JP2004054836A - Wall surface impact simulation method for solid-liquid mixed-phase fluid - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To properly simulate behavior of a solid-liquid mixed-phase fluid, and use it for service life prediction and design of a pump or the like. <P>SOLUTION: A flow velocity vector at each point of time at each point in a passage is calculated (S1). Solid particles are randomly arranged in a virtual sense in the passage (S3), and by solving the equation of motion regarding a rigid sphere model and the equation of motion regarding torque, the acceleration vector and the rotational angular velocity vector of each particle at each point of time is calculated, and the moving velocity vector of the particle is calculated (S4). Particles colliding with a wall surface or other particles up until a next point of time are determined (S5), and the impact vector with the wall surface is calculated by calculating the velocity vector and the rotational angular velocity after collision of the particle (S6). Position of the particle at the next point of time is determined (S9), and after repetitively executing the calculation a predetermined number of times, the magnitude of the impact vector, impact angle and impact frequency in each point of the passage wall surface are determined, and they are displayed along with an image of the wall surface (S10). <P>COPYRIGHT: (C)2004,JPO

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a simulation of a wall-collision situation of a solid-liquid multiphase fluid, and more specifically, is executed by a computer to simulate a state in which particles in a solid-liquid multiphase fluid collide with a pump impeller or the like inside a pump or the like. And a program for performing such a method.
[0002]
[Prior art]
Today, water is pumped from rivers and used for industrial and agricultural purposes, and floods caused by torrential rains are prevented. In addition, pumps are disposed in sewage, piping, and tanks, and are used to suck and discharge liquid. When the pump is used in such an application, the fluid in which the pump is disposed is, for example, a fluid in which fine particles are mixed, such as a sediment in a river or sewage, that is, a `` solid-liquid multiphase fluid '' It is often. Therefore, in general, particles in the solid-liquid multiphase fluid wear the impeller of the pump and the like, and have a relatively short life.
However, since a system that can appropriately simulate the effect of a solid-liquid multiphase fluid in a river or the like on a pump used in the fluid has not been proposed, the life of a pump used in such an environment is appropriately adjusted. It was impossible to predict.
[0003]
Under such circumstances, the pump in use may be damaged or otherwise damaged, or the pump may be operated in consideration of safety, despite the fact that a relatively long life expectancy remains. They are being replaced early. If a pump failure occurs, it is indispensable to affect industrial activities such as industry and agriculture, and if it is used for drainage of rivers, flooding may occur due to concentrated torrential rain, etc. Is extremely dangerous. On the other hand, replacing the pump early is extremely uneconomical.
Furthermore, when designing a pump or the like, it is necessary to properly understand the effects of the solid-liquid multiphase fluid on the pump, such as which parts should be reinforced to extend the life of the pump. There is no tool that properly simulates such effects.
The present invention has been made in view of such problems of the related art, and an object of the present invention is to provide a method of appropriately simulating the flow of a solid-liquid multi-phase fluid, thereby driving the solid-liquid multi-phase fluid. The purpose of the present invention is to appropriately estimate the service life of a pump or the like to be used and to help the design of the pump or the like.
The present invention also provides a program for executing such a simulation method.
[0004]
[Means for Solving the Problems]
To achieve the above-mentioned object, according to the present invention, a method executed by a computer to simulate a collision state of a solid particle in a solid-liquid multiphase fluid against a channel wall surface includes:
The motion of a fine solid particle is expressed by a Lagrangian equation using a hard sphere model between the solid particle and the solid particle, and between the wall and the solid particle. By tracking the behavior of the solid particles based on the free motion time of the particles, at least one distribution of the collision angle, the collision speed, and the collision frequency of the solid particles on the flow path wall surface is simulated.
[0005]
The present invention is also a computer-implemented method for achieving the above-described object, wherein the method simulates a collision state of solid particles in a solid-liquid multiphase fluid against a channel wall surface.
