Numerical method for calculating sediment wear based on modified impact angle function

Abstract

The application discloses a numerical calculation method of sediment wear based on a modified impact angle function, and the method comprises the following steps: based on the particle wear removal mechanism, the contact characteristics between particles and damaged materials under the solid-liquid two-phase flow condition are analyzed, and a modified impact angle function introducing the particle motion state is established; based on the discrete phase model, the water and sediment transportation process is simulated, the particle impact speed and impact angle information on the wear wall surface are calculated and obtained by using a preset code; based on the particle impact speed and impact angle information and the modified impact angle function introducing the particle motion state, a material wear rate model is established, and a material wear depth calculation equation is obtained; and based on the material wear depth calculation equation, the wear amount of the flow channel area in the water and sediment transportation process is obtained. Thus, the problems in the related art that with the increase of the liquid viscosity, the model has deviation between the wear prediction and experimental data, the accuracy of the wear prediction of the hydraulic machine is reduced, and the demand of the wear prediction of the hydraulic machine cannot be met are solved.

Description

Technical Field

[0001] This application relates to the field of fluid machinery engineering technology, and in particular to a numerical calculation method for sediment wear based on a modified impact angle function. Background Technology

[0002] Due to the high sediment content in my country's rivers, hydraulic machinery operates under sediment-laden conditions for extended periods. The continuous impact of sediment particles on the equipment surface causes wear, resulting in insufficient unit output, shortened lifespan, reduced efficiency, and decreased operational reliability. Therefore, achieving high-precision prediction of wear on hydraulic machinery is not only crucial for maintaining the safe operation of the equipment but also helps in designing wear-resistant equipment, making it a key technical challenge that urgently needs to be addressed.

[0003] In related technologies, wear models can be established based on gas-solid tests. Currently, widely used wear models include those proposed by Neilson and Gilchrist, Mclury, Huang, Oka, and Zhang, which have been directly used by scholars to predict wear in both gas-solid and liquid-solid systems.

[0004] However, as the viscosity of the liquid increases, the model's prediction of wear deviates from the experimental data, reducing the accuracy of hydraulic machinery wear prediction and failing to meet the needs of predicting wear in both gas-solid and liquid-solid systems, which urgently needs to be addressed. Summary of the Invention

[0005] This application provides a numerical calculation method for sediment wear based on a modified impact angle function, in order to solve the problems in related technologies, such as the deviation between the model's wear prediction and experimental data caused by the increase of liquid viscosity, which reduces the accuracy of hydraulic machinery wear prediction and fails to meet the needs of predicting wear in both gas-solid and liquid-solid systems.

[0006] This application provides a numerical calculation method for sediment wear based on a modified impact angle function, comprising the following steps: based on the particle wear removal mechanism, analyzing the contact characteristics between particles and damaged materials under solid-liquid two-phase flow conditions, and establishing a modified impact angle function that incorporates the particle motion state; simulating the water and sediment transport process based on a discrete phase model, and calculating and obtaining the particle impact velocity and impact angle information on the wear wall surface using a preset code; establishing a material wear rate model based on the particle impact velocity and impact angle information and the modified impact angle function that incorporates the particle motion state, and obtaining a material wear depth calculation equation; and obtaining the wear amount in the flow channel region during water and sediment transport based on the material wear depth calculation equation.

[0007] Optionally, in one embodiment of this application, the expression for the modified impact angle function is:

[0008]

[0009]

[0010]

[0011]

[0012] Where f(α) is the impact angle function, α is the angle at which the particle impacts the wall, K is a constant, taken as 3, and St p Let τ be the Stokes number of the particle. p τ is the time required for a particle to respond to changes in fluid flow. f ρ is the time required for these changes in fluid flow to occur. p For particle density, d p Where μ is the particle diameter f This refers to the fluid dynamic viscosity.

[0013] Optionally, in one embodiment of this application, the step of calculating and obtaining the particle impact velocity and impact angle information on the worn wall surface using a preset code includes: dividing the wall surface into several wall surfaces according to the grid nodes; determining whether the particle impacts the several wall surfaces; if it impacts the several wall surfaces, extracting the velocity vector of the particle at the wall surface and the unit normal vector perpendicular to the wall surface; using the velocity vector to solve for the absolute velocity magnitude, and using the velocity vector and the unit normal vector to decompose the particle velocity into the velocity perpendicular to the wall surface and the velocity parallel to the wall surface, calculating the collision angle between the particle path and the wall surface; statistically averaging all the calculated absolute velocities of the particles to obtain the particle impact velocity, and statistically averaging all the calculated collision angles of the particles to obtain the particle impact angle.

