Numerical simulation method of gas-solid two-phase flow with two-way coupling between non-spherical particles and flow field

Abstract

The application discloses a kind of non-spherical particle and flow field two-way coupling gas-solid two-phase flow numerical simulation method, belong to biomass fuel utilization technical field, including the following processes: constructing flow field model in Fluent and corresponding setting initial boundary condition of flow field;Non-spherical particle initialization condition is set in UDF;Inertial coordinate system and particle coordinate system are established, and the coupling of two coordinate systems is carried out;Translation motion table / rotary motion representation equation is obtained, and the position and direction of particle are determined by solving two equations, to correct flow field parameters and iteratively calculate particle motion parameters, realize the two-way coupling of non-spherical particle and flow field.The numerical simulation method in the application can accurately simulate the interaction between non-spherical particle and flow field through Fluent-UDF numerical simulation, ensure the accuracy of gas-solid two-phase flow numerical simulation, deepen the understanding of the complex process of direct combustion coupling biomass particle in coal-fired boiler, and provide theoretical support for optimizing burner design and combustion process.

Description

Technical Field

[0001] This invention belongs to the field of biomass fuel utilization technology, specifically relating to a numerical simulation method for gas-solid two-phase flow with bidirectional coupling of non-spherical particles and flow field. Background Technology

[0002] Blending biomass in coal-fired boilers is an effective way to reduce carbon emissions and recycle biomass solid waste, and it has been increasingly studied and applied. However, because biomass particles typically have a large particle size and exhibit irregular, non-spherical geometric characteristics, their kinetic characteristics in the gas-solid two-phase flow of coal-fired boilers differ significantly from those of conventional spherical pulverized coal fuel particles, making it difficult to accurately predict and simulate their kinetic behavior in gas-solid two-phase flow.

[0003] Compared to spherical particles, non-spherical particles have more complex gas-solid two-phase flow dynamics, especially in suspension combustion technology. Their asymmetric shape and the drag, lift, and torque generated by rotational effects can significantly affect their motion trajectory during combustion.

[0004] Currently, the dynamic behavior of particles in a flow field can be simulated using CFD (Computational Fluid Dynamics) modeling methods. It is usually done in conjunction with the commercial numerical software Fluent, which has advantages such as efficient numerical model setting, free user-defined model setting, good model prediction performance and fast result display, and is widely used in various numerical simulation scenarios.

[0005] However, existing numerical simulation methods are generally applicable to the simulation of spherical particles, and modeling non-spherical particles still presents some limitations and challenges. For example, Fluent's Discrete Phase Model (DPM) defaults to treating particles as spherical, which excessively simplifies the calculation and influence of forces such as drag, lift, and torque. Since the gas-solid phase flow behavior of non-spherical particles (such as biomass particles with an average equivalent diameter on the order of 2-3 mm) is more complex, this can lead to deviations in the simulated particle trajectory and residence time results. Furthermore, for real biomass particles, traditional drag models used in DPM (such as the Stokes drag model) cannot accurately describe their dynamic behavior. This is mainly because the drag coefficient, lift coefficient, and torque coefficient of non-spherical particles are not only related to the Reynolds number but also affected by shape parameters (such as aspect ratio) and orientation angles, which are not fully reflected in the existing default Fluent model. Therefore, existing numerical simulation methods are difficult to directly apply to the simulation of the dynamic behavior of non-spherical particles. Furthermore, in existing numerical simulation studies of biomass co-firing in coal-fired boilers, most studies use simplified particle dynamics models. In particular, the particle shape is usually assumed to be spherical, ignoring the rotational effect of the particles, which leads to a large deviation between the simulation results and the actual situation. Summary of the Invention

[0006] To address one or more of the above-mentioned deficiencies or improvement needs of existing technologies, this invention provides a numerical simulation method for gas-solid two-phase flow with bidirectional coupling between non-spherical particles and flow field. This method can effectively simulate the dynamic state of non-spherical particles in gas-solid two-phase flow, accurately capture the complex behavior of non-spherical particles, fully consider the rotational effect of non-spherical particles in the flow field, and significantly improve the accuracy of numerical simulation of non-spherical particles.

