基于TFM-PBM耦合模型的离心泵内微气泡破碎合并的模拟研究

doi:10.11949/0438-1157.20210355

摘要/Abstract

摘要：

了解离心泵内微气泡的发生特性，对于优化现有基于旋转流场的微气泡发生装置的性能、提高工业废水废气的污染物去除率至关重要。在考虑气泡破碎合并的前提下，通过将双流体模型（TFM）与群体平衡模型（PBM）进行耦合，求解离心泵内气液两相旋转流场，研究了入口体积气含率（IGVF）、入口气泡尺寸对泵内气泡沿程尺寸变化、出口气泡尺寸分布的影响，并结合Luo等的破碎合并模型分析成因。结果表明，随IGVF增加，叶轮内气体聚集引起局部气含率陡升，气泡由破碎主导转变为合并主导，而后在蜗壳内气含率恢复正常，气泡又变为破碎主导，总体上出口气泡尺寸逐渐增大。另外，入口气泡尺寸对出口气泡尺寸的影响对IGVF敏感，当IGVF较低时，随入口气泡尺寸增大，出口气泡尺寸先增大后减小；而当IGVF较高时，由于泵内气体聚集，入口气泡尺寸的影响并不明显。

关键词: 离心泵, 微气泡, 气液两相流, TFM-PBM耦合模型, 气含率, 粒度分布

Abstract:

Understanding the generation characteristics of microbubbles in centrifugal pumps is essential for optimizing the performance of existing microbubble generation devices based on rotating equipment and improving the pollutant removal rate of industrial wastewater and waste gas. Recognizing bubble break-up and coalescence, this paper examines how microbubbles evolve under different inlet gas volume fraction (IGVF) and different inlet bubble size in two-phase rotating flow field by coupling two fluid model (TFM) and population balance model (PBM), which was verified to be effective through comparing with experimental head and average bubble size. The results show that gas accumulation in impeller to be the main factor affecting the performance of bubbles with IGVF increasing, which causes bubble size increase as break-up dominated turn to coalescence dominated in impeller. Furthermore, the influence of inlet bubble size on outlet bubble size is sensitive to IGVF. Outlet bubble size increases first and then decreases with inlet bubble size increasing at low IGVF, while this influence is not obvious at high IGVF by gas accumulation in impeller.

Key words: centrifugal pump, microbubble, gas-liquid flow, TFM-PBM coupling model, gas holdup, size distribution

中图分类号:

TQ 021.1

高颂,徐燕燕,李继香,叶爽,黄伟光. 基于TFM-PBM耦合模型的离心泵内微气泡破碎合并的模拟研究[J]. 化工学报, 2021, 72(10): 5082-5093.

Song GAO,Yanyan XU,Jixiang LI,Shuang YE,Weiguang HUANG. Simulation study of microbubbles' break-up and coalescence in centrifugal pump based on TFM-PBM coupling model[J]. CIESC Journal, 2021, 72(10): 5082-5093.

图/表 18

表 1 离心泵的主要设计参数

Table 1 Parameters of centrifugal pump

流量	扬程	转速	叶轮入口直径	叶轮出口直径	叶片出口宽度	出口直径D₃/mm	叶片数Z
Q/(m³/h)	H/mm	n/(r/min)	D₁/mm	D₂/mm	b₂/mm	出口直径D₃/mm	叶片数Z
15	17	3000	50	115	9.2	40	7

图1 离心泵流体域几何建模

Fig.1 Geometric modeling of centrifugal pump fluid domain

图2 1500 r/min工况网格无关性验证

Fig.2 Mesh independence verification at 1500 r/min

表2 PBM模型气泡尺寸离散

Table 2 Discrete bubble sizes in PBM

气泡组	直径/mm
bin0	10
bin1	5.99
bin2	3.59
bin3	2.15
bin4	1.29
bin5	0.77
bin6	0.46
bin7	0.28
bin8	0.17
bin9	0.1

