A single-layer boundary simulation method for the SPH multiphase flow model of bridge scour

Abstract

The present invention discloses a single-layer boundary simulation method for a SPH multiphase flow model of bridge scour, comprising the following steps: establishing a SPH multiphase flow model and a single-layer particle boundary model of a scour pier; constructing a ghost particle mapping boundary according to the single-layer particle boundary of the scour pier obtained in the previous step; completing the retrieval of fluid particles around all ghost particles by using a kernel function based on the mapping boundary obtained in the previous step; reversely obtaining the density of the boundary particles of the scour pier based on the ghost particles and the corresponding retrieved particles obtained in the previous step; applying an artificial repulsive force according to the relative distance to the fluid particles i within the retrieval radius of any boundary particle b of the scour pier according to the boundary particles of the scour pier with the updated density obtained in the previous step; calculating the resultant force of the fluid particles on the boundary of the scour pier by the artificial repulsive force obtained in the previous step. The present invention can reduce the modeling scale of the SPH multiphase flow model of bridge scour and improve the stability and accuracy of the calculation of the particle position and pressure near the wall of the scour pier.

Description

Technical Field

[0001] The invention relates to the technical field of numerical simulation calculation, in particular to a single-layer boundary simulation method for a bridge scour SPH multiphase flow model. Background Art

[0002] The smoothed particle hydrodynamics (SPH) method is a numerical solution method based on the Lagrangian form. Compared with the Euler method, the particles themselves have mass, and mass conservation can be guaranteed without additional calculations; when simulating complex free surface flows, there is no need to track fluid boundaries and interfaces between different fluids, which is suitable for simulating large deformation problems such as bridge scour. Bridge scour SPH modeling requires the use of a multiphase flow model, among which scour pier boundary particle modeling is one of the key points in SPH simulation. The currently widely used method is multi-layer boundary particle modeling. However, bridge scour piers are mostly single cylindrical piers, and the normal direction of their boundary surfaces changes dramatically. Even if multi-layer particles are divided, a small number of penetrating particles will still appear. In addition, the bridge scour SPH multiphase flow model uses the state equation to estimate the fluid gradient pressure based on the change of particle density. Near the wall of the scour pier, the search radius of the kernel function is truncation by the boundary, so the fluid pressure used for interpolation fitting usually has a large error, which further affects the accuracy of scour simulation. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a single-layer boundary simulation method for the SPH multiphase flow model of bridge scour, so as to achieve the reduction of the modeling scale of the SPH multiphase flow model of bridge scour, improve the stability and accuracy of the particle position and pressure calculation near the wall of the scour pier, and have the characteristics of easy programming, high accuracy and strong operability.

[0004] In order to solve the above technical problems, the present invention provides a single-layer boundary simulation method for a bridge scour SPH multiphase flow model, comprising the following steps:

[0005] Step 1: Establish an SPH multiphase flow model, determine the fluid particle parameters, set the particle spacing, establish the kernel function form, and establish a target boundary single-layer particle model;

[0006] Step 2, constructing a ghost particle mapping boundary according to the single-layer particle boundary of the scour pier obtained in step 1;

[0007] Step 3: Based on the mapping boundary obtained in step 2, the mapping ghost particles corresponding to all the scour pier boundary particles are constructed cyclically, and the fluid particles around all the ghost particles are retrieved using the kernel function;

[0008] Step 4: Based on the ghost particles obtained in step 3 and the corresponding search particles, the equivalent density method is introduced to update the ghost particle density, and the particle density of the scour pier boundary is obtained inversely;

[0009] Step 5. For any fluid particle i within the retrieval radius of the updated density scouring pier boundary particle obtained in Step 4, apply an artificial repulsive force according to the relative distance r bi to avoid the penetration phenomenon of fluid particles;

[0010] Step 6. Calculate the resultant force F exerted on the fluid particle i by the scouring pier boundary by combining the artificial repulsive force obtained in Step 5 with the particle gradient pressure and the viscosity coefficient of the scouring pier boundary particle. bi .

[0011] Preferably, in Step 1, establishing an SPH multiphase flow model, determining fluid particle parameters, setting the particle spacing, and establishing a single-layer particle boundary model of the scouring pier specifically include the following steps:

[0012] Step 11. Set the initial particle spacing d p , determine the form of the kernel function adopted by the SPH algorithm, and adopt the Wendland equation:

[0013]

[0014] where W ij is the kernel function value of particle j relative to particle i, α is the dimensional coefficient, taking 21 / 16πh 3 , h is the kernel function search radius, and the recommended value is 2d p , r ij =r i -r j , r i is the coordinate of particle i;

[0015] Step 12. Determine the density ρ w , mass m w of the low-water particles, determine the density ρ s , mass m s of the sediment particles, and determine the particle volume V; the mass and volume of the fluid particles are calculated as follows:

[0016] V = d p 3 , m w =ρ w V, m s =ρ s V;

[0017] Step 13. Divide the single-layer particle boundary of the scouring pier according to the initial particle spacing d p .