[0007] To achieve the above objectives, this invention provides a numerical simulation method for gas-solid two-phase flow involving bidirectional coupling of non-spherical particles and the flow field, comprising the following steps:

[0008] (1) Set the flow field model and initial boundary conditions, and solve the Navier-Stokes equations;

[0009] (2) Set the initialization conditions for non-spherical particles and determine the physical parameters and initial motion parameters of the particles;

[0010] (3) Establish an inertial coordinate system for the flow field and a particle coordinate system for the non-spherical particles, and couple the two coordinate systems to obtain Euler angles. ;

[0011] (4) Establish the translation equations controlling the motion of non-spherical particles, treating the non-spherical particles as discrete phases, and obtain the following translation characterization equations:

[0012]

[0013] In the formula, , , , These represent the undisturbed velocity, mass, volume, and density of the particle, respectively. , , , , These are the drag force, lift force, virtual mass force, pressure gradient force, and gravity acting on the particle, respectively. The drag force and lift force are determined by the particle's orientation angle. θ Decide;

[0014] (5) Establish the rotational equations for controlling the motion of non-spherical particles, and obtain the rotational motion characterization equations considering the triaxial torque of the non-spherical particles:

[0015]

[0016] In the formula, , and These represent the components of the particle's angular velocity, moment of inertia, and torque along the three axial directions; and for cylindrical particles, , ;

[0017] (6) Solve the translation and rotation characterization equations, iteratively calculate the motion parameters of the flow field and non-spherical particles respectively, and update the position and orientation of the non-spherical particles;

[0018] (7) Feed the particle motion parameters obtained by iterative calculation into the flow field model, and correct the flow field simulation calculation based on the particle motion parameters of non-spherical particles; thereafter, iteratively perform the simulation calculation of the non-spherical particle motion process based on the corrected flow field parameters.

[0019] (8) Repeat the calculation process in (3) to (7) until the particle reaches the outlet boundary and the calculation converges.

[0020] As a further improvement of the present invention, when coupling the two coordinate systems in process (3), a quaternion is introduced to describe the direction in the particle coordinate system, that is... And through an orthogonal transformation matrix A From the inertial coordinate system , The particle coordinate system is obtained in the middle and ;

[0021]

[0022]

[0023]

[0024] In the formula, , These are the particle angular velocities in the inertial coordinate system and the particle coordinate system, respectively. , The torque is given in both the inertial coordinate system and the particle coordinate system.

[0025] As a further improvement of the present invention, the quaternion is expressed through Euler angles. The calculations are performed to obtain the following equation; and the quaternion is continuously updated over time and normalized at each time point, i.e. ;

[0026]

[0027] .

[0028] As a further improvement of the present invention, in the translation characterization equation, the forces acting on the non-spherical particles are calculated by the following formula:

[0029]

[0030]

[0031]

[0032]

[0033] In the formula, Let be the projected area perpendicular to the direction of motion during the particle's fall, and ; , These are the undisturbed velocity and density of the airflow / fluid, respectively. This is the acceleration due to gravity of the particle; , and These represent the drag coefficient, lift coefficient, and torque coefficient of the particle at the corresponding angle.

[0034] As a further improvement of the present invention, corresponding to the drag coefficient Lift coefficient and torque coefficient The calculation, performed using the open-source software OpenFOAM, satisfies the following condition: 0.1 ≤ length-to-diameter ratio. Ar ≤0.9, 0°≤direction angle θ ≤90°, 1≤Reynolds number ReCylindrical particles ≤2000 were subjected to direct numerical simulation under a body-fitted mesh to obtain OpenFOAM simulation values.

[0035] As a further improvement of the present invention, the drag coefficient The calculation is performed using the following formula:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] In the formula, The particle angle in the flow field is The drag coefficient at that time; This is the drag coefficient when the particle angle in the flow field is 0° or 90°; ( i =2,3,4,5) are the fitting coefficients, and correlation fitting coefficients are introduced. The calculated correlation coefficients are... Numerical selection was performed using OpenFOAM simulation.

[0043] As a further improvement of the present invention, the lift coefficient The calculation is performed using the following formula:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] In the formula, The particle angle in the flow field is The lift coefficient at that time; The parameters were calculated using the corresponding formulas and numerical simulations, respectively, to define the parameters. These are parameters used in numerical simulation, and they are selected through OpenFOAM simulation.

[0053] As a further improvement of the present invention, in process (5), the torque components in each direction of the particle rotational motion are... The calculation is performed using the following formula:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] In the formula, These are the rate of change of stress at the particle location, the fluid angular velocity, and the diagonal drag tensor relative to the particle angular velocity and strain rate, respectively. The particle angle in the flow field is The torque coefficient at that time.

[0061] As a further improvement of the present invention, the torque coefficient The calculation is performed using the following formula:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] In the formula, These are defined parameters, which are then calculated using corresponding formulas and numerical simulations. These are parameters used in numerical simulation, and they are selected through OpenFOAM simulation.

[0070] As a further improvement of the present invention, the motion process of the continuous phase gas flow field is continuously run in the Fluent module, and the motion process of the non-spherical particles is continuously iterated in the UDF module. The initial gas field conditions required for the motion of the non-spherical particles are provided to the UDF module by the Fluent module. After multiple iterations of calculation, the particle motion in the UDF module is transferred from the UDF module to the Fluent module to correct the running parameters of the airflow field. The corrected airflow field parameters are then transferred to the UDF module as the initial conditions for the gas field in the next round of iterative calculation.

