Please wait a minute...
浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (8): 1620-1627    DOI: 10.3785/j.issn.1008-973X.2020.08.022
    
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
Download: HTML     PDF(1278KB) HTML
Export: BibTeX | EndNote (RIS)      

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     
Received: 21 July 2019      Published: 28 August 2020
CLC:  TQ 022.1  
Corresponding Authors: Yao YANG     E-mail: 974003446@qq.com;yangyao306@gmail.com
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Yan-ni GUO
Yao YANG
Zheng-liang HUANG
Jing-dai WANG
Yong-rong YANG
Cite this article:

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.

URL:

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


缠绕管结构参数对管内压降的影响及压降模型

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 
Fig.1 Experimental device for pressure drop measurement in helical coil
Fig.2 Structure diagram of helical coil
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
Tab.1 Structure parameters of different helical coils
Fig.3 Variation diagram of pressure drop with flow rate in helical coils with different coiling diameters
Fig.4 Variation diagram of pressure drop with flow rate in helical coils with different coiling angles
Fig.5 Variation diagram of pressure drop with flow rate in helical coils with different tube diameters
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
Tab.2 Empirical correlation of friction coefficient in helical coil
Fig.6 Comparison of pressure drop calculated by empirical formula of literature and experimental results
Fig.7 Comparison of relative error of pressure drop between prediction model of Mccann and experimental results
Fig.8 Comparison of predicted theoretical and experimental pressure drops in different structural helical coils
Fig.9 Comparison of predicted theoretical and experimental pressure drops in different structural helical coils (Pressure drop greater than 8500 Pa)
Fig.10 Comparison between calculation results of Mccann model and results of proposed model with experimental values
Fig.11 Streamline diagram of fluid entering helical coil
Fig.12 Diagram of velocity distribution (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
Tab.3 Critical flow rate, d/D, Re and Dn of helical coil when pressure drop in helical coil reaches 8500 Pa
Fig.13 Relationship between $\xi $ and pressure drop under different experimental conditions
[1]   WANG G, WANG D, PENG X, et al Experimental and numerical study on heat transfer and flow characteristics in the shell side of helically coiled trilobal tube heat exchanger[J]. Applied Thermal Engineering, 2019, 149: 772- 787
doi: 10.1016/j.applthermaleng.2018.11.055
[2]   SEPEHR M, HASHEMI S S, RAHJOO M, et al Prediction of heat transfer, pressure drop and entropy generation in shell and helically coiled finned tube heat exchangers[J]. Chemical Engineering Research and Design, 2018, 134: 277- 291
doi: 10.1016/j.cherd.2018.04.010
[3]   FSADNI A M, WHITTY J P M A review on the two-phase pressure drop characteristics in helically coiled tubes[J]. Applied Thermal Engineering, 2016, 103: 616- 638
doi: 10.1016/j.applthermaleng.2016.04.125
[4]   REDDY K V K, KUMAR B S P, GUGULOTHU R, et al CFD analysis of a helically coiled tube in tube heat exchanger[J]. Materials Today: Proceedings, 2017, 4 (2): 2341- 2349
doi: 10.1016/j.matpr.2017.02.083
[5]   KUMAR V, SAINI S, SHARMA M, et al Pressure drop and heat transfer study in tube-in-tube helical heat exchanger[J]. Chemical Engineering Science, 2006, 61 (13): 4403- 4416
