A Discrete Particle Trajectory Prediction Method for Pipeline Centrifugal Separators Based on Surrogate Models

Abstract

The object of the present invention is to provide a method for predicting the discrete particle trajectories of a pipeline centrifugal separator based on a surrogate model, which comprises the following steps: planning the experimental matrix of the structural parameters and flow field distribution of the pipeline centrifugal separator; obtaining the corresponding matrix between each structural parameter and flow field characteristic parameter according to the simulation experimental data; conducting a sensitivity analysis of the input variables, selecting a modeling technique, and constructing a surrogate model for the key input parameters and response values; comparing the results of the surrogate model with the experimental data; constructing a force model for discrete particles in the swirling flow field; establishing a transient motion trajectory equation for discrete particles by using the Euler method, and coupling and solving the flow field calculation model and the particle force model to obtain a discrete particle motion prediction model. The present invention can predict the motion trajectories of discrete particles in the separator under conditions of different physical property parameters, different structural parameters, and different flow parameters, so as to provide guidance for the structural design and application of the pipeline centrifugal separator.

Description

Technical Field

[0001] The present invention relates to a two-phase separation method, specifically a method for predicting the motion trajectories of discrete particles. Background Art

[0002] A pipeline centrifugal separator generates a swirling flow by means of a guiding impeller arranged in a pipeline, and can be directly arranged in a flow pipeline. Compared with common centrifugal separation equipment such as a hydrocyclone, it has a more compact structure and smaller pressure loss. In recent years, it has been successfully applied to gas-liquid separation and liquid-liquid separation, and has broad application prospects in two-phase separation. Since the separation performance of the centrifugal separator is highly sensitive to fluid parameters, once the physical properties of the fluid change, the separation efficiency may change drastically, and the original separator structure is no longer applicable. Therefore, it is necessary to propose a general and universal calculation method for evaluating the applicability of the separator under different separation media and expanding the application of this pipeline centrifugal separator in two-phase separation.

[0003] The motion trajectories of discrete particles in a continuous phase determine the separation performance of the separator. According to the working principle of the separator, if the discrete particles can quickly gather at the center of the pipeline, they can be discharged from the outlet, achieving a high separation efficiency. If the centrifugal force acting on the discrete particles is insufficient and they cannot move to the center of the pipeline, they cannot be separated at this time. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the motion trajectories of discrete particles in a pipeline centrifugal separator based on a surrogate model, which can accurately and quickly predict the motion trajectories of discrete particles.

[0005] The purpose of the present invention is achieved as follows:

[0006] A method for predicting the motion trajectories of discrete particles in a pipeline centrifugal separator based on a surrogate model according to the present invention is characterized in that:

[0007] (1) The Latin hypercube experimental design method is adopted to plan the experimental matrix of the structural parameters and flow field distribution of the pipeline centrifugal separator;

[0008] (2) The geometric parameters of the separator are input, and the CFD solver is used to calculate the internal flow field of the separator to obtain the characteristic parameters in the flow field calculation relation, and the corresponding matrix between each structural parameter and the flow field characteristic parameter is obtained according to the simulation experimental data;

[0009] (3) According to the experimental data in step (2), a sensitivity analysis of the input variables is carried out, insensitive variables are eliminated, and then a modeling technique is selected to construct a surrogate model for the key input parameters and the response value;

[0010] (4) Randomly extract data from the matrix of structural parameters and flow field characteristic parameters, compare the results of the surrogate model with the experimental data. If the requirements are met, the surrogate model meets the requirements.

[0011] (5) Construct a force model for discrete particles in the swirling flow field, considering the centrifugal force caused by the radial pressure gradient, the drag force generated by the relative motion between the discrete phase particles and the continuous phase, the buoyancy force of the continuous phase on it, the Magnus force caused by the rotation of the moving particles, the Saffman force caused by the velocity gradient, and the virtual mass force. Establish the force balance equations in the axial, radial, and tangential directions.

[0012] (6) Use the Euler method to establish the transient motion trajectory equation of discrete particles, and couple and solve the flow field calculation model and the particle force model to obtain the discrete particle motion prediction model.