[0071] The aforementioned improved technical features can be combined with each other as long as they do not conflict with each other.

[0072] In summary, the beneficial effects of the above-described technical solutions conceived by this invention compared with the prior art include:

[0073] (1) The numerical simulation method for gas-solid two-phase flow with bidirectional coupling of non-spherical particles and flow field of the present invention includes the following process: constructing a flow field model in Fluent and setting the initial boundary conditions of the flow field accordingly; setting the initialization conditions of non-spherical particles in UDF; establishing an inertial coordinate system and a particle coordinate system and coupling the two coordinate systems; obtaining the translational motion characterization equation and the rotational motion characterization equation, and determining the position and direction of the particles by solving the two equations, and then correcting the flow field parameters and iteratively calculating the particle motion parameters by coupling the motion parameters of the particles with the flow field model, realizing the bidirectional coupling of non-spherical particles and flow field, improving the accuracy of the simulation of the motion process of non-spherical particles in the flow field, providing a basis for the real feedback of the motion process of non-spherical particles in the gas field, and also providing theoretical support for the application of non-spherical biomass particles.

[0074] (2) The gas-solid two-phase flow numerical simulation method of bidirectional coupling between non-spherical particles and flow field in this invention, by optimizing the conversion method of the two coordinate systems and the calculation method of the forces on the non-spherical particles, combined with the OpenFOAM direct numerical simulation, fully ensures the calculation of the drag coefficient, lift coefficient, torque coefficient and corresponding forces on the non-spherical particles, and fully considers the coupling of translational motion and rotational motion of non-spherical particles in the air field, so that the simulation calculation of the motion process of non-spherical particles is closer to the actual situation, and improves the accuracy and reliability of the simulation calculation results.

[0075] (3) The numerical simulation method for gas-solid two-phase flow with bidirectional coupling of non-spherical particles and flow field in this invention can accurately simulate the interaction between non-spherical particles and flow field through Fluent-UDF numerical simulation. It can not only handle the translational and rotational motion of non-spherical particles, but also fully consider the interaction between gas and solid phases. It has significant advantages, especially in handling large particle size and irregular shape of biomass particles. It can effectively deepen the understanding of the complex process of direct combustion coupled non-spherical biomass particles in coal-fired boilers and provide theoretical support for optimizing burner design and combustion process. Attached Figure Description

[0076] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0077] Figure 1 This is a flowchart illustrating the operational logic of the numerical simulation method for gas-solid two-phase flow with bidirectional coupling between non-spherical particles and the flow field in this embodiment of the invention.

[0078] Figures 2-3 This is a schematic diagram of the inertial coordinate system and particle coordinate system constructed for non-spherical particles in the numerical simulation method of this invention embodiment;

[0079] Figure 4 This is a schematic diagram of the motion trajectory of non-spherical particles under different models in specific embodiments of the present invention;

[0080] Figure 5 This is a schematic diagram comparing the drag coefficient and particle velocity under different models in a specific embodiment of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0082] In the description of this invention, it should be understood that, unless otherwise expressly specified and limited, the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," etc., indicating the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0083] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0084] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0085] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0086] Specifically, in a preferred embodiment of the present invention, a numerical simulation method for gas-solid two-phase flow with bidirectional coupling between non-spherical particles and the flow field is provided. By considering the coupling effects of various forces such as drag, lift, torque, virtual mass, and pressure gradient force of non-spherical particles in the gas-solid two-phase flow, it aims to achieve bidirectional coupling calculation between non-spherical particles and fluid. While considering the effect of the flow field on the particles, it also fully considers the influence of particle motion on the flow field, solves the translational and rotational coupling problem of non-spherical particles, accurately simulates the motion process of non-spherical particles, and improves the accuracy of the simulation.

[0087] Please see Figure 1 In a preferred embodiment, the numerical simulation method for gas-solid two-phase flow with bidirectional coupling of non-spherical particles and flow field includes the following process:

[0088] (1) Set the flow field model and initial boundary conditions, and solve the Navier-Stokes equations.

[0089] In practice, the gas phase flow field is initialized using the commercial numerical software Fluent, and the fluid velocity is set. Pressure, temperature, and other important parameters.

[0090] Meanwhile, the solution to the Navier-Stokes equations can be performed using the standard method described in any computational fluid dynamics code. This is a relatively mature existing technology and will not be elaborated upon here.

[0091] (2) Set the initialization conditions for non-spherical particles and determine the physical parameters and initial motion parameters of the particles;

[0092] In practical settings, it is preferable to determine the particle initialization conditions and related parameters in a UDF (User Defined Function), and the determined parameters preferably include the number of non-spherical particles, initial position, and initial velocity. Shape parameters (length of the major axis of the particle) b and bottom diameter a ), length-to-diameter ratio The angle between the fluid direction and the long axis of the particle equivalent diameter and initial conditions of motion (mass flow rate).