(A) By analyzing the motion of the solid-liquid multiphase fluid based on the Navier-Stokes equation, each position of the flow path wall surface and the solid particles in the flow path and each time point (t _j : j) of a plurality of calculation steps = 0, 1, 2,...) To calculate and store a flow velocity vector (V _{f, i} ) representing the velocity and direction of the fluid;
(B) randomly arranging solid particles according to a predetermined particle concentration in the fluid in the flow path, and setting the position of each solid particle at an initial time point (t ₀ );
(C) The drag vector (F _{drag, i} ) and the lift vector (F _{lift, i} ) acting on each solid particle in the flow path at the current time point (t _j ) are represented by the solid particle diameter (d _p ) and the fluid density. , And the flow velocity vector (V _{f, i} ) of the fluid at the current time point (t _j ) of the fluid corresponding to the position of the solid particles, and the centrifugal force vector (F _{cent, i} ) is calculated as the solid particle diameter (d _p ), The particle density (ρ), the rotation speed of the rotating body disposed in the flow path, the particle speed, and the rotation radius of the solid particles, and calculate the Coriolis force vector (F _{cor, i} ) as the solid particle diameter (d _p ), A particle density (ρ), a rotation speed of a rotating body disposed in the flow path, a particle speed, and a step of calculating from a radius of rotation of the solid particles;
(D) Substituting these force vectors acting on each solid particle into the equation of motion of the hard sphere model to calculate an acceleration vector (dup _{, i} / dt) at the current time point (t _j ) of each solid particle. When,
(E) calculating a rotational angular velocity vector (ω _{p, i} ) at a current time point (t _j ) of each solid particle from an equation of motion regarding a rotational moment;
(F) motion velocity vector of each solid particle at the current time point _{(t j) (V p,} i) the current point in time _{(t j)} velocity in the vector of the fluid corresponding to the position of the solid particles _{(V f, i} ) And the acceleration vector (dup _{, i} / dt) of the solid particles;
(G) The next time point (t _j ) from the current time point (t _j ) based on the motion velocity vector (V _{p, i} ) and the rotational angular velocity vector (ω _{p, i} ) of each solid particle at the current time point (t _j ). _{j + 1} ) determining the solid particles that collide with the channel walls and other solid particles by the time of
(H) The motion velocity vector (V _{p, i (2)} ) and the rotational angular velocity vector (ω _{p, i (2)} ) of each solid particle colliding with the wall of the flow path are calculated as the motion velocity vector of the solid particle. (V _{p, i} ) and the rotational angular velocity vector (ω _{p, i} ) are defined as a motion velocity vector (V _{p, i (1)} ) and a rotational angular velocity vector (ω _{p, i (1)} ) at the time of a wall collision. Calculating from an equation;
(I) The velocity vector (V _{p, i (1)} ) and the rotational angular velocity vector (ω _{p, i (1)} ) of each solid particle colliding with the channel wall surface at the current time point (t _j ) at the time of wall collision are Calculating a collision velocity vector (V _{collision, i} ) for each solid particle based on:
(J) determining the position and the motion state of each solid particle at the next time point (t _{j + 1} );
(K) By repeatedly performing steps (c) to (j), the motion velocity vector (V _{p, i (1)} ) and the rotational angular velocity vector (ω _{p, i (1)} ), and determining the solid particles that collide with the flow path wall surface and calculating the collision velocity vector (V _{collision, i} );
(L) displaying the calculated magnitude of the collision velocity vector ( _{Vcollision, i} ) of the solid particles in association with the position of the flow path wall surface.
[0006]
The above-described simulation method according to the present invention further includes:
(M) At each time point (t _j ), the collision angle (α ₁ ) of each solid particle colliding with the channel wall surface at the time of wall collision is determined by the motion velocity vector (V _{p, i (1 A)} calculating based on:
(N) displaying the magnitude of the obtained collision angle (α ₁ ) in association with the position of the channel wall surface;
(O) calculating a wall collision frequency of each solid particle colliding with the flow path wall surface at all time points in association with the position of the flow path wall surface;
(P) displaying the magnitude of the obtained wall collision frequency in association with the position of the channel wall surface.
[0007]
The present invention is further a program executed by a computer to execute a method for simulating a state of collision of solid particles in a solid-liquid multiphase fluid against a channel wall surface, wherein the method is the simulation method described above. Provide a program characterized by the following.
[0008]
BEST MODE FOR CARRYING OUT THE INVENTION
The simulation method according to the present invention performs a flow analysis of a solid-liquid multiphase fluid using a computer, and a mathematical analysis thereof will be described below with reference to FIG.
