CN106021638A - Modelling method for bubbling fluidized bed based on random motion of bubbles and particles - Google Patents
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Abstract
本发明公开了一种基于气泡和颗粒随机运动的鼓泡流化床建模方法。该方法包括：(1)统计CFD‑DEM计算的鼓泡床颗粒运动规律，建立颗粒相的Markov链随机模型；(2)对CFD‑DEM计算的鼓泡床颗粒瞬时分布图进行图像识别，统计气泡的产生、运动及长大的规律，建立气泡随机发展模型；(3)利用气泡形状的棒球帽模型将颗粒相Markov过程与气泡随机模型耦合，建立鼓泡流化床颗粒运动的随机模型。本发明的方法，解决了单纯颗粒相Markov过程无法体现气泡信息和其对颗粒运动影响的缺点，在保证鼓泡床颗粒运动准确性的前提下，大幅度降低计算负荷，提高计算速度。
The invention discloses a modeling method of a bubbling fluidized bed based on the random movement of bubbles and particles. The method includes: (1) counting the movement law of the bubbling bed particles calculated by CFD-DEM, and establishing a Markov chain random model of the particle phase; (2) performing image recognition on the instantaneous distribution diagram of the bubbling bed particles calculated by CFD-DEM, and statistically The generation, movement and growth of bubbles are established to establish a random development model of bubbles; (3) The particle phase Markov process is coupled with the bubble random model by using the bubble-shaped baseball cap model to establish a stochastic model of particle motion in a bubbling fluidized bed. The method of the invention solves the disadvantage that the simple particle phase Markov process cannot reflect the bubble information and its influence on the particle movement, and greatly reduces the calculation load and improves the calculation speed under the premise of ensuring the accuracy of the particle movement in the bubbling bed.
Description
技术领域technical field
本发明涉及一种基于气泡和颗粒随机运动的鼓泡流化床建模方法，属于气固两相流动计算机数值模拟技术领域。The invention relates to a modeling method of a bubbling fluidized bed based on the random movement of bubbles and particles, and belongs to the technical field of computer numerical simulation of gas-solid two-phase flow.
背景技术Background technique
鼓泡流化床具有非常高的传热和传热速率，在化工、能源、食品及药品加工等领域有着广泛应用。对鼓泡流化床进行计算机数值模拟有助于系统的优化设计，能够大幅度降低试验成本。Bubbling fluidized beds have very high heat transfer and heat transfer rates, and are widely used in chemical, energy, food and pharmaceutical processing and other fields. The computer numerical simulation of the bubbling fluidized bed is helpful to the optimal design of the system and can greatly reduce the test cost.
传统的经验和半经验模型(例如平推流模型和鼓泡两相模型)计算效率高，模型响应速度快，但此类模型无法提供详细的颗粒和气泡运动规律，计算精度很低。目前流行的基于计算流体力学和颗粒动力学的数值模拟方法，因其基于求解基本的物理学公式，能够较为准确的计算出颗粒的运动规律，以及浓度分布等，特别是欧拉-拉格朗日方法考虑了气相和颗粒相的相互作用。其中，CFD-DEM模型还考虑了颗粒间的相互作用，使其能够更为准确的模拟气固两相流，但计算时间长和计算负荷高一直是这类模型进一步放大和应用于实际的瓶颈。而随机模型则是能够快速而准确模拟颗粒系统的一种潜在方法，尤其是基于CFD-DEM计算结果的Markov链随机模型具有模型简单、样本信息丰富、计算速度快的特点，已经在滚筒混合器这类纯颗粒系统中有了初步应用。鼓泡流化床气固两相之间的相互作用十分强烈，更存在气泡的出现对颗粒运动带来的影响，当使用和应用于纯颗粒系统相同的方法将Markov链随机模型应用于鼓泡流化床系统时，只能得到十分宏观的颗粒运动规律，无法模拟出床内复杂的气固两相流型。寻找合适的方法将鼓泡流化床中气泡对颗粒运动的影响与颗粒的Markov过程相耦合成为进一步发展鼓泡流化床随机模型的关键。Traditional empirical and semi-empirical models (such as plug flow model and bubbling two-phase model) have high calculation efficiency and fast model response, but such models cannot provide detailed particle and bubble motion laws, and the calculation accuracy is very low. Currently popular numerical simulation methods based on computational fluid dynamics and particle dynamics, because they are based on solving basic physical formulas, can more accurately calculate the movement laws of particles, as well as concentration distribution, etc., especially Euler-Lagrang The Japanese method takes into account the interaction of the gas phase and the particle phase. Among them, the CFD-DEM model also considers the interaction between particles, so that it can simulate the gas-solid two-phase flow more accurately, but the long calculation time and