A review on direct numerical simulation of gas-liquid-solid fluidized bed

doi:10.11949/0438-1157.20250035

Abstract

Abstract:

Gas-liquid-solid fluidized bed has broad industrial application in chemical and other process industries. However, due to the complexity of the flow (with characteristics of multi-scale, non-stationary, nonlinear, etc.) and the limitations of multi-phase flow measuring techniques and mechanism models, it is still difficult to scientifically design it. At this time, numerical simulations based on computational fluid dynamics have become an effective way to quantitatively describe three-phase flow. The numerical simulation methods for three-phase flow are generally divided into modeling and direct numerical simulation. Among them, direct numerical simulation is to analyze the interaction between bubbles, particles and fluids at the microscopic scale without introducing drag models, which can reveal the interaction mechanisms between gas, liquid and solid phases and is a method that focuses on. The commonly used direct numerical simulation methods for multi-phase flow, such as volume of fluid, level-set, front tracking, immersed boundary, distributed lagrange multiplier/fictitious-domain, lattice Boltzmann and smoothed particle hydrodynamics are outlined, and the advantages and disadvantages of various simulation methods are compared. Afterwards, the research progress on direct numerical simulation of three-phase flow is reviewed. Finally, the existing problems in direct numerical simulation and future research directions are pointed out.

Key words: gas-liquid-solid flow, multi-phase flow, fluidization, computational fluid dynamics, direct numerical simulation

摘要：

气液固流化床在化工等过程工业中有着广阔的应用前景。但是，由于流动的复杂性（多尺度、非稳态和非线性等）和测试方法以及机理模型的局限性，还难以对其进行科学设计和放大。基于计算流体力学的数值模拟是量化描述三相流动的有效途径。三相流数值模拟方法分为模型化方法和直接数值模拟方法。其中，直接数值模拟是在没有引入曳力模型等的条件下，从微观尺度解析气泡、颗粒和流体间的相互作用，可以揭示气液固三相间的相互作用机理，是重点关注的方法。综述了常用的多相流动直接数值模拟方法，包括流体体积法、水平集法、界面跟踪法、浸没边界法、虚拟区域法、格子玻尔兹曼法和光滑粒子动力学法等，并分析了各种模拟方法的优势和不足，之后对三相流直接数值模拟的研究进展进行了评述，最后给出了目前三相流数值模拟方法存在的问题以及今后进一步研究的方向。

关键词: 气液固流, 多相流, 流态化, 计算流体力学, 直接数值模拟

CLC Number:

TQ 018

Yongli MA, Shu AN, Jie YANG, Mingyan LIU. A review on direct numerical simulation of gas-liquid-solid fluidized bed[J]. CIESC Journal, 2025, 76(8): 3772-3788.

马永丽, 安澍, 杨捷, 刘明言. 气液固流化床直接数值模拟研究进展[J]. 化工学报, 2025, 76(8): 3772-3788.

Figures/Tables 18

Fig.1 Schematic diagram of gas-liquid phase interface correlation algorithmnumber—the liquid volume fraction in the local grid; φ—the symbolic distance function; solid dots—Lagrange tracking points

Table 1 Comparison of VOF method， LS method and FT method

方法	优势	劣势
VOF	简便；质量守恒性好；自动处理界面的合并、破裂	界面重构复杂，特别是三维情况；无法直接获取界面信息；界面不连续
LS	易于三维并行；自动处理合并、破裂；易获得界面信息，如曲率；界面形状更加光滑	质量不守恒；重初始化增加计算成本
FT	精确的界面追踪；质量守恒	计算复杂度高；无法自动处理合并、破裂

Fig.2 Schematic of DLM/FD[29-30]

Fig.3 Schematic of IBM

Fig.4 The collision between 50 μm particles and 130 μm bubbles in liquid phase used by directly numerical simulation[38]a—light particles and spherical bubbles; b—light particles and deformed bubbles; c—heavy particles and deformed bubbles

Fig.5 Simulated liquid bridge under stretching at different time instants[41]: (a) t = 12.5 ms, (b) t = 125 ms, (c) t = 170 ms, (d) t = 175 ms

Fig.6 Liquid bridges in tetrahedral (left) and triangular (right) particle configurations[41]

Fig.7 Interaction between bubble and suspended rigid particles(ψ represents the ratio of bubble size to particle size)[43]

Fig.8 Spatiotemporal evolution of the bubble-particle interaction dynamics (the contours on the left-hand part of each panel show the logarithm of the viscous dissipation function log10ξ in the fluid, and the contours on the right-hand part show the velocity magnitude in the fluid)[48]

Fig.9 Collision process between a single spherical particle (blue) of 0.01 m diameter and a single rising bubble (red) of 0.02 m diameter[49]

Fig.10 Direct numerical simulation of 2D bubbles and their wake vortex trajectories in a gas-liquid-solid fluidized bed[8]

Fig.11 Directly numerical simulation and experimental comparison of single bubble formation and rising movements[55](a) gas-liquid single bubble VOF simulation; (b) gas-liquid-solid flow simulation when the solid holdup is 0.3%; (c) gas-liquid single bubble VOF experimental diagram; (d) gas-liquid-solid flow experimental diagram when the solid holdup is 0.3%

Fig.12 Motion behavior of single bubble and its trailing vortices when it leaves the three-phase fluidized bed and enters the free space[55]

Fig.13 Vector diagram of solid particle velocity during the condensation of bubbles[56]

Fig.14 Five bubbles with an initial diameter of 0.016 m pass through the ascent process of a sediment layer of 60000 particles[57]

Fig.15 The changes of radial distribution functions (pairs of particle-particle, bubble-bubble and particle-bubble)[72]

Fig.16 Three different flow patterns of bubbles passing through the particle layer (Ⅰ: connected finger flow, Ⅱ: transitional flow, Ⅲ: dispersed bubble flow)[73]

Fig.17 Coupled model of SPH and DEM[76]

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