In the following description, it is assumed that the motion of the mixed solid particles does not affect the flow of the fluid itself, and the analysis is performed using a PI-Cell (Particle-in-cell) method. In addition, fluid motion is analyzed by solving the Navier-Stokes equation Euler-like with Dawes code or other fluid numerical analysis code, which is a standard tool of hydro design, and the motion of solid particles is the force acting on solid particles. By using the hard sphere model, the behavior of the particles is tracked between the solid particles and between the solid particles and between the wall and the solid particles in a Lagrangian manner.
[0009]
The following factors are used as factors affecting the flow phenomenon in a solid-liquid multiphase fluid.
(A) Angle of impact of particles (sand, etc.) on the wall surface (α ₁ )
(B) Speed at collision (Vcollision)
(C) Collision frequency (d) Particle size (d _p )
(E) Physical properties of particle surface (f) Shape of particle surface (g) Stress level of particle surface (h) Particle shape and hardness (i) Particle density (ρ)
(J) particle concentration in the fluid _(C v)
(K) fluid properties and temperature (l) flow path shape and boundary conditions
Among these factors, (d) to (l) are factors relating to physical quantities of particles and fluids, and are input by an operator. In the present invention, by using the factors (d) to (l) and tracking the behavior of the solid particles in the solid-liquid multiphase fluid by the steps described below, the collision angle of the solid particles to the channel wall surface is determined. (Factor (a)), speed at the time of collision (factor (b)), and collision frequency (factor (c)) are obtained by simulation.
[0011]
Analysis of fluid motion First, in step S1, in order to analyze the motion of the fluid in the flow path (flow path space), the properties and temperature (factor (k)) of the fluid, the flow path shape and the boundary The Navier-Stokes equation is solved using the condition (factor (l)). As a result, a flow velocity vector _{Vf, i} representing the instantaneous flow velocity and the flow direction at each point in time t _j (j = 0, 1, 2,...) Of each point in the flow path is obtained. The flow velocity vector is stored in association with time points t ₀ , t ₁ , t ₂ ,..., T _j , t _{j + 1,.} The stored flow velocity vectors V _{f, i} are sequentially read out and used when solving the equation of motion of solid particles described below.
[0012]
In this specification, a suffix i attached to a symbol indicates that the symbol is a vector of a magnitude and a direction in an xyz coordinate space. Further, the suffixes f and p added to the symbols indicate that they are symbols relating to fluid and solid particles, respectively. Therefore, _{Vf, i} described above is a vector represented by the velocity components {Vx, Vy, Vz} of the fluid in the x-axis, y-axis, and z-axis directions (vector _{Vf, i).} = {Vx, Vy, Vz}).
The suffix (1) attached to the symbol indicates the state before the collision of the solid particles, and the suffix (2) indicates the state after the collision.
[0013]
<br/> solving the kinetic equation for the solid particles is then set to j = 0 in step S2, then in step S2, the fluid in the flow path, depending on particle concentration C _v in the fluid, hard sphere model Are randomly arranged. Then, the process proceeds to step S3 to solve the equation of motion of the solid particles.
FIG. 2 illustrates a state in which one solid particle P collides with the channel wall surface W and is reflected to make the following description clearer. 2, _also, V p, _{i (1)} and V _{p, i (2)} is the velocity vector of the particles representing the speed and direction after the collision before and collision of the solid particles, n _i is the impact surface Normal vector. Further, α ₍₁₎ and α ₍₂₎ are the collision angle and the reflection angle of the solid particles with respect to the channel wall surface W, and ω _{p, i (1)} and ω _{p, i (2)} are before and after the solid particles collide. It is a rotational angular velocity vector (a rotational angular velocity component and a rotational direction component) after the collision.
In this specification, the “rotational angular velocity” means the rotational angular velocity of a particle in a coordinate system, while the “relative rotational angular velocity” described below refers to the relative rotation of a particle with respect to a fluid in a coordinate system. Means angular velocity.
[0014]
In step S4, the flow rate and direction, that is flow velocity vector V _f at time t _j of the fluid portion corresponding to each solid particle coordinates in the flow _path, the _i, searches extracted from the stored data in step S1.
