基于三流体模型物理引导神经网络的扰动波速预测

doi:10.16085/j.issn.1000-6613.2024-1757

摘要/Abstract

摘要：

扰动波广泛存在于蒸发器、天然气等环雾状两相流工业环境中，其中扰动波速是气液界面动量传递、传热和摩擦压降的重要参数。为提高扰动波大范围预测精度，本文以气相-液滴-液膜三流体模型为基础，考虑夹带液滴影响对气芯参数和液膜参数进行修正，提出了基于物理引导神经网络（PGNN）的扰动波速预测方法。利用环雾状流实验装置进行不同载气工况和液相流量实验，利用双电导环液膜传感器获得扰动波速，利用液膜提取装置测量液滴夹带率，并以气相韦伯数和液相雷诺数为参数建立了夹带率关联式。对提出的物理引导神经网络进行了超参数优化，利用不同工况（口径、压力、介质物性、流动方向）下的288组公开扰动波数据进行预测，76.74%的数据点在±5.0%误差带以内，94.10%的数据点在±15.0%误差带以内，相较于其他扰动波关联式和机器学习模型，本文提出的PGNN模型预测精度和可拓展性均大大提升。

关键词: 预测, 气液两相流, 神经网络, 扰动波速, 夹带率

Abstract:

Disturbance waves widely exist in evaporators, natural gas and other industrial environments in annular mist flow pattern, among which the disturbance wave velocity is an important parameter for gas-liquid momentum transfer, heat-transfer and friction pressure drop prediction. To improve the predicted accuracy, the physical-guided neural network (PGNN) was proposed based on the three-fluid model, where the gas core mixture parameters and liquid film parameter were revised by considering the effect of droplet entrained in the gas core. For the experiments, flow tests on various carrier gas parameter and liquid flow rate were conducted, the wave velocities were obtained by using dual conductivity ring liquid film sensor, and the droplet entrainment was measured by using the developed liquid film extraction and metering device. The entrainment correlation was developed with the parameters of gas Weber number and liquid Reynolds number. The hyperparameters of the proposed physical-guided neural network was optimized, and the database of 288 set covering various two-phase flow conditions (pipe diameter, operational pressure, physical properties of the medium, flow direction) was used for the prediction. The results indicated that 76.74% data were within ±5.0% error bands and 94.10% data were within ±15.0% error bands. The predicted accuracy and scalability could be largely enhanced for the proposed PGNN method.

Key words: prediction, gas-liquid two-phase flow, neural networks, disturbance wave velocity, entrainment

中图分类号:

TP212.9

李金霞, 茹浩然, 刘文凯, 孙宏军, 丁红兵. 基于三流体模型物理引导神经网络的扰动波速预测[J]. 化工进展, 2025, 44(4): 1815-1824.

LI Jinxia, RU Haoran, LIU Wenkai, SUN Hongjun, DING Hongbing. Physical-guided neural network based on three-fluid model for disturbance wave velocity prediction[J]. Chemical Industry and Engineering Progress, 2025, 44(4): 1815-1824.

图/表 15

图1 气相-液滴-液膜三流体模型

表1 Kumar等[4]和Sun等[7]建模对比

参数	Kumar等^[4]	Sun等^[7]
扰动波速	$V w = Ψ V s g + V s l 1 + Ψ$	$V w = Ψ' V g c + u ¯ i 1 + Ψ'$
界面滑移速度比参数	$Ψ = 5.5 ρ g ρ l 0.5 R e l R e g 0.25$	$Ψ' = 10.6 ρ g c ρ l 0.5 R e l f R e g' 0.25$
气相特征速度	$V s g = W g A ρ g$	$V g c = W g A c o r e ρ g + W l E A c o r e ρ l$
特征密度	$ρ g$	$ρ g c = ρ g + W l E A c o r e V g c$
液相特征速度	$V s l = W l A ρ l$	$u ¯ i = 1 - E V s l$
气相特征雷诺数	$R e g = V s g ρ g D μ g$	$R e g' = ρ g V g c D μ g$
液相特征雷诺数	$R e l = ρ l V s l D μ l$	$R e l f = ρ l u ¯ i D μ l$