high calculation load have always been the bottlenecks for the further expansion and application of this type of model . The stochastic model is a potential method that can quickly and accurately simulate particle systems, especially the Markov chain stochastic model based on CFD-DEM calculation results has the characteristics of simple model, rich sample information, and fast calculation speed. This type of pure particle system has preliminary applications. The interaction between the gas-solid two phases in a bubbling fluidized bed is very strong, and the appearance of bubbles has an impact on the particle movement. When using the same method as applied to the pure particle system, the Markov chain stochastic model is applied to the bubbling In the case of a fluidized bed system, only very macroscopic particle motion laws can be obtained, and the complex gas-solid two-phase flow pattern in the bed cannot be simulated. Finding a suitable method to couple the effect of bubbles on particle motion in the bubbling fluidized bed with the particle Markov process becomes the key to further develop the stochastic model of the bubbling fluidized bed.
发明内容Contents of the invention
发明目的：为了克服现有技术中存在的不足，本发明提供一种基于气泡和颗粒随机运动的鼓泡流化床建模方法，该方法建立了气泡的随机发展模型，将气泡对颗粒运动的影响与颗粒的Markov过程耦合，建立鼓泡流化床颗粒运动随机模型。在保证低负荷、快速计算的同时，大大提高鼓泡流化床随机模型数值计算精度。Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a method for modeling a bubbling fluidized bed based on the random motion of bubbles and particles. The effect is coupled with the Markov process of particles, and a random model of particle motion in a bubbling fluidized bed is established. While ensuring low load and fast calculation, the numerical calculation accuracy of the stochastic model of the bubbling fluidized bed is greatly improved.
技术方案：为实现上述目的，本发明采用的技术方案为：Technical scheme: in order to achieve the above object, the technical scheme adopted in the present invention is:
一种基于气泡和颗粒随机运动的鼓泡流化床建模方法，包括以下步骤：A method for modeling a bubbling fluidized bed based on the random motion of bubbles and particles, comprising the following steps:
步骤1，将鼓泡流化床划分网格，统计前期CFD-DEM模型的模拟结果得到颗粒分布图。计算颗粒在网格间的转移概率，根据转移概率建立颗粒相的Markov链随机模型。通过Markov链随机模型得到颗粒位置信息。In step 1, the bubbling fluidized bed is divided into grids, and the simulation results of the previous CFD-DEM model are counted to obtain a particle distribution map. The transition probability of particles between grids is calculated, and the Markov chain stochastic model of particle phase is established according to the transition probability. The particle position information is obtained by the Markov chain stochastic model.
步骤2，对CFD-DEM模型模拟得到的颗粒分布图进行图像识别，统计气泡的产生、运动及长大的规律，建立气泡随机发展模型，根据气泡随机发展模型确定气泡相对位置。Step 2: Carry out image recognition on the particle distribution map simulated by the CFD-DEM model, count the generation, movement and growth of the bubbles, establish a random development model of the bubbles, and determine the relative positions of the bubbles according to the random development model of the bubbles.
步骤3，利用气泡形状的棒球帽模型将步骤1中的Markov链随机模型与步骤2中的气泡随机发展模型进行耦合，建立鼓泡流化床颗粒运动的随机模型。将步骤1)得到的颗粒位置信息和步骤2)确定的气泡相对位置代入鼓泡流化床颗粒运动的随机模型得到耦合气泡后颗粒的位置。In step 3, the Markov chain stochastic model in step 1 is coupled with the bubble stochastic development model in step 2 by using the bubble-shaped baseball cap model to establish a stochastic model of particle motion in the bubbling fluidized bed. Substitute the particle position information obtained in step 1) and the relative position of the bubbles determined in step 2) into the stochastic model of particle motion in the bubbling fluidized bed to obtain the position of the particles after coupling the bubbles.
