Rainwater pipeline siltation-flow velocity response characteristic research method

Abstract

The invention discloses a rainwater pipeline siltation-flow velocity response characteristic research method. A rainwater pipeline siltation fluid-solid coupling equation and a hydrodynamic siltation method are utilized to construct a rainwater pipeline siltation water flow mechanical analysis model; a multiphase flow control equation is used as boundary constraint, a computational fluid dynamics and discrete element method coupled numerical simulation method is adopted, and a computational fluid dynamics and discrete element method coupled model of the high-resolution rainwater pipeline with siltation is built; and the optimized computational fluid dynamics and discrete element method coupling model is utilized to analyze the influence of sedimentation on the flow velocity, and the distribution difference of the average flow velocity of the section under different rainwater pipeline sedimentation conditions is determined. And constructing a Manning formula in which the deposition strength parameter is introduced to calculate the average flow velocity of the rainwater pipeline inlet section. According to the invention, the influence of the rainwater pipeline siltation strength on different section flow velocities is explored, and powerful technical support is provided for municipal rainwater pipeline disease detection and urban inland inundation intelligent early warning.

Description

Technical Field

[0001] The present invention belongs to the fields of fluid mechanics and computational fluid dynamics, and relates to a research method for the deposition-velocity response characteristics of rainwater pipes. Background Art

[0002] In the field of engineering technology, especially in the design and maintenance of urban drainage systems, rainwater pipes are widely used due to their large hydraulic radius, material saving, good mechanical properties, etc. However, with the increase in the service life of rainwater pipes, problems such as the precipitation of solid particles and silt deposition inside are becoming increasingly serious, resulting in a reduction in the flow area of rainwater pipes, and thus affecting their flow capacity. Under extreme weather conditions, rainwater pipe deposition may even cause urban waterlogging, threatening the safety of residents' lives and property.

[0003] Traditionally, the research on the internal flow characteristics of rainwater pipes mainly relies on experimental measurements. However, limited by experimental conditions, it is often impossible to accurately capture the complex changes in hydraulic characteristics inside rainwater pipes. Therefore, computational fluid dynamics (CFD), as an effective alternative method for fluid experimental research, has gradually become an important means for studying the flow characteristics of rainwater pipes. Through computational fluid dynamics (CFD) simulation, the flow motion under different working conditions can be accurately simulated, providing strong support for optimizing the design and maintenance of rainwater pipes.

[0004] In recent years, with the continuous development of computing technology, the coupled application of computational fluid dynamics (CFD) and discrete element method (DEM) (CFD-DEM) has become an effective method for studying the flow of liquid-solid multiphase models. Through CFD-DEM modeling and calculation, the flow situation of the interaction between fluid and particles can be clarified, providing a new perspective for analyzing the influence of deposited particles in rainwater pipes on flow characteristics. However, the existing research results in the application of rainwater pipes mostly focus on fields such as scour, erosion, and sediment bed seepage. The research on the change of hydraulic conditions in rainwater pipes caused by the formation of deposited particle beds inside rainwater pipes and the influence on the flow velocity in the time coordinate of the flow field inside rainwater pipes is still insufficient.

[0005] Therefore, the purpose of this study is to use the fluid-structure interaction equation of deposited rainwater pipes and the hydrodynamic deposition method to construct a hydrodynamic analysis model of deposited rainwater pipes, and through the CFD-DEM numerical simulation method, deeply explore the influence of deposited particles in rainwater pipes on flow characteristics. Summary of the Invention

[0006] Aiming at the above problems, the purpose of the present invention is to develop a model that couples the finite element and the discrete element to accurately restore the influence of deposited particles in rainwater pipes on flow characteristics, and construct a modified Manning formula considering the deposition intensity parameter to calculate the average velocity of the inlet section of rainwater pipes considering deposition.

[0007] The present invention proposes a research method for the deposition-velocity response characteristics of rainwater pipes. First, the Reynolds-averaged Navier-Stokes equations and the Navier-Stokes equations are established, and the volume of fluid method is used to capture the fluid interaction data at the gas-liquid interface to obtain the fluid-phase constraint equations. At the same time, the particle-particle collision equation, the particle-wall collision equation, and the single-particle motion equation are established to constrain the particle phase and transfer the spatio-temporal information. Then, based on the particle collision model output of the dry particle collision restitution coefficient, a calculation model for the wet particle phase restitution coefficient is constructed, and the momentum loss and energy dissipation are predicted considering the interstitial fluid effect. Secondly, the deposition mass strength is quantified, and a fluid resistance model for the non-uniform flow of the deposited rainwater pipe is constructed in combination with the hydrodynamic theory. Thirdly, a high-resolution CFD-DEM coupling model for the deposited rainwater pipe is built. Finally, the accuracy of the CFD-DEM coupling model for the deposited rainwater pipe is verified by setting up a rainwater pipe test device in the Water Conservancy Hall of Zhengzhou University. The CFD-DEM coupling model for the deposited rainwater pipe is optimized by comparing the experimental and simulation data. The influence of deposition on the flow velocity is analyzed using the optimized CFD-DEM coupling model for the deposited rainwater pipe. The distribution difference of the cross-sectional average flow velocity under different deposition conditions of the rainwater pipe is determined, and the Manning formula with the deposition strength parameter is constructed to calculate the cross-sectional average flow velocity at the inlet of the rainwater pipe considering deposition.

[0008] The technical solution adopted by the present invention is as follows: a research method for the deposition-velocity response characteristics of rainwater pipes, the method comprising:

[0009] Step S1: Establish the Reynolds-averaged Navier-Stokes equations and the Navier-Stokes equations, and capture the fluid interaction data at the gas-liquid interface by the volume of fluid method. Based on the fluid interaction data at the gas-liquid interface, obtain the fluid-phase constraint equations;

[0010] Step S2: On the basis of the fluid-phase constraint equations in Step S1, establish the particle-particle collision equation, the particle-wall collision equation, and the single-particle motion equation to perform particle-phase constraint on the particles in the rainwater pipe with deposition, and at the same time transfer the spatio-temporal transport state information of the particles in the rainwater pipe;

[0011] Step S3: Based on the particle-phase constraint in Step S2, establish a particle collision model and output the dry particle collision restitution coefficient; combine the energy dissipation theory to construct a calculation model for the wet particle phase restitution coefficient; combine the elastohydrodynamic principle, fully consider the interparticle damping effect caused by the interstitial fluid, and predict the momentum loss and energy dissipation between the wet deposited particles under the flow-through state in the rainwater pipe;

[0012] Step S4: Quantify the overall siltation intensity of the silt in the rainwater pipe with siltation into two indicators: siltation height and siltation length; based on the prediction results of the momentum loss and energy dissipation between the wet silt particles in Step S3, combined with the fluid dynamics theory, fully consider the shear force at the junction of the silt and water and the gravity of the upstream water body, and construct a fluid resistance model for the non-uniform flow of the rainwater pipe with siltation.