表1 Kumar等[4]和Sun等[7]建模对比

参数	Kumar等^[4]	Sun等^[7]
扰动波速	$V w = Ψ V s g + V s l 1 + Ψ$	$V w = Ψ' V g c + u ¯ i 1 + Ψ'$
界面滑移速度比参数	$Ψ = 5.5 ρ g ρ l 0.5 R e l R e g 0.25$	$Ψ' = 10.6 ρ g c ρ l 0.5 R e l f R e g' 0.25$
气相特征速度	$V s g = W g A ρ g$	$V g c = W g A c o r e ρ g + W l E A c o r e ρ l$
特征密度	$ρ g$	$ρ g c = ρ g + W l E A c o r e V g c$
液相特征速度	$V s l = W l A ρ l$	$u ¯ i = 1 - E V s l$
气相特征雷诺数	$R e g = V s g ρ g D μ g$	$R e g' = ρ g V g c D μ g$
液相特征雷诺数	$R e l = ρ l V s l D μ l$	$R e l f = ρ l u ¯ i D μ l$

图2 物理引导BP神经网络结构loss—均方误差；Ψ(i)'—第i个样本的预测值

表2 扰动波速数据库

D/10^-3m	P/10⁶Pa	V_sg/m·s^-1	V_sl/m·s^-1	数量	介质	流动方向	扰动波速测量不确定度	参考文献
50	0.1~0.7	10~35	0.006~0.6	42	空气、水	水平	±10.6%	[6]
15	0.15~0.35	18.9~37.7	0.0028~0.028	81	空气、水	竖直	±12.5%	[7]
31.8	0.25	23.4~50.7	0.01~0.12	25	空气、水	竖直	—	[10]
9.525	0.1	5.22~22.05	0.056~0.318	36	空气、水	竖直	—	[11]
9.4	0.12~0.4	6~88	0.052~0.577	40	空气、水	竖直	—	[12]
5	0.1	13.6~43.2	0.0013~0.004	24	空气、水	竖直	—	[13]
11	0.1	12~28	0.023~0.089	28	空气、水	竖直	±11%	[14]
11.6×36	0.1	7.5~13.6	0.008~0.027	12	空气、饱和五氟丙烷（R245fa）	竖直	±22.9%	[15]

图3 实验装置与测量技术

表3 实验主要性能参数

参数	范围	不确定度	绝对/相对
管径D/10^-3m	15	$± 0.1$	绝对
两个传感器的距离L/10^-3m	30	$± 0.14$	绝对
工作压力P/10³Pa	150~350	$± 0.7$ %	相对
气体密度ρ_g/kg·m^-3	1.79~4.24	$± 2.4 %$	相对
气体表观流速V_sg/m·s^-1	18.86~37.73	$± 2.6 %$	相对
液体表观流速V_sl/10^-3m·s^-1	2.8~28	$± 2.0 %$	相对
液膜的质量流量W_lf/10^-3kg·s^-1	0.44~4.08	$± 3.2 %$	相对
夹带率E/%	4.89~19.06	$± 3.8 %$	相对
气体流量Q_g/10^-3m³·s^-1	1.39~ 6.94	$± 1.0 %$	相对
液相流量Q_l/10^-6m³·s^-1	0~4.72	$± 2.0 %$	相对

表3 实验主要性能参数

参数	范围	不确定度	绝对/相对
管径D/10^-3m	15	$± 0.1$	绝对
两个传感器的距离L/10^-3m	30	$± 0.14$	绝对
工作压力P/10³Pa	150~350	$± 0.7$ %	相对
气体密度ρ_g/kg·m^-3	1.79~4.24	$± 2.4 %$	相对
气体表观流速V_sg/m·s^-1	18.86~37.73	$± 2.6 %$	相对
液体表观流速V_sl/10^-3m·s^-1	2.8~28	$± 2.0 %$	相对
液膜的质量流量W_lf/10^-3kg·s^-1	0.44~4.08	$± 3.2 %$	相对
夹带率E/%	4.89~19.06	$± 3.8 %$	相对
气体流量Q_g/10^-3m³·s^-1	1.39~ 6.94	$± 1.0 %$	相对
液相流量Q_l/10^-6m³·s^-1	0~4.72	$± 2.0 %$	相对