优选的：所述步骤1中所述Markov链随机模型的建立方法，根据颗粒在网格间的转移概率构建颗粒运动的Markov链转移概率矩阵。通过转移概率矩阵计算得到颗粒网格信息，通过颗粒网格信息得到颗粒位置信息。Preferably: the establishment method of the Markov chain stochastic model described in step 1 is to construct a Markov chain transition probability matrix of particle movement according to the transition probability of particles between grids. The particle grid information is obtained through the calculation of the transition probability matrix, and the particle position information is obtained through the particle grid information.
优选的：所述步骤2中气泡随机发展模型的建立方法：分别统计不同高度下气泡质心水平位置及等效直径的概率分布，据此概率分布利用随机数来模拟鼓泡流化床中气泡的产生、运动及长大得到气泡随机发展模型。Preferably: the establishment method of the bubble random development model in the step 2: respectively count the probability distribution of the horizontal position of the bubble center of mass and the equivalent diameter under different heights, and use random numbers to simulate the bubble in the bubbling fluidized bed according to the probability distribution Generate, move and grow to get the random development model of bubbles.
优选的：所述步骤2得到气泡随机发展模型中的气泡总个数在床内保持不变，气泡总个数由CFD-DEM模型模拟的床内平均气泡数确定，当一个气泡质心上升超过床层平均高度时，一个新气泡即从床底部产生。气泡在发展过程中不断上升、长大。Preferably: the total number of bubbles in the random development model obtained in step 2 remains unchanged in the bed, and the total number of bubbles is determined by the average number of bubbles in the bed simulated by the CFD-DEM model. When a bubble centroid rises above the bed When the average height of the layer is reached, a new bubble is created from the bottom of the bed. Bubbles rise and grow continuously during the development process.
优选的：颗粒在网格内均匀随机分布。Preferably: the particles are uniformly and randomly distributed in the grid.
优选的：所述步骤3中气泡形状的棒球帽模型：气泡的主体是半径为rt圆C1被同等大小的圆C2截取后的剩余部分，包括三个部分，分别为第一区域I、第二区域II以及第三区域III，第三区域III为圆C2截取掉的部分，第二区域II为圆C2截取掉的部分中圆C2上的弧以及该弧的两端点分别与圆心C1连线所围成的区域，第一区域I为圆C1剩余的弧以及该弧的两端点分别与圆心C1连线所围成的区域。Preferably: the baseball cap model of the shape of the bubble in the step 3: the main body of the bubble is the remaining part after the circle C1 with a radius of r t is intercepted by the circle C2 of the same size, including three parts, which are respectively the first area I and the second area. The second area II and the third area III, the third area III is the part cut off by the circle C2, the second area II is the arc on the circle C2 in the part cut off by the circle C2 and the two ends of the arc are respectively connected with the center C1 The enclosed area, the first area I is the area enclosed by the remaining arc of the circle C1 and the lines connecting the two ends of the arc and the center C1 respectively.
优选的：耦合前处于三种区域的颗粒与气泡发生耦合作用，分别是气泡上部、气泡下部及气泡尾涡。Preferably: before the coupling, the particles in three regions are coupled with the bubbles, namely the upper part of the bubbles, the lower part of the bubbles and the wake of the bubbles.
优选的：采用Davison模型描述的气泡附近颗粒运动规律计算三种区域颗粒与气泡的耦合。Preferably: using the particle motion law described by the Davison model near the bubble to calculate the coupling between the particles and the bubble in the three regions.