[0013] Step S5: Propose a "fluid-solid" phase coupling method for the rainwater pipe with siltation that integrates the fluid resistance model in Step S4 and the liquid phase constraint equation in Step S1; to ensure the accuracy of the fluid-solid coupling mechanical interaction, combine the drag resistance, pressure gradient force, and virtual mass force quantization theory to establish a high-resolution coupled model of computational fluid dynamics and discrete element method for the rainwater pipe with siltation.

[0014] Step S6: Build a rainwater pipe test device, measure the water level and flow velocity of the rainwater pipe test device, compare the errors between the measured water level and flow velocity data of the rainwater pipe test device and the simulation data of the high-resolution coupled model of computational fluid dynamics and discrete element method for the rainwater pipe with siltation in Step S5, and then optimize the parameters of the coupled model of computational fluid dynamics and discrete element method for the rainwater pipe, and verify the accuracy of the high-resolution coupled model of computational fluid dynamics and discrete element method for the rainwater pipe with siltation in Step S5 through experiments.

[0015] Step S7: For the coupled model of computational fluid dynamics and discrete element method for the rainwater pipe with siltation after parameter optimization in Step S6, set different flow rates and siltation degrees, use the simulation results of the coupled model of computational fluid dynamics and discrete element method for the rainwater pipe to analyze the influence of siltation on the cross-sectional average flow velocity of the rainwater pipe, and determine the difference in the cross-sectional average flow velocity between the silted rainwater pipe and the non-silted rainwater pipe under the same hydraulic conditions and fullness; use the Manning formula corrected by adding the siltation intensity parameter to accurately calculate the cross-sectional average flow velocity at the inlet of the rainwater pipe considering siltation.

[0016] Furthermore, in Step S2, establish a particle-particle collision equation, a particle-wall collision equation, and a single-particle motion equation to perform particle-phase constraints on the particles in the rainwater pipe with siltation, and at the same time transmit the spatio-temporal transport state information of the particles in the rainwater pipe; specifically as follows:

[0017] The particle-particle collision equation uses the midpoint method to detect particle-particle contacts and solves the non-linear equation related to the midpoint through the Newton iteration method to determine the degree of particle overlap.

[0018] The particle-wall collision equation represents the wall equation as an optimization problem by specifying points on the wall and the corresponding unit normal vectors, and uses the Lagrange multiplier method to solve the optimization problem to determine the contact points between the particles and the wall;

[0019] The motion of a single particle in the single-particle motion equation is described by a first-order ordinary differential equation; in the Lagrangian coordinate system, the dynamics of particle rotation and translation are described by Newton's second law; according to the soft-sphere model, the contact force between two particles is separated into a normal vector and a tangential vector, and the equivalent local curvature radius is introduced to calculate the contact force between the particles and calculate the torque generated by the normal and tangential contact forces, so as to obtain the distance vector from the particle center to the contact point.

[0020] Furthermore, in step S3, based on the particle-phase constraints in step S2, a particle collision model is established and the collision restitution coefficient of dry particulate matter is output; in combination with the energy dissipation theory, a calculation model for the normal restitution coefficient of wet particles is constructed; in combination with the elastohydrodynamic principle, fully considering the inter-particle damping effect caused by the interstitial fluid, the momentum loss and energy dissipation between wet and silted particles under the flow state in the rainwater pipe are predicted; the specific steps are as follows:

[0021] Step S31: Generalize the normal restitution coefficient as a function of the Stokes number based on the normal component of the wall-impact velocity; the normal restitution coefficient e is defined as:

[0022] e = -U r / U i (1);

[0023] where, U r and U i are the relative velocities before and after particle collision;

[0024] Step S32: Based on step S31, from the perspective of energy dissipation theory, obtain the calculation model for the normal restitution coefficient of wet particles:

[0025]

[0026] where, e wet represents the normal restitution coefficient of wet particles, e dry is the normal restitution coefficient of dry particle collision, ρ l is the liquid-phase density, ρ p represents the particle-phase density, δ is the liquid film thickness, d p is the equivalent diameter of the particle, e dry represents the normal restitution coefficient of dry particles, S t is the Stokes number, S t = ρ l d p U i / 9μl , ρ l is the liquid-phase density, μ l is the kinematic viscosity of the liquid phase;

[0027] Step S33: Convert the normal restitution coefficient of the wet particles in the normal restitution coefficient calculation model of the wet particles in Step S32 into a damping coefficient that reflects energy dissipation, and predict the momentum loss and energy dissipation between the wet and silted particles under the flowing state in the rainwater pipeline; According to the theory of elastic fluid mechanics, the damping coefficient η wet is expressed as:

[0028]

[0029] where κ represents the curvature of the boundary surface, and m represents the mass of the wet particles.

[0030] Furthermore, in Step S4, the overall siltation intensity of the silt in the silted rainwater pipeline is quantified into two indicators: siltation height and siltation length; Based on the prediction results of the momentum loss and energy dissipation between the wet and silted particles in Step S3, combined with the theory of hydrodynamics, fully considering the shear force at the junction of the silt and water and the gravity of the upstream water body, construct a fluid resistance model for the non-uniform flow of the silted rainwater pipeline; The specific steps are as follows:

[0031] Step S41: For the silt in uniform flow, quantitatively calculate the shear force F τ , F τ = F G1 , F G1 is the gravity of the upper-layer water flow, that is, F τ = ρg(V BHL )J; where ρ is the density of water, g is the acceleration due to gravity, V BHL is the volume of the unit water body above the silt, and J is the hydraulic gradient;

[0032] Step S42: Combining the theory of hydrodynamics, the silt resistance F D , the water gravity F G2 and the shear force F τ reach an equilibrium state, that is, F D = F τ + F G2 ; F G2 = ρg(1 - β)V BTL J, where V BTL is the volume of water in the silt, β represents the solid volume ratio of the particles, that is, the proportion of the solid part excluding pores in the particles; The silt resistance is quantified as: where λ represents the friction factor, V BHL is the volume of the unit water body, V represents the cross-sectional average velocity; CD Denote the sediment resistance coefficient in the rainwater pipeline;

[0033] Step S43: Combine the sediment resistance obtained in step S42 to obtain the fluid resistance model of the non-uniform flow of the rainwater pipeline where sedimentation occurs in step S4. Its formulaic expression is as follows:

[0034] F G = F V + F B + F′ (4);

[0035] Among them, F G denotes gravity, F V is the resistance of the sediment, F B is the frictional resistance of the side wall and the bottom surface, and F' is the acceleration force of the local unit water body; F G = ρg(V BHL )S f , S f is the hydraulic gradient.