[0093] In a preferred embodiment, the non-spherical particles are preferably cylindrical biomass particles.

[0094] (3) Establish an inertial coordinate system for the flow field, and establish a particle coordinate system for non-spherical particles in the flow field;

[0095] In a preferred embodiment, the motion of non-spherical particles in the flow field is a coupling of translational and rotational motions, which are described using different coordinate systems. Translational motion can be viewed as a motion process relative to the global coordinate system of the flow field, while rotational motion can be viewed as a motion process relative to the particle's own coordinate system.

[0096] In a preferred embodiment, to characterize the translational motion of the particles, a global coordinate system is established for the flow field, i.e., as follows: Figure 2 The inertial coordinate system shown .

[0097] At the same time, a particle coordinate system is established for the particles. At this point, it is preferable to use the central axis of the particle as the Z' axis, and the two mutually perpendicular radial axes as the X' and Y' axes, such as... Figure 2 As shown in the image.

[0098] Euler angles are obtained by coupling the inertial coordinate system and the particle coordinate system. ,like Figure 3 As shown in the image.

[0099] Furthermore, in a preferred embodiment, quaternions are introduced to describe the orientation in the particle coordinate system, i.e. Through an orthogonal transformation matrix A From the inertial coordinate system , The particle coordinate system is obtained in the middle and This ensures that singularities are avoided when determining the rate of change of Euler angles, and that the elements of the transformation matrix represent the direction cosines of the particle axes in the inertial coordinate system. Specifically:

[0100]

[0101]

[0102]

[0103] In the formula, , These are the particle angular velocities in the inertial coordinate system and the particle coordinate system, respectively. , The torque is given in both the inertial coordinate system and the particle coordinate system.

[0104] Furthermore, in the preferred embodiment, the quaternion is represented by Euler angles. The calculations are performed and updated continuously over time. In practice, quaternions need to be normalized at each time point, i.e. This is to prevent the accumulation of numerical errors. Specifically,

[0105]

[0106]

[0107] In the formula, These represent the particle angular velocities along the three particle axes in the particle coordinate system.

[0108] (4) Establish the translational equations for the motion control of non-spherical particles. Treat the non-spherical particles as discrete phases and solve the particle motion control equations based on Euler's equations and Newton's second law:

[0109]

[0110] In the formula, , , , These represent the undisturbed velocity, mass, volume, and density of the particle, respectively. , , , , These are the drag force, lift force, virtual mass force, pressure gradient force, and gravity acting on the particle, respectively. The drag force and lift force are determined by the particle's orientation angle. θ Decide.

[0111] In practice, the particle motion control equations are written using UDFs (user-defined functions), and all particles in the model's computational domain are tracked in the Lagrange coordinate system. By fully considering the drag force, lift force, virtual mass force, pressure gradient force, and gravity exerted on the particles by the fluid, the force state of non-spherical particles in the flow field is characterized, and the calculation is performed in conjunction with the local velocities and orientations of the fluid and particles.

[0112] Preferably, in this model, the effects of thermophoretic force, Brownian force, and Magnus rotational lifting force and Saffman shear lifting force due to rotation relative to the long axis of the particle on the non-spherical particles (biomass particles) of the gas-solid flow under co-firing in a coal-fired boiler are relatively small and therefore neglected in the motion control equation.

[0113] Furthermore, in the above-mentioned particle motion control equations, the forces acting on the particles are preferably calculated using the following formulas:

[0114]

[0115]

[0116]

[0117]

[0118] In the formula, Let be the projected area perpendicular to the direction of motion during the particle's fall, and ; , These are the undisturbed velocity and density of the airflow / fluid, respectively. This is the acceleration due to gravity of the particle; , and These represent the drag coefficient, lift coefficient, and torque coefficient of the particle at the corresponding angle.

[0119] Furthermore, in a preferred embodiment, the open-source software OpenFOAM is preferably used to satisfy the following condition: 0.1 ≤ aspect ratio. Ar ≤0.9, 0°≤direction angle θ ≤90°, 1≤Reynolds number Re Cylindrical particles ≤2000 were subjected to direct numerical simulation (DNS) on a body-fitted mesh. OpenFOAM simulation values ​​were obtained and drag coefficients were fitted. Lift coefficient and torque coefficient The calculation formula.

[0120] Specifically, the drag coefficient in the preferred embodiment The calculation is performed using the following formula:

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127] In the formula, The particle angle in the flow field is The drag coefficient at that time; This is the drag coefficient when the particle angle in the flow field is 0° or 90°; ( i =2,3,4,5) are the fitting coefficients, and correlation fitting coefficients are introduced. The calculated correlation coefficients are... The numerical values ​​selected through OpenFOAM simulation are shown in Table 1 below. It should be noted that the data in Table 1 were obtained after the aforementioned numerical simulation of DNS, and the drag coefficient... The calculation uses known quantities that can be directly selected.