[0013] The present invention may further include:

[0014] 1. The Navier-Stokes equations in the cylindrical coordinate system (r, θ, z) are as follows

[0015]

[0016]

[0017]

[0018] The equations are simplified to:

[0019]

[0020]

[0021]

[0022] According to the above equations, the tangential velocity u is obtained θ General solution form:

[0023]

[0024] Further derivation gives the expression of the axial velocity u z :

[0025]

[0026] l = -RS

[0027] At the same time, the axial velocity satisfies the law of conservation of mass,

[0028]

[0029] where, W 1 , W 2And S are unknown parameters to be solved;

[0030] Latin hypercube design is adopted to plan test points, and then CFD is used to calculate these test points to obtain the flow field of the separator under different structural parameters, and then the response values W 1 , W 2 and S. Based on these sample points, a modeling technique is selected to construct a surrogate model, and sample points are randomly selected for model verification. If the verification results meet the error requirements, the flow field distribution under each structural parameter is determined through this surrogate model;

[0031] For discrete particles in the swirling flow field, the forces acting on them include the centrifugal force Fc caused by the pressure gradient, the drag force Fd generated by the relative motion between the discrete-phase particles and the continuous phase, the buoyancy force Fg of the continuous phase on them, the Magnus force Fm caused by the rotation of the moving particles, the Saffman force Fs caused by the velocity gradient, and the virtual mass force Fa, etc. The motion of discrete particles in the swirling flow field satisfies the following equilibrium relationship:

[0032]

[0033] In the formula, ρ b is the density of discrete particles, D b is the particle diameter, and V b is the particle velocity;

[0034] The force model of discrete particles is coupled with the flow field model established by using the surrogate model, and the particle trajectory equation in the cylindrical coordinate system is further established by using the Euler method, and finally the motion trajectories of discrete particles under different structural parameters and different physical property parameters can be predicted:

[0035]

[0036] The advantages of the present invention are as follows:

[0037] 1. The velocities of the continuous phase and discrete particles at each position in the separator under different impeller structural parameters and different flow velocities can be obtained;

[0038] 2. By calculating the discrete particle force model embedded in the calculation model, the magnitudes and variation conditions of the forces acting on the discrete particles during the motion process can be obtained;

[0039] 3. The motion trajectories of discrete particles in the separator under different physical property parameters, different structural parameters and different flow parameters can be predicted, thereby providing guidance for the structural design and application of the pipeline centrifugal separator. Brief Description of the Drawings

[0040] Figure 1 is the flow chart of the present invention;

[0041] Figure 2The building process of the surrogate model;

[0042] Figure 3 The prediction result of the motion trajectories of discrete particles. Specific implementation manners

[0043] The present invention will be described in more detail with reference to the accompanying drawings as follows:

[0044] Combined with Figures 1 - 3 , a method for predicting the trajectories of discrete particles in a pipe-type centrifugal separator based on a surrogate model according to the present invention includes three parts as shown in Figure 1 :

[0045] I. Computational model of the internal flow field of the separator

[0046] (1) Using the Latin hypercube experimental design method, planning the experimental matrix of the structural parameters and flow field distribution of the pipe-type centrifugal separator;

[0047] (2) Inputting the geometric parameters of the separator, using CFD to solve and calculate the internal flow field of the separator, obtaining the characteristic parameters in the flow field calculation relational expression, and obtaining the corresponding matrix between each structural parameter and the flow field characteristic parameter according to a large amount of simulation experimental data;

[0048] (3) According to the experimental data in (2), performing sensitivity analysis on the input variables, eliminating the insensitive variables, and then selecting an appropriate modeling technique to construct a surrogate model for the key input parameters and the response values;

[0049] (4) Randomly extracting several groups of data from the matrix of the structural parameters and the flow field characteristic parameters, comparing the results of the surrogate model with the experimental data. If the requirements are met, it is considered that the surrogate model meets the requirements;

[0050] II. Force model of discrete particles

[0051] Construct a force model of discrete particles in the swirling flow field, considering the centrifugal force caused by the radial pressure gradient, the drag force generated by the relative motion between the discrete phase particles and the continuous phase, the buoyancy force of the continuous phase on it, the Magnus force caused by the rotation of the moving particles, the Saffman force caused by the velocity gradient, and the virtual mass force, etc., and establishing the force balance equations in the axial, radial, and tangential directions;

[0052] III. Prediction model of the motion trajectories of discrete particles

[0053] Using the Euler method to establish the transient motion orbit equation of discrete particles, and coupling and solving the flow field calculation model and the particle force model to obtain the discrete particle motion prediction model. Specific embodiment:

[0055] The Navier-Stokes equations in the cylindrical coordinate system (r, θ, z) are as follows

[0056]

[0057]

[0058]

[0059] Considering that in a stable swirling flow field, the flow field has symmetry, and the radial velocity is often negligible, and at the same time, the velocity gradient in the radial direction is significantly greater than that in the axial direction, the equation can be simplified as:

[0060]

[0061]

[0062]

[0063] According to the above equation, the tangential velocity u can be obtained θ General solution form:

[0064]

[0065] By further derivation, the axial velocity u z expression:

[0066]

[0067] l = -RS (9)

[0068] At the same time, the axial velocity satisfies the law of conservation of mass,

[0069]

[0070] where, W 1 ,W 2 and S are unknown parameters to be solved.

