计及气泡诱导与剪切湍流的气泡破碎、湍流相间扩散及传质模型

doi:10.11949/0438-1157.20220465

化工学报 ›› 2022, Vol. 73 ›› Issue (6): 2573-2588.doi: 10.11949/0438-1157.20220465

计及气泡诱导与剪切湍流的气泡破碎、湍流相间扩散及传质模型

施炜斌^1,²(),龙姗姗²,杨晓钢²(),蔡心悦²

^1.华侨大学机电及自动化学院，福建厦门 361021
^2.宁波诺丁汉大学机械、材料与制造工程系，浙江宁波 315100

收稿日期:2022-03-31 修回日期:2022-05-18 出版日期:2022-06-05 发布日期:2022-06-30
通讯作者: 杨晓钢 E-mail:weibin.shi@hqu.edu.cn;Xiaogang.Yang@nottingham.edu.cn
作者简介:施炜斌（1991—），男，博士，讲师，weibin.shi@hqu.edu.cn
基金资助:
国家自然科学基金项目(91534118);福建省自然科学基金项目(2021J01296)

Bubble breakage, turbulence dispersion and mass transfer model considering the joint effects of bubble-induced turbulence and shear turbulence

Weibin SHI^1,²(),Shanshan LONG²,Xiaogang YANG²(),Xinyue CAI²

^1.College of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, Fujian, China
^2.Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Ningbo 315100, Zhejiang, China

Received:2022-03-31 Revised:2022-05-18 Published:2022-06-05 Online:2022-06-30
Contact: Xiaogang YANG E-mail:weibin.shi@hqu.edu.cn;Xiaogang.Yang@nottingham.edu.cn

摘要/Abstract

摘要：

在以鼓泡塔为代表的气液鼓泡流动中，存在着气泡诱导湍流（BIT）和剪切湍流两种湍流机制，并且二者在不同的时间、空间范围内既相互竞争又共同作用。受制于BIT动能能谱的形式和特性不够完整清晰，过去的研究中关于BIT如何对气泡破碎聚并、相间作用力、相间传热传质等相间相互作用过程产生影响的结论比较模糊。因此，本文在具有波数κ^-3特性的BIT能谱的基础上，提出了在不同工况下考虑BIT与剪切湍流共同作用的研究思路。研究结果表明，考虑两种湍流机制的气泡破碎模型和湍流相间扩散模型对BIT在整体或局部占据不同程度主导地位的情况，都能很好地捕捉气液鼓泡流动的动力学特性，为进一步准确揭示气液相间传质过程的内在机理提供了基础。

关键词: 气泡, 湍流, 传质, 种群平衡, 大涡模拟, 气液两相流, 鼓泡塔

Abstract:

In the gas-liquid bubbling flow represented by the bubble column, there are two turbulence mechanisms, the bubble induced turbulence (BIT) and the shear turbulence, and they both compete and work together in different time and space ranges. There are uncertainties remain in how BIT affects the bubble breakage and coalescence, the interphase interaction forces and the mass transfer, due to the limited understanding of the BIT energy spectrum. Considering the joint effects of bubble-induced turbulence and shear turbulence, we proposed the bubble breakage model and the turbulence dispersion force model in dealing with the global or the local dominance of BIT. For different operating conditions, these models have performed well in capturing the dynamic behaviors of both the gas- and the liquid-phase, which offers fresh insights into understanding the mechanisms of the interphase mass transfer process in the gas-liquid bubbly flows.

Key words: bubble, turbulent flow, mass transfer, population balance, large eddy simulation, gas-liquid flow, bubble column

中图分类号:

TQ 021.1

施炜斌, 龙姗姗, 杨晓钢, 蔡心悦. 计及气泡诱导与剪切湍流的气泡破碎、湍流相间扩散及传质模型[J]. 化工学报, 2022, 73(6): 2573-2588.

SHI Weibin, LONG Shanshan, YANG Xiaogang, CAI Xinyue. Bubble breakage, turbulence dispersion and mass transfer model considering the joint effects of bubble-induced turbulence and shear turbulence[J]. CIESC Journal, 2022, 73(6): 2573-2588.

图/表 15

表1

RSM湍流模型方程"

