Analysis and calculation of friction resistance of gas-liquid flow in inclined riser pipe under fluctuating vibration

doi:10.11949/0438-1157.20211106

Abstract

Abstract:

Accurate calculation of frictional pressure drop of gas-liquid two-phase flow under fluctuating vibration is of great significance to the development of marine nuclear power. The variation of frictional pressure drop of gas-liquid two-phase flow in a 30° inclined riser pipe under different vibration and flow conditions was studied by experiment. The results show that the fluctuation amplitude and average value of friction pressure drop increase significantly under fluctuating vibration. Compared with the static state, the multi-scale entropy of friction pressure drop increases obviously except bubble flow, and the phenomenon of large-scale oscillation is present, which indicates that the instability of gas-liquid two-phase flow is more significant. The calculated results of the static friction pressure drop model are quite different from the experimental values, and the existing models are not suitable for the fluctuating vibration state. It is found that the friction coefficient is inversely proportional to the homogeneous Reynolds number and directly proportional to the vibration amplitude and frequency. Based on a large number of experimental data, the calculation formula of friction resistance coefficient suitable for fluctuating vibration state is established, and the calculation results are in good agreement with the experimental results.

Key words: gas-liquid flow, fluctuating vibration, inclined riser pipe, friction resistance, prediction, model

摘要：

起伏振动下气液两相流摩擦压降的准确计算对海洋核动力的发展有重要意义。实验研究了不同振动和流动工况下30°倾斜上升管气液两相流摩擦压降的变化规律。结果表明，起伏振动下摩擦压降波动幅度和平均值显著增大。与静止状态相比，起伏振动下摩擦压降的多尺度熵值除泡状流外明显增大，且呈现大幅振荡现象，流动不稳定性更加显著。静止状态摩擦压降模型计算结果与实验值误差较大，现有模型对于起伏振动状态不适用。分析流动和振动参数对摩擦阻力系数的影响，发现其与均相雷诺数成反比，与振动幅值以及频率成正比。以大量实验数据为基础，建立了适用于起伏振动状态的摩擦阻力系数计算关系式，计算与实验结果吻合较好。

关键词: 气液两相流, 起伏振动, 倾斜上升管, 摩擦压降, 预测, 模型

CLC Number:

TL 334

Yunlong ZHOU, Qichao LIU. Analysis and calculation of friction resistance of gas-liquid flow in inclined riser pipe under fluctuating vibration[J]. CIESC Journal, 2022, 73(2): 643-652.

周云龙, 刘起超. 起伏振动倾斜上升管气液两相流摩擦阻力分析与计算[J]. 化工学报, 2022, 73(2): 643-652.

Figures/Tables 15

Fig.1 Experimental system

Table 1 Experimental instrument and uncertainty

仪器	量程	精度	不确定度
电磁流量计	0~10 m³/h	0.5%	0.94%~4.03%
质量流量计	0~30 m³/h	1%	1.8%~5.59%
差压变送器	0~25 kPa	0.1%	0.326%~2.002%

Table 2 Calculation model of two phase dynamic viscosity

模型	关系式
McAdams^[2]	$1 / μ t p = x / μ g + (1 - x) / μ w$
Beattie-Whalley^[3]	$μ t p = β μ g + (1 - β) (1 + 2.5 β) μ w$
Duckler^[4]	$μ t p = β μ g + (1 - β) μ w$
Awad-Muzychka^[5]	$μ t p = μ g 2 μ g + μ w - 2 (μ g - μ w) (1 - x) 2 μ g + μ w + (μ g - μ w) (1 - x)$

Table 2 Calculation model of two phase dynamic viscosity

模型	关系式
McAdams^[2]	$1 / μ t p = x / μ g + (1 - x) / μ w$
Beattie-Whalley^[3]	$μ t p = β μ g + (1 - β) (1 + 2.5 β) μ w$
Duckler^[4]	$μ t p = β μ g + (1 - β) μ w$
Awad-Muzychka^[5]	$μ t p = μ g 2 μ g + μ w - 2 (μ g - μ w) (1 - x) 2 μ g + μ w + (μ g - μ w) (1 - x)$

Fig.2 Calculation errors distribution of different models of static pipe

Table 3 The errors between calculated values of different models and experimental values in static pipe

