微小通道内过冷流动沸腾阻力特性实验及预测研究

doi:10.11949/0438-1157.20221317

摘要/Abstract

摘要：

实验探究了微小圆管内(内径1 mm)过冷水流动沸腾的阻力特性，参数范围：热通量4.0~5.6 MW/m²，压力3.0~5.0 MPa，质量流速2000~4200 kg/(m²‧s)，进口热力学干度-0.50~-0.10。获取了质量流速、压力、热通量等参数对过冷沸腾阻力的影响，并重点关注其预测方法。将测试数据与典型阻力关联式对比，结果表明，由于高热流、微通道等特殊因素，导致大部分阻力关联式的预测精度不够理想。为更准确预测高热流过冷沸腾阻力，基于LeakyReLU函数，建立了遗传算法优化的极限学习机模型(GA-ELM)，其预测精度优于传统关联式(平均绝对误差为2.0%)，且泛化性良好。研究工作可为微小尺度流动换热系统设计优化提供支撑。

关键词: 过冷沸腾, 微小通道, 对流, 两相流, 流动阻力, 遗传算法, 极限学习机

Abstract:

The pressure drop characteristics of subcooled water flow boiling in a mini-tube (1 mm) were experimentally investigated. The experimental parameters were as follows: heat flux 4.0—5.6 MW/m², pressure 3.0—5.0 MPa, mass flow rate 2000—4200 kg/(m²‧s), and inlet thermodynamic quality -0.50—-0.10. The effects of mass flow rate, pressure, heat flux and other parameters on the subcooling boiling resistance were obtained, and the prediction method was focused on. Comparison of the experimental data with typical pressure drop correlations indicates that the accuracy of the prediction for most pressure drop correlations is not sufficient due to special factors such as high heat flux and micro-channels. In order to predict the pressure drop of subcooled boiling of high heat flux more accurately, the extreme learning machine model optimized by genetic algorithm (GA-ELM) is established based on LeakyReLU function. The prediction accuracy of GA-ELM is better than the traditional correlations (the average absolute error is 2.0%), with well generalization ability. This study will support design optimization of micro/mini-scale flow heat transfer systems.

Key words: subcooled boiling, mini-channel, convection, two-phase flow, flow resistance, genetic algorithm, extreme learning machine

中图分类号:

TK 124

郑书闽, 郭鹏程, 颜建国, 王帅, 李文博, 周淇. 微小通道内过冷流动沸腾阻力特性实验及预测研究[J]. 化工学报, 2023, 74(4): 1549-1560.

Shumin ZHENG, Pengcheng GUO, Jianguo YAN, Shuai WANG, Wenbo LI, Qi ZHOU. Experimental and predictive study on pressure drop of subcooled flow boiling in a mini-channel[J]. CIESC Journal, 2023, 74(4): 1549-1560.

图/表 16

图1 实验回路示意图

Fig.1 Schematic diagram of experimental loop

图2 实验段示意图

Fig.2 Schematic diagram of experimental section

表 1 实验工况

Table 1 Test conditions

实验参数	数值
热通量q/(MW/m²)	4.0~5.6
压力p/MPa	3.0、4.0、5.0
质量流速G/(kg/(m²‧s))	2000~4200
进口温度T_in/℃	20~180