有益效果：本发明提供的一种基于气泡和颗粒随机运动的鼓泡流化床建模方法，相比现有技术，具有以下有益效果：Beneficial effects: The present invention provides a bubbling fluidized bed modeling method based on the random motion of bubbles and particles, which has the following beneficial effects compared with the prior art:
本发明的基于气泡和颗粒随机运动的鼓泡流化床建模方法，通过统计鼓泡流化床的CFD-DEM模拟结果，获得颗粒和气泡的运动规律，首次建立了鼓泡流化床气泡的随机发展模型，并建立气泡形状的棒球帽模型，在颗粒的Markov随机过程中引入气泡对其运动的影响；本发明避免了求解复杂的计算流体力学和颗粒动力学方程，大幅度提高了计算效率，同时，气泡随机发展模型与颗粒Markov过程的耦合保证了鼓泡流化床随机模型的计算精度。The bubbling fluidized bed modeling method based on the random motion of bubbles and particles of the present invention obtains the movement law of particles and bubbles by counting the CFD-DEM simulation results of the bubbling fluidized bed, and establishes the bubble fluidized bed bubble model for the first time. The random development model of the bubble shape is established, and the impact of the bubble on its movement is introduced in the Markov random process of the particle; Efficiency, meanwhile, the coupling of the stochastic development model of the bubbles with the particle Markov process ensures the calculation accuracy of the stochastic model of the bubbling fluidized bed.
附图说明Description of drawings
图1是气泡形状的棒球帽模型和气泡与颗粒耦合算法示意图。Figure 1 is a schematic diagram of the bubble-shaped baseball cap model and the coupling algorithm between bubbles and particles.
图2是统计CFD-DEM计算结果得到的气泡产生概率分布图。Figure 2 is the probability distribution diagram of bubble generation obtained from statistical CFD-DEM calculation results.
图3是统计CFD-DEM计算结果得到的气泡质心位置分布图。Figure 3 is the position distribution diagram of the bubble centroid obtained from the statistical CFD-DEM calculation results.
图4是统计CFD-DEM计算结果得到的气泡直径沿床高分布图。Fig. 4 is a diagram of the distribution of bubble diameter along the bed height obtained from statistical CFD-DEM calculation results.
图5(a)是耦合气泡随机发展模型前鼓泡流化床颗粒随机运动效果图。Fig. 5(a) is the effect diagram of random movement of particles in a bubbling fluidized bed before coupling the random development model of bubbles.
图5(b)是耦合气泡随机发展模型后鼓泡流化床颗粒随机运动效果图。Figure 5(b) is the effect of random movement of particles in a bubbling fluidized bed after coupling the random development model of bubbles.
图6(a)是随机模型耦合气泡前后及CFD-DEM的颗粒径向混合曲线对比图。Figure 6(a) is a comparison of particle radial mixing curves before and after the random model coupling bubbles and CFD-DEM.
图6(b)是随机模型耦合气泡前后及CFD-DEM的颗粒轴向混合曲线对比图。Figure 6(b) is a comparison of particle axial mixing curves before and after the random model coupling bubbles and CFD-DEM.
具体实施方式detailed description
下面结合附图和具体实施例，进一步阐明本发明，应理解这些实例仅用于说明本发明而不用于限制本发明的范围，在阅读了本发明之后，本领域技术人员对本发明的各种等价形式的修改均落于本申请所附权利要求所限定的范围。Below in conjunction with accompanying drawing and specific embodiment, further illustrate the present invention, should be understood that these examples are only for illustrating the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various aspects of the present invention All modifications of the valence form fall within the scope defined by the appended claims of the present application.
一种基于气泡和颗粒随机运动的鼓泡流化床建模方法，包括以下步骤：A method for modeling a bubbling fluidized bed based on the random motion of bubbles and particles, comprising the following steps:
步骤1，将鼓泡流化床划分网格，统计前期CFD-DEM模型的模拟结果得到颗粒分布图。计算经过某一个时间步时，颗粒在网格间的转移概率，根据转移概率建立颗粒相的Markov链随机模型。通过Markov链随机模型得到颗粒位置信息。In step 1, the bubbling fluidized bed is divided into grids, and the simulation results of the previous CFD-DEM model are counted to obtain a particle distribution map. After a certain time step, the transition probability of the particles between the grids is calculated, and the Markov chain random model of the particle phase is established according to the transition probability. The particle position information is obtained by the Markov chain stochastic model.
