Numerical prediction method for wet particle behavior in fluidized bed

Abstract

The present application provides a numerical prediction method for wet particle behavior in a fluidized bed, belonging to the technical field of wet particle behavior prediction in a fluidized bed. The limitations of traditional methods in dealing with complex wet particle systems are solved. It includes the following steps: step one: establishing a full-analytical non-spherical wet particle CFD-DEM model, modeling the particle shape, size and liquid properties; step two: at the particle scale, different working conditions are simulated based on the full-analytical model, the formation, evolution of liquid bridge force and its influence on particle motion are explored, and the dynamic characteristics and interaction data of the liquid bridge between wet particles are obtained through direct numerical simulation; step three: extracting and establishing a liquid bridge force model suitable for describing high liquid content, large contact angle and non-spherical particles from the liquid bridge dynamics data; step four: the obtained non-spherical liquid bridge force model is substituted into the non-analytical CFD-DEM framework to predict the fluidization behavior of wet particles in a fluidized bed. It is mainly used for wet particle prediction.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wet particle behavior prediction in fluidized bed, and particularly relates to a numerical prediction method for wet particle behavior in fluidized bed. BACKGROUND

[0002] Fluidized bed technology is widely used in chemical industry, pharmaceutical industry, energy industry and material processing industry, and becomes the core unit in many key process flows due to its excellent heat transfer and mass transfer performance and high reaction capacity. However, in actual industrial processes, the particles processed in the fluidized bed are mostly non-spherical and contain a certain amount of moisture, which makes the fluidization behavior extremely complex. The irregular shape of non-spherical particles and the different surface properties, combined with the liquid bridge dynamics behavior between particles, result in significant differences in the movement, aggregation and dispersion characteristics of wet particles in the fluidized bed from those of ideal spherical particles. Traditional experimental methods face many challenges in studying the fluidization behavior of non-spherical wet particles. First, the multiphase flow process of non-spherical wet particles is very complex, and experimental methods are difficult to fully capture the dynamic characteristics of particles. Second, the interaction force between wet particles due to liquid bridge effect, as well as the particle aggregation and sedimentation phenomenon caused thereby, makes the experimental results often have great uncertainty. In addition, the fluidized bed under actual industrial conditions is large in scale, and the scaling effect of the experimental device may make it difficult to directly apply the experimental data to the actual production process. These factors make it extremely difficult to obtain accurate data on the fluidization behavior of non-spherical wet particles in the fluidized bed through experimental methods.

[0003] The numerical simulation method can effectively save manpower, material resources and time cost. The various liquid bridge force models obtained through theoretical analysis are usually only applicable to low liquid content, small contact angle and spherical particle shape, but such assumptions are not common in practice, which limits their application in non-spherical particle systems. SUMMARY

[0004] Therefore, the application aims to provide a numerical prediction method for wet particle behavior in fluidized bed to solve the limitations of traditional methods in dealing with complex wet particle systems.

[0005] To achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0006] A numerical prediction method for wet particle behavior in fluidized bed, comprising the following steps:

[0007] Step 1: Establish a fully analytical non-spherical wet particle CFD-DEM model to model the particle shape, size and liquid properties;

[0008] Step 2: On the particle scale, different working conditions are simulated based on the CFD-DEM model to explore the formation, evolution of liquid bridge force and its influence on particle motion, obtain the dynamic characteristics and interaction data of wet particle liquid bridge, and establish a database;

[0009] Step 3: Based on symbolic regression technology, the liquid bridge force model for describing liquid content, large contact angle and non-spherical particles is extracted and established from the database, and genetic algorithm is used to search for specific function form and parameter value in the database, and to predict the liquid bridge force model of liquid content, contact angle and non-spherical particles;

[0010] Step 4: The obtained liquid bridge force model of non-spherical particles is substituted into the non-analytical CFD-DEM model to predict the fluidization behavior of wet particles in the fluidized bed.

[0011] Further, the particle geometry modeling in step 1 uses a super-ellipse model to describe the particle, and its standard equation is:

[0012]

[0013] Where a, b and c are the semi-axis lengths in the main axis direction of the particle, and n1 and n2 are shape indexes used to control the sharpness of the particle edge. The larger the shape index, the greater the gradient of the shape function is:

[0014]

[0015] Where the quaternion method is used to process variables related to particle rotation, and the equation is as follows:

[0016] s=qs0q -1 (7)

[0017]

[0018] Further, the translational and rotational behavior of particles in step 1 is described by Newton's second law:

[0019]

[0020] Where F C is the contact force between particles, F VP is the fluid / particle interaction force, F CAP is the capillary force on the particle, and F G is the gravity on the particle. The particle rotation equation is as follows:

[0021]

[0022] Where I i is the particle rotational inertia in the local coordinate system, and ω iM is the contact torque experienced by the particle Cij M is the contact torque experienced by the particle VPi M is the fluid-structure interaction force torque experienced by the particle CAPi M is the capillary force torque experienced by the particle.