Then, the following forces acting on the individual solid particles are calculated.
The drag vector F _{drag, i} and the lift vector F _{lift, i} are calculated from the particle diameter d _p , the fluid density (factor k), and the flow velocity vector V _{f, i} .
The centrifugal force vector F _{cent, i} is calculated from the particle diameter d _p , the particle density ρ, the rotation speed of a rotating body such as an impeller inside the pump, the particle speed, and the rotation radius of the solid particles.
The Coriolis force vector F _{cor, i} is calculated from the particle diameter d _p , the particle density ρ, the rotation speed of a rotating body such as an impeller inside the pump, the particle speed, and the rotation radius of the solid particles.
[0015]
These calculated forces are substituted into the equation of motion of the rigid body model shown as equation (1) below.
(Equation 1)
_{m p · du p, i /} dt
_{= F drag, i + F lift} , i + F cent, i + F cor, i + g i (1)
In the formula (1), _{g i} is the gravitational acceleration at time _{t j, m p} is the particle mass calculated from the particle size _{d p} and the particle density _{ρ, du p,} i / dt is the acceleration vector of the solid particles at time _{t j} is there.
Then, by solving the above-described equation of motion (1), the acceleration vector _{du p} at time _{t j} for each solid particle to obtain a i / dt.
[0016]
Next, from the relative rotational angular velocity vectors ω _{R, i} of the individual solid particles with respect to the surrounding fluid, the equation of motion relating to the rotational moment shown as the following equation (2) is solved to obtain the rotational angular velocity vectors ω _{p, i of the} solid particles. Is calculated. The relative rotational angular velocity vector omega _{R, i} is the rotational angular velocity vector omega _{p, i} and change rate _{dV f} of the velocity vector of the fluid of the solid particles is calculated from the i / dt.
(Equation 2)
I · dω _{p, i} / dt
= −C _r · ρ / 2 (d _p / 2) ² · | ω _{R, i} | · ω _{R, i} (2)
In equation (2), I is the polar moment of inertia of the solid particles, _Cr is an experimental coefficient relating to the relative rotational angular velocity between the fluid and the solid particles, and | ωR _{, i} | is the relative rotational angular velocity vector ωR _{, i.} , That is, the rotation angular velocity component.
[0017]
Further, the motion velocity vector _{Vp, i} of the solid particles is obtained by substituting the fluid velocity vector _{Vf, i} into the following equation (3).
[Equation 3]
V _{p, i} = V _{f, i} + Δτ · a _i (3)
In Expression (3), Δτ is a time interval for advancing the calculation, that is, Δτ = t _{j + 1} −t _j . a _i is the acceleration vector du _pi / dt of the solid particle one step before, and therefore, as shown in equation (1), together with the drag vector F _{drag, i} and the lift vector F _{lift, i} , the centrifugal force vector F _{cent , I} and the action of the Coriolis force vector F _{cor, i} .
[0018]
Calculation of various momentums due to collision of solid particles Next, in step S5, the velocity vectors _{Vp, i of} the individual solid particles calculated in step S4 by the equations (1) and (3). And the position of the solid particles at that point in time, determine the solid particles that collide with the wall and other solid particles (ie, the solid interface) until the next time point tj _{+ 1} . This determination determines that the solid particles collide when the position of the solid particles moving up to the next point is within the diameter of an adjacent solid particle and when the particle surface contacts a wall surface.
Then, in step S6, for the solid particles colliding with the wall surface or other solid particles, the velocity vector V _{p, i (2)} and the rotational angular velocity vector ω _{p, i (2)} after the collision are expressed by the following equation (4). And (5) by substituting the velocity vector _{Vp, i (1)} = _{Vp, i} of the colliding solid particles before collision into the collision equation.
(Equation 4)
_{V p, i (2) =} V p, i (1) + J / m p (4)
_{ω p, i (2) =} ω p, i (1) + d p / 2 · n × J / I (5)
In Equations (4) and (5), J is a momentum vector affected by the coefficient of restitution and the friction coefficient of the collision portion, and the like, and the physical properties of the particle surface (factor (e)) and the particle surface shape (factor) (F)), the particle surface stress level (factor (g)), and the particle shape and hardness (factor (h)). Further, as described above, n represents a normal vector of the impact surface, I is a polar moment of inertia of the particles determined from the particle size d _p. “×” indicates the cross product of the vectors.