[0036] Furthermore, a "fluid-solid" interphase coupling method for rainwater pipelines with sedimentation is proposed by integrating the fluid resistance model in step S4 and the liquid-phase constraint equation in step S1; to ensure the accuracy of the fluid-solid coupling mechanical interaction, a coupled model of computational fluid dynamics and discrete element method for rainwater pipelines with sedimentation at high resolution is established by combining the drag resistance, pressure gradient force, and virtual mass force quantization theory; the specific steps are as follows:

[0037] Step S51: Discretize the computational domain into polyhedral meshes. The mesh size is further checked according to the aspect ratio, skewness, and minimum orthogonality, and the mesh size is set to 2 times the particle size;

[0038] Step S52: Set the time step of the discrete element method simulation to 20% of the maximum Rayleigh time step, and set the time step of the computational fluid dynamics simulation to be less than or equal to 1; it is obtained that the time steps of the computational fluid dynamics simulation and the discrete element method simulation of the coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline in step S5 are 7e-8 and 1.8e-9 respectively;

[0039] Step S53: Analyze and calculate the free surface turbulence in the computational fluid dynamics simulation in step S52 using the renormalized turbulence model and the fluid multiphase flow model; after connecting to the coupled server, enable the Lagrangian discrete phase model in the computational fluid dynamics simulation, and simulate the particle phase of the coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline in step S5 as the Lagrangian discrete phase model injection;

[0040] Step S54: Using the grid size and time step determined in Steps S51 and S52, and combining the analytical calculation of free surface turbulence and the injection of the Lagrangian discrete phase model in Step S53, a high-resolution coupled model of computational fluid dynamics and discrete element method for stormwater pipes is constructed to analyze the deposition-velocity response characteristics of sedimented stormwater pipes.

[0041] Further, Step S6: Set up a stormwater pipe test device, measure the water level and flow velocity of the stormwater pipe test device, compare the measured water level and flow velocity data of the stormwater pipe test device with the simulation data of the high-resolution coupled model of computational fluid dynamics and discrete element method for sedimented stormwater pipes in Step S5, and then optimize the parameters of the coupled model of computational fluid dynamics and discrete element method for stormwater pipes. Verify the accuracy of the high-resolution coupled model of computational fluid dynamics and discrete element method for sedimented stormwater pipes in Step S5 through experiments. The specific steps are as follows:

[0042] Step S61: Select a PVC stormwater pipe with a diameter of DN300, its diameter is 300 mm, wall thickness is 5 mm, length is 10 m, slope is 0.003, and an angle steel bracket is set every 2 m to prevent the gravity deformation of the stormwater pipe.

[0043] Step S62: Select gravel with an average particle size of 6 mm as the sediment, and set different sediment lengths of 1 m, 2 m, 3 m, and 4 m in the PVC pipe in Step S61, with corresponding sediment heights of 0.1, 0.2, and 0.3, for a total of 12 different sedimentation conditions.

[0044] Step S63: The stormwater pipe test device uses a water pump to transport the fluid from the underground reservoir to the water tower. A stabilizer is placed at the outlet of the water tower; a vibration damping net with a diameter of 300 mm is placed behind the valve, and the fluid flows through an electromagnetic flowmeter and then into the pipe to achieve stable circulation.

[0045] Step S64: In the stormwater pipe test device in Step S63, compare the simulated values and experimental values at different measurement points, and analyze the reasons for the errors, including the influence of measurement errors and model simplification assumptions on the results.

[0046] Step S65: According to the comparison results in Step S64, correct the parameters in the fluid phase and particle phase calculation modules of the coupled model of computational fluid dynamics and discrete element method for stormwater pipes to improve the accuracy and reliability of the coupled model of computational fluid dynamics and discrete element method for stormwater pipes; optimize the coupling method of the coupled model of computational fluid dynamics and discrete element method for stormwater pipes, and improve the calculation method in the fluid-solid phase coupling process.

[0047] Further, in step S7, for the coupled computational fluid dynamics and discrete element method model of the silted stormwater pipeline after parameter optimization in step S6, different flow rates and siltation degrees are set, and the influence of siltation on the cross-sectional average velocity of the stormwater pipeline is analyzed using the simulation results of the coupled computational fluid dynamics and discrete element method model of the stormwater pipeline to determine the difference in cross-sectional average velocity between the silted stormwater pipeline and the non-silted stormwater pipeline under the same hydraulic conditions and degree of fullness; the Manning formula modified by adding the siltation intensity parameter is used to accurately calculate the cross-sectional average velocity at the inlet of the stormwater pipeline considering siltation. The specific steps are as follows:

[0048] Step S71: Considering the influence of the presence of silt on the cross-sectional average velocity at the inlet and outlet of the stormwater pipeline, two variables, namely the transverse siltation intensity and the longitudinal siltation intensity, are introduced, and the structural formula for the cross-sectional average velocity V of the non-full-flow stormwater pipeline with siltation is constructed as:

[0049]

[0050] where f(t, l) is the influence function of the presence of silt in the stormwater pipeline on the cross-sectional average velocity at the inlet of the stormwater pipeline. The longitudinal siltation intensity t represents the ratio of the height of the silt to the pipe diameter, the transverse siltation intensity l represents the ratio of the length of the silt to the length of the stormwater pipeline, i is the slope, n is the roughness coefficient, and α represents the fullness coefficient;

[0051] Step S72: The relationship between f(t, l) and (t, l) is determined through simulation. In a certain value range (l ~ (0.1, 0.4) and t ~ (0.1, 5)), the fitting degree between the original data and the fitting surface is good (such as the fitting degree = 0.99877). The cross-sectional average velocity V of the non-full-flow stormwater pipeline with siltation is corrected, and the Manning formula modified by adding the siltation intensity parameter is constructed, that is to obtain the cross-sectional average velocity at the inlet of the stormwater pipeline that can accurately calculate considering siltation. Where A represents the cross-sectional area of flow, and χ represents the wetted perimeter.