[0023] Further, the fluid volume method is used to describe the gas-liquid two-phase behavior in step 1:

[0024]

[0025] Where U is the fluid velocity, p is the fluid density, p is the fluid pressure, t is the fluid viscous stress tensor, f s is the surface tension, g is the gravitational acceleration, t is time, f VP M is the fluid-structure interaction force;

[0026] Where the viscous stress tensor expression is:

[0027]

[0028] Where m is the fluid dynamic viscosity, T is the transpose operation.

[0029] Further, the fluid force and torque on the particle in step 1 are obtained by surface integration around the particle, and the surface integration is converted to volume integration using the following divergence theorem:

[0030]

[0031] The surface tension line integral of the three-phase contact line is equivalent to the surface area integral of the surface tension of the immersed free surface, which is converted to volume integral using the Gauss divergence theorem, and the solution formula is as follows:

[0032]

[0033] Further, in step 2, the dynamic characteristics and interaction data of the liquid bridge between wet particles are obtained by direct numerical simulation.

[0034] Further, the symbolic regression technique in step 3 includes the following steps:

[0035] S1: Clean, filter, filter, normalize the data in the database, and obtain the non-spherical liquid bridge force characteristics;

[0036] S2: Extract the partial derivative between the variables in the database;

[0037] S3: Generate candidate symbolic functions:

[0038] S4: Derive the partial derivative of each candidate symbolic function:

[0039] S5: According to the error function, the best function is reserved, when the prediction energy of the obtained symbol equation reaches the required accuracy, the simplest equation is output, and the liquid bridge force model is obtained.

[0040] Compared with the prior art, the present application has the beneficial effects that:

[0041] The present application is based on a DNS and symbol regression fluidized bed wet particle fluidization behavior prediction method, which uses the DNS method to study the liquid bridge dynamic behavior between non-spherical wet particles at the particle scale and establish a database, and combines the symbol regression algorithm to obtain a model suitable for describing the liquid bridge dynamic behavior of high liquid content, large contact angle and non-spherical particles, and further substitutes the model into the unanalytical CFD-DEM model for predicting the fluidization behavior of wet particles in the fluidized bed. The method does not need to perform complex sampling analysis on the actual running fluidized bed, greatly saving the manpower, physical and time cost. BRIEF DESCRIPTION OF DRAWINGS

[0042] The accompanying drawings, which form a part of the present application, are intended to provide further understanding of the present application, and the illustrative embodiments of the present application and their descriptions serve to explain the present application, and do not constitute improper limitations on the present application. In the drawings:

[0043] Figure 1 A flowchart of a numerical prediction method for wet particle behavior in a fluidized bed according to the present application. DETAILED DESCRIPTION

[0044] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict, and the described embodiments are only part of the embodiments of the present application, not all the embodiments.

[0045] Specific embodiment one: see Figure 1 To illustrate this embodiment, a numerical prediction method for wet particle behavior in a fluidized bed,

[0046] Step 1: Establish a fully analytical non-spherical wet particle CFD-DEM model, model the particle shape, size and liquid properties;

[0047] Step 2: On the particle scale, different working conditions are set based on the CFD-DEM model for simulation, the formation, evolution and influence of the liquid bridge force on the particle motion are explored, the dynamic characteristics and interaction data of the wet particle liquid bridge are obtained, and a database is established;

[0048] Step 3: Based on symbolic regression technique, extract and establish liquid bridge force model for describing high liquid content, large contact angle and non-spherical particles from the database, use genetic algorithm to collect specific function form and optimal parameter value from the database, and derive the liquid bridge force model for high liquid content, large contact angle and non-spherical particles;

[0049] Step 4: Substitute the obtained liquid bridge force model of non-spherical particles into the non-analytical CFD-DEM model for predicting the fluidization behavior of wet particles in the fluidized bed.

[0050] Further, in step 2, the dynamic characteristics and interaction data of the liquid bridge between wet particles are obtained by DNS direct numerical simulation.