模型		E_MA/%	30%以内占比/%
均相模型	McAdams	27.86	47.85
	Beattie-Whalley	31.93	38.04
	Duckler	31.76	34.36
	Awad-Muzychka	33.45	30.06
分相模型	Chisholm	28.32	53.99
	Sun and Mishima	29.87	44.17
	Müller and Heck	27.22	51.53

Fig.3 Friction pressure drop fluctuation of static and fluctuating vibration pipe

Fig.4 Power spectrum of frictional pressure drop in static and fluctuating vibration pipeline

Fig.5 Multi scale entropy of frictional pressure drop in fluctuating and stationary pipes under different flow conditions

Fig.6 Vibration acceleration and friction pressure drop fluctuation and frequency analysis

Fig.7 Friction coefficient at different Reynolds numbers

Fig.8 Friction coefficient under different vibration amplitude

Fig.9 Friction coefficient under different vibration frequencies

Fig.10 Friction coefficient under different tilt angle

Fig.11 Comparison between calculated and experimental values of friction coefficient of vibration

Fig.12 Error distribution of new model calculation results

References 31

1	阎昌琪. 气液两相流[M].哈尔滨: 哈尔滨工程大学出版社, 2007.
	Yan C Q. Gas and Liquid Two-Phase Flow [M]. Harbin: Harbin Engineering University Press, 2007.
2	McAdams W H, Woods W K, Herman L C. Vaporization inside horizontal tubes (Ⅱ): Benzene oil mixture[J]. Trans. ASME, 1942, 64: 193-200.
3	Beattie D R H, Whalley P B. A simple two-phase frictional pressure drop calculation method[J]. International Journal of Multiphase Flow, 1982, 8(1): 83-87.
4	Duckler A E,Wicks M,Cleveland R G.Pressure drop and hold-up in two phase flow[J]. AIChE Journal,1964,10:38-51.
5	Awad M M, Muzychka Y S. Effective property models for homogeneous two-phase flows[J]. Experimental Thermal and Fluid Science, 2008, 33(1): 106-113.
6	Lin S, Kwok C C K, Li R Y, et al. Local frictional pressure drop during vaporization of R-12 through capillary tubes[J]. International Journal of Multiphase Flow, 1991, 17(1): 95-102.
7	Lockhart R W, Martinelli R C. Proposed correlation of data for isothermal two-phase two-component flow in pipes[J].Chemical Engineering Progress,1949,45:39–45.
8	Chisholm D. A theoretical basis for the Lockhart-Martinelli correlation for two-phase flow[J]. International Journal of Heat and Mass Transfer, 1967, 10(12): 1767-1778.
9	Sun L C, Mishima K. Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels[J]. International Journal of Multiphase Flow, 2009, 35(1): 47-54.
10	Müller-Steinhagen H, Heck K. A simple friction pressure drop correlation for two-phase flow in pipes[J]. Chemical Engineering and Processing: Process Intensification, 1986, 20(6): 297-308.
11	高璞珍, 庞凤阁, 王兆祥. 核动力装置一回路冷却剂受海洋条件影响的数学模型[J]. 哈尔滨工程大学学报, 1997, 18(1): 24-27.
	Gao P Z, Pang F G, Wang Z X. Mathematical model of primary coolant in nuclear power plant influenced by ocean conditions[J]. Journal of Harbin Engineering University, 1997, 18(1): 24-27.
12	Xing D C, Yan C Q, Sun L C, et al. Effect of rolling motion on single-phase laminar flow resistance of forced circulation with different pump head[J]. Annals of Nuclear Energy, 2013, 54: 141-148.
13	Xing D C, Yan C Q, Sun L C, et al. Effects of rolling on characteristics of single-phase water flow in narrow rectangular ducts[J]. Nuclear Engineering and Design, 2012, 247: 221-229.
14	曹夏昕, 阎昌琪, 孙立成, 等. 摇摆状态下竖直管内单相水阻力特性实验研究[J]. 核动力工程, 2007, 28(3): 51-55.
	Cao X X, Yan C Q, Sun L C, et al. Pressure drop characteristics of single-phase flow in vertical rolling pipes[J]. Nuclear Power Engineering, 2007, 28(3): 51-55.
15	张金红, 阎昌琪, 曹夏昕, 等. 摇摆状态下水平管中单相水的摩擦阻力实验研究[J]. 核动力工程, 2008, 29(4): 44-49.