[0052] The present invention proposes a research method for the deposition-flow velocity response characteristics of rainwater pipelines. First, establish the Reynolds-averaged Navier-Stokes equations, the Navier-Stokes equations, and capture the fluid interaction data at the gas-liquid interface using the volume of fluid method to obtain the fluid phase constraint equations. At the same time, establish the particle-particle collision equation, the particle-wall collision equation, and the single-particle motion equation to constrain the particle phase and transfer the spatio-temporal information. Then, based on the output of the particle collision model for the dry particulate matter collision restitution coefficient, construct a calculation model for the wet particle phase restitution coefficient, and consider the interstitial fluid effect to predict the momentum loss and energy dissipation. Secondly, quantify the deposition mass strength, and combine with the hydrodynamic theory to construct a fluid resistance model for the non-uniform flow of the deposited rainwater pipeline. Thirdly, fully consider the relevant factors and combine multiple equations and forces to build a high-resolution CFD-DEM coupling model for the deposited rainwater pipeline. Finally, prove the accuracy of the CFD-DEM coupling model for the deposited rainwater pipeline by building a rainwater pipeline test device in the Water Conservancy Hall of Zhengzhou University, compare the experimental and simulation data to optimize the CFD-DEM coupling model for the deposited rainwater pipeline, use the optimized CFD-DEM coupling model for the deposited rainwater pipeline to analyze the influence of deposition on the flow velocity, determine the distribution difference of the cross-sectional average flow velocity under different rainwater pipeline deposition conditions, and construct a modified Manning formula considering the deposition strength parameter to calculate the cross-sectional average flow velocity at the inlet of the rainwater pipeline considering deposition.

[0053] The beneficial effects of the present invention: Compared with the prior art, the present invention provides valuable insights into exploring the influence of the deposition strength of the deposited rainwater pipeline on the flow velocity of different cross-sections of the rainwater pipeline, and gives the cross-sectional average flow velocity formula of the rainwater pipeline after optimization and fully considering the deposition strength. These research works provide strong technical support for the detection of municipal pipeline diseases and the intelligent early warning of urban waterlogging. Brief Description of the Drawings

[0054] Figure 1 Shows the overall flow chart of a research method for the deposition-flow velocity response characteristics of a rainwater pipeline according to the present invention. Detailed Embodiments

[0055] As Figure 1 shown, a research method for the deposition-flow velocity response characteristics of a rainwater pipeline according to the present invention has the following steps:

[0056] Step S1: Establish the Reynolds-averaged Navier-Stokes equations, the Navier-Stokes equations, and capture the fluid interaction data at the gas-liquid interface using the volume of fluid method. Based on the fluid interaction data at the gas-liquid interface, obtain the fluid phase constraint equations;

[0057] Step S2: On the basis of the fluid phase constraint equations in Step S1, establish the particle-particle collision equation, the particle-wall collision equation, and the single-particle motion equation to constrain the particles in the rainwater pipeline with deposition, and at the same time transfer the spatio-temporal transport state information of the particles in the rainwater pipeline;

[0058] Step S3: Based on the particle-phase constraints in Step S2, establish a particle collision model and output the collision restitution coefficient of dry particulate matter; combine the energy dissipation theory to construct a calculation model for the normal restitution coefficient of wet particles; combine the elastohydrodynamics principle, fully consider the inter-particle damping effect caused by the interstitial fluid, and predict the momentum loss and energy dissipation between the wet and deposited particles under the flow condition in the rainwater pipeline.

[0059] Step S4: Quantify the overall deposition intensity of the deposited sediment in the rainwater pipeline with deposition as two indicators: deposition height and deposition length; based on the prediction results of the momentum loss and energy dissipation between the wet and deposited particles in Step S3, combine the fluid dynamics theory, fully consider the shear force at the junction of the deposited sediment and water and the gravity of the upstream water body, and construct a fluid resistance model for the non-uniform flow in the rainwater pipeline with deposition.

[0060] Step S5: Propose a "fluid-solid" interphase coupling method for the rainwater pipeline with deposition that integrates the fluid resistance model in Step S4 and the liquid-phase constraint equation in Step S1; to ensure the accuracy of the fluid-structure coupling mechanical interaction, combine the drag resistance, pressure gradient force, and virtual mass force quantization theory to establish a high-resolution coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline with deposition.

[0061] Step S6: Build a rainwater pipeline test device, measure the water level and flow velocity of the rainwater pipeline test device, compare the errors between the measured water level and flow velocity data of the rainwater pipeline test device and the simulation data of the high-resolution coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline with deposition in Step S5, and then optimize the parameters of the coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline, and verify the accuracy of the high-resolution coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline with deposition in Step S5 through experiments.

[0062] Step S7: For the coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline with deposition after parameter optimization in Step S6, set different flow rates and deposition degrees, use the simulation results of the coupled model of computational fluid dynamics and discrete element method for the rainwater pipeline to analyze the influence of deposition on the cross-sectional average flow velocity of the rainwater pipeline, and determine the difference in the cross-sectional average flow velocity between the rainwater pipeline with deposition and the non-deposited rainwater pipeline under the same hydraulic conditions and fullness; use the Manning formula corrected by adding the deposition intensity parameter to accurately calculate the cross-sectional average flow velocity at the inlet of the rainwater pipeline considering deposition.

[0063] Further, in step S2, a particle-particle collision equation, a particle-wall collision equation, and a single-particle motion equation are established to impose particle-phase constraints on the particles in the silted rainwater pipeline, and at the same time, the spatio-temporal transport state information of the particles in the pipeline is transmitted, as follows:

[0064] The particle-particle collision equation uses the midpoint method for particle contact detection and solves the non-linear equation related to the midpoint by the Newton iteration method to determine the degree of overlap between particles. The particle-wall collision equation expresses the wall equation as an optimization problem by specifying points on the wall and the corresponding unit normal vectors, and solves the optimization problem using the Lagrange multiplier method to determine the contact points between the particles and the wall. The motion of a single particle in the single-particle motion equation is described by a first-order ordinary differential equation; in the Lagrangian coordinate system, the dynamics of particle rotation and translation are described by Newton's second law; according to the soft-sphere model, the contact force between two particles is separated into a normal vector and a tangential vector, and the equivalent local curvature radius is introduced to calculate the contact force between the mass points and calculate the torque generated by the normal and tangential contact forces, so as to obtain the distance vector from the particle center to the contact point.