[0018] Preferably, in Step 2, the ghost particle mapping boundary should be constructed at a normal distance d from the boundary plane​p At the 1 / 2 position, the boundary normal vector should point to the fluid direction in the computational domain.

[0019] Preferably, in step 3, the fluid particles i retrieved around the ghost particle g should satisfy:

[0020] |r gi | ≤ h.

[0021] Preferably, in step 4, based on the ghost particles and the corresponding retrieved particles obtained in step 3, the equivalent density method is introduced to update the density of the ghost particles, and the density of the scouring pier boundary particles is inversely obtained, which specifically includes the following steps:

[0022] Step 41: Introduce the equivalent density method to convert the mass of the sediment particles retrieved for each ghost particle to obtain the equivalent mass

[0023] Step 42: According to the equivalent mass of the sediment particles obtained in step 41 The estimated density ρ of the corresponding ghost particle is fitted according to the kernel function normalization formula; g ;

[0024] Step 43: According to the estimated density ρ of the ghost particle obtained in step 42 g , based on the change property of the SPH algorithm gradient value, the density ρ of the corresponding scouring pier boundary particle is inversely obtained b .

[0025] Preferably, in step 41, based on the equivalent mass of the equivalent density method The calculation is as follows:

[0026]

[0027] where the subscript j represents the physical parameters of sediment particle j, is the sound speed, which is taken as 10 times the maximum particle speed in the computational domain, P is the pressure, P0 is the reference pressure, taken as 0, ρ i0 is the initial density of the fluid particle, and for water particles, it is ρ w , and for sediment particles, it is ρ s , γ is a coefficient, taken as 7.0, ρ0 is the reference density of the fluid particle, taken as 1000 kg / m 3 .

[0028] Preferably, in step 42, the estimated density ρ of the ghost particle g The calculation is as follows:

[0029]

[0030] where the subscript g represents the physical parameters of ghost particle g, and the subscript j represents the fluid particle j searched within the kernel radius of ghost particle g.

[0031] Preferably, in step 43, the particle density ρ at the boundary of the scouring pier b is calculated as follows:

[0032]

[0033] where x, y, and z represent the XYZ-axis coordinate values of the position where the particle is located, is the Hamiltonian operator.

[0034] Preferably, in step 5, the artificial repulsive force is calculated as follows:

[0035]

[0036]

[0037] where ξ is a constant coefficient with a value of 0.5, the subscript b represents the physical parameters of the particle b at the boundary of the scouring pier, and the subscript f represents the physical parameters of the fluid particle f.

[0038] Preferably, in step 6, the resultant force F on the fluid particle i exerted by the boundary of the scouring pier bi is calculated as follows:

[0039]

[0040] where ψ is a boundary coefficient with a value of 0 - 1; μ is the viscosity coefficient of particle i, ε takes a value of 0.01, u is the velocity, u ib = u i - u b .

[0041] The beneficial effects of the present invention are as follows: Based on the SPH single-phase flow single-layer boundary algorithm and considering the density difference between different water and sediment, the present invention constructs a single-layer boundary algorithm for the SPH multiphase flow model that can be used for bridge scour, which has the characteristics of easy programming implementation, high accuracy, and strong operability; when used for the construction of the SPH multiphase flow model for bridge scour, it can effectively reduce the magnitude of particle modeling, improve the simulation calculation accuracy near the wall of the scouring pier, prevent particle penetration, and improve calculation stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a schematic flow chart of the method of the present invention.

[0043] Figure 2 is a diagram of the fluid particle distribution and retrieval mechanism simulated by the present invention.

[0044] Figure 3 is a diagram of the construction of the ghost particle mapping surface and the particle retrieval mechanism proposed by the present invention.