	Zhang J H, Yan C Q, Cao X X, et al. Experimental study on single-phase liquid friction factor in rolling horizontal pipe[J]. Nuclear Power Engineering, 2008, 29(4): 44-49.
16	Yu Z T, Tan S C, Yuan H S, et al. Experimental investigation on flow instability of forced circulation in a mini-rectangular channel under rolling motion[J]. International Journal of Heat and Mass Transfer, 2016, 92: 732-743.
17	张金红. 摇摆状态下气水两相流流型及阻力特性研究[D]. 哈尔滨: 哈尔滨工程大学, 2009.
	Zhang J H. Study on flow pattern and resistance characteristics of air-water two-phase flow in rolling motion[D]. Harbin: Harbin Engineering University, 2009.
18	栾锋. 摇摆对水平管内气水两相流影响的研究[D]. 哈尔滨: 哈尔滨工程大学, 2009.
	Luan F. Research on effect of rolling condition on gas-water flow in horizontal tubes[D]. Harbin: Harbin Engineering University, 2009.
19	刘传成, 阎昌琪, 孙立成, 等. 摇摆运动下矩形窄通道内摩擦压降特性研究[J]. 原子能科学技术, 2013, 47(4): 576-581.
	Liu C C, Yan C Q, Sun L C, et al. Characteristics of frictional pressure drop in narrow rectangular channel in rolling motion[J]. Atomic Energy Science and Technology, 2013, 47(4): 576-581.
20	Jin G Y, Yan C Q, Sun L C, et al. Effect of rolling motion on transient flow resistance of two-phase flow in a narrow rectangular duct[J]. Annals of Nuclear Energy, 2014, 64: 135-143.
21	Li S L, Cai W H, Jiang Y Q, et al. The pressure drop and heat transfer characteristics of condensation flow with hydrocarbon mixtures in a spiral pipe under static and heaving conditions[J]. International Journal of Refrigeration, 2019, 103: 16-31.
22	Iliuta I, Larachi F. CO₂ and H₂S absorption by MEA solution in packed-bed columns under inclined and heaving motion conditions — hydrodynamics and reactions performance for marine applications[J]. International Journal of Greenhouse Gas Control, 2018, 79: 1-13.
23	Pendyala R, Jayanti S, Balakrishnan A R. Flow and pressure drop fluctuations in a vertical tube subject to low frequency oscillations[J]. Nuclear Engineering and Design, 2008, 238(1): 178-187.
24	Li J R, Hu H T, Xie Y, et al. Two-phase flow boiling characteristics in plate-fin channels at offshore conditions[J]. Applied Thermal Engineering, 2021, 187: 116595.
25	Hong G, Yan X, Yang Y H, et al. Experimental study on onset of nucleate boiling in narrow rectangular channel under static and heaving conditions[J]. Annals of Nuclear Energy, 2012, 39(1): 26-34.
26	Yu S C, Chen J, Mi X G, et al. Experimental and numerical investigation of two-phase flow outside tube bundle of liquefied natural gas spiral wound heat exchangers under offshore conditions[J]. Applied Thermal Engineering, 2019, 152: 103-112.
27	周云龙, 刘起超, 汪俊超. 起伏振动下倾斜管内单相流流动阻力特性分析[J]. 原子能科学技术, 2020, 54(3): 421-428.
	Zhou Y L, Liu Q C, Wang J C. Analysis of flow resistance characteristic of single-phase flow in inclined pipe under undulating vibration[J]. Atomic Energy Science and Technology, 2020, 54(3): 421-428.
28	周云龙, 常赫, 刘起超. 非线性振动下水平通道气液两相流动[J]. 化工学报, 2019, 70(7): 2512-2519.
	Zhou Y L, Chang H, Liu Q C. Gas-liquid two-phase flow in horizontal channel under nonlinear vibration[J]. CIESC Journal, 2019, 70(7): 2512-2519.
29	Zhou Y L, Chang H, Lv Y. Gas-liquid two-phase flow in a horizontal channel under nonlinear oscillation: flow regime, frictional pressure drop and void fraction[J]. Experimental Thermal and Fluid Science, 2019, 109: 109852.
30	张华高. 船舶静稳性与航行安全博弈[J]. 中国水运, 2015(9): 56.
	Zhang H G. Game between ship static stability and navigation safety[J].China Water Transportation, 2015(9): 56.
31	钱政, 贾果欣. 误差理论与数据处理[M]. 北京: 科学出版社, 2013.
	Qian Z, Jia G X. Error Theory and Data Processing [M]. Beijing: Science Press, 2013.

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