[0128] Table 1 C D The correlation coefficients used

[0129]

[0130] Furthermore, the lift coefficient in the preferred embodiment The calculation is performed using the following formula:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] In the formula, The particle angle in the flow field is The lift coefficient at that time; The parameters were calculated using the corresponding formulas and numerical simulations, respectively, to define the parameters. These are numerical simulation parameters, selected through OpenFOAM numerical simulation, and the selected values ​​are shown in Table 2 below;

[0140] Table 2 C L The correlation coefficients used

[0141]

[0142] By calculating the drag coefficient and lift coefficient of particles at different angles, the drag and lift forces acting on non-spherical particles can be determined. Furthermore, by transforming the translation equation controlling the motion of non-spherical particles, the following translational motion characterization equation can be obtained:

[0143]

[0144] By calculating and selecting the parameters in the translation characterization equation, the translation state of non-spherical particles at different time points can be fed back in real time.

[0145] (5) Establish the rotation equation for controlling the motion of non-spherical particles, and obtain the rotational motion characterization equation considering the triaxial torque of non-spherical particles;

[0146] The rotational motion of non-spherical particles can be viewed as the process in which the fluid exerts torques on the particle particles in the three axis directions of the particle coordinate system, causing the particles to rotate around the principal axis of the particles at an angular velocity; that is, considering the pitching torque of the non-spherical particles in the airflow field caused by aerodynamics, the flow resistance torque caused by the relative rotation between the particles and the local fluid flow around the particles, and the torque caused purely by flow separation damping.

[0147]

[0148] In the formula, , and The components representing the particle's angular velocity, moment of inertia, and torque along the three axial directions are: For cylindrical particles, the moment of inertia is further preferably expressed as: , .

[0149] Spherical particles, due to their uniform orientation, typically have their rotational motion neglected in the Lagrange DPM model. However, for non-spherical particles, when... When the torque is applied, its importance cannot be ignored. Therefore, in the preferred embodiment, the pitching torque of the non-spherical particle caused by aerodynamics in the airflow field, the flow resistance torque caused by the relative rotation between the particle and the local fluid flow around the particle, and the torque caused purely by flow separation damping are considered respectively.

[0150] Furthermore, for the torque components in each direction during the particle's rotational motion... The calculation is preferably performed using the following formula:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] In the formula, These are the rate of change of stress at the particle location, the fluid angular velocity, and the diagonal drag tensor relative to the particle angular velocity and strain rate, respectively. The particle angle in the flow field is The torque coefficient at that time is calculated using the following formula:

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165] In the formula, These are defined parameters, which are then calculated using corresponding formulas and numerical simulations. These are numerical simulation parameters, selected through OpenFOAM numerical simulation, and the selected values ​​are shown in Table 3 below;

[0166] Table 3 C T The correlation coefficients used

[0167]

[0168] By setting the above formula and selecting the parameters, the rotational equation for controlling the motion of non-spherical particles in the preferred embodiment can be deformed to obtain the following rotational motion characterization equation:

[0169]

[0170] (6) Solve the translation and rotation characterization equations, iteratively calculate the motion parameters of the flow field and non-spherical particles respectively, and update the position and orientation of the non-spherical particles;

[0171] Based on the acquisition and calculation of the translational motion characterization equation and the rotational motion characterization equation, the translational motion and rotational motion of non-spherical particles are characterized respectively. By coupling the translational motion and rotational motion of non-spherical particles, the trajectory of non-spherical particles in the airflow field can be accurately characterized, and the position and orientation of the particles can be updated in real time.

[0172] (7) Couple the motion process of particles with the motion process of fluid, feed back the particle motion parameters obtained by iterative calculation in UDF model to the fluid operation in Fluent, consider the feedback effect of particles on the flow field, and correct the simulation calculation of the flow field in real time based on the influence of non-spherical particle motion on the flow field; thereafter, iteratively perform simulation calculation of non-spherical particle motion process based on the corrected flow field parameters.

[0173] (8) Repeat the calculation process in (3) to (7) until the particle reaches the outlet boundary and the calculation converges.

[0174] For the simulation method in the preferred embodiment, compared with the existing CFD-DPM model simulation, it not only considers the effect of the flow field on the particles, but also fully considers the feedback effect of the particles on the flow field, realizing the transformation from unidirectional coupling to bidirectional coupling. Simultaneously, when calculating the motion of non-spherical particles in the flow field, it can not only accurately handle the translational motion of non-spherical particles, but also solve the coupling problem of their rotational motion. By introducing the calculation of lift, pressure gradient force, virtual mass force, etc., into the equation of motion, and considering the complex mechanical effects generated by the rotation of particles in the fluid (such as torque changes), it fully ensures the coupling of translational and rotational motions during the motion of non-spherical particles, thereby achieving a more accurate flow simulation of non-spherical particles.