[0014] Optionally, in one embodiment of this application, the equation for calculating the material wear depth is:

[0015]

[0016]

[0017]

[0018] Where Δh is the material wear depth, ρ wall Where is the density of the wall material, ER is the wear rate, and N is the density of the wall material. p This represents the total number of particles. Let A be the mass flow rate of particle p. face Let p be the area of ​​particle p impacting the wall, Er be the wear ratio, k be a constant coefficient, and F be the area of ​​particle p impacting the wall. S V is the particle shape factor. pLet p be the velocity of particle p impacting the wall, n be the velocity exponent, and f(α) be the modified impact angle function.

[0019] This application's embodiments can analyze the contact characteristics between particles and damaged materials under solid-liquid two-phase flow conditions based on the particle wear removal mechanism. A modified impact angle function incorporating particle motion is established, and the water-sediment transport process is simulated based on a discrete phase model. Custom coding is used to calculate and obtain the particle impact velocity and impact angle information on the worn wall surface. Based on the particle impact velocity and impact angle information and the modified impact angle function incorporating particle motion, a material wear rate model is established, resulting in an equation for calculating the material wear depth. This allows for the acquisition of wear in the flow channel region during water-sediment transport, effectively calculating the wear rate under solid-liquid two-phase flow conditions and improving the accuracy of predicting wear in hydraulic machinery under sediment-laden conditions. Therefore, this solves the problems in related technologies where increasing liquid viscosity leads to discrepancies between model wear predictions and experimental data, reducing the accuracy of hydraulic machinery wear prediction and failing to meet the needs of predicting wear in both gas-solid and liquid-solid systems.

[0020] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0021] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0022] Figure 1 This is a flowchart illustrating a numerical calculation method for sediment abrasion based on a modified impact angle function, according to an embodiment of this application.

[0023] Figure 2 This is a schematic diagram of the force balance of a moving particle during its contact with a wall surface, according to a specific embodiment of this application.

[0024] Figure 3 This is a schematic diagram of the computational domain for a water and sand transport pipeline with an elbow, according to a specific embodiment of this application.

[0025] Figure 4 This is a schematic diagram of the computational domain mesh for a water and sand transport pipeline with an elbow, according to a specific embodiment of this application.

[0026] Figure 5 This is a schematic diagram of the wear distribution of a water and sand transport pipeline calculated according to a specific embodiment of this application. Detailed Implementation

[0027] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0028] The following describes, with reference to the accompanying drawings, a numerical calculation method for sediment wear based on a modified impact angle function, according to embodiments of this application. Addressing the problem mentioned in the background art that as liquid viscosity increases, discrepancies arise between model predictions of wear and experimental data, reducing the accuracy of hydraulic machinery wear prediction and failing to meet the requirements for predicting wear in both gas-solid and liquid-solid systems, this application provides a numerical calculation method for sediment wear based on a modified impact angle function. In this method, based on the particle wear removal mechanism, the contact characteristics between particles and damaged materials under solid-liquid two-phase flow conditions are analyzed. A modified impact angle function incorporating particle motion is established, and the water-sediment transport process is simulated based on a discrete phase model. Custom coding is used to calculate and obtain particle impact velocity and impact angle information on the wear wall surface. Based on the particle impact velocity and impact angle information and the modified impact angle function incorporating particle motion, a material wear rate model is established, yielding a material wear depth calculation equation. This allows for the acquisition of wear in the flow channel region during water-sediment transport, effectively calculating the wear rate under solid-liquid two-phase flow conditions and improving the accuracy of predicting wear in hydraulic machinery under sediment-laden conditions. This solves the problems in related technologies, such as the discrepancy between model wear predictions and experimental data caused by increasing liquid viscosity, which reduces the accuracy of hydraulic machinery wear prediction and fails to meet the needs of predicting wear in both gas-solid and liquid-solid systems.

[0029] Specifically, Figure 1 This is a flowchart illustrating a numerical calculation method for sediment abrasion based on a modified impact angle function, provided in an embodiment of this application.

[0030] like Figure 1 As shown, the numerical calculation method for sediment wear based on the modified impact angle function includes the following steps:

[0031] In step S101, based on the particle wear removal mechanism, the contact characteristics between particles and damaged materials under solid-liquid two-phase flow conditions are analyzed, and a modified impact angle function that introduces the particle motion state is established.

[0032] It is understood that the embodiments of this application can analyze the contact characteristics between particles and damaged materials under solid-liquid two-phase flow conditions based on the particle wear removal mechanism, and introduce the Stokes number representing the particle motion state into the relevant function of the obtained impact angle, thereby establishing a modified impact angle function that incorporates the particle motion state, thereby improving the feasibility of numerical calculation of sediment wear.