[0045] Among them, 1. Fluid particle; 2. Central fluid particle to be searched; 3. Kernel function radius h; 4. Spacing between the mapped boundary surface and the actual boundary surface; 5. Boundary particle; 6. Fluid particle; 7. Kernel function search radius; 8. Mapped ghost particle; 9. Mapped boundary surface. Specific implementation manner

[0046] Such as Figure 1 And Figure 2 As shown, a single - layer boundary simulation method for a bridge scour SPH multiphase flow model includes the following steps:

[0047] Step 1: Establish an SPH multiphase flow model, determine fluid particle parameters, set the particle spacing, establish the form of the kernel function, and establish a single - layer particle model of the target boundary; the specific steps are as follows:

[0048] Step 1.1: Set the initial particle spacing d p , determine the form of the kernel function adopted by the SPH algorithm, and it is recommended to adopt the Wendland equation:

[0049]

[0050] Among them, W ij is the kernel function value of particle j relative to particle i, α is the dimensional coefficient, taking 21 / (16πh) 3 , h is the kernel function search radius, and it is recommended to take the value of 2d p , r ij = r i - r j r i is the coordinate of particle i; Step 1.2: Determine the density ρ w of the water particles, the mass m w , determine the density ρ s of the sediment particles, the mass m s , determine the particle volume V, and the mass and volume of the fluid particles are calculated as follows:

[0051] V = d p 3 , m w = ρ w V, m s = ρ s V

[0052] Step 1.3: Divide the single - layer particle boundary of the scour pier according to the initial particle spacing d p ;

[0053] Step 2: According to the single - layer particle boundary of the scour pier obtained in Step 1, construct a ghost particle mapped boundary, and the ghost particle mapped boundary should be constructed at a normal distance d pAt 1 / 2, the boundary normal vector should point to the fluid direction in the computational domain. As shown in Figure 3 the figure, the normal of the scouring pier surface should be the vector direction from the center of the cylinder to the fluid;

[0054] Step 3: Based on the mapped boundary obtained in Step 2, circularly construct the mapped ghost particles corresponding to all the boundary particles of the scouring piers, and use the kernel function to complete the retrieval of the fluid particles around all the ghost particles. The fluid particle i retrieved around the ghost particle g should satisfy:

[0055] |r gi | ≤ h

[0056] Step 4: Based on the ghost particles and the corresponding retrieved particles obtained in Step 3, introduce the equivalent density method to update the density of the ghost particles, and inversely obtain the density of the boundary particles of the scouring piers. The specific steps are as follows:

[0057] Step 4.1: Introduce the equivalent density method, perform mass conversion on the sediment particles retrieved by each ghost particle, and obtain the equivalent mass The equivalent mass based on the equivalent density method is calculated as follows:

[0058]

[0059] where the subscript j represents the physical parameters of sediment particle j, is the speed of sound, taken as 10 times the maximum particle speed in the computational domain, P is the pressure, P0 is the reference pressure, recommended to be taken as 0, ρ i0 is the initial density of the fluid particle, the water particle is ρ w , the sediment particle is ρ s , γ is a coefficient, taken as 7.0, ρ0 is the reference density of the fluid particle, taken as 1000 kg / m 3 ;

[0060] Step 4.2: According to the equivalent mass of the sediment particles obtained in Step 4.1 Fit the estimated density ρ of the corresponding ghost particle according to the kernel function normalization formula g , the estimated density ρ of the ghost particle g is calculated as follows:

[0061]

[0062] where the subscript g represents the physical parameters of ghost particle g, and the subscript j represents the fluid particle j searched within the kernel radius of ghost particle g;

[0063] Step 4.3: According to the estimated density ρ of the corresponding ghost particle obtained in Step 4.2 g , based on the property of the gradient value change of the SPH algorithm, inversely obtain the density ρ of the corresponding boundary particle of the scouring pier b, which is calculated as follows:

[0064]

[0065] where x, y, and z represent the XYZ-axis coordinate values of the position of the particle, is the Hamiltonian operator, and the rest is the same as above;

[0066] Step 5. For the fluid particle i within the retrieval radius of any scour pier boundary particle b among the updated density scour pier boundary particles obtained in Step 4, apply an artificial repulsive force according to the relative distance r bi to avoid the penetration phenomenon of fluid particles. The artificial repulsive force is calculated as follows:

[0067]

[0068]

[0069] where ξ is a constant coefficient, and the recommended value is 0.5. The subscript b represents the physical parameters of the scour pier boundary particle b, and the subscript f represents the physical parameters of the fluid particle f. The rest is the same as above;

[0070] Step 6. Combine the artificial repulsive force obtained in Step 5 with the particle gradient pressure and the viscosity coefficient of the scour pier boundary particle to calculate the boundary resultant force F exerted on the fluid particle i bi . The boundary resultant force F exerted on the fluid particle i bi is calculated as follows:

[0071]

[0072] where ψ is the boundary coefficient, with a value range of 0 - 1; μ is the viscosity coefficient of the particle i, and ε takes 0.01.

