Flow characteristics of liquid-liquid Taylor flow in mini channels with circular and flat cross-sections: a numerical study

doi:10.11949/0438-1157.20200471

Abstract

Abstract:

Taylor flows in mini tubes have been widely adopted in energy and chemical industrials. In order to study characteristics of two-phase interfaces and frictional pressure drops, the liquid-liquid Taylor flow in mini channels with circular and flat cross sections are studied numerically using the moving frame reference method. Effects of Reynolds number, ratio of width to height, and volume fraction of the dispersed phase on two-phase interfaces, liquid film thickness, and pressure drops are analyzed. The numerical results show that the dispersed droplets in circular tubes are consist of spherical nose and tail. The dispersed flows in flat tubes are confined by the channel wall, leading to flat droplets. The two-phase interfaces shrink with increasing Re for all tubes, leading to a higher liquid film thickness between interfaces and channel walls at a higher Re. The liquid film thickness is uniformly distributed along the circumferential direction in circular tubes, while the liquid film in flat tube is much thinner at the flattened part compared with the arc corner. Two-phase pressure drops increase with increasing Re and ratio of width to height, while they decrease with increase in droplet volume fraction. Three components contribute to the two-phase pressure drops, which are the continuous pressure drop, the dispersed pressure drop, and the interfacial pressure drops. Compared with the other two, the interfacial pressure drop contributes more to the total pressure drop. A new correlation to predict the pressure drops in circular and flat tubes is developed.

Key words: liquid-liquid two-phase flow, mini channel, numerical simulation, flat tubes, pressure drops

摘要：

微细通道内Taylor流动广泛应用于能源化工领域，为分析其相界面及阻力特性，利用相对坐标系的方法，研究了竖直圆管及扁平管内的液-液Taylor流动，讨论了通道宽高比、Reynolds数（Re）及分散相体积分数对液膜厚度和两相压降的影响。结果表明：圆管内液滴头部和尾部可以膨胀至近似球形，而扁平管内壁面的限制作用较强，液滴呈现扁平状。随Reynolds数增大，两相界面逐渐收缩，液膜厚度逐渐上升。圆管内液膜厚度比较均匀，扁平管内液膜在通道顶部较薄，而圆弧部分较厚。两相压降随Re和宽高比的增大而增大，随分散相体积分数的增大而降低。相比连续相和分散相压降，界面压降所占的比重最高，并依据模拟结果，提出了圆管及扁平管内液-液Taylor流动的压降预测公式。

关键词: 液液两相流, 小通道, 数值模拟, 扁平管, 压降

CLC Number:

TK 124

Jingzhi ZHANG, Naixiang ZHOU, Guanmin ZHANG, Maocheng TIAN. Flow characteristics of liquid-liquid Taylor flow in mini channels with circular and flat cross-sections: a numerical study[J]. CIESC Journal, 2020, 71(S2): 70-79.

张井志, 周乃香, 张冠敏, 田茂诚. 微细圆管及扁平管内液-液Taylor流动特性的数值研究[J]. 化工学报, 2020, 71(S2): 70-79.

Figures/Tables 13

Fig.1 Computational model

Table 1 Geometrical parameters of investigated channels

管道	宽高比	W/mm	H/mm	P_w /mm	d_h/mm
圆管（AR0）	—	—	—	6.28	2.00
扁平管（AR1）	1	1.22	1.22	6.28	1.70
扁平管（AR2）	2	1.76	0.88	6.28	1.37

Fig.2 Mesh independence

Table 2 Solution method and discretization scheme

Variable	Methods
VOF scheme	Explicit
pressure–velocity coupling	Fractional Step
gradients	Green-Gauss node based
pressure	Body Force Weighted
volume fraction	Geo-Reconstruct
momentum	Second Order Upwind

Fig.3 Comparison of droplet velocities between numerical and experimental data

Fig.4 3D interfaces of dispersed liquid droplets under different working conditions

Fig.5 Cross-sectional profiles of liquid droplets

Fig.6 Circumferential distribution of continuous phase film thicknesses

Fig.7 Dimensionless continuous phase film thicknesses plot against capillary number

Fig.8 Effects of Re and εd on two-phase frictional pressure drops

Fig.9 Static pressure distributions along flow direction and component ratios of pressure drops

Table 3 Correlations for two-phase pressure drops

Authors	?p_c	?p_d	?p_I	C	MAD/%
Authors	?p_c	?p_d	?p_I	C	AR0	AR1	AR2
Jovanovi?等^[23]	$a v c μ c L c R 2$	$a v d L d R 2 - R - δ 2 μ c + 0.5 R - δ 2 μ d$	$C λ d h × C a d 2 / 3$	14.89	4.9	13.6	12.1
?adosz等^[24]	$a v c μ c L c + β A$	$a v c L d - β 1 μ d - 1 μ c A d 2 A 2 + 1 μ c$		7.106	29.3	33.1	31.4
Yue等^[28]	$a v c μ c L c 2 d h 2$	$a v c μ d L d - d h 2 d h 2$		32	62.3	41.7	40.8
本研究	$f × R e 2 v c μ c L c d h 2$	$f × R e 2 v c L d d h 2 1 1 μ d - 1 μ c A d 2 A 2 + 1 μ c$		AR0: 14.89 AR1: 17.58 AR2: 16.54	5.0	5.1	2.2

Table 3 Correlations for two-phase pressure drops

Authors	?p_c	?p_d	?p_I	C	MAD/%
Authors	?p_c	?p_d	?p_I	C	AR0	AR1	AR2
Jovanovi?等^[23]	$a v c μ c L c R 2$	$a v d L d R 2 - R - δ 2 μ c + 0.5 R - δ 2 μ d$	$C λ d h × C a d 2 / 3$	14.89	4.9	13.6	12.1
?adosz等^[24]	$a v c μ c L c + β A$	$a v c L d - β 1 μ d - 1 μ c A d 2 A 2 + 1 μ c$		7.106	29.3	33.1	31.4
Yue等^[28]	$a v c μ c L c 2 d h 2$	$a v c μ d L d - d h 2 d h 2$		32	62.3	41.7	40.8
本研究	$f × R e 2 v c μ c L c d h 2$	$f × R e 2 v c L d d h 2 1 1 μ d - 1 μ c A d 2 A 2 + 1 μ c$		AR0: 14.89 AR1: 17.58 AR2: 16.54	5.0	5.1	2.2

Fig.10 Comparison of numerical two-phase frictional pressure drops with empirical correlations

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