[0065] Further, in step S3, based on the particle-phase constraints in step S2, a particle collision model is established and the collision restitution coefficient of dry particulate matter is output. On this basis, combined with the energy dissipation theory, a calculation model for the normal restitution coefficient of wet particles is constructed. Combining the principles of elastohydrodynamics, fully considering the inter-particle damping effect caused by the interstitial fluid, the momentum loss and energy dissipation between the wet silted particles under the flow state in the pipeline are predicted. The specific steps are as follows:

[0066] Step S31: Based on the normal component of the wall-impinging velocity, the normal restitution coefficient is generalized as a function of the Stokes number. The normal restitution coefficient e is defined as:

[0067] e = -U r / U i (1);

[0068] where U r and U i are the relative velocities before and after particle collision.

[0069] Step S32: Based on step S31, from the perspective of energy dissipation theory, a calculation model for the normal restitution coefficient of wet particles is obtained:

[0070]

[0071] where e wet represents the normal restitution coefficient of wet particles, e dry is the normal restitution coefficient of dry particle collision, ρ l is the liquid phase density, ρ prepresents the particle-phase density, δ is the liquid film thickness, d p is the equivalent diameter of the particle, e dry represents the normal restitution coefficient of the dry particle, S t is the Stokes number, S t = ρ l d p U i / 9μ l ρ l is the liquid-phase density, μ l is the kinematic viscosity of the liquid phase

[0072] Step S33: Convert the normal restitution coefficient of the wet particles in the wet particle normal restitution coefficient calculation model described in Step S32 into a damping coefficient reflecting energy dissipation, and predict the momentum loss and energy dissipation between the wet and silted particles under the flowing state in the pipeline. According to the theory of elastic fluid mechanics, this damping coefficient η wet can be expressed as:

[0073]

[0074] where κ represents the curvature of the interface surface, m represents the mass of the wet particle, e wet represents the normal restitution coefficient of the wet particle.

[0075] Furthermore, in Step S4, the overall siltation intensity of the silt in the rainwater pipeline where siltation occurs is quantified into two indicators: siltation height and siltation length. Based on the prediction results of the momentum loss and energy dissipation between the wet and silted particles in Step S3, combined with the theory of hydrodynamics, fully considering the shear force at the junction of the silt and water and the gravity of the upstream water body, a fluid resistance model for non-uniform flow in the rainwater pipeline where siltation occurs is constructed. The specific steps are as follows:

[0076] Step S41: For the silt in uniform flow, quantitatively calculate the shear force F τ at the junction between the silted particles and the upper-layer water flow, F τ = F G1 where F G1 is the gravity of the upper-layer water flow, so F τ = ρg(V BHL )J. Where ρ is the density of water, g is the acceleration due to gravity, V BHL is the volume of the unit water body above the silt, and J is the hydraulic gradient.

[0077] Step S42: On the basis of the calculation method of the shear force F τ described in Step S41, combined with the theory of hydrodynamics, the silt resistance F D , the water gravity F G2 and the shear force F τ reach an equilibrium state, that is, FD = F τ + F G2 。F G2 = ρg(1 - β)V BTL J, where V BTL is the volume of water in the sediment, and β represents the solid volume fraction of the particles, that is, the proportion of the solid part excluding pores in the particles. The sediment resistance can be quantified as: where λ represents the friction factor along the way, and V BHL is the volume of a unit water body, V represents the cross-sectional average velocity, and C D represents the sediment resistance coefficient in the rainwater pipeline;.

[0078] Step S43: Combining the sediment resistance obtained in step S42, obtain the fluid resistance model of the non-uniform flow of the rainwater pipeline with sediment deposition described in step S4, and its formulaic expression is as follows:

[0079] F G = F V + F B + F'(4);

[0080] where F G represents gravity, F V is the resistance of the sediment, F B is the friction resistance of the side wall and the bottom surface, and F' is the accelerating force of the local unit water body. F G = ρg(V BHL )S f , V BHL is the volume of a unit water body, and S f is the hydraulic gradient.

[0081] Furthermore, in step S5, a "fluid-solid" interphase coupling method for rainwater pipelines with sediment deposition that integrates the fluid resistance model in step S4 and the liquid phase constraint equation in step S1 is proposed. To ensure the accuracy of the fluid-solid coupling mechanical interaction, a high-resolution coupled model of computational fluid dynamics (CFD) and discrete element method (DEM) for rainwater pipelines with sediment deposition is established by combining the drag resistance, pressure gradient force, and virtual mass force quantization theories. The specific steps are as follows:

[0082] Step S51: Discretize the computational domain into polyhedral meshes, and the mesh size is further checked according to the aspect ratio, skewness, and minimum orthogonality. The mesh size is set to 2 times the particle size.

[0083] Step S52: Based on Step S51, the time step of the Discrete Element Method (DEM) simulation is set to 20% of the maximum Rayleigh time step, and the time step of the Computational Fluid Dynamics (CFD) simulation is set to be less than or equal to 1. Based on this, the time steps of the Computational Fluid Dynamics (CFD) simulation and the Discrete Element Method (DEM) simulation of the rainwater pipeline Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) coupling model described in Step S5 are 7e-8 and 1.8e-9 respectively

[0084] Step S53: The renormalization turbulence model and the fluid multiphase flow model are used to analyze and calculate the free surface turbulence in the Computational Fluid Dynamics (CFD) simulation described in Step S52. After connecting to the coupling server, the Lagrangian discrete phase model in the Computational Fluid Dynamics (CFD) simulation is enabled, and the particle phase of the rainwater pipeline Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) coupling model described in Step S5 is simulated as the Lagrangian discrete phase model injection

[0085] Step S54: Using the grid size and time step determined in Step S52 and Step S51, combined with the analysis and calculation of the free surface turbulence and the Lagrangian discrete phase model injection in Step S53, a high-resolution rainwater pipeline Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) coupling model is constructed to analyze the deposition-velocity response characteristics of the silted rainwater pipeline

