

3. The method for simulating a turbulent flow field and a suspended sediment concentration field under grid disturbance according to claim 1, wherein the specific steps of the step S2 are as follows:

s21, the level set function phi is a signed distance function, the water phase is positive, the air phase is negative, the density and viscosity in each phase are constant values, the transition is smooth near the crossing interface and varies along with the distance 2 epsilon, the density and viscosity in the water phase and the air phase are calculated by using the level set function phi,

ρ(φ)＝ρ _air +(ρ _water -ρ _air )h(φ)

μ(φ)＝μ _air +(μ _water -μ _air )h(φ)

h (φ) is a smooth Heaviside function defined as follows:

s22, the free water surface is a set with a distance function phi of zero, and a level set equation is solved to obtain:

s23, after solving the level set convection equation, the distance function is not guaranteed to be a unit gradient, the conservation of mass of two phases is guaranteed, and in order to solve the problem of non-conservation, the model solves the mass conservation constant weight initialization equation.

4. The method for simulating a turbulent flow field and a suspended sediment concentration field under grid disturbance according to claim 1, wherein the specific steps of the step S3 are as follows:

s31, dividing the flocculation group into N discrete groups, and using the parting dimension N _f Fractal characteristics describing the ith flocculation group:

wherein m is _i ，D _i ，ρ _f,i Respectively representing the mass, diameter and density of the ith flocculation group, D _p Is the major particle diameter;

s32, each flocculation group corresponds to a representative size, and the grouping size is the main particle diameter D _p To the maximum floc size D _max Logarithmic distribution between the flocculation groups according to the size range [ D ] _min ，D _max ]Automatically adjusting;

s33, sediment particle exchange among flocculation groups adopts a double-body interaction mode, is controlled by aggregation, shearing crushing and collision crushing of flocculation groups, and causes the capture and loss of sediment particles, and the general equation is as follows:

wherein n is _k The number (m-3) of sediment particles in the kth group of flocculation groups; g _aggr And L _aggr The sediment particle capturing and losing number (m-3) caused by the flocculation polymerization; g _break-shear And L _break-shear The sediment particle capturing and losing number (m-3) caused by shearing and crushing respectively; g _break-call And L _break-call The number (m-3) of sediment particle capturing and losing caused by collision and breaking of the flocculation.

5. The method for simulating the turbulence field and the suspended sediment concentration field under the disturbance of the grid according to claim 1, wherein the specific implementation step of the step S4 is as follows:

s41, taking the grid as a solid and taking the water body in the water tank as a fluid in an intrusion boundary method; the aperture ratio of the grid meets the condition of generating turbulence similar to isotropy, and the local encryption grid can reflect the shape and the spacing of local grid holes;

s42, simulating an approximately isotropic turbulence field generated by grid oscillation by using an LES method, wherein the grid moves in a sine function mode in the transverse direction:

L＝A·sin(f·2πt)

wherein A is amplitude, f is vibration frequency, t is time, and L is grid position;

s43, various working conditions of a physical model test can be generated by adjusting the vibration frequency and amplitude of the grid so as to realize effective simulation of a turbulence field and a suspended mass sediment concentration field under grid disturbance.

6. The method for simulating the turbulence field and the suspended sediment concentration field under the disturbance of the grid according to claim 1, wherein the specific implementation step of the step S5 is as follows:

s51, solving a fluid control equation by adopting a split-step method, wherein a momentum equation adopts a 2-order precision central differential format discrete space-time term comprising viscosity, pressure gradient and SGS term, adopts a 3-order precision WENO format or a 2-order central differential format discrete convection term, and adopts a 2-order precision Crank-Nicholson format to perform time propulsion:

where n represents the previous time step, Δt is the time step, F is the right hand term excluding the pressure term in the 2 nd control equation in step S1, and P is the pressure term.

S52, applying a continuity condition at the 2 nd stage of the splitting step by adopting a 3-point center differential format, and solving the following poisson pressure equation:

where n is a pressure correction term used to update the pressure and velocity fields calculated in step 1 of the splitting step:

p ⁿ⁺¹ ＝p ⁿ +Π

7. the method for simulating the turbulence field and the suspended sediment concentration field under the disturbance of the grid according to claim 1, wherein the specific implementation step of the step S6 is as follows:

s61, setting initial conditions and boundary conditions of a mathematical model, wherein the initial conditions are set to turbulent flow velocity and suspended sediment concentration, and the boundary conditions are set to be periodic boundaries.

S62, operating the model, and outputting a turbulent flow field and a suspended solid sediment concentration field under the simulated grid disturbance.