[0051] First, according to the structure of the fluidized bed, the simulation system is meshed, the basic parameters are set, the particle properties and fluid content, viscosity and other parameters are input, the inlet and boundary conditions are defined, the time step and convergence conditions are set to start solving. When solving, first solve the fluid continuity equation and momentum equation, then solve the interphase momentum exchange force according to the flow field information, and finally solve the particle DEM equation. Repeat this process until the calculation is stopped, and export the particle velocity, angular velocity, density and geometric shape to obtain the fluidization behavior of wet particles in the fluidized bed. The DNS method is used to study the liquid bridge dynamics between non-spherical wet particles at the particle scale and establish a database. Combined with the symbolic regression algorithm, a model suitable for describing the liquid bridge dynamics of high liquid content, large contact angle and non-spherical particles is obtained. Further, this model is substituted into the non-analytical CFD-DEM model to predict the fluidization behavior of wet particles in the fluidized bed. This method does not require complex sampling analysis of the actual running fluidized bed, greatly saving manpower, physical and time costs.

[0052] The DNS method is a direct numerical simulation method used to solve the Navier-Stokes equation in fluid dynamics to completely analyze all scales of turbulence. The DNS method can provide detailed information of fluid flow, including velocity, pressure and temperature, which is irreplaceable for understanding and studying the physical mechanism of turbulence. It can completely analyze all scales of fluid motion, from the largest vortex to the smallest turbulence scale. It can provide sufficient accuracy while significantly reducing computational cost.

[0053] The fully analytical non-spherical wet particle CFD-DEM model can fully analyze all movements and interactions of particles, including the shape, trajectory, and interaction with the fluid of the particles. In the fully analytical CFD-DEM model, the movement of each particle is directly solved by DEM in the Lagrangian framework, which can accurately calculate the force (such as drag force, lift force, etc.) of the fluid on each particle and the influence of the particle on the fluid. In the fully analytical model, the shape of the non-spherical particle can be accurately represented by a complex geometric description, rather than being simplified as a sphere or other regular shape. This allows the model to more accurately capture the influence of particle shape on flow and interaction.

[0054] Specific embodiment two: on the basis of specific embodiment one, the initial conditions of this embodiment are given as follows: particle diameter is 1.0 mm, axial length is 1.0 mm, liquid volume between particles is cylindrical, volume is 0.144 mm3, which is applied by the Monte Carlo method, calculation area is 8a x 2.7a x 1.5a, liquid density is 1000 kg / m3, liquid viscosity is 0.01 Pa·s, gas viscosity is 1.8 x 10-5 Pa·s, gas density is 1.2 kg / m3, surface tension coefficient is 0.07 N / m, and the fluidization behavior of wet particles in the fluidized bed is predicted by using embodiment one.

[0055] First, the particle geometry is modeled, and a super-ellipse model is used to describe the particle, and the standard equation is as follows:

[0056]

[0057] Where a, b, and c are the semi-axial lengths in the main axial direction of the particle, and n1 and n2 are shape indices used to control the sharpness of the particle edge. The greater the shape index, the greater the gradient of the shape function is:

[0058]

[0059]

[0060] Where the quaternion method is used to handle variables related to particle rotation, and the equation is as follows:

[0061] s = qs0q -1 (7)

[0062]

[0063] The translational and rotational behavior of the particle is described by Newton's second law:

[0064]

[0065] Where F C is the contact force between particles, and F VPFor fluid / particle interaction force, F CAP F is the capillary force acting on the particle. G Let gravitational force act on the particle, and the equation of motion for the particle is as follows:

[0066]

[0067] Among them, I i Let ω be the moment of inertia of the particle in the local coordinate system. i M is the particle rotational velocity in the local coordinate system. Cij M is the contact torque experienced by the particle. VPi M represents the torque caused by the fluid-structure interaction force acting on the particle. CAPi The capillary force and torque experienced by the particles.

[0068] The gas-liquid two-phase behavior is described using the fluid volume method:

[0069]

[0070] Where U is the fluid velocity, ρ is the fluid density, p is the fluid pressure, τ is the fluid viscous stress tensor, and f is the fluid velocity. s Surface tension, g-force acceleration, t-time, f VP This refers to fluid / particle interaction forces.

[0071] The expression for the viscous stress tensor is:

[0072]

[0073] Where μ is the fluid dynamic viscosity, and T is the transpose operation.

[0074] The fluid forces and torques on the particles are obtained by performing surface integration around the particles, and the surface integration is converted into a volume integration using the following divergence theorem:

[0075]

[0076] The surface tension linear integral of the three-phase contact line is equivalent to the surface tension integral of the surface tension submerged in a free surface. Using Gauss's divergence theorem, it is transformed into a volume integral, and the solution formula is as follows:

[0077]

[0078] At the particle scale, simulations were conducted under different operating conditions based on a fully analytical model to investigate the formation, evolution, and fracture of liquid bridge forces and their impact on particle motion. Through direct numerical simulation, the dynamic characteristics and interaction data of liquid bridges between wet particles were obtained, and a database was established.