[0019]
In step S6, the collision velocity vector V _{collision, i} of each solid particle colliding with the wall surface is calculated using the following equation (6).
(Equation 5)
V _{collision, i
= V p, i (1)} -d p / 2 · ω p, i (1) × n (6)
In the equation (6), the vector V _{p, i (1)} represents a translation component at the time of collision of a particle with a wall, and −d _p / 2 · ω _{p, i (1)} × n is a rotation component at the time of collision of a particle with a wall. Is represented. Therefore, the collision velocity vector is expressed as the sum of the velocity of the center of gravity of the solid particle and the rotational velocity of the particle surface.
[0020]
Iterative calculation at next time When step S6 ends, in step S7, it is determined whether the time, that is, the calculation step j is equal to a preset maximum value j _max (for example, j _max = about 5000 times). It is determined, and j = j + 1 is set in step S8. Then, in step S9, the position and the motion state of each solid particle at the time point t _{j + 1} (= t _j + Δτ) are calculated. The motion state indicates the state of the velocity vector and the rotational angular velocity vector of the solid particles. At this time, for each solid particle that collides with the wall surface and other solid particles, V _{p, i (2)} and ω _{p, i (2)} calculated from Expressions (4) and (5), and time t computed based on the force acting on the fluid velocity vector V _{f, i} and the solid particles in the _j. On the other hand, with respect to each solid particles do not collide, computed on the basis of the velocity vector V _p of the rotational angular velocity vector omega _{p, i} and equation (3) by the resulting particles calculated by the equation _(2), on the _i.
Then, returning to step S4, using the obtained position and motion state of each solid particle and the fluid velocity vector V _{f, i} at time t _{j + 1} (calculated and stored in advance in step S1), time t _The velocity vector Vp _{, i} and the rotational angular velocity vector ωp _{, i} of the individual solid particles at _{j + 1} are obtained, and in step S5, the particles that collide with the wall surface W during Δτ, that is, by the time tj _{+ 2} , are specified. In S6, the velocity vector _{Vp, i (2)} and the rotational angular velocity vector ωp _{, i (2)} after the collision are calculated, and the collision velocity vector _{Vcollision, i} is calculated.
[0021]
In this manner, steps S4 to S8 are repeatedly executed by the predetermined number of repetitions j _max , and the collision velocity vector V _{collision, i} on the wall surface of the solid particles at all time points is calculated.
Note that the collision velocity vector V _{collision, i} does not necessarily need to be obtained at each time point (each operation step), and after V _{p, i (1)} and ω _{p, i (1)} have been obtained at all time points, The calculations may be performed collectively.
[0022]
Statistical processing and display of collision state of solid particles If it is determined in step S7 that j = _jmax , the process proceeds to step S10, where the collision velocity of each solid particle calculated as described above is calculated. The magnitude of the vector _{Vcollision, i} is determined, and is associated with the position of the wall.
Further, the collision angle α ₁ of each solid particle at the time of collision with the wall surface is calculated from the motion velocity vector V _{p, i (1)} before the collision obtained in step S6, and is associated with the position of the wall surface.
Further, the wall collision frequency of each solid particle colliding with the channel wall surface is counted as the number of times the solid particle collides with each position on the wall surface, and is associated with the wall position.
Then, these data are processed into image display data, and the obtained image is displayed on the monitor screen together with the wall image.
[0023]
FIG. 3 shows a result of predicting how particles in a fluid in a pump having an impeller with a side plate affect the inner surface of the side plate by a simulation method according to the present invention. 3A shows the collision angle α ₁ of the solid particles, FIG. 3B shows the collision frequency, and FIG. 3C shows the collision velocity | V _{collision, i} |, both of which are on the shroud surface side, that is, the inner surface of the side plate. This shows a collision state with. In FIG. 3, the size is indicated by the contour display method. Therefore, the smaller the enclosed area, the larger the value indicated by the enclosed line. In this simulation, the following factors were employed.