所述步骤1中所述Markov链随机模型的建立方法：任意两个网格间的转移概率构成这个时间步长颗粒运动的Markov链转移概率矩阵，统计时间段内所有转移概率矩阵的平均值作为颗粒Markov过程最终的转移概率矩阵。通过转移概率矩阵计算得到颗粒网格信息，通过颗粒网格信息得到颗粒位置信息。颗粒在网格内均匀随机分布。The establishment method of the Markov chain stochastic model described in the step 1: the transition probability between any two grids constitutes the Markov chain transition probability matrix of this time step particle motion, and the average value of all transition probability matrices in the statistical time period is used as Final transition probability matrix of the granular Markov process. The particle grid information is obtained through the calculation of the transition probability matrix, and the particle position information is obtained through the particle grid information. Particles are uniformly and randomly distributed within the grid.
步骤2，对统计时间段内每个时间步长通过CFD-DEM模型模拟得到的颗粒分布图进行图像识别，统计气泡的产生、运动及长大的规律，建立气泡随机发展模型，根据气泡随机发展模型确定气泡相对位置。Step 2: Perform image recognition on the particle distribution map simulated by the CFD-DEM model at each time step within the statistical time period, count the generation, movement and growth of the bubbles, and establish a random development model of the bubbles, according to the random development of the bubbles The model determines the relative positions of the bubbles.
所述步骤2中气泡随机发展模型的建立方法：分别统计不同高度下气泡质心水平位置及等效直径的概率分布，据此概率分布，利用电脑产生的随机数的蒙特卡洛方法来模拟鼓泡流化床中气泡的产生、运动及长大得到气泡随机发展模型。The establishment method of the bubble random development model in the step 2: separately count the probability distribution of the horizontal position of the bubble center of mass and the equivalent diameter at different heights, and use the Monte Carlo method of random numbers generated by the computer to simulate the bubbling according to the probability distribution The generation, movement and growth of bubbles in the fluidized bed obtain the random development model of bubbles.
气泡的上升速度由经验公式计算；气泡总个数在床内保持不变，气泡总个数由CFD-DEM模型模拟的床内平均气泡数确定，当一个气泡质心上升超过床层平均高度时，一个新气泡即从床底部产生。气泡在发展过程中不断上升、长大。The rising speed of the bubbles is calculated by an empirical formula; the total number of bubbles remains unchanged in the bed, and the total number of bubbles is determined by the average number of bubbles in the bed simulated by the CFD-DEM model. When a bubble centroid rises above the average height of the bed, A new bubble is created from the bottom of the bed. Bubbles rise and grow continuously during the development process.
步骤3，利用气泡形状的棒球帽模型将步骤1中的Markov链随机模型与步骤2中的气泡随机发展模型进行耦合，建立鼓泡流化床颗粒运动的随机模型。将步骤1)得到的颗粒位置信息和步骤2)确定的气泡相对位置代入鼓泡流化床颗粒运动的随机模型得到耦合气泡后颗粒的位置。In step 3, the Markov chain stochastic model in step 1 is coupled with the bubble stochastic development model in step 2 by using the bubble-shaped baseball cap model to establish a stochastic model of particle motion in the bubbling fluidized bed. Substitute the particle position information obtained in step 1) and the relative position of the bubbles determined in step 2) into the stochastic model of particle motion in the bubbling fluidized bed to obtain the position of the particles after coupling the bubbles.
所述步骤3中气泡形状的棒球帽模型：如图1所示，气泡的主体是半径为rt圆C1被同等大小的圆C2截取后的剩余部分，包括三个部分，分别为第一区域I、第二区域II以及第三区域III，第三区域III为圆C2截取掉的部分，第二区域II为圆C2截取掉的部分中圆C2上的弧以及该弧的两端点分别与圆心C1连线所围成的区域，第一区域I为圆C1剩余的弧以及该弧的两端点分别与圆心C1连线所围成的区域。The baseball cap model in the shape of the bubble in step 3: as shown in Figure 1, the main body of the bubble is the remaining part after the circle C1 with a radius of r t is intercepted by a circle C2 of the same size, including three parts, which are respectively the first area I. The second area II and the third area III, the third area III is the part cut off by the circle C2, the second area II is the arc on the circle C2 in the part cut off by the circle C2 and the two ends of the arc are respectively connected with the center of the circle The area enclosed by the line connecting C1, the first area I is the area enclosed by the remaining arc of the circle C1 and the two ends of the arc and the line connecting the center C1 respectively.