[0086] Furthermore, in Step S6, a rainwater pipeline test device is built, the water level and flow velocity of the rainwater pipeline test device are measured, and the error between the measured water level and flow velocity data of the rainwater pipeline test device and the simulation data of the high-resolution silted rainwater pipeline Computational Fluid Dynamics and Discrete Element Method coupling model in Step S5 is compared, so as to optimize the parameters of the rainwater pipeline Computational Fluid Dynamics and Discrete Element Method coupling model, and verify the accuracy of the high-resolution silted rainwater pipeline Computational Fluid Dynamics and Discrete Element Method coupling model in Step S5 through experiments; the specific steps are as follows

[0087] Step S61: Select a PVC rainwater pipeline with a diameter of DN300, its diameter is 300mm, the wall thickness is 5mm, the length is 10m, the slope is 0.003, and an angle steel bracket is set every 2m to prevent the rainwater pipeline from deforming due to gravity

[0088] Step S62: Select gravel with an average particle size of 6mm as the sediment, and set different sediment lengths of 1m, 2m, 3m, and 4m in the PVC rainwater pipeline in Step S61, and the corresponding sediment heights are 0.1, 0.2, and 0.3 respectively, with a total of 12 different sediment conditions

[0089] Step S63: The rainwater pipeline test device uses a water pump to transport fluid from the underground reservoir to the water tower. A stabilizer is disposed at the outlet of the water tower. A vibration damping net with a diameter of 300 mm is placed behind the valve. The fluid flows through the electromagnetic flowmeter and then into the pipeline, finally achieving stable circular flow.

[0090] Step S64: In the rainwater pipeline test device in Step S63, compare the simulated values and test values at different measurement points, and analyze the causes of errors, including the influence of factors such as measurement errors and model simplification assumptions on the results.

[0091] Step S65: According to the comparison results in Step S64, correct the parameters in the fluid phase and particle phase calculation modules of the coupled model of computational fluid dynamics and discrete element method for rainwater pipelines to improve the accuracy and reliability of the coupled model of computational fluid dynamics and discrete element method for rainwater pipelines. Optimize the coupling method of the coupled model of computational fluid dynamics and discrete element method for rainwater pipelines, and improve the calculation method in the fluid-solid interface coupling process.

[0092] Furthermore, in Step S7, for the coupled model of computational fluid dynamics and discrete element method for rainwater pipelines with siltation after the model parameters are optimized in Step S6, set different flow rates and siltation degrees, and use the simulation results of the coupled model of computational fluid dynamics and discrete element method for rainwater pipelines to analyze the influence of siltation on the cross-sectional average velocity of the rainwater pipeline, and determine the difference in the cross-sectional average velocity between the silted rainwater pipeline and the non-silted rainwater pipeline under the same hydraulic conditions and fullness degree. Use the Manning formula corrected by adding the siltation intensity parameter to accurately calculate the cross-sectional average velocity at the inlet of the rainwater pipeline considering siltation. The specific steps are as follows:

[0093] Step S71: In order to further consider the influence of the presence of silt on the cross-sectional average velocity at the inlet and outlet of the pipeline, introduce two variables, the transverse siltation intensity and the longitudinal siltation intensity, and construct the structural formula for the cross-sectional average velocity V when the rainwater pipeline with silt is not full:

[0094]

[0095] Among them, f(t, l) is the influence function of the presence of silt in the rainwater pipeline on the cross-sectional average velocity at the inlet of the rainwater pipeline. The longitudinal siltation intensity t represents the ratio of the silt height to the pipe diameter, the transverse siltation intensity l represents the ratio of the silt length to the rainwater pipeline length, i is the slope, n is the roughness coefficient, and α represents the fullness coefficient.

[0096] Step S72: Determine the relationship between f(t, l) and (t, l) through simulation. In a certain value range (l ~ (0.1, 0.4) and t ~ (0.1, 5)), the original data has a good fitting degree with the fitting surface (such as the fitting degree = 0.99877). Thus, on the basis of Step S71, the cross-sectional average velocity V of the non-full-flow silted rainwater pipe is corrected, and the Manning formula with the siltation intensity parameter correction is constructed, that is The cross-sectional average velocity at the inlet of the rainwater pipe considering siltation can be accurately calculated. Among them, A represents the cross-sectional area of flow, and χ represents the wetted perimeter.

[0097]

[0098] Furthermore, the rainwater pipe test device is built in the Water Conservancy Hall of Zhengzhou University to verify the accuracy statistics of the research method for the siltation-velocity response characteristics of a rainwater pipe. The statistical results are shown in the above table. The average value is taken after five measurements. The average error rate between the fitted value and the measured value of the cross-sectional average velocity at the inlet of the rainwater pipe is 5.7%.