表3 TFM-PBM数值模拟方案

Table 3 TFM-PBM simulation scheme

固定参数	对照组
1500，bin4，7.7 m3/h (42%Q_max)	$α$ (IGVF)/%：0.32，0.60，1.04，2.21，2.61，3.25，4.86
1800，bin4，9.16 m3/h (42%Q_max)	$α$ (IGVF)/%：0.32，1.04，3.28，4.86
1500，0.32%，7.7 m3/h (42%Q_max)	bin2,bin3,bin4,bin5,bin6,bin7
1500，3.25%，7.7 m3/h (42%Q_max)	bin2,bin3,bin4,bin5,bin6,bin7
1500，4.86%，7.7 m3/h (42%Q_max)	bin3,bin4,bin5,bin6

表3 TFM-PBM数值模拟方案

Table 3 TFM-PBM simulation scheme

固定参数	对照组
1500，bin4，7.7 m3/h (42%Q_max)	$α$ (IGVF)/%：0.32，0.60，1.04，2.21，2.61，3.25，4.86
1800，bin4，9.16 m3/h (42%Q_max)	$α$ (IGVF)/%：0.32，1.04，3.28，4.86
1500，0.32%，7.7 m3/h (42%Q_max)	bin2,bin3,bin4,bin5,bin6,bin7
1500，3.25%，7.7 m3/h (42%Q_max)	bin2,bin3,bin4,bin5,bin6,bin7
1500，4.86%，7.7 m3/h (42%Q_max)	bin3,bin4,bin5,bin6

图3 扬程的TFM-PBM仿真结果与实验测量结果[30]对比

Fig.3 Head comparison of TFM-PBM data and experimental values[30]

图4 相分布的TFM-PBM仿真结果与可视化结果[30]对比

Fig.4 Phase distribution comparison of TFM-PBM data and visualization values[30]

图5 泵内沿程气泡尺寸随IGVF变化 (din=bin4)

Fig.5 Average bubble size of each flow domain under different inlet gas volume fraction (din=bin4)

图6 有效破碎频率ω(B)、有效合并频率ω(C) 随体积气含率(α)的变化

Fig.6 Effective break-up frequency ω(B) and effective coalescence frequency ωC under different gas volume fraction α

表4 蜗壳内湍流耗散率随IGVF变化

Table 4 Turbulent dissipation rate of impeller and volute under different inlet gas volume fraction

入口体积气含率IGVF/%	蜗壳内平均湍流耗散率ε/(m²/s³)
0.32	17
0.60	17
1.04	19
2.21	26
3.25	38
4.86	42

图7 有效破碎频率ω(B)、有效合并频率ω(C)随体积气含率(α)的变化

Fig.7 Effective break-up frequency ω(B) and effective coalescence frequency ωC under different gas volume fraction α

图8 泵出口气泡数密度分布随IGVF变化(din=bin4)

Fig.8 Bubble number density distribution at outlet of pump under different IGVF(din=bin4)

图9 泵出口气泡尺寸分布随IGVF变化（占气相，din=bin4）

Fig.9 Bubble size distribution at outlet of pump under different inlet gas volume fraction (by air, din=bin4)

图10 泵出口气泡尺寸分布随IGVF变化（占两相，din=bin4）

Fig.10 Bubble size distribution at outlet of pump under different inlet gas volume fraction (by two-phase, din=bin4)

图11 泵内沿程气泡尺寸随入口气泡尺寸变化(IGVF=0.32%）

Fig.11 Average bubble size of each flow domain under different inlet bubble size(IGVF=0.32%)

图12 叶轮内破碎效率P′(B)、合并效率P′(C)随入口气泡尺寸的变化 (IGVF=0.32%)

Fig.12 Break-up efficiency P′(B) and coalescence efficiency P′(C) in impeller under different inlet bubble size (IGVF=0.32%)

图13 泵出口气泡尺寸分布随入口气泡尺寸变化（占两相，IGVF=0.32%）

Fig.13 Bubble size distribution at outlet of pump under different inlet bubble size (by two-phase, IGVF=0.32%)

图14 泵出口气泡尺寸分布随入口气泡尺寸变化（占两相，IGVF=3.25%）

Fig.14 Bubble size distribution at outlet of pump under different inlet bubble size (by two-phase, IGVF=3.25%)

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