微通道内低黏聚合物流体的停留时间分布研究

doi:10.11949/0438-1157.20201758

摘要/Abstract

摘要：

以低分子量的聚丙二醇为流动介质、酸性橙的N,N-二甲基乙酰胺溶液为示踪剂，采用脉冲响应法测定了螺旋型微通道（MC）反应器内的停留时间分布（RTD），验证了平行多釜串联（PTIS）模型与RTD实验数据的匹配性，系统考察了MC长度和Reynolds数（Re）对RTD的影响，并讨论了流体径向速度分布指数y和Peclet数（Pe）的变化规律。结果表明，RTD随MC长度的增加而变窄。当通过降低黏度来增大Re时，RTD随之变窄。当通过增大流速来增大Re时，若管径较大，则RTD随之变窄。但若管径较小且管长不长时，则RTD随Re的增加而变宽；如管长较长，则RTD随Re（或流速）的增加先变宽后变窄，即存在临界Reynolds数（Re_c）。RTD的这些变化规律表明，二次流动和径向分子扩散对细小管径的MC的RTD有显著的影响。

关键词: 微通道, 停留时间分布, 混合, 模型

Abstract:

Residence time distribution (RTD) in the spiral microchannel (MC) was determined by the impulse response method using polypropylene glycol with low molecular weight as the fluid carrier and N,N- dimethylmethylacetamide solution of acid orange as the tracer. The fittingness between parallel tanks-in-series (PTIS) model and RTD experimental data was verified. The influence of MC's length and Reynolds number (Re) on RTD was systematically studied. Additionally, the change law of radial velocity index y and Peclet number (Pe) of the fluid was thoroughly discussed. The results indicated that RTD became narrower with the increase of MC's length. When Re was increased by reducing viscosity, RTD became narrowed with Re increasing. When Re was increased by increasing flow rate, RTD would also become narrower as Re grew if the MC's diameter was large. However, if the MC's diameter was small and length was short, RTD would be widened as Re increased; on condition of longer length, RTD could become widened first and then narrowed with the increase of Re (or velocity). That is, there was a critical Reynolds number (Re_c). These changes of RTD indicate that secondary flow and radial molecular diffusion have a significant effect on the RTD of MC with small diameters.

Key words: microchannel, residence time distribution, mixing, modeling

中图分类号:

TQ 021.4

赵晶, 李伯耿, 卜志扬, 范宏. 微通道内低黏聚合物流体的停留时间分布研究[J]. 化工学报, 2021, 72(8): 4030-4038.

Jing ZHAO, Bogeng LI, Zhiyang BU, Hong FAN. Research on residence time distribution of the low-viscous polymer fluid in microchannel[J]. CIESC Journal, 2021, 72(8): 4030-4038.

图/表 9

图1 RTD测量的设备示意图(a) loading state; (b) injection state

Fig.1 Equipment diagram for RTD measurement

表1 v、vˉ、r以及?r与y（或m）的关系

Table 1 Relationship between v， vˉ， r， ?r and y （or m）

参数	PTIS-y	PTIS-m
v	$1 - r y$	$1 - r m$
$v ˉ$	$2 y + 1 y + 2$	$m m + 2$
r	$1 - v 1 / y$	$1 - v 1 / m$
?r	$- v 1 / y - 1 y$	$- 1 - v 1 / m - 1 m$

表1 v、vˉ、r以及?r与y（或m）的关系

Table 1 Relationship between v， vˉ， r， ?r and y （or m）

参数	PTIS-y	PTIS-m
v	$1 - r y$	$1 - r m$
$v ˉ$	$2 y + 1 y + 2$	$m m + 2$
r	$1 - v 1 / y$	$1 - v 1 / m$
?r	$- v 1 / y - 1 y$	$- 1 - v 1 / m - 1 m$