图4 夹带率建模结果

图5 夹带率建模与测量结果

表4 各参数不确定度及合成不确定度

参数	不确定度/%	合成不确定度
液相表观流速V_sl	±2.0	$u c R e l R e l = ± 2.5 %$
液相密度ρ_l	±0.22
管道公称直径D	±0.67
液相动力黏度µ_l	±1.33
气体密度ρ_g	±2.4	$u c W e g W e g = ± 5.6 %$
气相表观流速V_sg	±2.6
液相表面张力系数σ	±0.96
液相质量流量W_l	±2.0	$u c E E = ± 3.8 %$
液膜质量流量W_lf	±3.2

表4 各参数不确定度及合成不确定度

参数	不确定度/%	合成不确定度
液相表观流速V_sl	±2.0	$u c R e l R e l = ± 2.5 %$
液相密度ρ_l	±0.22
管道公称直径D	±0.67
液相动力黏度µ_l	±1.33
气体密度ρ_g	±2.4	$u c W e g W e g = ± 5.6 %$
气相表观流速V_sg	±2.6
液相表面张力系数σ	±0.96
液相质量流量W_l	±2.0	$u c E E = ± 3.8 %$
液膜质量流量W_lf	±3.2

表5 神经网络参数取值

参数	搜索范围	优化结果
层数	2~5	4
每层神经元数	10~30	20
训练次数	1000~10000	10000
学习率	0.0001~0.1	0.001
动量因子	0.5~1	0.9
最小性能梯度	e^-10	e^-10

图6 学习率超参数优化对比

图7 动量因子超参数优化对比

表6 预测模型列表

预测模型	预测公式	重要中间参数
Schubring等^[2]	$V w = 2.55 V s g R e g x - 13$	$x = W g W g + W l$
Ju等^[3]	$V w = 10.1 V s l W e l - 0.392 W e g 0.227$
Wang等^[8]	$V w = Ψ V g c + u ¯ i 1 + Ψ, Ψ = 0.0017 ρ g c ρ l - 0.5 R e l f R e g - 0.24 P s y s t e m P a t m 0.48$	$u ¯ i = 1.8 V s l 1 - α, R e l < 2100 V s l 1 - α, R e l > 2100$
Sun等^[7]	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = 10.6 ρ g c ρ l 0.5 R e g' R e l f - 0.25$	$u ¯ i = 1 - E V s l$
Sun等^[9]	$V w = Ψ V s g + V s l 1 + Ψ, Ψ = B P N N ρ g ρ l, R e g, R e l$
本文	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = B P N N ρ g c ρ l, R e g', R e l f$

表6 预测模型列表

预测模型	预测公式	重要中间参数
Schubring等^[2]	$V w = 2.55 V s g R e g x - 13$	$x = W g W g + W l$
Ju等^[3]	$V w = 10.1 V s l W e l - 0.392 W e g 0.227$
Wang等^[8]	$V w = Ψ V g c + u ¯ i 1 + Ψ, Ψ = 0.0017 ρ g c ρ l - 0.5 R e l f R e g - 0.24 P s y s t e m P a t m 0.48$	$u ¯ i = 1.8 V s l 1 - α, R e l < 2100 V s l 1 - α, R e l > 2100$
Sun等^[7]	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = 10.6 ρ g c ρ l 0.5 R e g' R e l f - 0.25$	$u ¯ i = 1 - E V s l$
Sun等^[9]	$V w = Ψ V s g + V s l 1 + Ψ, Ψ = B P N N ρ g ρ l, R e g, R e l$
本文	$V w = Ψ' V g c + u ¯ i 1 + Ψ', Ψ' = B P N N ρ g c ρ l, R e g', R e l f$