Particle density ρ: 2670 kg / m ³
Particle diameter d _p : 25 μm
Particle concentration C _{v in} fluid: 32 kg / m ³
Total number of solid particles to be calculated: 20,000
Time interval Δτ: 0.00005 sec
Iteration number j _max: In the simulation example of the shroud surface side (the side plate inner surface) shown in 5000 Figure 3, the impact angle, collision frequency, and impact velocity shows a tendency to very close.
[0024]
In order to verify the validity of the above-described simulation method according to the present invention, the inventor applied paint to the inner surface of the side plate of the impeller of the pump, and allowed the solid-liquid multiphase fluid to flow through the pump, The state of paint remaining on the inner surface was measured. As a result, a result as shown in FIG. 4 was obtained. In FIG. 4, the darker the area, the more paint is removed.
Comparing the experimental results of FIG. 4 with the results of the simulation according to the present invention shown in FIG. 3, it can be seen that substantially the same results are obtained. Therefore, it can be seen that the image obtained by the simulation method according to the present invention appropriately represents the actual collision state of the particles on the inner surface of the side plate of the impeller.
[0025]
When executing the simulation method according to the present invention, the operator specifies a factor representing the actual state of the solid-liquid multiphase fluid such as a river and the shape of the pump to be arranged in the river (flow path shape and boundary conditions). Is input to the simulation system. Then, the effect of the solid-liquid mixed-phase fluid on the pump is estimated by analyzing an image showing the state of collision of the solid particles in the solid-liquid mixed-phase fluid with the pump obtained by operating the simulation system. be able to. Thereby, for example, information such as which part of the pump impeller or the like to be reinforced can be obtained.
On the other hand, in the case of a pump in use (or before use) in an actual river or the like, the remaining life (life) can be estimated. In this life estimation, at least one of the material of the pump impeller, the collision angle of solid particles, the collision frequency, and the collision speed is obtained from a database obtained by conducting experiments under various conditions using a sand wear model. Based on the two analysis results, the pump life (affected by the solid-liquid multiphase fluid) can be estimated.
[0026]
In the above description, an example of simulating the effect of the solid particles of the solid-liquid mixed-phase fluid in the pump on the pump has been described. However, the simulation method of the present invention is not limited to the pump. It can also be applied to simulate the effect of
Since the simulation method according to the present invention is configured as described above, it is possible to appropriately simulate the effect of the solid particles of the solid-liquid multiphase fluid on the wall surface of the pump impeller or the like. Therefore, it is a very effective system for designing the pump and the like and estimating the life.
[Brief description of the drawings]
FIG. 1 is a flowchart illustrating a method of simulating a wall collision of a solid-liquid multiphase fluid according to the present invention.
FIG. 2 is a schematic diagram illustrating a state of collision of solid particles with a channel wall for explaining a simulation method according to the present invention.
FIGS. 3A to 3C show collision angles and collisions of solid particles on the inner surface of a side plate, which is one of flow path walls of a pump impeller with a side plate, obtained by a simulation method according to the present invention. It is a figure of the monitor screen which illustrates a frequency and a collision speed.
FIG. 4 shows the remaining state of paint applied in advance to the inner surface of the side plate of the pump impeller with the side plate by actually flowing a solid-liquid mixed-phase fluid in the pump in order to verify the validity of the simulation method according to the present invention. It is a figure showing the result of the experiment which measured.