图2 RTD实验结果及模型回归图（T=110℃, d=1 mm, D=140 mm）、

Fig.2 RTD experimental data and regression results of models

图3 活塞流与层流示意图

Fig.3 Schematic diagram of plug flow and laminar flow

表2 RTD的模型回归结果

Table 2 Comparison of regression results with various RTD models

Run	d/mm	L/m	Q/(ml/min)	u/(m/s)	$t ˉ$ /s	Re	RSSE/%
Run	d/mm	L/m	Q/(ml/min)	u/(m/s)	$t ˉ$ /s	Re	PTIS-y model	PTIS-m model	TIS model	AD model
1	0.5	6	0.5	0.043	142	2.5	1.4	3.4	3.6	7.9
2	0.5	6	1.0	0.085	71	5	2.2	2.9	6.1	11.8
3	0.5	6	2.0	0.170	35.5	10	1.4	3.1	2.3	4.9
4	0.5	6	5.0	0.425	14.2	25	1.2	1.9	3.7	11.1
5	0.5	12	0.5	0.043	284	2.5	0.4	6	1.1	3.7
6	0.5	12	1.0	0.085	142	5	4.2	8.3	5.8	9.9
7	0.5	12	2.0	0.170	71	10	0.8	3	3.9	8.8
8	0.5	12	5.0	0.425	28.4	25	3.6	5	6.3	10
9	0.5	30	0.5	0.043	709.4	2.5	0.3	2.7	0.8	3.2
10	0.5	30	1.0	0.085	354.7	5	1	2.3	2.1	4.9
11	0.5	30	2.0	0.170	177.5	10	2.1	4.5	4.7	7.9
12	0.5	30	5.0	0.425	70.9	25	0.4	6.7	1.7	3.7
13	1.0	6	0.5	0.011	567.5	1.25	0.3	5.8	0.9	2.5
14	1.0	6	1.0	0.021	283.7	2.5	0.8	14.7	16.1	20.5
15	1.0	6	2.0	0.042	142	5	5.7	6.8	16.2	20.2
16	1.0	6	5.0	0.106	56.7	12.5	5.5	6.6	34.2	38.8
17	1.0	12	0.5	0.011	1135	1.25	3.1	3.9	9.6	13.8
18	1.0	12	1.0	0.021	567.5	2.5	2.2	3.1	11	15.6
19	1.0	12	2.0	0.043	283.7	5	3	5	13.2	15.4
20	1.0	30	0.5	0.011	2837	1.25	0.6	7.7	2.12	4.1
21	1.0	30	1.0	0.021	1419	2.5	1.3	6.7	4.2	7.1
22	1.0	30	2.0	0.043	709.3	5	5.4	12.6	11.7	13.3
23	1.0	30	0.5^①	0.011	2837	0.5	1.4	2.6	5.7	12.6
24	1.0	30	0.5^②	0.011	2837	0.21	2.4	3.3	4.8	9.1

表2 RTD的模型回归结果

Table 2 Comparison of regression results with various RTD models

Run	d/mm	L/m	Q/(ml/min)	u/(m/s)	$t ˉ$ /s	Re	RSSE/%
Run	d/mm	L/m	Q/(ml/min)	u/(m/s)	$t ˉ$ /s	Re	PTIS-y model	PTIS-m model	TIS model	AD model
1	0.5	6	0.5	0.043	142	2.5	1.4	3.4	3.6	7.9
2	0.5	6	1.0	0.085	71	5	2.2	2.9	6.1	11.8
3	0.5	6	2.0	0.170	35.5	10	1.4	3.1	2.3	4.9
4	0.5	6	5.0	0.425	14.2	25	1.2	1.9	3.7	11.1
5	0.5	12	0.5	0.043	284	2.5	0.4	6	1.1	3.7
6	0.5	12	1.0	0.085	142	5	4.2	8.3	5.8	9.9
7	0.5	12	2.0	0.170	71	10	0.8	3	3.9	8.8
8	0.5	12	5.0	0.425	28.4	25	3.6	5	6.3	10
9	0.5	30	0.5	0.043	709.4	2.5	0.3	2.7	0.8	3.2
10	0.5	30	1.0	0.085	354.7	5	1	2.3	2.1	4.9
11	0.5	30	2.0	0.170	177.5	10	2.1	4.5	4.7	7.9
12	0.5	30	5.0	0.425	70.9	25	0.4	6.7	1.7	3.7
13	1.0	6	0.5	0.011	567.5	1.25	0.3	5.8	0.9	2.5
14	1.0	6	1.0	0.021	283.7	2.5	0.8	14.7	16.1	20.5
15	1.0	6	2.0	0.042	142	5	5.7	6.8	16.2	20.2
16	1.0	6	5.0	0.106	56.7	12.5	5.5	6.6	34.2	38.8
17	1.0	12	0.5	0.011	1135	1.25	3.1	3.9	9.6	13.8
18	1.0	12	1.0	0.021	567.5	2.5	2.2	3.1	11	15.6
19	1.0	12	2.0	0.043	283.7	5	3	5	13.2	15.4
20	1.0	30	0.5	0.011	2837	1.25	0.6	7.7	2.12	4.1
21	1.0	30	1.0	0.021	1419	2.5	1.3	6.7	4.2	7.1
22	1.0	30	2.0	0.043	709.3	5	5.4	12.6	11.7	13.3
23	1.0	30	0.5^①	0.011	2837	0.5	1.4	2.6	5.7	12.6
24	1.0	30	0.5^②	0.011	2837	0.21	2.4	3.3	4.8	9.1

图4 RTD方差及PTIS-y模型参数随MC管长变化曲线（T= 110℃, μ= 8.5 mPa·s, D= 140 mm）

Fig.4 Variance of RTD and parameters of PTIS-y model vs MC of different length

图5 流体黏度变化时RTD方差及PTIS-y模型参数随Re变化曲线（T=110℃, d=1 mm, L=30 m, u=0.011 m/s, D=140 mm, μ=8.5~50.3 mPa·s）

Fig.5 Variance of RTD and parameters of PTIS-y model with Re when changing viscosity

图6 流速改变时MC中的RTD方差及PTIS-y模型参数随Re变化曲线（T=110℃, μ=8.5 mPa·s, D=140 mm, u=0.011~0.425 m/s）

Fig.6 Variance of RTD and parameters of PTIS-y model with Re when changing flow rate

图7 模型参数Pey与RTD方差的关系(T=110℃, d=1 mm, D=140 mm)

Fig.7 Relationship between Pey and variance of RTD

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