[0175] Clearly, the "two-way coupling" simulation method in the preferred embodiment not only makes the simulation results more accurate in the particle motion trajectory, but also improves the simulation accuracy of the fluid field, especially for simulation in application scenarios with high particle density, fully meeting the simulation requirements of motion processes under complex motion of non-spherical particles.

[0176] During the actual execution of the simulation model, the model for fluid motion and the model for particle motion run separately but are interconnected. Their execution process is as follows: Figure 1 As shown in the image.

[0177] The process involves continuously running the motion of the continuous phase gas flow field in the Fluent module and continuously iterating the motion of the non-spherical particles in the UDF module. The initial gas field conditions required for the motion of the non-spherical particles are provided to the UDF module by the Fluent module. After multiple iterations of the particle motion calculation in the UDF module (e.g., after every 20 iterations), the UDF module transmits the position and orientation data of the particles to the Fluent module to correct the operating parameters of the airflow field. The corrected airflow field parameters are then transmitted back to the UDF module as the initial conditions for the airflow field in the next round of iterative calculation. This process is repeated until the particles move to the outlet boundary and the entire simulation calculation converges.

[0178] The operation process and effects of the aforementioned simulation calculation method will be further illustrated through the following specific embodiments:

[0179] In this embodiment, the simulation is based on the movement and combustion process of cylindrical biomass particles in a 660MW counterboiler of a power plant.

[0180] In the actual simulation, a 3D model of the opposed boiler was first created, and then meshed. In the preferred embodiment, the boiler body dimensions are 68.7 m × 37.402 m × 19.4192 m (height × width × depth). The burners are arranged in an opposed configuration with front and rear walls, with a total of 24 swirl burners arranged in three layers on the spiral water-cooled walls of the furnace, four burners on each of the front and rear walls. Except for the bottom layer on the rear wall, which contains four plasma pulverized coal burners, the remaining layers are all low-NOx burners. x Swirl pulverized coal burners; one layer of burnout air is arranged above the swirl pulverized coal burners on both the front and rear walls, with two side burnout air nozzles and four burnout air nozzles in each layer. To achieve the co-firing of straw biomass, the original coal-fired boiler is being modified by arranging two layers of swirl biomass burners on each of the left and right side walls of the boiler, with one burner in each layer, for a total of four biomass burners.

[0181] It should be noted that the modeling and mesh generation of the counter-pressure boiler can be accomplished using mature existing technologies, which are not the focus of this embodiment and will not be elaborated here.

[0182] Meanwhile, to better demonstrate the adaptability and effectiveness of the numerical simulation method in the preferred embodiment for calculating the dynamic characteristics of non-spherical particles, this specific embodiment simulates the movement and combustion process of cylindrical biomass particles in a coal-fired boiler. Pulverized coal is injected into the furnace from the pulverized coal burner nozzles on the front and rear walls of the opposed boiler, while biomass particles enter from the biomass burner nozzles on the left and right walls of the boiler, and their specific parameter settings are shown in Table 4.

[0183] Table 4 Calculation parameters in specific embodiments

[0184]

[0185] After completing the modeling, set up the mathematical model, boundary conditions, etc., and then perform iterative calculations.

[0186] First, cold-state calculations are performed using only the flow equations (continuity equation, momentum conservation equation) and turbulence equations to obtain a fully developed flow field. Then, other equations are selected for hot-state calculations, which yield the distribution characteristics of furnace temperature, combustion components, etc. The discrete terms for pulverized coal particles are set using a built-in model, while biomass pellets are simulated using a user-defined function (UDF). The specific method for coupled calculations is as follows:

[0187] (1) Numerical simulation of biomass pellets (non-spherical / long cylindrical pellets) in coal-fired boilers was carried out in FLUENT to obtain the flow field information of the entire furnace.

[0188] (2) Use UDF to read the flow field information data, including kinematic viscosity, flow field velocity, density, etc., and use this to calculate the trajectory of biomass particles;

[0189] Specifically, DEFINE_DPM_INIT (existing program code) is used to set the geometry of the cylindrical particles (e.g., length and bottom diameter are 1mm and 4mm respectively, aspect ratio is 0.25, and this particle shape parameter corresponds to the largest proportion of particles in the co-fired biomass particles), incident direction, velocity, particle size, and other initialization conditions. Further, DEFINE_DPM_DRAG and DEFINE_DPM_BODY_FORCE (existing program code) are used to calculate the particle's gravity, drag, lift, pressure gradient force, and virtual mass force, and to solve the motion control translation equation, completing the calculation of the translational motion characterization equation. Subsequently, DEFINE_DPM_SCALAR_UPDATE (existing program code) is used to describe the torque coefficient and the rotational motion caused by the fluid's viscous torque on the particles, and to update the discrete parameters of the entire particle.