Claims

1. A method for studying the siltation-flow rate response characteristics of a rainwater pipe, characterized in that: The method comprises: Step S1: Establish the Reynolds time-averaged turbulence equation, the Navier-Stokes equation, and capture the gas-liquid interface fluid interaction data using the fluid volume function method, and obtain the fluid phase constraint equation based on the gas-liquid interface fluid interaction data; Step S2: Based on the fluid phase constraint equation in step S1, a particle-particle collision equation, a particle-wall collision equation and a single particle motion equation are established to perform particle phase constraints on the particles in the rainwater pipe where siltation occurs, and at the same time transmit the spatiotemporal transport state information of the particles in the rainwater pipe; Step S3: Based on the particle phase constraint of step S2, a particle collision model is established, and the collision recovery coefficient of dry particles is output; in combination with the energy dissipation theory, a normal phase recovery coefficient calculation model of wet particles is constructed; in combination with the principle of elastic fluid dynamics, the inter-particle damping effect caused by the interstitial fluid is fully considered, and the momentum loss and energy dissipation between wet sedimentation particles under the flow state in the rainwater pipe are predicted; Step S4: quantify the overall siltation intensity of the silted material in the silted rainwater pipe into two indicators: siltation height and siltation length; based on the momentum loss and energy dissipation prediction results between the wet silted particles in step S3, combined with fluid dynamics theory, fully consider the shear force at the interface between the silted material and water and the gravity of the upstream water body, and construct a fluid resistance model for non-uniform flow in the silted rainwater pipe; Step S5: A "fluid-solid" phase coupling method for a rainwater pipe with siltation is proposed, which integrates the fluid resistance model of step S4 and the liquid phase constraint equation of step S1. To ensure the accuracy of the fluid-solid coupling mechanical interaction, a high-resolution computational fluid dynamics and discrete element method coupling model of a rainwater pipe with siltation is established by combining the drag resistance, pressure gradient force and virtual mass force quantification theory. Step S6: constructing a rainwater pipe test device, measuring the water level and flow rate of the rainwater pipe test device, performing error comparison between the measured water level and flow rate data of the rainwater pipe test device and the simulation data of the high-resolution computational fluid dynamics and discrete element method coupling model of the rainwater pipe with siltation in step S5, and then optimizing the parameters of the computational fluid dynamics and discrete element method coupling model of the rainwater pipe with siltation, and verifying the accuracy of the high-resolution computational fluid dynamics and discrete element method coupling model of the rainwater pipe with siltation in step S5 through experiments; Step S7: For the computational fluid dynamics and discrete element method coupling model of the rainwater pipe with siltation after the parameters of the computational fluid dynamics and discrete element method coupling model of the rainwater pipe are optimized in step S6, different flow rates and siltation degrees are set, and the influence of siltation on the average flow velocity of the rainwater pipe section is analyzed by using the simulation results of the computational fluid dynamics and discrete element method coupling model of the rainwater pipe, and the difference in the average flow velocity of the section between the silted rainwater pipe and the non-silted rainwater pipe under the same hydraulic conditions and fullness is determined; the Manning formula after adding the correction of the siltation intensity parameter is used to accurately calculate the average flow velocity of the rainwater pipe inlet section considering the siltation condition.

2. A method for studying the siltation-flow rate response characteristics of a rainwater pipe according to claim 1, characterized in that: In step S2, a particle-particle collision equation, a particle-wall collision equation and a single particle motion equation are established to constrain the particles in the rainwater pipe where siltation occurs, and at the same time transmit the spatiotemporal transport state information of the particles in the rainwater pipe; the details are as follows: The particle-particle collision equation uses the midpoint method to detect inter-particle contact, and the nonlinear equation associated with the midpoint is solved by the Newton iteration method to determine the degree of overlap between particles; The particle-wall collision equation is formulated as an optimization problem by specifying points on the wall and the corresponding unit normal vectors, and the Lagrange multiplier method is used to solve the optimization problem to determine the contact points between the particle and the wall; The motion of a single particle in the single particle motion equation is described by a first-order ordinary differential equation; in the Lagrangian coordinate system, the dynamics of particle rotation and translation are described by Newton's second law; according to the soft sphere model, the contact force between two particles is separated into a normal vector and a tangential vector, and the equivalent local radius of curvature is introduced to calculate the contact force between the particles and the torque generated by the normal and tangential contact forces, thereby obtaining the distance vector from the center of the particle to the contact point.

3. A method for studying the siltation-flow rate response characteristics of a rainwater pipe according to claim 1, characterized in that: Step S3, based on the particle phase constraint of step S2, establish a particle collision model and output the collision recovery coefficient of dry particles; combine the energy dissipation theory to build a normal phase recovery coefficient calculation model for wet particles; combine the principles of elastic fluid dynamics, fully consider the inter-particle damping effect caused by the gap fluid, and predict the momentum loss and energy dissipation between wet sedimentation particles under the flow state in the rainwater pipe; the specific steps are as follows: Step S31: Based on the normal component of the wall impact velocity, the normal restitution coefficient is generalized as a function of the Stokes number; the normal restitution coefficient e is defined as: e=-U r / IN i (1); Among them, U r and U i is the relative speed of the particles before and after the collision; Step S32: Based on step S31, from the perspective of energy dissipation theory, a calculation model for the normal phase restitution coefficient of wet particles is obtained: Among them, e wet represents the normal restitution coefficient of wet particles, e dry is the normal restitution coefficient of dry particle collision, ρ l is the liquid density, ρ p represents the particle phase density, δ is the liquid film thickness, d p is the equivalent diameter of the particle, e dry represents the normal restitution coefficient of dry particles, S t is the Stokes number, S t =ρ l d p U i / 9μ l , ρ l is the liquid density, μ l is the liquid phase kinematic viscosity; Step S33: The normal restitution coefficient of wet particles in the normal restitution coefficient calculation model of wet particles in step S32 is converted into a damping coefficient of reaction energy dissipation, and the momentum loss and energy dissipation between wet sedimentation particles under the flow state in the rainwater pipe are predicted; according to the elastic fluid mechanics theory, the damping coefficient η wet It is expressed as: Among them, κ represents the curvature of the interface surface, and m represents the mass of the wet particle.

4. A method for studying the siltation-flow rate response characteristics of a rainwater pipe according to claim 1, characterized in that: In step S4, the overall siltation intensity of the silted material in the silted rainwater pipe is quantified into two indicators: siltation height and siltation length. Based on the momentum loss and energy dissipation prediction results between the wet silted particles in step S3, combined with fluid dynamics theory, the shear force at the interface between the silted material and water and the gravity of the upstream water body are fully considered to construct a fluid resistance model for non-uniform flow in the silted rainwater pipe. The specific steps are as follows: Step S41: For the sediment in the uniform flow, quantitatively calculate the shear force F at the interface between the sediment particles and the upper water flow. τ , F τ =F G1 , F G1 is the gravity of the upper water flow, that is, F τ =ρg(V BHL )J; where ρ is the density of water, g is the acceleration due to gravity, V BHL is the volume of the unit water body above the sediment, J is the hydraulic slope; Step S42: Combined with the fluid dynamics theory, the sediment resistance F D , water gravity F G2 and shear force F τ The three reach a state of equilibrium, that is, F D =F τ +F G2 ; F G2 =ρg(1-β)V BTL J, where V BTL is the volume of water in the sediment, β represents the solid volume ratio of the particles, that is, the proportion of the solid part of the particles after removing the pores; the sediment resistance is quantified as: Among them, λ represents the resistance coefficient along the way, V BHL is the volume of the unit water body, V is the average flow velocity of the section; C D It represents the resistance coefficient of sediment in the stormwater pipe; Step S43: Combined with the silt resistance obtained in step S42, a fluid resistance model for the non-uniform flow in the rainwater pipe with siltation described in step S4 is obtained, which is formulated as follows: F G =F V +F B +F′ (4); Among them, F G Represents gravity, F V is the resistance of the sediment, F B is the friction resistance of the wall and bottom surface, F' is the acceleration force of the local unit water body; F G =ρg(V BHL )S f , S f is the hydraulic slope.

