Method for predicting behavior numerical value of wet particles in fluidized bed

Abstract

The invention provides a method for predicting behavior numerical values of wet particles in a fluidized bed, and belongs to the technical field of behavior prediction of wet particles in fluidized beds. And the problem of limitation of a traditional method in treatment of a complex wet particle system is solved. The method comprises the following steps: 1, establishing a full-analysis non-spherical wet particle CFD-DEM model, and modeling particle shape, size and liquid attribute; 2, on the particle size, setting different working conditions based on a full-analysis model for simulation, exploring formation and evolution of liquid bridge force and the influence of the liquid bridge force on particle motion, and obtaining dynamic characteristics and interaction data of a liquid bridge between wet particles through direct numerical simulation; 3, extracting and establishing a liquid bridge force model suitable for describing high liquid content, large contact angle and non-spherical particles from liquid bridge dynamic data; and 4, substituting the obtained non-spherical liquid bridge force model into an unanalyzed CFD-DEM framework to predict the fluidization behavior of wet particles in a fluidized bed. The method is mainly used for wet particle prediction.

Description

Technical Field

[0001] The invention belongs to the technical field of wet particle behavior prediction in a fluidized bed, and in particular relates to a numerical prediction method for wet particle behavior in a fluidized bed. Background Art

[0002] Fluidized bed technology is widely used in many industrial fields such as chemical, pharmaceutical, energy and material processing. With its excellent heat transfer, mass transfer performance and efficient reaction ability, it has become the core unit in many key process flows. However, in actual industrial processes, most of the particles processed in the fluidized bed are non-spherical and contain a certain amount of water, which makes their fluidization behavior extremely complex. The non-spherical particles have irregular shapes and different surface characteristics. In addition, the liquid bridge dynamics between particles lead to significant differences in the movement, aggregation and dispersion characteristics of wet particles in the fluidized bed and those of spherical particles under ideal conditions. Traditional experimental methods are not very effective in studying non-spherical particles. There are many challenges in studying the fluidization behavior of 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 the particles. Second, the interaction force between wet particles due to the liquid bridge effect, and the resulting particle agglomeration and sedimentation, make 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 means.

[0003] The numerical simulation method can effectively save manpower, material resources and time costs. 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. However, this assumption is not common in practice, which limits its application in non-spherical particle systems. Summary of the invention

[0004] In view of this, the present invention aims to propose a numerical prediction method for the behavior of wet particles in a fluidized bed to solve the problem of limitations of traditional methods in dealing with complex wet particle systems.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for numerically predicting the behavior of wet particles in a fluidized bed comprises 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: At the particle scale, different working conditions are set up for simulation based on the CFD-DEM model to explore the formation and evolution of liquid bridge forces and their influence on particle movement, obtain the dynamic characteristics and interaction data of wet particle liquid bridges, and establish a database;

[0009] Step 3: Based on the symbolic regression technology, a liquid bridge force model for describing liquid content, large contact angle and non-spherical particles is extracted and established from the database. A genetic algorithm is used to collect specific function forms and parameter values ​​from the database to deduce the liquid bridge force model of liquid content, contact angle and non-spherical particles;

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

[0011] Furthermore, the particle geometry modeling in step 1 uses a superellipse model to describe the particles, and its standard equation is:

[0012]

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

[0014]

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

[0016] s=qs0q -1 (7)

[0017]

[0018] Furthermore, the translational and rotational behavior of the 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, F G is the gravity on the particle, and the particle rotation equation is as follows:

[0021]

[0022] Among them, I i is the particle moment of inertia in the local coordinate system, ω iis the particle rotation speed in the local coordinate system, M Cij is the contact torque on the particle, M VPi is the fluid-solid interaction torque on the particle, M CAPi The capillary torque on the particle.

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

[0024]

[0025] 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 gravity acceleration, t time, f VP is the fluid / particle interaction force;

[0026] The expression of viscous stress tensor is:

[0027]

[0028] where μ is the dynamic viscosity of the fluid and T is the transpose operation.