[0190] (3) Feed the particle trajectory calculation results back to the FLUENT module to update the position and orientation of the particles, perform coupling iteration of the FLUENT gas continuous phase and the UDF biomass particle discrete term, and then update the information data of the flow field in the furnace. Repeat the operation until the numerical simulation of biomass co-firing in coal-fired boilers converges.

[0191] Furthermore, the simulation results of the Cylindrical aerodynamic model (CAM) in the specific embodiment are compared with the simulation results of the existing Spherical drag model (SDM) and Shape Factor Drag Model (SFDM) of DPM. The comparison results are as follows: Figure 4 As shown in the figure, (a) represents the simulation results under the SDM model; (b) represents the simulation results under the SFDM model; and (c) represents the simulation results under the CAM model.

[0192] according to Figure 4The results show significant differences in the simulation outcomes across the three models. Because factors such as drag, lift, and torque from rotational motion of large non-spherical particles were not incorporated, both the SFDM and SDM models, starting from the same position, show a large number of biomass particles falling into the cold ash hopper. This is particularly pronounced in the SDM model. This simulation result further affects the thermochemical conversion process of the particles and contradicts the actual situation in power plants where there is no significant change in the fly ash at the bottom of the furnace before and after biomass co-firing.

[0193] Furthermore, in Figure 5 In this study, aerodynamic characteristic parameters of the same biomass pellet under different models were compared, specifically the drag coefficient and velocity of the pellets at the nozzles of the upper and lower layers of biomass pellets. Figure 5 In the table, (a) compares the drag coefficients of particles at the upper biomass nozzle; (b) compares the velocities of particles at the upper biomass nozzle; (c) compares the drag coefficients of particles at the lower biomass nozzle; and (d) compares the velocities of particles at the lower biomass nozzle.

[0194] according to Figure 5 The comparison results show that by using the aerodynamic model (CAM) that accurately considers the shape of cylindrical particles, the drag coefficients of the upper and lower layers of biomass particles at the nozzles are increased by 22.18% and 20.91% respectively compared to the data under the shape factor drag model (SFDM).

[0195] Furthermore, the CAM model simultaneously considers the combined effects of non-spherical lift, virtual mass force, pressure gradient force, gravity, and torque, resulting in a significant increase in the average velocity of the lower layer biomass particles compared to the spherical model (SDM). This allows for a more accurate prediction of their complex motion states (since 70.84% ​​of the particles in the spherical model land on the cold ash hopper, these particles were selected for comparison). The reason for these results is primarily that the drag coefficient of the biomass particles calculated using the cylindrical particle aerodynamic model is consistently greater than that of the spherical drag coefficient model at any given moment. The combined effect of more forces increases the average particle velocity and reduces the residence time, leading to a significant difference in the biomass particle trajectory, which better reflects actual motion conditions.

[0196] In summary, the numerical simulation method in this specific embodiment can solve for the motion of particles during the gas-solid (air, pulverized coal, and biomass pellets) two-phase mixing process in a complex and chaotic furnace combustion environment. Based on the design of the numerical simulation method, the coupled effects of the translational and rotational motions of non-spherical particles are fully considered. Compared with the simulation calculation methods of conventional SDM and SFDM models, it can more accurately complete the simulation calculation of the dynamic parameters of non-spherical particles in the gas-solid two-phase flow, improve the accuracy of the numerical simulation of non-spherical particles, and provide a reliable basis and support for the subsequent design and operation optimization of the combustion system.

[0197] The numerical simulation method for gas-solid two-phase flow with bidirectional coupling of non-spherical particles and flow field in this invention, through Fluent-UDF numerical simulation, can accurately simulate the interaction between non-spherical particles and flow field. It can not only handle the translational and rotational motion of non-spherical particles, but also fully consider the interaction between gas and solid phases. It has significant advantages, especially in dealing with large particle size and irregular shape of biomass particles. It can effectively deepen the understanding of the complex process of direct combustion coupled with non-spherical biomass particles in coal-fired boilers, and provide theoretical support for optimizing burner design and combustion process.