耦合前处于三种区域的颗粒与气泡发生耦合作用，分别是气泡上部、气泡下部及气泡尾涡。Before the coupling, the particles and the bubbles are coupled in three regions, namely the upper part of the bubble, the lower part of the bubble and the wake of the bubble.
三种区域颗粒与气泡耦合算法符合Davison模型描述的气泡附近颗粒运动规律。因此可以采用Davison模型描述的气泡附近颗粒运动规律计算三种区域颗粒与气泡的耦合。The three regional particle-bubble coupling algorithms conform to the particle motion rules around the bubble described by the Davison model. Therefore, the particle motion law near the bubble described by the Davison model can be used to calculate the coupling between particles and bubbles in the three regions.
下面结合具体实施例对本发明做进一步的解释。The present invention will be further explained below in conjunction with specific examples.
实施例以二维鼓泡流化床情形进行叙述，三维情形可以此类推：The embodiment is described with the situation of two-dimensional bubbling fluidized bed, and the three-dimensional situation can be deduced by analogy:
(1)首先将二维鼓泡流化床划分网格，统计前期CFD-DEM的模拟结果，计算经过某一个时间步时，颗粒在网格间的转移概率，任意两个网格间的转移概率构成这个时间步长颗粒运动的Markov链转移概率矩阵，统计时间段内所有转移概率矩阵的平均值作为颗粒Markov过程最终的转移概率矩阵。通过转移概率矩阵计算得到颗粒网格信息后，颗粒在网格内均匀随机分布。(1) First divide the two-dimensional bubbling fluidized bed into grids, count the simulation results of CFD-DEM in the previous stage, and calculate the transfer probability of particles between grids after a certain time step, and the transfer between any two grids The probability constitutes the Markov chain transition probability matrix of particle movement at this time step, and the average value of all transition probability matrices in the statistical time period is used as the final transition probability matrix of the particle Markov process. After the particle grid information is obtained through the calculation of the transition probability matrix, the particles are uniformly and randomly distributed in the grid.
(2)对统计时间段内每个时间步长CFD-DEM模拟的鼓泡流化床颗粒分布图进行图像识别，分别统计不同高度下气泡质心水平位置及等效直径的概率分布，如图2、3、4所示。据此分布，利用电脑产生随机数，根据蒙特卡洛方法来判断鼓泡流化床中气泡的产生、运动及长大。气泡产生位置由随机数r0和公式(1)计算：(2) Perform image recognition on the particle distribution map of the bubbling fluidized bed simulated by CFD-DEM at each time step within the statistical time period, and count the probability distribution of the horizontal position of the center of mass and the equivalent diameter of the bubbles at different heights, as shown in Figure 2 , 3, 4 shown. According to this distribution, use the computer to generate random numbers, and judge the generation, movement and growth of bubbles in the bubbling fluidized bed according to the Monte Carlo method. The bubble generation position is calculated by the random number r 0 and the formula (1):
其中，r0表示随机数，random(a,b)表示电脑产生a到b之间的一个随机数，w0表示根据随机数r0计算出的鼓泡床底部气泡产生位置的横坐标，f(w)表示鼓泡床底部横坐标w处产生气泡的概率，w表示气泡在鼓泡床底部产生位置的横坐标。Among them, r 0 represents a random number, random(a,b) represents a random number between a and b generated by the computer, w 0 represents the abscissa of the bubble generation position at the bottom of the bubbling bed calculated according to the random number r 0 , f (w) represents the probability of generating bubbles at the abscissa w at the bottom of the bubbling bed, and w represents the abscissa of the position where the bubbles are generated at the bottom of the bubbling bed.
