Experimental and predictive study on pressure drop of subcooled flow boiling in a mini-channel

doi:10.11949/0438-1157.20221317

Abstract

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

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

CLC Number:

TK 124

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.

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.

Figures/Tables 16

Fig.1 Schematic diagram of experimental loop

Fig.2 Schematic diagram of experimental section

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

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

Fig.3 Typical pressure drop curve for subcooled flow boiling

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

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

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

Table 3 Empirical correlations for subcooled boiling pressure drop

文献	关联式	应用范围
[29]	$Φ^{2} = 0.97 + 0.028 e x p (6.13 \frac{L_{s b}}{L_{s a t}})$	p=0.34~2.76 MPa，G=1143~5322 kg/(m²∙s)， q=0.675~4 MW/m²，d=3、 4.63 mm
[30]	$Φ^{2} = 1 + B o^{0.7} {(\frac{ρ_{l}}{ρ_{g}})}^{0.78} \frac{20 L_{s b} / L_{s a t}}{1.315 - L_{s b} / L_{s a t}}$	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]	$Φ^{2} = 1 + C B o^{1.6} J a^{- 1.2} \frac{ρ_{l}}{ρ_{g}} \times \frac{d_{h e a t e d}}{d_{w e t t e d}}$ （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]	$Φ^{2} = {(\frac{L_{s b}}{L_{s a t}})}^{1.3} e x p (\frac{L_{s b}}{L_{s a t}} + 1.35)$ ， $\frac{L}{d} = 25$ $Φ^{2} = {(\frac{L_{s b}}{L_{s a t}})}^{1.3} e x p (\frac{L_{s b}}{L_{s a t}} + 0.4)$ ， $\frac{L}{d} = 50$	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]	$Φ^{2} = 1 + 2250 B o^{1.5} J a^{- 1.43} {(\frac{ρ_{l}}{ρ_{g}})}^{0.2}$	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]	$Φ^{2} = 1 + 4.86 \times 10^{6} \times B o^{2.4657} {(\frac{L}{L_{s a t}})}^{1.9505} J a^{- 2.1436}$	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

Table 3 Empirical correlations for subcooled boiling pressure drop

文献	关联式	应用范围
[29]	$Φ^{2} = 0.97 + 0.028 e x p (6.13 \frac{L_{s b}}{L_{s a t}})$	p=0.34~2.76 MPa，G=1143~5322 kg/(m²∙s)， q=0.675~4 MW/m²，d=3、 4.63 mm
[30]	$Φ^{2} = 1 + B o^{0.7} {(\frac{ρ_{l}}{ρ_{g}})}^{0.78} \frac{20 L_{s b} / L_{s a t}}{1.315 - L_{s b} / L_{s a t}}$	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]	$Φ^{2} = 1 + C B o^{1.6} J a^{- 1.2} \frac{ρ_{l}}{ρ_{g}} \times \frac{d_{h e a t e d}}{d_{w e t t e d}}$ （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]	$Φ^{2} = {(\frac{L_{s b}}{L_{s a t}})}^{1.3} e x p (\frac{L_{s b}}{L_{s a t}} + 1.35)$ ， $\frac{L}{d} = 25$ $Φ^{2} = {(\frac{L_{s b}}{L_{s a t}})}^{1.3} e x p (\frac{L_{s b}}{L_{s a t}} + 0.4)$ ， $\frac{L}{d} = 50$	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]	$Φ^{2} = 1 + 2250 B o^{1.5} J a^{- 1.43} {(\frac{ρ_{l}}{ρ_{g}})}^{0.2}$	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]	$Φ^{2} = 1 + 4.86 \times 10^{6} \times B o^{2.4657} {(\frac{L}{L_{s a t}})}^{1.9505} J a^{- 2.1436}$	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

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

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

Fig.8 Topological graph of extreme learning machine

Fig.9 Flow chart of GA-ELM model program

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

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

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

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