图8 不同扰动波速预测结果对比

表7 预测数据对比

模型	R²	MPE/%	MAPE/%	U_nc,pre/%	ξ_5%/%	ξ_15%/%	ξ_30%/%
Schubring等^[2]	0.93	13.39	54.68	58.30	1.04	6.25	18.50
Ju等^[3]	0.72	3.51	22.97	32.32	13.89	36.11	85.41
Wang等^[8]	0.56	2.37	29.62	27.03	17.71	50.34	74.65
Sun等^[7]	0.89	4.48	12.61	18.15	39.58	78.47	93.06
Sun等^[9]	0.85	1.03	7.12	11.50	73.96	89.93	96.18
本文	0.99	0.41	4.29	10.02	76.74	94.10	98.26

参考文献 18

1	孙宏军, 李腾, 李金霞, 等. 基于Kelvin-Helmholtz不稳定性和界面剪切作用的扰动波高预测模型[J]. 化工进展, 2024, 43(2): 609-618.
	SUN Hongjun, LI Teng, LI Jinxia, et al. Disturbance wave height prediction model based on Kelvin-Helmholtz instability and interfacial shear[J]. Chemical Industry and Engineering Progress, 2024, 43(2): 609-618.
2	SCHUBRING D, SHEDD T A. Wave behavior in horizontal annular air-water flow[J]. International Journal of Multiphase Flow, 2008, 34(7): 636-646.
3	JU Peng, LIU Yang, YANG Xiaohong, et al. Wave characteristics of vertical upward adiabatic annular flow in pipes[J]. International Journal of Heat and Mass Transfer, 2019, 145: 118701.
4	KUMAR Ranganathan, GOTTMANN Matthias, SRIDHAR K R. Film thickness and wave velocity measurements in a vertical duct[J]. Journal of Fluids Engineering, 2002, 124(3): 634-642.
5	SETYAWAN Andriyanto, INDARTO, DEENDARLIANTO. The effect of the fluid properties on the wave velocity and wave frequency of gas-liquid annular two-phase flow in a horizontal pipe[J]. Experimental Thermal and Fluid Science, 2016, 71: 25-41.
6	WANG Mi, ZHENG Dandan, WU Yazhou. Experimental and modeling study on interfacial disturbance wave velocity in horizontal gas-liquid flow by ultrasonic method[J]. Experimental Thermal and Fluid Science, 2019, 109: 109908.
7	SUN Hongjun, LI Teng, LI Jinxia, et al. Generalization of disturbance wave velocity of vertical annular flow considering entrained droplets effect[J]. Experimental Thermal and Fluid Science, 2024, 151: 111102.
8	WANG Chao, ZHAO Ning, FENG Yue, et al. Interfacial wave velocity of vertical gas-liquid annular flow at different system pressures[J]. Experimental Thermal and Fluid Science, 2018, 92: 20-32.
9	SUN Hongjun, HUANG Yi, LI Jinxia, et al. Disturbance wave velocity model based on physics-guided backpropagation neural network[C]//2024 IEEE International Instrumentation and Measurement Technology Conference (I2MTC). Glasgow, United Kingdom: IEEE, 2024: 1-6.
10	WOLF A, JAYANTI S, HEWITT G F. Flow development in vertical annular flow[J]. Chemical Engineering Science, 2001, 56(10): 3221-3235.
11	DE JONG Pieter, GABRIEL Kamiel S. A preliminary study of two-phase annular flow at microgravity: Experimental data of film thickness[J]. International Journal of Multiphase Flow, 2003, 29(8): 1203-1220.
12	SAWANT Pravin, ISHII Mamoru, HAZUKU Tatsuya, et al. Properties of disturbance waves in vertical annular two-phase flow[J]. Nuclear Engineering & Design, 2008, 238(12):3528-3541.
13	AlAMU Mhunir Bayonle. Investigation of periodic structures in gas-liquid flow[D]. Nottingham: University of Nottingham, 2010.
14	DASGUPTA A, CHANDRAKER D K, KSHIRASAGAR S,et al. Experimental investigation on dominant waves in upward air-water two-phase flow in churn and annular regime[J]. Experimental Thermal and Fluid Science, 2017, 81:147-163.
15	MOREIRA Tiago Augusto, MORSE Roman William, DRESSLER Kristofer M, et al. Liquid-film thickness and disturbance-wave characterization in a vertical, upward, two-phase annular flow of saturated R245fa inside a rectangular channel[J]. International Journal of Multiphase Flow, 2020, 132:103412.
16	LI Jinxia, WANG Chao, DING Hongbing, et al. EMD and spectrum-centrobaric-correction-based analysis of vortex street characteristics in mist annular flow of wet gas[J]. IEEE Transactions on Instrumentation and Measurement, 2018, 67(5): 1150-1160.
17	LI Jinxia, WANG Chao, DING Hongbing, et al. Wet gas metering using a vortex cross-correlation meter based on fluctuating pressure measurement[J]. Journal of Petroleum Science and Engineering, 2020, 195: 107855.
18	AL-SARKHI A, SARICA C, MAGRINI K. Inclination effects on wave characteristics in annular gas-liquid flows[J]. AIChE Journal, 2012, 58(4): 1018-1029.