表 2 参数不确定度

Table 2 Parameter uncertainties

实验参数	不确定度/%
压力	±0.26
压差	±0.78
流体温度	±0.4
壁面温度	±0.5
质量流速	±1.01
热通量	±5.35

图3 典型过冷沸腾阻力特性曲线

Fig.3 Typical pressure drop curve for subcooled flow boiling

图4 质量流速对过冷沸腾阻力的影响

Fig.4 Effect of mass flow rate on pressure drop of subcooled boiling

图5 压力对过冷沸腾阻力的影响

Fig.5 Effect of pressure on pressure drop of subcooled boiling

图6 热通量对过冷沸腾阻力的影响

Fig.6 Effect of heat flux on pressure drop of subcooled boiling

表 3 过冷沸腾阻力关联式

Table 3 Empirical correlations for subcooled boiling pressure drop

文献	关联式	应用范围
[29]	$Φ 2 = 0.97 + 0.028 e x p 6.13 L s b L s a t$	p=0.34~2.76 MPa，G=1143~5322 kg/(m²∙s)， q=0.675~4 MW/m²，d=3、 4.63 mm
[30]	$Φ 2 = 1 + B o 0.7 ρ l ρ g 0.78 20 L s b / L s a t 1.315 - L s b / L s a t$	p=0.98~19.6 MPa，G=1400~3000 kg/(m²∙s), q=0.58~1.75 MW/m²，d=2.89、 6.34、 8.31 mm
[31]	$Φ 2 = 1 + C B o 1.6 J a - 1.2 ρ l ρ g × d h e a t e d d w e t t e d$ （水，C=80；R12和R134a，C=500）	p=0.8~2 MPa，G=750~3000 kg/(m²∙s)，q<0.208 MW/m²，ΔT_sub=2.0~47.6℃，d=5.5~9.5 mm
[32]	$Φ 2 = L s b L s a t 1.3 e x p L s b L s a t + 1.35$ ， $L d = 25$ $Φ 2 = L s b L s a t 1.3 e x p L s b L s a t + 0.4$ ， $L d = 50$	p=0.4~1.6 MPa，G=25000~45000 kg/(m²∙s)， q_cr=50~80 MW/m²，T_{b, in}=22~66℃， d=1.05~2.44 mm
[12]	$Φ 2 = 1 + 2250 B o 1.5 J a - 1.43 ρ l ρ g 0.2$	p=3~5 MPa，G=6000~10000 kg/(m²∙s)，q=7.5~12.5 MW/m²，T_{b, in}=80~220℃， ΔT_{sub, in}=40~185℃，d=9 mm，L=400 mm
[14]	$Φ 2 = 1 + 4.86 × 106 × B o 2.4657 L L s a t 1.9505 J a - 2.1436$	p=2~16 MPa，G=3000~45000 kg/(m²∙s)，q<80 MW/m²，T_{b, in}=22~63℃，L=25~125 mm，d=1.05~2.44 mm，25≤L/d≤50

表 3 过冷沸腾阻力关联式

Table 3 Empirical correlations for subcooled boiling pressure drop

文献	关联式	应用范围
[29]	$Φ 2 = 0.97 + 0.028 e x p 6.13 L s b L s a t$	p=0.34~2.76 MPa，G=1143~5322 kg/(m²∙s)， q=0.675~4 MW/m²，d=3、 4.63 mm
[30]	$Φ 2 = 1 + B o 0.7 ρ l ρ g 0.78 20 L s b / L s a t 1.315 - L s b / L s a t$	p=0.98~19.6 MPa，G=1400~3000 kg/(m²∙s), q=0.58~1.75 MW/m²，d=2.89、 6.34、 8.31 mm
[31]	$Φ 2 = 1 + C B o 1.6 J a - 1.2 ρ l ρ g × d h e a t e d d w e t t e d$ （水，C=80；R12和R134a，C=500）	p=0.8~2 MPa，G=750~3000 kg/(m²∙s)，q<0.208 MW/m²，ΔT_sub=2.0~47.6℃，d=5.5~9.5 mm
[32]	$Φ 2 = L s b L s a t 1.3 e x p L s b L s a t + 1.35$ ， $L d = 25$ $Φ 2 = L s b L s a t 1.3 e x p L s b L s a t + 0.4$ ， $L d = 50$	p=0.4~1.6 MPa，G=25000~45000 kg/(m²∙s)， q_cr=50~80 MW/m²，T_{b, in}=22~66℃， d=1.05~2.44 mm
[12]	$Φ 2 = 1 + 2250 B o 1.5 J a - 1.43 ρ l ρ g 0.2$	p=3~5 MPa，G=6000~10000 kg/(m²∙s)，q=7.5~12.5 MW/m²，T_{b, in}=80~220℃， ΔT_{sub, in}=40~185℃，d=9 mm，L=400 mm
[14]	$Φ 2 = 1 + 4.86 × 106 × B o 2.4657 L L s a t 1.9505 J a - 2.1436$	p=2~16 MPa，G=3000~45000 kg/(m²∙s)，q<80 MW/m²，T_{b, in}=22~63℃，L=25~125 mm，d=1.05~2.44 mm，25≤L/d≤50

图7 过冷沸腾阻力经验关联式的预测性能

Fig.7 Prediction performance of empirical correlations for subcooled boiling pressure drop

表 4 过冷沸腾阻力预测模型的预测性能

Table 4 Prediction performances of prediction models for subcooled boiling pressure drop

