亲油型聚结滤芯饱和度预测模型研究

doi:10.11949/0438-1157.20200426

摘要/Abstract

摘要：

纤维聚结滤芯广泛用于压缩空气净化、发动机曲轴箱通风、加工和切割等一系列工艺过程中，用于除去气流中的液体气溶胶颗粒。由于聚结滤芯饱和度对于过滤效率及阻力具有重要影响，因此建立饱和度与滤材参数及操作条件之间的关系将有助于优化滤芯结构并提高过滤性能。目前实际工业用聚结滤芯通常由多层微米级玻璃纤维材料组成，然而现有计算模型无法用于此类滤芯的饱和度预测。因此，本文基于多种常用亲油型聚结滤芯压降及饱和度实验测试结果，根据“跳跃-通道”模型及毛细管理论建立了新的饱和度预测模型。通过与大量已发表文献数据对比发现，当饱和值大于0.2时，预测值与实验结果吻合度较好，相对偏差≤20%。随着饱和度的降低，滤芯润湿区域和非润湿区域之间界限逐渐明显，此时无需对毛细管半径进行修正。然而，新模型仍然要依靠压降测量值进行计算，这一问题需在后续工作中加以解决。

关键词: 聚结, 过滤, 气溶胶, 饱和度, 模型

Abstract:

Fibrous coalescing filters are widely used in a series of processes such as compressed air purification, engine crankcase ventilation, processing and cutting, and are used to remove liquid aerosol particles in the airflow. Pressure drop and ef?ciency of coalescence filters are greatly affected by saturation. It is of importance to establish the relationship among saturation, filter media parameters and operating conditions, which is helpful to optimize the filter design. Coalescence ?lters composed of thin glass fibrous media with micron fiber diameters are widely used in industry, while the saturation of which cannot be accurately predicted by the existing saturation models. This work investigated the relationship between pressure drop and saturation of multi-layered filters with different oleophilic filter media. In this study, there was no sharp boundary between wetting and non-wetting regions within filter media, thus a filter was regarded as a whole capillary system. According to the Jump-and-Channel model and capillary theory, a saturation model was developed. Compared with a large number of published literature data, it is found that when the saturation value is greater than 0.2, the predicted value is in good agreement with the experimental results, and the relative deviation is ≤20%. With the decrease in saturation, the boundaries become more and more obvious between the wetting and non-wetting regions. In this case, there is no need to modify to the capillary radius in the developed model. However, the developed model was also limited by the need for the channel pressure drop measurement, which should be solved in further work.

Key words: coalescence, filtration, aerosol, saturation, model

中图分类号:

TE 832

常程,姬忠礼,刘佳霖. 亲油型聚结滤芯饱和度预测模型研究[J]. 化工学报, 2020, 71(12): 5610-5619.

CHANG Cheng,JI Zhongli,LIU Jialin. Saturation models of oleophilic coalescing filters[J]. CIESC Journal, 2020, 71(12): 5610-5619.

图/表 13

表1 现有聚结滤芯饱和度模型及所适用的滤材参数

Table 1 Saturation models and the applicable filter material parameters

Ref.	Model	Filter material	Fiber diameter/μm	Thickness/mm
[11]	$S e = 0.0829 α Z d f - 0.321 C a n - 0.431$ (1) $C a n = Q μ g A f σ c o s θ Δ P e Δ P d r y$ (2)	stainless steel fiber	4—22	7.1—7.8
[12]	$S e = α 0.39 ± 0.09 B o 0.47 ± 0.06 + 0.24 ± 0.07 l n B o C a 0.11 ± 0.04 × e x p - 0.04 ± 0.36 + 6.6 ± 1.5 × 105 D r$ (3) $B o = ρ l g d f 2 σ × 105$ (4) $C a = μ g u σ × 105$ (5) $D r = μ l D σ Z W$ (6)	glass fiber	2.9, 8.5	8.8
[13]	$x ∞ = - Δ P c r c + 2 σ c o s θ r c ρ l g$ (7) $Δ P c = (π + 1) π r f r c Δ P e$ (8) $r c = - A l o g e α r f - B c f$ (9)	glass fiber	0.62—1.24	0.53—0.65
[13]		stainless steel fiber	4.0—6.4	5.16—6.90
[14]	$S c h a n n e l = 1 1 + u u *$ (10)	glass fiber	2.99	0.5