[0198] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A numerical simulation method of gas-solid two-phase flow with two-way coupling between non-spherical particles and flow field, characterized in that, The process comprises the following steps: (1) setting a flow field model and initial boundary conditions, and solving N-S equations; (2) setting initial conditions of the non-spherical particles, determining the state parameters and initial motion parameters of the particles; (3) The inertial coordinate system is established for the flow field and the particle coordinate system is established for the non-spherical particles, and the coupling of the two coordinate systems is carried out to obtain Euler angles ; (4) establishing a motion control translation equation of the non-spherical particles, regarding the non-spherical particles as discrete phases, and obtaining the following translation motion representation equation: wherein, , , , represent the undisturbed velocity, mass, volume and density of the particle, respectively; , , , , are the drag force, lift force, virtual mass force, pressure gradient force and gravity acting on the particle, respectively, wherein the drag force and lift force are determined by the orientation angle In the translation representation equation, forces borne by the non-spherical particles are calculated by the following formula: of the particle; and Re wherein, is the projected area of the particle perpendicular to the direction of motion during the falling process, and ; , are the undisturbed velocity and density of the gas flow, respectively; is the gravitational acceleration of the particle; , and are the drag coefficient, lift coefficient and torque coefficient of the particle at the corresponding angle, respectively; the long axis length of the particle b , the bottom surface diameter a , the aspect ratio ; and the calculation of the corresponding drag coefficient , lift coefficient and torque coefficient is carried out by directly simulating the body-fitted grid of the cylindrical particles satisfying the following conditions: 0.1≤aspect ratio Ar ≤0.9, 0°≤direction angle (5) establishing a motion control rotation equation of the non-spherical particles, and obtaining a rotation motion representation equation by considering the three-axis torque of the non-spherical particles: ≤90°, 1≤Reynolds number (6) solving the translation representation equation and the rotation representation equation, respectively iteratively calculating the motion parameters of the flow field and the non-spherical particles, and updating the position and direction of the non-spherical particles; ≤2000, by using the open source software OpenFOAM to obtain the OpenFOAM simulation values. (7) feeding back the particle motion parameters obtained by the iterative calculation to the flow field model, correcting the simulation calculation of the flow field based on the particle motion parameters of the non-spherical particles; thereafter, based on the corrected flow field parameters, iteratively performing the simulation calculation of the motion process of the non-spherical particles; where , and represent the components of the particle angular velocity, moment of inertia and torque in the three axes of the particle; and for a cylindrical particle, , ; wherein the calculation of the torque component in each direction of the particle rotational motion is calculated by the following equation: wherein respectively, the rate of change of stress experienced by the particle in position, the fluid angular velocity, the relative particle angular velocity and the rate of strain, respectively; A is the orthogonal transformation matrix; is the torque coefficient when the particle angle in the flow field is is the torque coefficient when the particle angle in the flow field is (8) cyclically performing the calculation process in (3)-(7) until the particles reach the outlet boundary and the calculation converges. The motion process of the continuous phase gas flow field is continuously run in the Fluent module, and the motion process of the non-spherical particles is continuously iteratively run in the UDF module; the initial conditions of the gas field required in the motion process of the non-spherical particles are provided by the Fluent module to the UDF module, and after multiple iterative calculations of the particle motion in the UDF module, the position and direction data of the particles are transmitted from the UDF module to the Fluent module to correct the running parameters of the gas flow field, and the corrected gas flow field parameters are transmitted to the UDF module as the initial conditions of the gas field for a new round of iterative calculation. ​ 2. The numerical simulation method of gas-solid two-phase flow of non-spherical particles bidirectionally coupled with flow field according to claim 1, characterized in that, When coupling the two coordinate systems in process (3), a quaternion is introduced to describe the direction in the particle coordinate system, i.e. , and the particle coordinate system and are obtained from the inertial coordinate system , through an orthogonal transformation matrix A . wherein , are the angular velocities of the particles in the inertial and particle coordinate systems, respectively; , are the torques in the inertial and particle coordinate systems, respectively.

3. The numerical simulation method of gas-solid two-phase flow of non-spherical particles bidirectionally coupled with flow field according to claim 2, characterized in that, The quaternions are calculated by Euler angles and the following equation is obtained; and the quaternions are constantly updated over time and normalized at each time node, i.e. ; 。 4. The numerical simulation method of gas-solid two-phase flow of non-spherical particles bidirectionally coupled with flow field according to any one of claims 1-3, characterized in that, the drag coefficient is calculated by the following relation: wherein is the drag coefficient when the particle angle in the flow field is is the drag coefficient when the particle angle in the flow field is 0° or 90°; i are fitting coefficients, which are calculated by introducing the relevant fitting coefficients and the relevant fitting coefficients are selected by OpenFOAM simulation values.​​ 5. The numerical simulation method of gas-solid two-phase flow of non-spherical particles bidirectionally coupled with flow field according to claim 4, characterized in that, the lift coefficient is calculated by the following relation: wherein is the lift coefficient for a particle angle in the flow field; is a defined parameter, calculated by the corresponding formula and numerical simulation parameter, respectively; is a numerical simulation parameter, selected by OpenFOAM simulation value.

6. The numerical simulation method of gas-solid two-phase flow of non-spherical particles bidirectionally coupled with flow field according to claim 5, characterized in that, the torque coefficient The calculation is made by the following formula: In the formula, are respectively defined parameters, which are calculated by corresponding formula and numerical simulation parameter respectively; is a numerical simulation parameter, which is selected by OpenFOAM simulation value.

7. The numerical simulation method of gas-solid two-phase flow of non-spherical particles bidirectionally coupled with flow field according to any one of claims 1-3, characterized in that, ​

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