doi: 10.1016/j.ces.2006.01.039
[6]   ANDRZEJCZYK R, MUSZYNSKI T, GOSZ M Experimental investigations on heat transfer enhancement in shell coil heat exchanger with variable baffles geometry[J]. Chemical Engineering and Processing-Process Intensification, 2018, 132: 114- 126
doi: 10.1016/j.cep.2018.08.017
[7]   陈永东, 吴晓红, 周兵 LNG 缠绕管式换热器试验研究中的热物性计算方法[J]. 天然气工业, 2011, 31 (6): 92- 97
CHEN Yong-dong, WU Xiao-hong, ZHOU Bing Calculation method of thermal properties in experimental study of LNG wound tubular heat exchangers[J]. Natural Gas Industry, 2011, 31 (6): 92- 97
doi: 10.3787/j.issn.1000-0976.2011.06.020
[8]   都跃良, 张贤安 缠绕管式换热器的管理及其应用前景分析[J]. 化工机械, 2005, 32 (3): 181- 185
DU Yue-liang, ZHANG Xian-an Management of winding tube heat exchanger and analysis of its application prospects[J]. Chemical Industry Machinery, 2005, 32 (3): 181- 185
doi: 10.3969/j.issn.0254-6094.2005.03.015
[9]   GOU J, MA H, YANG Z, et al An assessment of heat transfer models of water flow in helically coiled tubes based on selected experimental datasets[J]. Annals of Nuclear Energy, 2017, 110: 648- 667
doi: 10.1016/j.anucene.2017.07.015
[10]   BERSANO A, FALCONE N, BERTANI C, et al Conceptual design of a bayonet tube steam generator with heat transfer enhancement using a helical coiled downcomer[J]. Progress in Nuclear Energy, 2018, 108: 243- 252
doi: 10.1016/j.pnucene.2018.05.018
[11]   DEAN W R Note on the motion of fluid in a curved pipe[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1927, 4 (20): 208- 223
doi: 10.1080/14786440708564324
[12]   MOOSAVI A, ABBASALIZADEH M, DIZAJI H S Optimization of heat transfer and pressure drop characteristics via air bubble injection inside a shell and coiled tube heat exchanger[J]. Experimental Thermal and Fluid Science, 2016, 78: 1- 9
doi: 10.1016/j.expthermflusci.2016.05.011
[13]   MURATA S, MIYAKE Y, INABA T, et al Laminar flow in a helically coiled pipe[J]. Bulletin of JSME, 1981, 24 (188): 355- 362
doi: 10.1299/jsme1958.24.355
[14]   HüTTL T J, WAGNER C, FRIEDRICH R Navier-Stokes solutions of laminar flows based on orthogonal helical coordinates[J]. International Journal For Numerical Methods in Fluids, 1999, 29 (7): 749- 763
doi: 10.1002/(SICI)1097-0363(19990415)29:7<749::AID-FLD815>3.0.CO;2-4
[15]   ALI S Pressure drop correlations for flow through regular helical coil tubes[J]. Fluid Dynamics Research, 2001, 28 (4): 295
doi: 10.1016/S0169-5983(00)00034-4
[16]   GUO L, FENG Z, CHEN X An experimental investigation of the frictional pressure drop of steam-water two-phase flow in helical coils[J]. International Journal of Heat and Mass Transfer, 2001, 44 (14): 2601- 2610
doi: 10.1016/S0017-9310(00)00312-4
[17]   TRUESDELL J R L C, ADLER R J Numerical treatment of fully developed laminar flow in helically coiled tubes[J]. AIChE Journal, 1970, 16 (6): 1010- 1015
doi: 10.1002/aic.690160625
[18]   MCCANN R C. Frictional pressure loss during turbulent flow in coiled tubing [C]// SPD Gulf Coast Section/ICoTA North American Coiled Tubing Roundtable. Conroe: Society of Petroleum Engineers, 1996.
[19]   SRINIVASAN P S Pressure drop and heat transfer in coils[J]. Chemical Engineering, 1968, 218: 113- 119
[20]   MANLAPAZ R L, CHURCHILL S W Fully developed laminar flow in a helically coiled tube of finite pitch[J]. Chemical Engineering Communications, 1980, 7 (1?3): 57- 78
doi: 10.1080/00986448008912549