表1 现有聚结滤芯饱和度模型及所适用的滤材参数

Table 1 Saturation models and the applicable filter material parameters

Ref.	Model	Filter material	Fiber diameter/μm	Thickness/mm
[11]	$S e = 0.0829 α Z d f - 0.321 C a n - 0.431$ (1) $C a n = Q μ g A f σ c o s θ Δ P e Δ P d r y$ (2)	stainless steel fiber	4—22	7.1—7.8
[12]	$S e = α 0.39 ± 0.09 B o 0.47 ± 0.06 + 0.24 ± 0.07 l n B o C a 0.11 ± 0.04 × e x p - 0.04 ± 0.36 + 6.6 ± 1.5 × 105 D r$ (3) $B o = ρ l g d f 2 σ × 105$ (4) $C a = μ g u σ × 105$ (5) $D r = μ l D σ Z W$ (6)	glass fiber	2.9, 8.5	8.8
[13]	$x ∞ = - Δ P c r c + 2 σ c o s θ r c ρ l g$ (7) $Δ P c = (π + 1) π r f r c Δ P e$ (8) $r c = - A l o g e α r f - B c f$ (9)	glass fiber	0.62—1.24	0.53—0.65
[13]		stainless steel fiber	4.0—6.4	5.16—6.90
[14]	$S c h a n n e l = 1 1 + u u *$ (10)	glass fiber	2.99	0.5

表2 实验滤材参数

Table 2 Properties of experimental filter materials

Filter	Material	Thickness /mm	Packing density	Fiber diameter /μm	Contact angle/ (°)
A	glass fiber	0.51±0.01	0.063±0.001	2.92±0.10	35.3±1.9
B	glass fiber	0.62±0.02	0.062±0.001	2.00±0.08	39.1±1.7
C	glass fiber	0.41±0.01	0.072±0.001	1.79±0.06	46.2±2.1

图1 滤材B微观结构

Fig.1 SEM images of filter material B

图2 实验装置流程图

Fig.2 Schematic of experimental apparatus

图3 滤芯A4过程压降曲线

Fig.3 Pressure drop profile of filter A4

图4 各滤芯压降组成情况

Fig.4 Pressure drop of filters with different layers

图5 不同层滤芯总饱和度及其内部各层滤材饱和度

Fig.5 Total saturation and saturation profiles of filters with different layers

图6 现有饱和度模型对滤芯A4、B4和C4预测值与实验结果对比

Fig.6 Comparison of predicted saturation with experimental results of filters A4, B4 and C4

图7 滤芯A4、B4和C4内第三层滤材液体分布情况

Fig.7 Liquid distribution in layer 3 of filters A4, B4 and C4 at steady state

表3 滤芯A4、B4和C4饱和度预测所用参数

Table 3 All parameters used to predict the saturation of filters A4, B4 and C4

Parameter	Filter A4	Filter B4	Filter C4
d_f/μm	2.92	2.00	1.79
α	0.063	0.062	0.072
Z /mm	2.03	2.48	1.64
W /m	0.15	0.15	0.15
N	4	4	4
Q /(m³/s)	0.002124	0.002124	0.002124
A_f /m²	0.0177	0.0177	0.0177
u /(m/s)	0.12	0.12	0.12
u^*/(m/s)	0.0176	0.0176	0.0176
D /(m³/s)	9.69×10^-10	9.69×10^-10	9.69×10^-10
ΔP_dry/kPa	0.53	1.36	1.40
ΔP_e /kPa	4.55	7.38	10.11
ρ_l/(kg/m³)	912	912	912
σ /(N/m)	0.03	0.03	0.03
μ_g /(Pa·s)	17.9×10^-6	17.9×10^-6	17.9×10^-6
μ_l /(Pa·s)	0.023	0.023	0.023
θ[式(2)]/(°)	35.3	39.1	46.2
θ[式(7)]/(°)	65.8	67.4	71.6
c_f	1	1	1
A	50.7	50.7	50.7
B	42.1	42.1	42.1

图8 预测饱和度在不同特征毛细管半径及液膜厚度比值条件下对比情况

Fig.8 Comparison of predicted saturation with different characteristic capillary radii and fractions