[0033] In the solid-liquid two-phase flow field, the diameter of the added particles can be a single value or a random number with a certain distribution.

[0034] As one possible approach, the volume loss of material caused by particles can be estimated from the volume of material swept across a tough surface by a single rigid particle, such as... Figure 2 The diagram shown illustrates the force balance of a moving particle during its contact with a wall surface.

[0035] Next, based on the force analysis, the equations of motion of the particles in the horizontal and vertical directions are:

[0036]

[0037]

[0038] Where m is the mass of the particle, P is the Vickers hardness of the material, n is the ratio of the contact area to the removal area, R is the particle size, and K is a constant.

[0039] The particles can be quartz sand particles.

[0040] According to Hertzian contact stress, we have:

[0041] A y =2πRy

[0042] Assuming the particles are of arbitrary shape, the contact area in the x-direction is a portion of the contact area in the y-direction, and K depends on the shape of the particles and the deformation behavior of the material.

[0043] Using the initial velocity and position of the particle, integrate the equations of motion of the particle in the horizontal and vertical directions, i.e.:

[0044]

[0045]

[0046] Where U is the velocity of the particle impacting the wall, and t is the contact time between the particle and the wall.

[0047] in,

[0048]

[0049] Where m is the mass of the particle, P is the Vickers hardness of the material, n is the ratio of the contact area to the removal area, and R is the particle size.

[0050] The volume to be removed is:

[0051]

[0052] Where m is the mass of the particle, P is the Vickers hardness of the material, and K is a constant.

[0053] Furthermore, based on the material removal volume calculated according to the particle-wall contact mechanism, its correlation function with the impact angle can be obtained. Introducing the Stokes number, representing the particle's motion state, into this function yields the expression for the modified impact angle function:

[0054]

[0055]

[0056]

[0057]

[0058] Where f(α) is the impact angle function, α is the angle at which the particle impacts the wall, K is a constant, taken as 3, and St p Let τ be the Stokes number of the particle. p τ is the time required for a particle to respond to changes in fluid flow. f ρ is the time required for these changes in fluid flow to occur. p For particle density, d p Where μ is the particle diameter f This refers to the fluid dynamic viscosity.

[0059] Among them, St p The Stokes number of a particle is defined as the time τ required for the particle to respond to changes in fluid flow. p The time τ required for these changes in fluid flow to occur f The ratio of .

[0060] In step S102, the water and sediment transport process is simulated based on the discrete phase model, and the impact velocity and impact angle information of particles on the wear wall surface are calculated and obtained using a preset code.

[0061] It is understood that the embodiments of this application can simulate the water and sediment transport process based on a discrete phase model, use custom coding to calculate and obtain the particle impact velocity and impact angle information on the wear wall surface, and improve the accuracy of hydraulic mechanical wear prediction under solid-liquid two-phase flow conditions by considering important factors such as particle impact velocity, angle, particle properties and target material properties, and introducing the Stokes number representing the particle state.

[0062] It should be noted that the preset codes are set by those skilled in the art according to the actual situation, and no specific limitations are made here.

[0063] In actual implementation, the embodiments of this application can be based on the measured data of the pumping station to show that the volume fraction of the particle phase during water and sediment transport is small enough that their interaction can be ignored. The DPM model can be used to simplify the simulation of the particle phase movement and to calculate the particle trajectory.

[0064] For example, such as Figure 3 As shown, the object of calculation in this embodiment is a water and sand transport pipeline with an elbow, wherein the inner diameter of the pipeline is 50mm, the radius of curvature at the elbow is 76.9m, the flow velocity inside the pipe is 4m / s, the diameter of the transported particles is 0.45mm, and the particle volume fraction is 1.2%.

[0065] Furthermore, such as Figure 4 As shown, in this embodiment, a geometric model of the computational domain can be established based on the actual dimensions of the pipeline, and a hexahedral structured mesh is used for mesh generation, with a total of 2.8 million meshes. The fluid in the computational domain is set to liquid water, with a given velocity inlet and pressure outlet, and the wall is a non-slip wall. The unidirectional flow initial field is obtained by calculating and solving using the RANS (Reynolds Average Navier-Stokes) method. Based on the single-phase flow initial field results, discrete phase particles are released at the inlet surface, and the particle motion trajectory is obtained by solving in the Lagrange coordinate system.