[21]   OWHADI A, BELL K J, CRAIN JR B Forced convection boiling inside helically-coiled tubes[J]. International Journal of Heat and Mass Transfer, 1968, 11 (12): 1779- 1793
doi: 10.1016/0017-9310(68)90021-5
[22]   JU H, XU Y, HUANG Z, et al Research method and two-phase flow stability of the steam generator of HTR-10[J]. Journal of Nuclear Science and Technology, 2001, 38 (9): 739- 744
doi: 10.1080/18811248.2001.9715090
[23]   BANDARU S K, CHHABRA R P Pressure drop for single and two-phase flow of non-newtonian liquids in helical coils[J]. The Canadian Journal of Chemical Engineering, 2002, 80 (2): 315- 321
doi: 10.1002/cjce.5450800219
[24]   MANDAL S N, DAS S K Gas-liquid flow through helical coils in vertical orientation[J]. Industrial and Engineering Chemistry Research, 2003, 42 (14): 3487- 3494
doi: 10.1021/ie0200656
[25]   DOWNING R S, KOJASOY G Single and two-phase pressure drop characteristics in miniature helical channels[J]. Experimental Thermal and Fluid Science, 2002, 26 (5): 535- 546
[26]   TOHIDI A, GHAFFARI H, NASIBI H, et al Heat transfer enhancement by combination of chaotic advection and nanofluids flow in helically coiled tube[J]. Applied Thermal Engineering, 2015, 86: 91- 105
doi: 10.1016/j.applthermaleng.2015.04.043
[27]   MORAVEJI M K, HEJAZIAN M CFD examination of convective heat transfer and pressure drop in a horizontal helically coiled tube with CuO/Oil base nanofluid[J]. Numerical Heat Transfer, Part A: Applications, 2014, 66: 315- 329
doi: 10.1080/10407782.2013.872976
[28]   JAYAKUMAR J S, MAHAJANI S M, MANDAL J C, et al Experimental and CFD estimation of heat transfer in helically coiled heat exchangers[J]. Chemical Engineering Research and Design, 2008, 86 (3): 221- 232
doi: 10.1016/j.cherd.2007.10.021
[29]   LEMENAND T, PEERHOSSAINI H A thermal model for prediction of the Nusselt number in a pipe with chaotic flow[J]. Applied Thermal Engineering, 2002, 22 (15): 1717- 1730
doi: 10.1016/S1359-4311(02)00075-3
[30]   TARBELL J M, SAMUELS M R Momentum and heat transfer in helical coils[J]. The Chemical Engineering Journal, 1973, 5 (2): 117- 127
doi: 10.1016/0300-9467(73)80002-4
[31]   XIN R C, AWWAD A, DONG Z F, et al An experimental study of single-phase and two-phase flow pressure drop in annular helicoidal pipes[J]. International Journal of Heat and Fluid Flow, 1997, 18 (5): 482- 488
doi: 10.1016/S0142-727X(97)80006-9
[32]   WHITE C M Streamline flow through curved pipes[J]. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1929, 123 (792): 645- 663
doi: 10.1098/rspa.1929.0089
[33]   SCHMIDT E F W?rmeübergang und druckverlust in rohrschlangen[J]. Chemie Ingenieur Technik, 1967, 39 (13): 781- 789
doi: 10.1002/cite.330391302
[34]   ITō H Laminar flow in curved pipes[J]. Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 1969, 49 (11): 653- 663
doi: 10.1002/zamm.19690491104
[1] Le XIE,Xi-dan HENG,Yang LIU,Qi-long JIANG,Dong LIU. Transformer fault diagnosis based on linear discriminant analysis and step-by-step machine learning[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(11): 2266-2272.
[2] MENG Jia-hui, LIAO Zu-wei, JIANG Bin-bo, HUANG Zheng-liang, WANG Jing-dai, YANG Yong-rong. Influence of steam treatment on ZSM-5 catalyst and MTP reaction[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(12): 2451-2458.
[3] MAN Jun , DING Fan , LI Qi-peng , DA Jing , SHAO Sen-yin. Study of high-pressure high-speed on-off solenoid using
permanent magnet shield[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(2): 309-314.