模型	方程
$ρ u i' u j' ˉ$ 输运方程	$? α l ρ l u i' u j' ˉ ? t + ? α l ρ l u k u i' u j' ˉ ? x k = ? ? x k α l μ l + μ t σ k ? u i' u j' ˉ ? x k + α l P i j + α l ? i j - 23 δ i j α l ρ l ε + α l S i j B I T$ (3)
湍动能产生项	$P i j = - ρ l u i' u k' ˉ ? u j ? x k + u j' u k' ˉ ? u i ? x k$ (4)
压力-应变项	$? i j = ? i j, 1 + ? i j, 2 + ? i j, 1 W + ? i j, 2 W = - C 1 ρ l ε k u i' u j' ˉ - 23 k δ i j - C 2 ρ l ε k P i j - 13 t r P δ i j - C 1 W ρ l ε k u k' u m' ˉ n k n m δ i j - 32 u k' u i' ˉ n k n j - 32 u k' u j' ˉ n k n i k 3 / 2 ε 1 C l y W 2 - C 2 W ? k m, 2 n k n m δ i j - 32 ? i k, 2 n k n j - 32 ? j k, 2 n k n i k 3 / 2 ε 1 C l y W 2$ (5)
湍流耗散率输运方程	$? α l ρ l ε ? t + ? ? x i α l ρ l ε u i = ? ? x j α l μ l + μ t σ ε ? ε ? x j + α l ρ l ε k C 1 ε u' i u' j ˉ ? u i ? x k - C 2 ε ε + α l S ε B I T$ (6)
湍动能	$k = 12 ∑ i = 1,2, 3 u i' u j'$ (7)

表1

表2

相间作用力模型方程"

作用力	方程
曳力	$M D = 34 C D d b ρ l α g u g - u l u g - u l$ (15)
升力	$M l i f t = C l ρ l α g u g - u l × ? × u l$ (16)
虚拟质量力	$M V M = C V M ρ l α g d u l d t l - d u g d t g$ (17)

表2

表3

气泡破碎模型方程的比较"

项目	Luo and Svendsen模型	考虑BIT的气泡破碎模型
能谱函数	$E κ = C κ ε 23 κ - 53$ $C κ ≈ 1.5$	$E κ = δ l C l ε 23 κ - 53 + δ b C b α g U s l i p ν κ - 3$ (29) $δ l$ 、 $δ b$ 为开关函数 $C l$ 、 $C b$ 取动态变化值
涡旋平均脉动速度	$u ˉ λ = β 12 ε λ 13$ $β ≈$ 2.0	$u ˉ λ = C λ 12 C b α g U s l i p ν λ$ (30)
湍流涡旋数密度	$f λ = C 3 1 - α λ 4$ $C 3 = 15 2 2 π 23 Γ 13 ≈ 0.822$	$f λ = C 3 1 - α λ 4$ (31) $C 3 = 12 π C λ 2 π 2$
涡旋-气泡碰撞概率密度函数	$ω B T d i, λ = C 4 1 - α n i ε d i 13 1 + ξ 2 d i ξ 113$ $C 4 = π 4 C 3 β 12 ≈ 0.923$	$ω B T d i, λ = C 4 1 - α n i 1 + ξ 2 d i ξ 3 C b α g U s l i p ν$ (32) $C 4 = π 4 C 3 C λ C b 12$
平均湍动能	$e ˉ d i, λ = π β 12 ρ l ε d i 23 d i 3 ξ 113$	$e ˉ d i, λ = π 12 C λ ρ l λ 5 C b α g U s l i p ν$ (33)
破碎速率	$Ω B d i ∶ d j = 0.923 1 - α$ × $n i ε d 2 13 ∫ ξ m i n 1 1 + ξ 2 ξ 113 e x p - 12 σ C f β ρ l ε 23 d i 53 ξ 113 d ξ$	$Ω B d i ∶ d j = 0.923 1 - α n i ε d 2 13$ × $∫ Λ d i 1 1 + ξ 2 ξ 113 e x p - 12 σ C f β ρ l ε 23 d i 53 ξ 113 d ξ + C 4 1 - α$ × (34) $n i C b α g U s l i p ν ∫ ξ m i n Λ d i 1 + ξ 2 ξ 3 e x p - 12 σ C f β ρ l C b α g U s l i p ν d i 3 ξ 5 d ξ$

表3

图1

表4

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

参考文献 47

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Case	实验	塔径/m	高度/m	表观气速/(m/s)	静液位高度/m	测量高度/m	湍流模型	湍流扩散	破碎模型
Case 1	Gemello等^[36-37]	0.4	3.6	0.16	1.6	1.5	RSM	—	Luo and Sevndsen
Case 2	Gemello等^[36-37]	0.4	3.6	0.16	1.6	1.5	RSM	—	Luo and Sevndsen Ω_B’(d_i ∶d_j )=10Ω_B(d_i ∶d_j )
Case 3	Gemello等^[36-37]	0.4	3.6	0.16	1.6	1.5	RSM	—	式(34)
Case 4	Guan等^[38]	0.15	1.6	0.08	1.2	0.8	RSM	—	Luo and Sevndsen
Case 5	Guan等^[38]	0.15	1.6	0.08	1.2	0.8	RSM	—	式(34)
Case 6	Sommerfeld等^[17]	0.14	1.4	0.0029	0.65	0.325	LES	Burns等^[39]	—
Case 7	Sommerfeld等^[17]	0.14	1.4	0.0029	0.65	0.325	LES	式(43)	—

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计及气泡诱导与剪切湍流的气泡破碎、湍流相间扩散及传质模型

Bubble breakage, turbulence dispersion and mass transfer model considering the joint effects of bubble-induced turbulence and shear turbulence

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