[0029] Furthermore, the fluid forces and moments on the particles in step 1 are obtained by performing surface integration around the particles, and the surface integral is converted to volume integral using the following divergence theorem:

[0030]

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

[0032]

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

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

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

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

[0037] S3: Generate candidate symbol function:

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

[0039] S5: The best function is retained according to the error function. When the predicted energy of the obtained symbolic equation reaches the required accuracy, the simplest equation is output to obtain the liquid bridge force model.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The present invention discloses a method for predicting the fluidization behavior of wet particles in a fluidized bed based on DNS and symbolic regression. The method adopts the DNS method to study the liquid bridge dynamics behavior between non-spherical wet particles at the particle scale and establish a database, and combines the symbolic regression algorithm to obtain a model suitable for describing the liquid bridge dynamics behavior of high liquid content, large contact angle and non-spherical particles. The model is further substituted into an unresolved CFD-DEM model for predicting the fluidization behavior of wet particles in a fluidized bed. The method does not require complex sampling and analysis of the actual operating fluidized bed, which greatly saves manpower, physical and time costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0043] Figure 1 It is a schematic flow chart of a method for numerically predicting the behavior of wet particles in a fluidized bed according to the present invention. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely explain the technical solutions in the embodiments of the present invention. It should be noted that the embodiments of the present invention 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 invention, not all of the embodiments.

[0045] Specific implementation method 1: See Figure 1 To illustrate the present embodiment, a method for numerically predicting the behavior of wet particles in a fluidized bed is described.

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

[0047] Step 2: At the particle scale, different working conditions are set up for simulation based on the CFD-DEM model to explore the formation and evolution of liquid bridge forces and their influence on particle movement, obtain the dynamic characteristics and interaction data of wet particle liquid bridges, and establish a database;

[0048] Step 3: Based on the symbolic regression technology, a liquid bridge force model for describing high liquid content, large contact angle and non-spherical particles is extracted and established from the database. A genetic algorithm is used to collect specific function forms and optimal parameter values ​​from the database to derive a 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 unresolved CFD-DEM model to predict the fluidization behavior of wet particles in the fluidized bed.

[0050] Furthermore, in step 2, DNS direct numerical simulation is performed to obtain the dynamic characteristics and interaction data of the liquid bridge between wet particles.

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

[0052] The DNS method is a direct numerical simulation method used to solve the Navier-Stokes equations in fluid dynamics to fully resolve all scales of turbulence. The DNS method can provide detailed information on fluid flow, including velocity, pressure, and temperature, and plays an irreplaceable role in understanding and studying the physical mechanisms of turbulence. It can fully resolve fluid motion at all scales, from the largest vortex to the smallest turbulent scale. It can significantly reduce computational costs while providing sufficient accuracy.

[0053] The fully analytical non-spherical wet particle CFD-DEM model can fully analyze all the movements and interactions of particles, including the shape of particles, movement trajectory, and interaction with fluids. 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 of the fluid on each particle (such as drag, lift, etc.), as well as the influence of particles on the fluid. In the fully analytical model, the shape of non-spherical particles can be accurately represented by complex geometric descriptions, rather than being simplified to spheres or other regular shapes. This allows the model to more accurately capture the influence of particle shape on flow and interaction.

[0054] Specific implementation method 2: Based on specific implementation method 1, this embodiment gives the initial conditions that the particle diameter is 1.0 mm in axial length, the liquid volume between the particles is cylindrical, and the volume is 0.144 mm3. The Monte Carlo method is applied, the calculation area is 8a×2.7a×1.5a, the liquid density is 1000 kg / m3, the liquid viscosity is 0.01 Pa·s, the gas viscosity is 1.8×10-5 Pa·s, the gas density is 1.2 kg / m3, and the surface tension coefficient is 0.07 N / m. Implementation method 1 is used to predict the fluidization behavior of wet particles in the fluidized bed.

[0055] First, the particle geometry is modeled and the superellipse model is used to describe the particles. The standard equation is:

[0056]

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

[0058]

[0059]

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

[0061] s=qs0q -1 (7)

[0062]

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

[0064]

[0065] where F C is the contact force between particles, F VPis the fluid / particle interaction force, F CAP is the capillary force on the particle, F G is the gravity on the particle, and the particle rotation equation is as follows:

[0066]

[0067] Among them, I i is the particle moment of inertia in the local coordinate system, ω i is the particle rotation speed in the local coordinate system, M Cij is the contact torque on the particle, M VPi is the fluid-solid interaction torque on the particle, M CAPi The capillary torque on the particle.

