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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (8): 1620-1627    DOI: 10.3785/j.issn.1008-973X.2020.08.022
化学工程     
缠绕管结构参数对管内压降的影响及压降模型
郭燕妮(),杨遥*(),黄正梁,王靖岱,阳永荣
浙江大学 浙江省化工高效制造技术重点实验室，浙江 杭州 310027
Pressure drop model and influence of structure parameters of helical coil on pressure drop in tube
Yan-ni GUO(),Yao YANG*(),Zheng-liang HUANG,Jing-dai WANG,Yong-rong YANG
Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, Zhejiang University, Hangzhou 310027, China
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摘要：

为了研究缠绕管内流体的压降规律、建立具有较宽适用范围的压降预测模型，以水为介质，采用U型压差计测量缠绕管内流体进、出口的压降，实验考察缠绕直径、缠绕角度、管径等缠绕管结构参数对管内压降的影响. 结果表明，在流速及其他结构参数相同的情况下，缠绕直径或管径越小，单位长度缠绕管内压降越大；在不同流速区间，缠绕管结构参数对管内压降的影响程度不同. 在低流速（小于0.5 m/s）下，缠绕管结构对管内压降的影响较小；在高流速（大于0.5 m/s）下，缠绕管结构对管内压降的影响显著. 采用统一的压降预测模型对实验数据拟合会使得其在高压降区失准，进而提出由流动参数和缠绕管几何参数组合而成的分段特征参数，并构建分段式压降预测模型. 分段式压降模型的计算值与实验值的相对偏差小于10%.
关键词： 缠绕管;  二次流;  结构参数;  压降模型;  特征参数    
Abstract:

The pressure drops of the fluid in the helical coil were measured through the water as the medium and the U-shaped pressure instrument as the measuring tool, to study the law of pressure drop in the helical coil and establish a pressure drop prediction model with a wide range of applications. The effects of structure parameters including coiling diameter, coiling angle and tube diameter on the pressure drop were investigated experimentally. Results show that the pressure drop of the helical coil is larger if the coiling diameter or the tube diameter of the helical coil is smaller in the case of the same flow rate and other structure parameters. The structure parameters of the helical coil have different effects on the pressure drop at different flow rate ranges. The influence of the structure parameters on the pressure drop is small at low flow rates (u<0.5 m/s), and the structure parameters have a significant influence on the pressure drop at high flow rates (u>0.5 m/s). The uniform model parameters made the prediction model of the pressure drop in the helical coil misaligned in the high-pressure drop zone. Therefore, the segmentation characteristic parameter was proposed, which is composed of the flow parameters and the structure parameters. The relative deviation of the pressure drop between the calculated and the measured is less than 10%.
Key words: helical coil    secondary flow    structure parameter    pressure drop model    characteristic parameter
收稿日期: 2019-07-21 出版日期: 2020-08-28
CLC:  TQ 022.1  
基金资助: 国家自然科学基金资助项目（21808197，61621002）；国家杰出青年科学基金资助项目（21525627）
通讯作者: 杨遥     E-mail: 974003446@qq.com;yangyao306@gmail.com
作者简介: 郭燕妮（1993—），女，硕士生，从事化工过程方向研究. orcid.org/0000-0003-0046-4764. E-mail： 974003446@qq.com
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郭燕妮
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引用本文:

郭燕妮,杨遥,黄正梁,王靖岱,阳永荣. 缠绕管结构参数对管内压降的影响及压降模型[J]. 浙江大学学报(工学版), 2020, 54(8): 1620-1627.

Yan-ni GUO,Yao YANG,Zheng-liang HUANG,Jing-dai WANG,Yong-rong YANG. Pressure drop model and influence of structure parameters of helical coil on pressure drop in tube. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1620-1627.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.08.022    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I8/1620