5. The method for studying the siltation-flow rate response characteristics of a rainwater pipe according to claim 1, characterized in that: A "fluid-solid" phase coupling method for a rainwater pipe with siltation is proposed, which integrates the fluid resistance model in step S4 and the liquid phase constraint equation in step S1. In order to ensure the accuracy of the fluid-solid coupling mechanical interaction, a high-resolution computational fluid dynamics and discrete element method coupling model of a rainwater pipe with siltation is established by combining the quantification theory of drag resistance, pressure gradient force and virtual mass force. The specific steps are as follows: Step S51: discretize the computational domain into polyhedral grids, the grid size is further checked based on aspect ratio, skewness and minimum orthogonality, and the grid size is set to twice the particle size; Step S52: the time step of the discrete element method simulation is set to 20% of the maximum Rayleigh time step, and the time step of the computational fluid dynamics simulation is set to be less than or equal to 1; It is found that the time steps of the computational fluid dynamics simulation and the discrete element method simulation of the coupled computational fluid dynamics and discrete element method model of the stormwater pipe in step S5 are 7e-8 and 1.8e-9 respectively; Step S53: the free surface turbulence in the computational fluid dynamics simulation in step S52 is analyzed and calculated using the renormalized turbulence model and the fluid multiphase flow model; after connecting to the coupling server, the Lagrangian discrete phase model in the computational fluid dynamics simulation is enabled, and the particle phase of the stormwater pipe computational fluid dynamics and discrete element method coupling model in step S5 is simulated as a Lagrangian discrete phase model injection; Step S54: Using the grid size and time step determined in step S51 and step S52, combined with the analytical calculation of free surface turbulence and the Lagrangian discrete phase model injection in step S53, a high-resolution stormwater pipe computational fluid dynamics and discrete element method coupling model is constructed to analyze the siltation-flow velocity response characteristics of the silted stormwater pipe.

6. A method for studying the siltation-flow rate response characteristics of a rainwater pipe according to claim 1, characterized in that: Step S6: Build a rainwater pipe test device, measure the water level and flow rate of the rainwater pipe test device, compare the measured water level and flow rate data of the rainwater pipe test device with the simulation data of the high-resolution rainwater pipe computational fluid dynamics and discrete element method coupling model of step S5, and then optimize the parameters of the rainwater pipe computational fluid dynamics and discrete element method coupling model, and verify the accuracy of the high-resolution rainwater pipe computational fluid dynamics and discrete element method coupling model of step S5 through experiments; the specific steps are as follows: Step S61: Select a DN300 PVC rainwater pipe with a diameter of 300 mm, a wall thickness of 5 mm, a length of 10 m, and a slope of 0.003, and set an angle steel bracket every 2 m to prevent the rainwater pipe from deforming due to gravity; Step S62: gravel with an average particle size of 6 mm is selected as the sediment, and different sedimentation lengths of 1 m, 2 m, 3 m, and 4 m are set in the PVC rainwater pipe of step S61, and the corresponding sedimentation heights are 0.1, 0.2, and 0.3, respectively, for a total of 12 different sedimentation conditions; Step S63: The rainwater pipe test device uses a water pump to transport the fluid from the underground reservoir to the water tower. A stabilizer is placed at the outlet of the water tower. A vibration reduction net with a diameter of 300 mm is placed after the valve. The fluid flows through the electromagnetic flowmeter and then flows into the pipe to achieve stable circulation flow. Step S64: In the rainwater pipe test device in step S63, the simulation values ​​at different measurement points are compared with the test values ​​to analyze the causes of the errors, including the influence of measurement errors and model simplified assumptions on the results; Step S65: According to the comparison result in step S64, the parameters in the fluid phase and particle phase calculation modules in the stormwater pipe computational fluid dynamics and discrete element method coupling model are corrected to improve the accuracy and reliability of the stormwater pipe computational fluid dynamics and discrete element method coupling model; The coupling method of the stormwater pipe computational fluid dynamics and discrete element method coupling model is optimized to improve the calculation method in the fluid-solid phase coupling process.

7. A method for studying the siltation-flow rate response characteristics of a rainwater pipe according to claim 1, characterized in that: In step S7, for the computational fluid dynamics and discrete element method coupling model of the rainwater pipe with siltation after the parameters of the computational fluid dynamics and discrete element method coupling model of the rainwater pipe in step S6 are optimized, different flow rates and siltation degrees are set, and the influence of siltation on the average flow velocity of the rainwater pipe section is analyzed by using the simulation results of the computational fluid dynamics and discrete element method coupling model of the rainwater pipe, and the difference in the average flow velocity of the section between the silted rainwater pipe and the non-silted rainwater pipe under the same hydraulic conditions and fullness is determined; the Manning formula after adding the correction of the siltation intensity parameter is used to accurately calculate the average flow velocity of the rainwater pipe inlet section considering the siltation; the specific steps are as follows: Step S71: Considering the influence of the existence of sediment on the average flow velocity of the rainwater pipe inlet and outlet sections, two variables, the transverse sedimentation intensity and the longitudinal sedimentation intensity, are introduced to construct the structural formula of the average flow velocity V of the section of the sedimented rainwater pipe when it is not full: Among them, f(t,l) is the influence function of the existence of sediment in the rainwater pipe on the average flow velocity of the section at the inlet of the rainwater pipe, the longitudinal sedimentation intensity t represents the ratio of the sediment height to the pipe diameter, the transverse sedimentation intensity l represents the ratio of the sediment length to the length of the rainwater pipe, i is the slope, n is the roughness coefficient, and α represents the fullness coefficient; Step S72: Determine the relationship between f(t,l) and (t,l) through simulation. Within a certain range of values ​​(l to (0.1,0.4) and t to (0.1,5)), the original data has a good fit with the fitting surface. The average flow velocity V of the section of the silted rainwater pipe when it is not full is corrected, and the Manning formula with the correction of the siltation intensity parameter is constructed, that is, The average flow velocity of the rainwater pipe inlet section can be accurately calculated considering siltation; where A represents the water-passing cross-sectional area and χ represents the wetted perimeter.

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