[0066] Furthermore, in this embodiment, the particle trajectory can be tracked by integrating the differential equation of particle forces, and particle diffusion caused by liquid turbulence can be calculated using a random walk model. The solid particles moving in the solid-liquid flow field are subjected to resistance, buoyancy caused by gravity, pressure gradient force, and virtual mass force, which can be expressed as:

[0067]

[0068] in,

[0069]

[0070]

[0071]

[0072]

[0073] Among them, F D As resistance, F B The buoyant force caused by gravity, F VM For virtual mass force, F P Where F is the pressure gradient force, and m is another force. p For particle mass, u p C represents the particle velocity. d Re is the drag coefficient.p ρ is the particle Reynolds number. p Where ρ is the particle density, ρ is the fluid mass, and d is the fluid density. p Where is the particle diameter, u is the fluid velocity, and C is the fluid velocity. VM This is a virtual quality coefficient, taken as 0.5, where the subscript p represents a particle.

[0074] In one embodiment of this application, the impact velocity and impact angle information of particles on the worn wall surface are calculated and obtained using a preset code, including: dividing the wall surface into several wall surfaces according to the grid nodes; determining whether the particles collide with several wall surfaces; if they collide with several wall surfaces, extracting the velocity vector of the particles at the wall surface and the unit normal vector perpendicular to the wall surface; using the velocity vector to solve for the absolute velocity magnitude, and using the velocity vector and the unit normal vector to decompose the particle velocity into the velocity perpendicular to the wall surface and the velocity parallel to the wall surface, calculating the collision angle between the particle path and the wall surface; statistically averaging all the calculated absolute velocities of the particles to obtain the particle impact velocity, and statistically averaging all the calculated collision angles of the particles to obtain the particle impact angle.

[0075] In some embodiments, the present application embodiments can divide the wall surface into several wall surfaces i according to the grid nodes, determine whether the particle collides with the wall surface i, and when the particle collides with the wall surface i, extract the velocity vector of the particle at the wall surface i and the unit normal vector perpendicular to the wall surface i, use the particle velocity vector to solve the absolute velocity magnitude, and use the particle velocity vector and the wall normal vector to decompose the particle velocity into the velocity perpendicular to the wall surface and the velocity parallel to the wall surface, thereby calculating the collision angle between the particle path and the wall surface i. Finally, the absolute velocity magnitudes of all the calculated particles are statistically averaged to obtain the particle impact velocity, and the collision angles of all the calculated particles are statistically averaged to obtain the particle impact angle. In this way, by obtaining information on the impact of different particles on the wall surface, the accuracy of the numerical calculation of sediment wear can be improved, and the degree of material wear can be quantitatively predicted, which greatly reduces the cost of studying the wear and damage of hydraulic machinery under sediment-laden conditions.

[0076] In step S103, a material wear rate model is established based on the particle impact velocity and impact angle information and the modified impact angle function that incorporates the particle motion state, thereby obtaining the material wear depth calculation equation.

[0077] It is understood that the embodiments of this application can establish a material wear rate model based on the particle impact velocity and impact angle information in the above steps and the modified impact angle function that introduces the particle motion state. That is, the relationship between mass wear rate and wear ratio is established by using the obtained particle impact information, and the wear ratio is calculated based on the constructed modified impact angle function and the obtained particle impact information. Based on the calculated mass wear rate, the material wear depth calculation equation can be obtained, which can more accurately predict the wear under solid-liquid two-phase flow conditions and quantitatively predict the degree of material wear.

[0078] In actual operation, the wear pattern of particles on the wall surface is usually represented by the mass wear rate (ER) per unit area per unit time. For numerical calculations, the relationship between the obtained particle impact information and the wear ratio can be established as follows:

[0079]

[0080] Where ER is the wear rate, representing the mass loss of the wall material per unit area per unit time, N p This represents the total number of particles. Let A be the mass flow rate of particle p. face Let p be the area of ​​the wall surface impacted by particle p, and Er be the wear ratio, which represents the ratio of the mass of wall material lost to the total mass of the impacting particles.

[0081] Since the wear ratio is related to factors such as the impact velocity of the particle wall, the impact angle, and the particle shape, it can be calculated based on the modified impact angle function constructed in the above steps and the particle impact information obtained in the above steps. Its expression is as follows:

[0082]

[0083] Where k is a constant coefficient, F S V is the particle shape factor, with a value of 0.5. p Let p be the velocity of particle p impacting the wall, n be the velocity exponent, which is taken as 2.4, and f(α) be the modified impact angle function.

[0084] Based on the calculated mass wear rate, the material wear depth can be obtained, and its calculation equation is as follows:

[0085]

[0086] Where Δh is the material wear depth, ρ wall The density of the wall material is taken as 7850 kg / m³. 3 .