图 1  缠绕管压降测量实验装置
图 2  缠绕管结构示意图
编号 d/mm D/mm α/(°)
1 15.0 325 10
2 15.0 273 10
3 15.0 219 10
4 15.0 325 5
5 15.0 325 15
6 10.8 325 10
7 22.0 325 10
表 1  不同结构缠绕管的结构参数
图 3  不同缠绕直径缠绕管内压降随流速的变化规律
图 4  不同缠绕角度缠绕管内压降随流速的变化规律
图 5  不同管径缠绕管内压降随流速的变化规律
文献 缠绕管内摩擦系数关联式 流动条件 几何条件 研究体系
1）注：Dn为弯管中考虑曲率的流体力学无量纲参数，Dn=Re(d/D)0.5
文献[30] $\begin{aligned}\frac{ {f_{\rm c}} }{ {f_{\rm s}} } =& 1.0 + [8.279 \times {10^{ - 4} } + 7.964 \times {10^{ - 3} }/\lambda ]Re -\\& 2.096 \times {10^{ - 7} }R{e^2}\end{aligned}$ 34.64<Re<2 738.00 3<D/d<30 水、醋酸、正丁醇、二甘醇、酒精
文献[31] $\begin{aligned}f_{\rm c} = 0.029\;85 + \frac{ {75.89[0.5 - { {\tan }^{ - 1} }\left(\frac{ {Dn - 39.88} }{ {77.56} }\right)/\pi ]} }{ { { {\left(\frac{D}{ { {d_{ {{i} },{\rm{out} } } } - {d_{ {{o} },{\rm{in} } } } } }\right)}^{1.45} } } }\end{aligned}$ 210<Re<23000 di=12.700、9.525、6.350 mm分别对应
do=21.180、15.748、10.210 mm 		空气、水
文献[32] $\begin{aligned}\frac{{f_{\rm s}}}{{f_{\rm c}}} = 1 - {\left(1 - {\left(\frac{{11.6}}{{Dn}}\right)^{0.45}}\right)^{\frac{1}{0.45}1)}}\end{aligned}$ Re<13000 D/d=5、15、50、2 050 水
文献[33] $\begin{aligned}\frac{f}{{f_{\rm s}}} = 1 + 0.14{R_0}^{0.97}R{e^{(1 - 0.644{R_0}^{0.312})}}\end{aligned}$ Re<2500 di/D=0.0363、0.061 0、0.0882、0.1050 水
文献[18] $\begin{aligned} f = \frac{{0.084}}{{R{e^{0.2}}}}{\left( {\frac{d}{D}} \right)^{0.1}}\end{aligned}$ 2500<Re<24880 di=33.725、45.187、49.775 mm
D=2450 mm 		水
文献[19] $\begin{aligned} f = 1.334R{e^{ - 0.2}}{\left( {\frac{d}{D}} \right)^{0.1}}\end{aligned}$ Re<2100 0.0097<d/D<0.1350 水
文献[34] $\begin{aligned} f = 1.216R{e^{ - 0.25}} + 0.116{\left(\frac{d}{D}\right)^{0.5}}\end{aligned}$ Re<50000 di=31.54、31.92、32.08、32.46 mm
分别对应
D=258、1354、1606、10400 mm 		水
文献[35] $\begin{aligned} f = 0.06 + 0.12{\left(\frac{d}{D}\right)^{0.275}}R{e^{ - 0.4}}\end{aligned}$ Re>50000 di=19.8 mm 水-空气气体质量分数为0.04~0.60
表 2  缠绕管内摩擦系数的经验关联式
图 6  文献经验公式计算缠绕管内压降值与实验值比较
图 7  Mccann预测模型计算的压降与实验值的相对误差对比图
图 8  不同结构缠绕管内预测理论压降与实验压降的对比图
图 9  不同结构缠绕管内预测理论压降与实验压降的对比图（压降大于8500 Pa）
图 10  Mccann模型及本研究模型计算结果与实验值的对比图
图 11  流体进入缠绕管内的流线图
图 12  速度分布图（d=10.8 mm）
条件 u/(m·s?1) d/D Re Dn
D=219，d=15.0，α=10° 1.3 0.068 19500 5103
D=273，d=15.0，α=10° 1.4 0.055 21000 5274
D=325，d=15.0，α=10° 1.5 0.046 22500 5156
D=325，d=15.0，α=5° 1.5 0.046 22500 4833
D=325，d=15.0，α=15° 1.5 0.046 22500 4833
D=325，d=10.8，α=10° 1.2 0.033 12960 2362
表 3  缠绕管内压降达到8500 Pa时的临界u、d/D、Re及Dn
图 13  不同实验条件下 $\xi $与压降的关系
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