[0079] Based on symbolic regression technique, liquid bridge force model suitable for describing high liquid content, large contact angle and non-spherical particles is extracted and established from liquid bridge dynamics data; genetic algorithm is used to search for specific function form and optimal parameter value of data set, and liquid bridge force model of high liquid content, large contact angle and non-spherical wet particles is pushed.

[0080] S1: data cleaning, screening, filtering and normalization of the database, and obtaining non-spherical liquid bridge force characteristics;

[0081] S2: partial derivative between variables in the database;

[0082] S3: generating a candidate symbolic function;

[0083] S4: deriving partial derivative of each candidate symbolic function;

[0084] S5: retaining the best function according to the error function, and outputting the simplest equation as the liquid bridge force model of high liquid content, large contact angle and non-spherical wet particles when the predicted energy of the obtained symbolic equation reaches the required accuracy.

[0085] The obtained non-spherical liquid bridge force model is substituted into the unanalyzed CFD-DEM framework to predict the fluidization behavior of wet particles in a fluidized bed.

[0086] The above disclosed embodiments of the application are only used to help explain the application. The embodiments do not describe all the details, nor limit the application to the specific embodiments described. According to the content of the specification, many modifications and changes can be made. The specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the application, so that those skilled in the art can well understand and utilize the application.

Claims

1. A method for numerical prediction of wet particle behavior in a fluidized bed, characterized by: It comprises the following steps: Step 1: Establish a fully resolved CFD-DEM model of non-spherical wet particles, model the particle shape, size and liquid properties; Step 2: At the particle scale, based on the CFD-DEM model, different working conditions are set up for simulation, the formation, evolution of liquid bridge force and its influence on particle motion are explored, the dynamic characteristics and interaction data of wet particle liquid bridge are obtained, and a database is established; Step 3: Based on symbolic regression technology, extract and establish a liquid bridge force model for describing the liquid content, contact angle and non-spherical particles from the database, use genetic algorithm to search for specific function form and parameter value in the database, and derive the liquid bridge force model of liquid content, contact angle and non-spherical particles; Step 4: The obtained liquid bridge force model of non-spherical particles is substituted into the non-resolved CFD-DEM model to predict the fluidization behavior of wet particles in the fluidized bed; The particle geometry modeling in step 1 uses a super-elliptical model to describe the particle, and its standard equation is: （1） Where a, b, and c are the semi-axis lengths in the principal axis direction of the particle, n1 and n2 are shape indices to control the sharpness of the particle edge, and the larger the shape index, the greater the gradient of the shape function is: （2） （3） （4） （5） （6） Where the quaternion method is used to handle variables related to particle rotation, and the equation is as follows: （7） （8）。 2. The method of numerical prediction of the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: The translational and rotational behavior of particles in step 1 is described by Newton's second law: （9） where F C is the contact force between particles, F VP is the fluid / particle interaction force, F CAP is the capillary force experienced by the particles, F G is the gravitational force experienced by the particles, the particle rotation equation is as follows: （10） where I i is the particle rotational inertia in the local coordinate system, ω i is the particle rotational velocity in the local coordinate system, M Cij is the contact torque experienced by the particle, M VPi is the fluid-structure interaction force torque experienced by the particle, M CAPi is the capillary force torque experienced by the particle.

3. The method of numerical prediction of the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: The fluid volume method is used to describe the gas-liquid two-phase behavior in step 1: （11） （12） where U is the fluid velocity, p is the fluid density, p is the fluid pressure, T is the fluid viscous stress tensor, f s surface tension, g is the gravitational acceleration, t is time, f VP is the fluid / particle interaction force; Where the viscous stress tensor expression is: （13） Where μ is the fluid dynamic viscosity, and T is the transpose operation.

4. The method of numerical prediction of the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: The fluid force and torque on the particle in step 1 are obtained by surface integration around the particle, and the following divergence theorem is used to convert the surface integral to volume integral: （14） （15） The surface tension line integral of the three-phase contact line is equivalent to the surface area integral of the immersed free surface, and the Gauss divergence theorem is used to convert it to volume integral, and the solution formula is as follows: （16） （17） （18） （19）。 5. The method of numerical prediction of the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: In step 2, the dynamic characteristics and interaction data of wet particle liquid bridge are obtained by direct numerical simulation.

6. The method of numerical prediction of the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: The symbolic regression technology in step 3 includes the following steps: S1: Clean, filter, filter and normalize the data in the database to obtain the characteristics of non-spherical liquid bridge force; S2: Extract the partial derivatives between variables in the database; S3: Generate candidate symbolic functions: S4: Derive the partial derivative of each candidate symbolic function: S5: According to the error function, the best function is retained, when the predicted energy of the obtained symbolic equation reaches the required accuracy, the equation is output, and the liquid bridge force model is obtained.

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