文献	MAE/%	RMSE/%	文献	MAE/%	RMSE/%
[29]	103.19	150.78	[14]	55.32	63.94
[30]	151.26	182.23	[12]	8.75	10.84
[31]	33.07	34.40	本文（BP神经网络模型）	3.91	5.41
[32]	35.37	40.99	本文（GA-ELM模型）	2.00	2.71

图8 极限学习机示意图

Fig.8 Topological graph of extreme learning machine

图9 GA-ELM模型程序流程图

Fig.9 Flow chart of GA-ELM model program

图10 不同隐含层神经元数目预测性能对比

Fig.10 Prediction performance of different neuron number in hidden layer

图11 预测集的预测值与实验值比较

Fig.11 Comparison between prediction value of the prediction set and experimental value

图12 预测模型的预测性能

Fig.12 Prediction performance of prediction model for subcooled boiling pressure drop

参考文献 36

1	Devahdhanush V S, Mudawar I, Nahra H K, et al. Experimental heat transfer results and flow visualization of vertical upflow boiling in earth gravity with subcooled inlet conditions—in preparation for experiments onboard the International Space Station[J]. International Journal of Heat and Mass Transfer, 2022, 188: 122603.
2	Mudawar I. Assessment of high-heat-flux thermal management schemes[J]. IEEE Transactions on Components and Packaging Technologies, 2001, 24(2): 122-141.
3	Ongena J, Ogawa Y. Nuclear fusion: status report and future prospects[J]. Energy Policy, 2016, 96: 770-778.
4	Yan J G, Bi Q C, Zhu G, et al. Critical heat flux of highly subcooled water flow boiling in circular tubes with and without internal twisted tapes under high mass fluxes[J]. International Journal of Heat and Mass Transfer, 2016, 95: 606-619.
5	Fang X D, Yuan Y L, Xu A Y, et al. Review of correlations for subcooled flow boiling heat transfer and assessment of their applicability to water[J]. Fusion Engineering and Design, 2017, 122: 52-63.
6	Parizad Benam B, Sadaghiani A K, Yağcı V, et al. Review on high heat flux flow boiling of refrigerants and water for electronics cooling[J]. International Journal of Heat and Mass Transfer, 2021, 180: 121787.
7	Deng D X, Zeng L, Sun W. A review on flow boiling enhancement and fabrication of enhanced microchannels of microchannel heat sinks[J]. International Journal of Heat and Mass Transfer, 2021, 175: 121332.
8	Gugliermetti L, Caruso G, Saraceno L. Prediction of subcooled flow boiling pressure drops in small circular tubes[J]. International Journal of Heat and Mass Transfer, 2017, 115: 1074-1090.
9	杨宽, 阎昌琪, 曹夏昕. 自然循环窄矩形通道内过冷沸腾两相摩擦阻力特性[J]. 化工学报, 2020, 71(7): 3060-3070.
	Yang K, Yan C Q, Cao X X. Subcooled flow boiling resistance characteristics in narrow rectangular channel under natural circulation condition[J]. CIESC Journal, 2020, 71(7): 3060-3070.
10	Sharifi S, Aligoodarz M R, Rahbari A. Thermohydraulic performance of Al₂O₃-water nanofluid during single-phase flow and two-phase subcooled flow boiling[J]. International Journal of Thermal Sciences, 2022, 179: 107605.
11	Sadaghiani A K, Koşar A. Numerical and experimental investigation on the effects of diameter and length on high mass flux subcooled flow boiling in horizontal microtubes[J]. International Journal of Heat and Mass Transfer, 2016, 92: 824-837.
12	Yan J G, Guo P C, Bi Q C, et al. Pressure drop for highly subcooled water flow boiling under high heat and mass fluxes[J]. Applied Thermal Engineering, 2017, 124: 1061-1074.
13	Zhang X, Feng W P, Zhang J, et al. Study on the subcooled boiling pressure drop for downward flow in a narrow rectangular channel[J]. Annals of Nuclear Energy, 2021, 154: 108111.
14	Ramesh B, Gedupudi S. On the prediction of pressure drop in subcooled flow boiling of water[J]. Applied Thermal Engineering, 2019, 155: 386-396.
15	Baburajan P K, Bisht G S, Gupta S K, et al. Measurement of subcooled boiling pressure drop and local heat transfer coefficient in horizontal tube under LPLF conditions[J]. Nuclear Engineering and Design, 2013, 255: 169-179.
16	Liang X, Xie Y Q, Day R, et al. A data driven deep neural network model for predicting boiling heat transfer in helical coils under high gravity[J]. International Journal of Heat and Mass Transfer, 2021, 166: 120743.
17	He Y C, Hu C Z, Li H Y, et al. Reliable predictions of bubble departure frequency in subcooled flow boiling: a machine learning-based approach[J]. International Journal of Heat and Mass Transfer, 2022, 195: 123217.