Claims

1. A single-layer boundary simulation method for a SPH multiphase flow model of bridge scour, characterized in that It includes the following steps: Step 1: Establish an SPH multiphase flow model, determine fluid particle parameters, set the particle spacing, establish the form of the kernel function, and establish a single-layer particle model of the target boundary; specifically, it includes the following steps: Step 11. Set the initial particle spacing d p , determine the form of the kernel function used in the SPH algorithm, and adopt the Wendland equation: Among them, W ij is the kernel function value of particle j relative to particle i, α is the dimension coefficient, taking 21 / 16πh 3 , h is the kernel function search radius, taking the value of 2d p , r ij = r i - r j , r i is the coordinate of particle i; Step 12: Determine the density ρ of the low water particles w , mass m w , determine the density ρ of the sediment particles s , mass m s , determine the particle volume V; The mass and volume of the fluid particles are calculated as follows: V = d p 3 , m w = ρ w V, m s = ρ s V; Step 13: Divide the single-layer particle boundary of the scour pier according to the initial particle spacing d p ; Step 2: Construct a ghost particle mapping boundary according to the single-layer particle boundary of the scour pier obtained in Step 1. Step 3: Based on the mapping boundary obtained in Step 2, circularly construct the mapping ghost particles corresponding to all the boundary particles of the scour pier, and complete the retrieval of fluid particles around all the ghost particles using the kernel function. Step 4: Based on the ghost particles and the corresponding retrieved particles obtained in Step 3, introduce the equivalent density method to update the density of the ghost particles, and inversely obtain the density of the scour pier boundary particles. Step 5. For any fluid particle i within the retrieval radius of the scouring pier boundary particle b updated with the density obtained in Step 4, apply an artificial repulsive force according to the relative distance r bi to avoid the penetration phenomenon of fluid particles; ​ Step 6: Based on the artificial repulsive force obtained in Step 5 Combined with the particle gradient pressure and the viscous coefficient of the particles at the boundary of the scour pier, calculate the resultant force F exerted on the fluid particle i by the boundary of the scour pier bi .

2. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour according to claim 1, characterized in that In step 2, the ghost particle mapping boundary should be constructed at a normal distance d p / 2 from the boundary plane, and the boundary normal vector should point in the fluid direction in the computational domain.

3. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour as described in claim 1, characterized in that In Step 3, the fluid particle i retrieved around the ghost particle g should satisfy: |r gi |≤h。 4. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour as claimed in claim 1, wherein In Step 4, based on the ghost particles and the corresponding retrieved particles obtained in Step 3, introducing the equivalent density method to update the density of the ghost particles and inversely obtaining the density of the scour pier boundary particles specifically includes the following steps: Step 41: Introduce the equivalent density method to perform mass conversion on the sediment particles retrieved by each ghost particle to obtain the equivalent mass Step 42. According to the equivalent mass of sediment particles obtained in Step 41 Fit the corresponding estimated density ρ of ghost particles according to the kernel function normalization formula g ; Step 43. Estimate the density ρ of the ghost particles obtained in step 42, and inversely obtain the density ρ of the boundary particles corresponding to the scour pier according to the variation property of the gradient value of the SPH algorithm g , and inversely obtain the density ρ of the boundary particles corresponding to the scour pier according to the variation property of the gradient value of the SPH algorithm b .

5. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour as described in claim 4, characterized in that, In step 41, the equivalent mass based on the equivalent density method is calculated as follows: Among them, the subscript j represents the physical parameters of sediment particle j. is the sound speed, which is taken as 10 times the maximum particle velocity in the computational domain, P is the pressure, P0 is the reference pressure, taken as 0, ρ i0 is the initial density of fluid particles, and for water particles it is ρ w , and for sediment particles it is ρ s , γ is a coefficient, taken as 7.0, ρ0 is the reference density of fluid particles, taken as 1000 kg / m 3 .

6. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour according to claim 4, characterized in that In step 42, the estimated density ρ of the ghost particles g is calculated as follows: Among them, the subscript g represents the physical parameters of the ghost particle g, and the subscript j represents the fluid particle j searched within the kernel radius of the ghost particle g.

7. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour as described in claim 4, wherein In step 43, the boundary particle density ρ of the scour pier b is calculated as follows: where x, y, z represent the XYZ-axis coordinate values of the position where the particle is located, is the Hamiltonian operator.

8. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour as described in claim 1, wherein In step 5, the manual repulsion force is calculated as follows: Among them, the subscript b represents the physical parameters of the scour pier boundary particle b, and the subscript f represents the physical parameters of the fluid particle f.

9. The single-layer boundary simulation method for the SPH multiphase flow model of bridge scour according to claim 1, wherein In step 6, the resultant force F of the boundary of the scour pier on the fluid particle i bi is calculated as follows: Among them, ψ is the boundary coefficient, with a value range of 0 - 1; μ is the viscosity coefficient of particle i, and ε takes 0.01.

Images