Claims (6)

A method executed by a computer to simulate a collision state of solid particles in a solid-liquid multiphase fluid against a channel wall surface,
The motion of a fine solid particle is expressed by a Lagrangian equation using a hard sphere model between the solid particle and the solid particle, and between the wall and the solid particle. A method for simulating at least one distribution of a collision angle, a collision velocity, and a collision frequency of a solid particle on a channel wall surface by tracking a behavior of the solid particle based on a free movement time of the particle. . A method executed by a computer to simulate a collision state of solid particles in a solid-liquid multiphase fluid against a channel wall surface,
(A) By analyzing the motion of the solid-liquid multiphase fluid based on the Navier-Stokes equation, each position of the flow path wall surface and the solid particles in the flow path and each time point (t _j : j) of a plurality of calculation steps = 0, 1, 2,...) To calculate and store a flow velocity vector (V _{f, i} ) representing the velocity and direction of the fluid;
(B) randomly arranging solid particles according to a predetermined particle concentration in the fluid in the flow path, and setting the position of each solid particle at an initial time point (t ₀ );
(C) The drag vector (F _{drag, i} ) and the lift vector (F _{lift, i} ) acting on each solid particle in the flow path at the current time point (t _j ) are represented by the solid particle diameter (d _p ) and the fluid density. , And the flow velocity vector (V _{f, i} ) of the fluid at the current time point (t _j ) of the fluid corresponding to the position of the solid particles, and the centrifugal force vector (F _{cent, i} ) is calculated as the solid particle diameter (d _p ), The particle density (ρ), the rotation speed of the rotating body disposed in the flow path, the particle speed, and the rotation radius of the solid particles, and calculate the Coriolis force vector (F _{cor, i} ) as the solid particle diameter (d _p ), A particle density (ρ), a rotation speed of a rotating body disposed in the flow path, a particle speed, and a step of calculating from a radius of rotation of the solid particles;
(D) Substituting these force vectors acting on each solid particle into the equation of motion of the hard sphere model to calculate an acceleration vector (dup _{, i} / dt) at the current time point (t _j ) of each solid particle. When,
(E) calculating a rotational angular velocity vector (ω _{p, i} ) at a current time point (t _j ) of each solid particle from an equation of motion regarding a rotational moment;
(F) motion velocity vector of each solid particle at the current time point _{(t j) (V p,} i) the current point in time _{(t j)} velocity in the vector of the fluid corresponding to the position of the solid particles _{(V f, i} ) And the acceleration vector (dup _{, i} / dt) of the solid particles;
(G) The next time point (t _j ) from the current time point (t _j ) based on the motion velocity vector (V _{p, i} ) and the rotational angular velocity vector (ω _{p, i} ) of each solid particle at the current time point (t _j ). _{j + 1} ) determining the solid particles that collide with the channel walls and other solid particles by the time of
(H) The motion velocity vector (V _{p, i (2)} ) and the rotational angular velocity vector (ω _{p, i (2)} ) of each solid particle colliding with the flow path wall surface after the collision are determined by the current time point (t _i ) The motion velocity vector (V _{p, i} ) and the rotation angular velocity vector (ω _{p, i} ) of the solid particles at the time of collision with the motion velocity vector (V _{p, i (1)} ) and the rotation angular velocity vector (ω _{p, i (1)} calculating from the collision equation as:
(I) The velocity vector (V _{p, i (1)} ) and the rotational angular velocity vector (ω _{p, i (1)} ) of each solid particle colliding with the channel wall surface at the current time point (t _j ) at the time of wall collision are Calculating a collision velocity vector (V _{collision, i} ) for each solid particle based on:
(J) determining the position and the motion state of each solid particle at the next time point (t _{j + 1} );
(K) By repeatedly performing steps (c) to (j), the motion velocity vector (V _{p, i (1)} ) and the rotational angular velocity vector (ω _{p, i (1)} ), and determining the solid particles that collide with the flow path wall surface and calculating the collision velocity vector (V _{collision, i} );
(L) displaying the calculated magnitude of the collision velocity vector (V _{collision, i} ) of the solid particles in association with the position of the channel wall surface. 3. The simulation method according to claim 2, wherein the method further comprises:
(M) At each time point (t _j ), the collision angle (α ₁ ) of each solid particle colliding with the channel wall surface at the time of wall collision is determined by the motion velocity vector (V _{p, i (1 A)} calculating based on:
(N) displaying the magnitude of the obtained collision angle (α ₁ ) in association with the position of the flow channel wall surface. The simulation method according to claim 2, wherein the method further comprises:
(O) calculating a wall collision frequency of each solid particle colliding with the flow path wall surface at all time points in association with the position of the flow path wall surface;
(P) displaying the magnitude of the obtained wall collision frequency in association with the position of the flow path wall surface. 5. The simulation method according to claim 1, wherein the flow path is inside the pump. A program executed by a computer to execute a method for simulating a collision state of solid particles in a solid-liquid multiphase fluid against a channel wall surface, wherein the method is any one of claims 1 to 5. A program characterized by the above simulation method.

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