[1]	苏茜, 白凡, 刘振兴, 刘彰. 基于XGBoost的气液两相流流型超声识别方法[J]. 化工进展, 2025, 44(4): 1786-1793.
[2]	李凌涵, 张淑美, 董峰. 少样本场景下的气液两相流动状态识别[J]. 化工进展, 2025, 44(4): 1794-1805.
[3]	孙铭聪, 覃晴, 王彦晗, 赵宁, 闫晓丽. 基于集成学习的垂直管环状流界面波速预测模型[J]. 化工进展, 2025, 44(4): 1849-1858.
[4]	任世鹏, 安元, 娄春, 梅晟东, 刘凯, 陈新建. 融合深度学习算法的炉内燃烧温度场分布在线重建[J]. 化工进展, 2025, 44(4): 1923-1933.
[5]	孙悦鹏, 孙延吉, 潘艳秋, 王成宇. 基于BO-LSTM的低温甲醇洗净化气CO₂含量预测[J]. 化工进展, 2025, 44(2): 688-697.
[6]	孙俭, 张海勇, 王成秀, 孙泽能, 蓝兴英, 高金森, 祝京旭. 基于k-means机器学习方法的气固循环流化床颗粒聚团特性[J]. 化工进展, 2025, 44(2): 625-634.
[7]	李雪静, 崔哲, 刘彬, 李传坤, 田文德. 乙烯装置碳二加氢和脱乙烷塔系统智能风险分析与预测[J]. 化工进展, 2025, 44(2): 717-727.
[8]	潘家保, 李贻良, 王锦. 磁流变脂热效应行为的分析与预测[J]. 化工进展, 2025, 44(1): 415-423.
[9]	戴征舒, 左元浩, 陈孝罗, 张犁, 赵根, 张学军, 张华. 机器学习在喷射器研究中的应用进展[J]. 化工进展, 2024, 43(S1): 1-12.
[10]	邹志云, 于蒙, 刘英莉. 基于LSTM和BP神经网络的间歇蒸馏过程工况预测[J]. 化工进展, 2024, 43(S1): 21-31.
[11]	李依梦, 陈运全, 何畅, 张冰剑, 陈清林. 基于物理信息神经网络的甲烷无氧芳构化反应的正反问题[J]. 化工进展, 2024, 43(9): 4817-4823.
[12]	张佳鑫, 张淼, 戴一阳, 董立春. 面向实际化工过程故障诊断的强化深度卷积神经网络模型构建与应用[J]. 化工进展, 2024, 43(9): 4833-4844.
[13]	王亚男, 刘琳琳, 庄钰, 都健. 基于代理模型的环氧乙烷制乙二醇工艺优化同步热集成[J]. 化工进展, 2024, 43(9): 5234-5241.
[14]	李凯, 魏鹤琳, 尹志凡, 左夏华, 于晓宇, 尹宏远, 杨卫民, 阎华, 安瑛. 基于GA-BP神经网络模型预测水基炭黑-胶原蛋白纳米流体热导率和黏度[J]. 化工进展, 2024, 43(7): 4138-4147.
[15]	丁路, 王培尧, 孔令学, 白进, 于广锁, 李文, 王辅臣. 煤气化过程反应模型研究进展[J]. 化工进展, 2024, 43(7): 3593-3612.