表4 新建饱和度模型预测所用计算参数

Table 4 All parameters used for predicting saturation

Authors	d_f/μm	α	l/mm	n	A_f/m²	L/m	u/(m/s)	ΔP_channel/kPa	ρ_l/(kg/m³)	σ/(N/m)
this work-A	2.92	0.063	0.51	1~4	0.0177	0.15	0.12	0.82~1.64	912	0.03
this work-B	2.00	0.062	0.62	1~4	0.0177	0.15	0.12	1.81~4.06	912	0.03
this work-C	1.79	0.072	0.41	1~4	0.0177	0.15	0.12	2.21~5.46	912	0.03
Mead-Hunter等^[13]-GF1	1.1	0.064	0.53	1	0.0017	0.047	0.153	3.15	841	0.028
Mead-Hunter等^[13]-GF4	1.24	0.054	0.65	1	0.0017	0.047	0.153	2.28	841	0.028
Kolb等^[14]	2.99	0.05	0.5	10	0.0064	0.08	0.05~0.7	1.37~6.60	900	0.031
Chang等^[23]	1.93	0.076	0.52	4	0.0198	0.188	0.1	3.09	912	0.03
Kampa等^[3]	1	0.05	0.5	10	0.0064	0.08	0.3	21.35	900	0.03
Kolb等^[8]	4.0	0.061	0.64	3	0.0064	0.08	0.25	1.79	900	0.031
Chen等^[24]-A	4.08	0.072	0.41	4	0.0177	0.15	0.12	0.67	912	0.03
Chen等^[24]-B	3.07	0.067	0.46	4	0.0177	0.15	0.12	1.36	912	0.03
Chen等^[24]-C	2.33	0.070	0.46	4	0.0177	0.15	0.12	2.17	912	0.03
Chen等^[24]-D	1.92	0.071	0.45	4	0.0177	0.15	0.12	4.25	912	0.03
Frising等^[25]	1.21	0.078	0.409	1	0.0095	0.11	0.058~0.25	2.81~5.41	913.4	0.03

图9 新模型饱和度预测值与实验结果对比情况

Fig.9 Predicted and measured total saturation

参考文献 25

1	Mead-Hunter R, King A J C, Mullins B J. Aerosol-mist coalescing filters—a review[J]. Separation and Purification Technology, 2014, 133: 484-506.
2	Contal P, Simao J, Thomas D, et al. Clogging of fibre filters by submicron droplets. Phenomena and influence of operating conditions[J]. Journal of Aerosol Science, 2004, 35: 263-278.
3	Kampa D, Wurster S, Buzengeiger J, et al. Pressure drop and liquid transport through coalescence filter media used for oil mist filtration[J]. International Journal of Multiphase Flow, 2014, 58: 313-324.
4	Kampa D, Wurster S, Meyer J, et al. Validation of a new phenomenological “jump-and-channel” model for the wet pressure drop of oil mist filters[J]. Chemical Engineering Science, 2015, 122: 150-160.
5	常程, 姬忠礼, 黄金斌, 等. 气液过滤过程中液滴二次夹带现象分析[J]. 化工学报, 2015, 66(4): 1344-1352.
	Chang C, Ji Z L, Huang J B, et al. Analysis of re-entrainment in process of gas-liquid filtration[J]. CIESC Journal, 2015, 66(4): 1344-1352.
6	陈锋, 姬忠礼, 齐强强. 孔径梯度分布对亲油型滤材气液过滤性能的影响[J]. 化工学报, 2017, 68(4): 1442-1451.
	Chen F, Ji Z L, Qi Q Q. Influence of pore size distribution on gas-liquid filtration performance of oleophilic filters[J]. CIESC Journal, 2017, 68(4): 1442-1451.
7	Chen F, Ji Z, Qi Q. Effect of liquid surface tension on the ﬁltration performance of coalescing filters[J]. Separation and Purification Technology, 2019, 209: 881-891.
8	Kolb H E, Watzek A K, Zaghini F V, et al. A mesoscale model for the relationship between efficiency and internal liquid distribution of droplet mist filters[J]. Journal of Aerosol Science, 2018, 123: 219-230.
9	Penner T, Meyer J, Kasper G, et al. Impact of operating conditions on the evolution of droplet penetration in oil mist filters [J]. Separation and Purification Technology, 2019, 211: 697-703.
10	Kolb H E, Kasper G. Mist filters: how steady is their “steady state”? [J]. Chemical Engineering Science, 2019, 204: 118-127.
11	Liew T P, Conder J R. Fine mist filtration by wet filters(I): Liquid saturation and flow resistance of fibrous filters[J]. Journal of Aerosol Science, 1985, 16(6): 497-509.
12	Raynor P C, Leith D. The inﬂuence of accumulated liquid on fibrous ﬁlter performance[J]. Journal of Aerosol Science, 2000, 31: 19-34.
13	Mead-Hunter R, Braddock R D, Kampa D, et al. The relationship between pressure drop and liquid saturation in oil-mist filters—predicting filter saturation using a capillary based model[J]. Separation and Purification Technology, 2013, 104: 121-129.
14	Kolb H E, Meyer J, Kasper G. Flow velocity dependence of the pressure drop of oil mist filters[J]. Chemical Engineering Science, 2017, 166: 107-114.
15	Reed C M, Wilson N. The fundamentals of absorbency of fibers, textile structures and polymers(I): The rate of rise of a liquid in glass-capillaries[J]. Journal of Physics D: Applied Physics, 1993, 26(9): 1378-1381.
16	Mullins B J, Braddock R D. Capillary rise in porous, ﬁbrous media during liquid immersion[J]. International Journal of Heat and Mass Transfer, 2012, 55: 6222-6230.
17	Mullins B J, Braddock R D, Kasper G. Capillarity in fibrous filter media: relationship to filter properties[J]. Chemical Engineering Science, 2007, 62: 6191-6198.
18	Mullins B J, Mead-Hunter R, Pitta R N, et al. Comparative performance of philic and phobic oil-mist filters[J]. AIChE Journal, 2014, 60(8): 2976-2984.
19	Jaganathan S, Tafreshi H V, Pourdeyhimi B. A realistic modeling of fluid in filtration in thin fibrous sheets[J]. Journal of Applied Physics, 2009, 105(11): 8.
20	Bredin A, Mullins B J. Influence of flow-interruption on filter performance during the filtration of liquid aerosols by fibrous filters[J]. Separation and Purification Technology, 2012, 90: 53-63.
21	Davies C N. Air Filtration[M]. London: Academic Press, Inc., 1973.
22	Bitten J F, Fochtman E G. Water bed distribution in fiber-bed coalescers[J]. Journal of Colloid and Interface Science, 1971, 37: 312-317.
23	Chang C, Ji Z L, Zeng F Y. The effect of a drainage layer on filtration performance of coalescing filters[J]. Separation and Purification Technology, 2016, 170: 370-376.
24	Chen F, Ji Z L, Qi Q Q. Effect of pore size and layers on filtration performance of coalescing filters with different wettabilities[J]. Separation and Purification Technology, 2018, 201: 71-78.
25	Frising T, Thomas D, Bémer D, et al. Clogging of ﬁbrous ﬁlters by liquid aerosol particles: experimental and phenomenological modelling study[J]. Chemical Engineering Science, 2005, 60: 2751-2762.