[0068] The fluid volume method is used to describe the gas-liquid two-phase behavior:

[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 gravity acceleration, t time, f VP is the fluid / particle interaction force;

[0071] The expression of viscous stress tensor is:

[0072]

[0073] where μ is the dynamic viscosity of the fluid and T is the transpose operation.

[0074] The fluid forces and moments on the particles are obtained by performing surface integration around the particles, which is converted to volume integrals using the following divergence theorem:

[0075]

[0076] The surface tension line integral of the three-phase contact line is equivalent to the surface integral of the surface tension of the immersed free surface, and converted into volume integral using Gaussian divergence theorem. The solution formula is as follows:

[0077]

[0078] At the particle scale, different working conditions are set up for simulation based on the fully analytical model to explore the formation, evolution, fracture of liquid bridge forces and their influence on particle movement. Through direct numerical simulation, the dynamic characteristics and interaction data of liquid bridges between wet particles are obtained, and a database is established.

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

[0080] S1: Clean, screen, filter and normalize the data in the database to obtain the characteristics of non-spherical liquid bridge force;

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

[0082] S3: Generate candidate symbolic functions;

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

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

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

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

Claims

1. A method for numerically predicting the behavior of wet particles in a fluidized bed, characterized in that: It includes the following steps: Step 1: Establish a fully analytical non-spherical wet particle CFD-DEM model to model the particle shape, size and liquid properties; Step 2: At the particle scale, different working conditions are set up for simulation based on the CFD-DEM model to explore the formation and evolution of liquid bridge forces and their influence on particle movement, obtain the dynamic characteristics and interaction data of wet particle liquid bridges, and establish a database; Step 3: Based on the symbolic regression technology, a liquid bridge force model for describing liquid content, contact angle and non-spherical particles is extracted and established from the database. A genetic algorithm is used to collect specific function forms and parameter values ​​from the database to deduce the liquid bridge force model of liquid content, contact angle and non-spherical particles; Step 4: Substitute the obtained liquid bridge force model of non-spherical particles into the unresolved CFD-DEM model to predict the fluidization behavior of wet particles in the fluidized bed.

2. The method for numerically predicting the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: In step 1, the particle geometry modeling uses a superellipse model to describe the particles, and its standard equation is: Where a, b, and c are the semi-axis lengths of the particle in the direction of the main axis, respectively. n1 and n2 are shape indices used to control the sharpness of the particle edge. The larger the shape index, the gradient of the shape function is: The quaternion method is used to process the variables related to particle rotation, and the equation is as follows: s=qs0q -1 (7) 3. The method for numerically predicting the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: The translational and rotational behavior of the particles in step 1 is described by Newton's second law: Among them, 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, F G is the gravity on the particle, and the particle rotation equation is as follows: Among them, I i is the particle moment of inertia in the local coordinate system, ω i is the particle rotation speed in the local coordinate system, M Cij is the contact torque on the particle, M VPi is the fluid-solid interaction torque on the particle, M CAPi The capillary torque on the particle.

4. The method for numerically predicting the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: In step 1, the fluid volume method is used to describe the gas-liquid two-phase behavior: 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 gravity acceleration, t time, f VP is the fluid / particle interaction force; The expression of viscous stress tensor is: where μ is the dynamic viscosity of the fluid and T is the transpose operation.

5. The method for numerically predicting the behavior of wet particles in a fluidized bed according to claim 1, characterized in that: The fluid forces and moments on the particles in step 1 are obtained by performing surface integration around the particles, and the surface integrals are converted to volume integrals using the following divergence theorem: The surface tension line integral of the three-phase contact line is equivalent to the surface integral of the surface tension of the immersed free surface, and converted into volume integral using Gaussian divergence theorem. The solution formula is as follows:

6. The method for numerically predicting 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 the liquid bridge between wet particles are obtained through direct numerical simulation.

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

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