气泡的上升速度由经验公式(2)、(3)计算；The rising speed of bubbles is calculated by empirical formulas (2) and (3);
ht+1＝ht+Δt·ut (3)h t+1 ＝h t +Δt·u t (3)
其中，ut表示t时刻气泡上升速度，g表示重力加速度，dt表示t时刻气泡等面积圆直径，ht表示t时刻气泡质心高度，Δt表示一个时间步长。Among them, u t represents the rising speed of the bubble at time t, g represents the acceleration of gravity, d t represents the diameter of the equal-area circle of the bubble at time t, h t represents the height of the center of mass of the bubble at time t, and Δt represents a time step.
气泡总个数在床内保持不变，由CFD-DEM模拟的床内平均气泡数确定，当一个气泡质心上升超过床层平均高度时，一个新气泡即从床底部产生；气泡在发展过程中不断上升、长大，气泡质心水平位置由公式(4)计算：The total number of bubbles remains constant in the bed, which is determined by the average number of bubbles in the bed simulated by CFD-DEM. When the centroid of a bubble rises above the average height of the bed, a new bubble is generated from the bottom of the bed; Continuously rising and growing, the horizontal position of the bubble center of mass is calculated by the formula (4):
wt+1＝random(w(t+1),1,wt+1,2) (4)w t+1 ＝random(w (t+1),1 ,w t+1,2 ) (4)
其中，wt+1表示t+1时刻气泡质心横坐标，w(t+1),1表示t+1时刻已知气泡高度条件下根据图3计算出的气泡质心最小横坐标，wt+1,2表示t+1时刻已知气泡高度条件下根据图3计算出的气泡质心最大横坐标。Among them, w t+1 represents the abscissa of the bubble centroid at time t+1, w (t+1), 1 represents the minimum abscissa of the bubble center of mass calculated according to Figure 3 under the condition of known bubble height at time t+1, w t+ 1, 2 represent the maximum abscissa of the bubble centroid calculated according to Figure 3 under the condition of known bubble height at time t+1.
气泡大小由公式(5)计算：The bubble size is calculated by formula (5):
dt+1＝random(maximum(dt+1,5,dt+1,4,dt),dt+1,3) (5)d t+1 ＝random(maximum(d t+1,5 ,d t+1,4 ,d t ),d t+1,3 ) (5)
其中，dt+1表示t+1时刻气泡等面圆直径，dt+1,5表示t+1时刻已知气泡高度条件下根据图4计算的气泡等面积圆直径最小值，dt+1,4表示t+1时刻已知气泡高度条件下根据图4计算的气泡等面积圆直径最小值，dt表示t时刻气泡等面积圆直径，dt+1,3表示t+1时刻已知气泡高度条件下根据图4计算的气泡等面积圆直径最大值。Among them, d t+1 represents the diameter of the equal-area circle of the bubble at time t+1, d t+1,5 represents the minimum value of the diameter of the equal-area circle of the bubble calculated according to Figure 4 under the condition of known bubble height at time t+1, d t+ 1, 4 represent the minimum value of bubble equal-area circle diameter calculated according to Fig. 4 under the condition of known bubble height at time t+1, d t represents the diameter of bubble equal-area circle at time t, and d t+1, 3 represents the diameter of bubble equal-area circle at time t+1. The maximum value of the bubble equal-area circle diameter calculated according to Fig. 4 under the condition of knowing the bubble height.
(3)建立气泡形状的棒球帽模型，如图1所示。气泡的主体是圆C1被同等大小的圆C2截取后的剩余部分。分为白色区域I和灰色区域II，耦合前的颗粒位置根据步骤(1)计算，用空心点表示，耦合后的颗粒位置用实心点表示。根据耦合前颗粒所处的位置为气泡内的区域I还是区域II，或者是处在气泡尾涡部分的区域III，来判断耦合后颗粒的位置。三种区域颗粒与气泡耦合算法符合Davison模型描述的气泡附近颗粒运动规律，具体按照公式(6)、(7)、(8)计算。(3) Establish a bubble-shaped baseball cap model, as shown in Figure 1. The body of the bubble is what remains of circle C1 intercepted by circle C2 of equal size. Divided into white area I and gray area II, the particle position before coupling is calculated according to step (1), represented by hollow dots, and the particle position after coupling is represented by solid dots. The position of the particle after coupling can be judged according to whether the position of the particle before coupling is in region I or region II in the bubble, or in region III of the wake part of the bubble. The three regional particle-bubble coupling algorithms conform to the movement rules of particles near the bubble described by the Davison model, and are specifically calculated according to formulas (6), (7), and (8).