18	汪森林, 李照志, 邵应娟, 等. 超临界二氧化碳垂直管内传热恶化数值模拟研究[J]. 化工学报, 2022, 73(3): 1072-1082.
	Wang S L, Li Z Z, Shao Y J, et al. Numerical simulation on heat transfer deterioration of supercritical carbon dioxide in vertical tube[J]. CIESC Journal, 2022, 73(3): 1072-1082.
19	Guo P C, Zheng S M, Yan J G, et al. Experimental investigation on heat transfer of subcooled flow boiling of water in mini channels under high heat fluxes[J]. Experimental Thermal and Fluid Science, 2023, 142: 110831.
20	陈静妍, 徐荣吉, 吴青平, 等. 基于BP神经网络的不凝性气体对脉动热管传热影响的分析[J]. 化工进展, 2020, 39 (7): 2574-2582.
	Chen J Y, Xu R J, Wu Q P, et al. Heat transfer of non-condensable gas to pulsating heat pipe based on BP neural network model [J]. Chemical Industry and Engineering Progress, 2020, 39(7): 2574-2582.
21	Kuang Y W, Han F, Sun L J, et al. Saturated hydrogen nucleate flow boiling heat transfer coefficients study based on artificial neural network[J]. International Journal of Heat and Mass Transfer, 2021, 175: 121406.
22	Bard A, Qiu Y, Kharangate C R, et al. Consolidated modeling and prediction of heat transfer coefficients for saturated flow boiling in mini/micro-channels using machine learning methods[J]. Applied Thermal Engineering, 2022, 210: 118305.
23	O’Neill L E, Mudawar I. Review of two-phase flow instabilities in macro- and micro-channel systems[J]. International Journal of Heat and Mass Transfer, 2020, 157: 119738.
24	Saisorn S, Suriyawong A, Srithumkhant P, et al. An investigation of horizontal and vertical flow boiling in a single channel with a confinement number beyond the threshold of micro-scale flow[J]. Physics of Fluids, 2021, 33(11): 113302.
25	Sun F, Xie G N, Li S L. An artificial-neural-network based prediction of heat transfer behaviors for in-tube supercritical CO₂ flow[J]. Applied Soft Computing, 2021, 102: 107110.
26	齐咏生, 樊佶, 刘利强, 等. 基于形态学分形和极限学习机的风电机组轴承故障诊断[J]. 太阳能学报, 2020, 41(6): 102-112.
	Qi Y S, Fan J, Liu L Q, et al. Fault diagnosis of wind turbine bearings based on morphological fractal and extreme learning machine[J]. Acta Energiae Solaris Sinica, 2020, 41(6): 102-112.
27	Coleman H W, Steele W G. Engineering application of experimental uncertainty analysis[J]. AIAA Journal, 1995, 33(10): 888-1896.
28	Bergles A E, Rohsenow W M. The determination of forced-convection surface-boiling heat transfer[J]. Journal of Heat Transfer, 1964, 86(3): 365-372.
29	Owens W, Schrock V. Local pressure gradients for subcooled boiling of water in vertical tubes[R]. ASME Paper 60-WA-249, 1960.
30	Tarasova N V, Leontiev A I, Hlopushin V I, et al. Pressure drop of boiling subcooled water and steam-water mixture flowing in heated channels[C]//Proc. 3rd International Heat Transfer Conference. Chicago, 1966.
31	Hahne E, Spindler K, Skok H. A new pressure drop correlation for subcooled flow boiling of refrigerants[J]. International Journal of Heat and Mass Transfer, 1993, 36(17): 4267-4274.
32	Tong W, Bergles A E, Jensen M K. Pressure drop with highly subcooled flow boiling in small-diameter tubes[J]. Experimental Thermal and Fluid Science, 1997, 15 (3): 202-212.
33	Huang G, Huang G B, Song S, et al. Trends in extreme learning machines: a review[J]. Neural Networks, 2015, 61: 32-48.
34	崔江, 唐军祥, 张卓然, 等. 基于极限学习机的航空发电机旋转整流器快速故障分类方法研究[J]. 中国电机工程学报, 2018, 38(8): 2458-2466, 2555.
	Cui J, Tang J X, Zhang Z R, et al. Fast fault classification method research of aircraft generator rotating rectifier based on extreme learning machine[J]. Proceedings of the CSEE, 2018, 38(8): 2458-2466, 2555.
35	颜建国, 郑书闽, 郭鹏程, 等. 基于GA-BP神经网络的超临界CO₂传热特性预测研究[J]. 化工学报, 2021, 72(9): 4649-4657.
	Yan J G, Zheng S M, Guo P C, et al. Prediction of heat transfer characteristics for supercritical CO₂ based on GA-BP neural network[J]. CIESC Journal, 2021, 72(9): 4649-4657.
36	Guo X Y, Zhang L, Xing Y X. Study on analytical noise propagation in convolutional neural network methods used in computed tomography imaging[J]. Nuclear Science and Techniques, 2022, 33(6): 116-129.