[0071] In order to establish a calculation model for the flow field of the separator under different structural parameters, the modeling method shown in Figure 2 is adopted. The main structural parameters of the pipe-type centrifugal separator include the blade outlet angle, blade twist angle, blade thickness, number of blades, central axis diameter, etc. Since the amount of calculation in the database is relatively large, the Latin hypercube design test points are first used, and then CFD is used to calculate these test points to obtain the flow field of the separator under different structural parameters, and then the response values W 1 ,W 2And S, based on these sample points, perform sensitivity analysis, eliminate insensitive parameters, reduce the modeling difficulty, and then select appropriate modeling techniques to construct a surrogate model. Randomly select several sample points for model verification. If the verification results meet the error requirements, the flow field distribution under each structural parameter can be determined through this surrogate model.

[0072] For discrete particles in a swirling flow field, the main forces acting on them are the centrifugal force Fc caused by the pressure gradient, the drag force Fd generated by the relative motion between the discrete-phase particles and the continuous phase, the buoyancy force Fg of the continuous phase on them, the Magnus force Fm caused by the rotation of the moving particles, the Saffman force Fs caused by the velocity gradient, and the virtual mass force Fa, etc. Therefore, the motion of discrete particles in the swirling flow field satisfies the following equilibrium relation:

[0073]

[0074] In the formula, ρ b is the density of discrete particles, D b is the particle diameter, and V b is the particle velocity.

[0075] Couple the discrete particle force model with the flow field model established using the surrogate model, further establish the particle trajectory equation in the cylindrical coordinate system using the Euler method, and finally obtain the discrete particle motion trajectories that can predict different structural parameters and different physical property parameters.

[0076]

[0077] Figure 3 Shown are the discrete particle motion trajectories obtained by the above method.

Claims

1. A method for predicting the discrete particle trajectories of a pipeline centrifugal separator based on a surrogate model, characterized in that: (1) The Latin hypercube experimental design method is adopted to plan the experimental matrix of the structural parameters and flow field distribution of the pipeline centrifugal separator; (2) The geometric parameters of the separator are input, and the CFD is used to solve and calculate the internal flow field of the separator to obtain the characteristic parameters in the flow field calculation relationship, and the corresponding matrix between each structural parameter and the flow field characteristic parameter is obtained according to the simulation experimental data; (3) According to the experimental data in step (2), the sensitivity analysis of the input variables is carried out, the insensitive variables are removed, and then the modeling technology is selected to construct a surrogate model for the key input parameters and response values; (4) Data is randomly selected from the matrix of structural parameters and flow field characteristic parameters, and the results of the surrogate model are compared with the experimental data. If the requirements are met, the surrogate model meets the requirements; (5) A force model for discrete particles in the swirling flow field is constructed, considering the centrifugal force caused by the radial pressure gradient, the drag force generated by the relative motion between the discrete phase particles and the continuous phase, the buoyancy force of the continuous phase on it, the Magnus force caused by the rotation of the moving particles, the Saffman force caused by the velocity gradient, and the virtual mass force, and the force balance equations in the axial, radial, and tangential directions are established; (6) The Euler method is used to establish the transient motion trajectory equation of discrete particles, and the flow field calculation model and the particle force model are coupled and solved to obtain the discrete particle motion prediction model; The discrete particle force model is coupled with the flow field model established by using the surrogate model, and the particle trajectory equation in the cylindrical coordinate system is further established by using the Euler method, and finally the discrete particle motion trajectories under different structural parameters and different physical property parameters can be predicted:

2. The method for predicting the discrete particle trajectories of a pipeline centrifugal separator based on a surrogate model according to claim 1, characterized in that: The Navier-Stokes equation in the cylindrical coordinate system (r, θ, z) is as follows The equation is simplified to: According to the above equation, the tangential velocity u is obtained θ General solution form: Further derivation gives the expression for the axial velocity u z as follows: l = -RS At the same time, the axial velocity satisfies the law of conservation of mass, Among them, W 1 , W 2 and S are unknown parameters to be solved; Use Latin hypercube sampling to plan the test points, and then use CFD to calculate these test points to obtain the separator flow field under different structural parameters, and then obtain the response values W 1 、W 2 and S. Based on these sample points, select a modeling technique to construct a surrogate model, and randomly select sample points for model verification. If the verification results meet the error requirements, determine the flow field distribution under each structural parameter through this surrogate model; For the discrete particles in the swirling flow field, the forces acting on them include the centrifugal force Fc caused by the pressure gradient, the drag force Fd generated by the relative motion between the discrete phase particles and the continuous phase, the buoyancy force Fg of the continuous phase on it, the Magnus force Fm caused by the rotation of the moving particles, the Saffman force Fs caused by the velocity gradient, and the virtual mass force Fa. The motion of the discrete particles in the swirling flow field satisfies the following equilibrium relationship: where ρ b is the density of discrete particles, D b is the particle diameter, V b is the particle velocity.

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