[0087] Therefore, in one embodiment of this application, the equation for calculating the material wear depth is:

[0088]

[0089]

[0090]

[0091] Where Δh is the material wear depth, ρ wall Where is the density of the wall material, ER is the wear rate, and N is the density of the wall material. p This represents the total number of particles. Let A be the mass flow rate of particle p. face Let p be the area of ​​particle p impacting the wall, Er be the wear ratio, k be a constant coefficient, and F be the area of ​​particle p impacting the wall. S V is the particle shape factor. p Let p be the velocity of particle p impacting the wall, n be the velocity exponent, and f(α) be the modified impact angle function.

[0092] In step S104, the wear amount in the channel area during water and sediment transport is obtained based on the material wear depth calculation equation.

[0093] It is understood that the embodiments of this application can obtain the wear amount in the flow channel area during water and sediment transport based on the material wear depth calculation equation in the above steps, thereby enabling more accurate prediction of wear under solid-liquid two-phase flow conditions, and quantitative prediction of the degree of material wear, which greatly reduces the cost of studying the wear and damage of hydraulic machinery under sediment conditions.

[0094] In some embodiments, such as Figure 5 The figure shows the calculated wear distribution of the water-sediment transport pipeline. The most severe wear is located at the end of the bend, and the wear distribution is consistent with the experimental results. This can effectively improve the accuracy of predicting wear under solid-liquid two-phase flow conditions and quantitatively predict the degree of material wear, greatly reducing the cost of studying the wear and damage of hydraulic machinery under sediment conditions, thus having good economic benefits.

[0095] The numerical calculation method for sediment wear based on a modified impact angle function proposed in this application can analyze the contact characteristics between particles and damaged materials under solid-liquid two-phase flow conditions based on the particle wear removal mechanism. A modified impact angle function incorporating particle motion is established, and the water-sediment transport process is simulated based on a discrete phase model. Custom coding is used to calculate and obtain the particle impact velocity and impact angle information on the worn wall surface. Based on the particle impact velocity and impact angle information and the modified impact angle function incorporating particle motion, a material wear rate model is established, resulting in an equation for calculating the material wear depth. This allows for the acquisition of the wear amount in the flow channel region during water-sediment transport, effectively calculating the wear rate under solid-liquid two-phase flow conditions and improving the accuracy of predicting wear in hydraulic machinery under sediment-laden conditions. This solves the problems in related technologies where increasing liquid viscosity leads to discrepancies between model wear predictions and experimental data, reducing the accuracy of hydraulic machinery wear prediction and failing to meet the needs of predicting wear in both gas-solid and liquid-solid systems.

Claims

1. A numerical calculation method for sediment abrasion based on a modified impact angle function, characterized in that, Includes the following steps: Based on the particle wear removal mechanism, the contact characteristics between particles and damaged materials under solid-liquid two-phase flow conditions are analyzed, and a modified impact angle function incorporating the particle motion state is established. The expression for the modified impact angle function is as follows: ， ， ， ， in, For impact angle function, The angle at which the particles impact the wall. K Let 3 be a constant. The Stokes number of the particle. The time required for particles to respond to changes in fluid flow. The time required for these changes in fluid flow to occur. Particle density, The particle diameter is For fluid dynamic viscosity; Based on a discrete phase model to simulate the water and sediment transport process, the impact velocity and impact angle information of particles on the worn wall surface are calculated and obtained using a preset code. The calculation and acquisition of particle impact velocity and impact angle information on the worn wall surface using the preset code includes: dividing the wall surface into several wall surfaces according to a grid; determining whether a particle impacts one of the wall surfaces; if it impacts one of the wall surfaces, extracting the particle's velocity vector at the wall surface and the unit normal vector perpendicular to the wall surface; using the velocity vector to solve for the absolute velocity magnitude, and using the velocity vector and the unit normal vector to decompose the particle velocity into perpendicular wall surface velocity and parallel wall surface velocity, calculating the collision angle between the particle path and the wall surface; statistically averaging all the calculated absolute velocities of the particles to obtain the particle impact velocity, and statistically averaging all the calculated collision angles of the particles to obtain the particle impact angle. Based on the particle impact velocity and impact angle information and the modified impact angle function incorporating the particle motion state, a material wear rate model is established, yielding a material wear depth calculation equation. The material wear depth calculation equation is as follows: in, For material wear depth, The density of the wall material, For wear rate, This represents the total number of particles. Particles p It has mass flow rate, Particles p The area of ​​impact on the wall, The wear ratio, k The constant coefficient, For particle shape factor, Particles p The speed at which the object hits the wall. n For speed index, The corrected impact angle function; Based on the material wear depth calculation equation, the wear amount in the channel area during water and sediment transport is obtained.

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