[1]	周绍华, 詹飞龙, 丁国良, 张浩, 邵艳坡, 刘艳涛, 郜哲明. 短管节流阀内流动噪声的实验研究及降噪措施[J]. 化工学报, 2023, 74(S1): 113-121.
[2]	江河, 袁俊飞, 王林, 邢谷雨. 均流腔结构对微细通道内相变流动特性影响的实验研究[J]. 化工学报, 2023, 74(S1): 235-244.
[3]	肖明堃, 杨光, 黄永华, 吴静怡. 浸没孔液氧气泡动力学数值研究[J]. 化工学报, 2023, 74(S1): 87-95.
[4]	温凯杰, 郭力, 夏诏杰, 陈建华. 一种耦合CFD与深度学习的气固快速模拟方法[J]. 化工学报, 2023, 74(9): 3775-3785.
[5]	王玉兵, 李杰, 詹宏波, 朱光亚, 张大林. R134a在菱形离散肋微小通道内的流动沸腾换热实验研究[J]. 化工学报, 2023, 74(9): 3797-3806.
[6]	何松, 刘乔迈, 谢广烁, 王斯民, 肖娟. 高浓度水煤浆管道气膜减阻两相流模拟及代理辅助优化[J]. 化工学报, 2023, 74(9): 3766-3774.
[7]	袁佳琦, 刘政, 黄锐, 张乐福, 贺登辉. 泡状入流条件下旋流泵能量转换特性研究[J]. 化工学报, 2023, 74(9): 3807-3820.
[8]	高燕, 伍鹏, 尚超, 胡泽君, 陈晓东. 基于双流体喷嘴的磁性琼脂糖微球的制备及其蛋白吸附性能探究[J]. 化工学报, 2023, 74(8): 3457-3471.
[9]	邢雷, 苗春雨, 蒋明虎, 赵立新, 李新亚. 井下微型气液旋流分离器优化设计与性能分析[J]. 化工学报, 2023, 74(8): 3394-3406.
[10]	郭雨莹, 敬加强, 黄婉妮, 张平, 孙杰, 朱宇, 冯君炫, 陆洪江. 稠油管道水润滑减阻及压降预测模型修正[J]. 化工学报, 2023, 74(7): 2898-2907.
[11]	高金明, 郭玉娇, 鄂承林, 卢春喜. 一种封闭罩内顺流多旋臂气液分离器的分离特性研究[J]. 化工学报, 2023, 74(7): 2957-2966.
[12]	何宣志, 何永清, 闻桂叶, 焦凤. 磁液液滴颈部自相似破裂行为[J]. 化工学报, 2023, 74(7): 2889-2897.
[13]	牛超, 沈胜强, 杨艳, 潘泊年, 李熠桥. 甲烷BOG喷射器流动过程计算与性能分析[J]. 化工学报, 2023, 74(7): 2858-2868.
[14]	江锦波, 彭新, 许文烜, 门日秀, 刘畅, 彭旭东. 泵出型螺旋槽油气密封泄漏特性及参数影响研究[J]. 化工学报, 2023, 74(6): 2538-2554.
[15]	刘起超, 周云龙, 陈聪. 起伏振动垂直上升管气液两相流截面含气率分析与计算[J]. 化工学报, 2023, 74(6): 2391-2403.