D′I＝rt+random(0,1)·(rt-DI)2/rt (6)D′ I ＝r t +random(0,1)·(r t -D I ) 2 /r t (6)
D′II＝rt-random(0,1)·(rt-DII)2/rt (7)D′ II ＝r t -random(0,1)·(r t -D II ) 2 /r t (7)
D′III＝rt+random(0,1)·(rt-DIII)2/rt (8)D′ III ＝r t +random(0,1)·(r t -D III ) 2 /r t (8)
其中，D′I表示区域I中颗粒耦合气泡后与C1圆心的距离，rt表示圆C1和圆C2的半径，DI表示区域I中颗粒耦合气泡前与C1圆心的距离，D′II表示区域II中颗粒耦合气泡后与C1圆心的距离，DII表示区域II中颗粒耦合气泡前与C1圆心的距离，D′III表示区域III中颗粒耦合气泡后与C2圆心的距离，DIII表示区域III中颗粒耦合气泡前与C2圆心的距离。Among them, D' I represents the distance from the center of C1 circle after particle coupling bubbles in region I, rt represents the radius of circle C1 and circle C2, D I represents the distance from the center of C1 circle before particle coupling bubbles in region I, and D' II represents The distance between the particle-coupling bubble and the center of C1 in region II, D II represents the distance between the particle-coupling bubble and the center of C1 in region II, D′ III represents the distance between the particle-coupling bubble and the center of C2 in region III, and D III represents the area The distance between the particle coupling bubble and the center of C2 in III.
本实施例从15-20s的模拟，CFD-DEM需要耗费150小时左右，纯颗粒相的Markov随机过程需要100分钟左右，耦合气泡相后也只增加了25分钟左右，所以相比CFD-DEM，应用本发明使得计算速度提高了70倍左右。图5(a)和图5(b)是耦合气泡相前后的瞬时颗粒分布对比，直观上应用本发明将气泡和颗粒运动相耦合后，模拟结果成功复现了气泡的结构形态和发展过程，显著改进了颗粒分布均匀化的特点。图6(a)和图6(b)定量的比较了随机模型耦合气泡前后及CFD-DEM模拟的鼓泡流化床颗粒径向和轴向的混合曲线，应用本发明后，颗粒的Markov过程中成功引入了气泡对其运动的影响，显著改善了颗粒混合曲线过于平滑的缺点，大大提高了随机模型的精度。From the simulation of 15-20s in this example, CFD-DEM takes about 150 hours, and the Markov stochastic process of pure particle phase takes about 100 minutes. After coupling the bubble phase, it only increases by about 25 minutes. Therefore, compared with CFD-DEM, The application of the invention increases the calculation speed by about 70 times. Figure 5(a) and Figure 5(b) are the comparison of instantaneous particle distribution before and after coupling the bubble phase. Intuitively, after applying the present invention to couple the bubble and particle movement, the simulation results successfully reproduce the structure and development process of the bubble. Significantly improved particle distribution homogenization characteristics. Fig. 6 (a) and Fig. 6 (b) have quantitatively compared the mixing curves of the bubbling fluidized bed particle radial and axial directions before and after the stochastic model coupling bubble and CFD-DEM simulation, after applying the present invention, the Markov process of particle The influence of air bubbles on its movement has been successfully introduced in the model, which has significantly improved the defect that the particle mixing curve is too smooth, and greatly improved the accuracy of the stochastic model.
以上所述仅是本发明的优选实施方式，应当指出：对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications are also possible. It should be regarded as the protection scope of the present invention.
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