[1]	吴馨, 龚建英, 靳龙, 王宇涛, 黄睿宁. 超声波激励下铝板表面液滴群输运特性的研究[J]. 化工学报, 2023, 74(S1): 104-112.
[2]	吴延鹏, 李晓宇, 钟乔洋. 静电纺丝纳米纤维双疏膜油性细颗粒物过滤性能实验分析[J]. 化工学报, 2023, 74(S1): 259-264.
[3]	宋嘉豪, 王文. 斯特林发动机与高温热管耦合运行特性研究[J]. 化工学报, 2023, 74(S1): 287-294.
[4]	连梦雅, 谈莹莹, 王林, 陈枫, 曹艺飞. 地下水预热新风一体化热泵空调系统制热性能研究[J]. 化工学报, 2023, 74(S1): 311-319.
[5]	金正浩, 封立杰, 李舒宏. 氨水溶液交叉型再吸收式热泵的能量及分析[J]. 化工学报, 2023, 74(S1): 53-63.
[6]	李科, 文键, 忻碧平. 耦合蒸气冷却屏的真空多层绝热结构对液氢储罐自增压过程的影响机制研究[J]. 化工学报, 2023, 74(9): 3786-3796.
[7]	王浩, 王振雷. 基于自适应谱方法的裂解炉烧焦模型化简策略[J]. 化工学报, 2023, 74(9): 3855-3864.
[8]	李锦潼, 邱顺, 孙文寿. 煤浆法烟气脱硫中草酸和紫外线强化煤砷浸出过程[J]. 化工学报, 2023, 74(8): 3522-3532.
[9]	于旭东, 李琪, 陈念粗, 杜理, 任思颖, 曾英. 三元体系KCl + CaCl₂ + H₂O 298.2、323.2及348.2 K相平衡研究及计算[J]. 化工学报, 2023, 74(8): 3256-3265.
[10]	诸程瑛, 王振雷. 基于改进深度强化学习的乙烯裂解炉操作优化[J]. 化工学报, 2023, 74(8): 3429-3437.
[11]	闫琳琦, 王振雷. 基于STA-BiLSTM-LightGBM组合模型的多步预测软测量建模[J]. 化工学报, 2023, 74(8): 3407-3418.
[12]	郭雨莹, 敬加强, 黄婉妮, 张平, 孙杰, 朱宇, 冯君炫, 陆洪江. 稠油管道水润滑减阻及压降预测模型修正[J]. 化工学报, 2023, 74(7): 2898-2907.
[13]	刘春雨, 周桓宇, 马跃, 岳长涛. CaO调质含油污泥干燥特性及数学模型[J]. 化工学报, 2023, 74(7): 3018-3027.
[14]	李艳辉, 丁邵明, 白周央, 张一楠, 于智红, 邢利梅, 高鹏飞, 王永贞. 非常规服役超临界锅炉的微纳尺度腐蚀动力学模型建立及应用[J]. 化工学报, 2023, 74(6): 2436-2446.
[15]	刘起超, 周云龙, 陈聪. 起伏振动垂直上升管气液两相流截面含气率分析与计算[J]. 化工学报, 2023, 74(6): 2391-2403.