基于一维漂移流模型的低温管路预冷过程两相流动与换热特性研究

doi:10.11949/0438-1157.20250026

摘要/Abstract

摘要：

为进一步掌握低温管路预冷过程中两相流动与沸腾换热的特性规律，以液氮传输管路为对象构建低温管路预冷过程热流耦合数值模型，基于一维漂移流模型重点考虑了气液相间滑移速度的影响，计算得到了预冷过程中管壁温度、含气率、热通量与气液相间滑移速度的变化规律，并对比分析了不同时刻、不同管路位置及不同管长下平均速度和质量流速的波动情况。结果表明，漂移流模型能够更为准确地预测预冷过程的两相流动换热特性，壁面降温结果较均相流模型误差降低3.9%；预冷过程大部分为两相流动区间，气液相间滑移速度不可忽略，且含气率越高平均气相滑移速度较均相流模型偏移越大；预冷过程平均速度和质量流速存在显著波动，针对0.572 m长的管路，平均速度波动幅度接近1.5 m/s，平均质量流速波动的最大幅度接近45 kg/(m²·s)；管长对于质量流速波动影响显著，管路越长平均质量流速波动幅度越大，对于同一根管道，下游位置处的质量流速波动幅度比上游更剧烈。研究成果对于深入理解和优化低温管路的预冷过程具有重要意义。

关键词: 低温管路预冷, 预冷沸腾, 气液两相流, 数值模拟, 漂移流模型, 滑移速度, 不稳定性

Abstract:

To further grasp the characteristics and patterns of two-phase flow and boiling heat transfer during the precooling process of low-temperature pipelines, a coupled heat flux numerical model was developed for the precooling process of low-temperature pipelines, focusing on liquid nitrogen transfer pipelines. Utilizing the one-dimensional drift flow model, particular emphasis was placed on the influence of gas-liquid interphase slip velocity. The variations in pipe wall temperature, gas content, heat flux density, and gas-liquid interphase slip velocity during the precooling process were computed. Comparative analysis was conducted on the fluctuations of average velocity and mass flow rate at various times, pipeline positions, and lengths. The findings indicate that the drift flow model offers a more precise prediction of the two-phase flow and heat transfer characteristics during the precooling process, achieving a 3.9% reduction in error compared to the homogeneous flow model. The majority of the precooling process occurs within the two-phase flow regime, where the slip velocity between gas and liquid phases cannot be disregarded. Furthermore, an increase in gas content leads to a greater deviation in the average gas phase slip velocity compared to the homogeneous flow model. Significant fluctuations were observed in both average velocity and mass flow rate during the precooling process. For a 0.572 m long pipeline, the average velocity fluctuation amplitude neared 1.5 m/s, while the maximum amplitude of the average mass flow rate fluctuation is close to 45 kg/(m²·s). The length of the pipeline significantly impacts mass flow rate fluctuations, with longer pipelines experiencing greater average mass flow rate fluctuations. Within the same pipeline, the fluctuation amplitude of mass flow rate is more pronounced at downstream positions compared to upstream. The research results of this paper are of great significance for the in-depth understanding and optimization of the precooling process of cryogenic pipelines.

Key words: pre-cooling of low-temperature pipelines, pre-cooled boiling, gas-liquid flow, numerical simulation, drift-flux model, slip velocity, instability

中图分类号:

TK 91

张淇栋, 艾立强, 马原, 吴胜宝, 王磊, 厉彦忠. 基于一维漂移流模型的低温管路预冷过程两相流动与换热特性研究[J]. 化工学报, 2025, 76(8): 3842-3852.

Qidong ZHANG, Liqiang AI, Yuan MA, Shengbao WU, Lei WANG, Yanzhong LI. Research on two-phase flow and heat transfer characteristics in precooling process of low-temperature pipelines based on one-dimensional drift-flux model[J]. CIESC Journal, 2025, 76(8): 3842-3852.

图/表 14

表1 分布参数和加权滑移速度计算公式

Table 1 Calculation formula for distribution parameters and weighted slip velocity

含气率

分布参数C₀

加权滑移速度

V d j

$α g$ <0.4

0.4< $α g$ <0.6

0.6< $α g$ <0.8

1.2 - 0.2 ρ g ρ l

$2 σ g ρ l - ρ g ρ l 2 1 / 4 1 - α g 1.75$

$0.35 g D ρ l - ρ g ρ l$

$2 σ g ρ l - ρ g ρ l 2 1 / 4$

α g

>0.8

1 + 1 - α g α g + 4 ρ g ρ l

1 - α g α g + 4 ρ g ρ l ρ l - ρ g g D 1 - α g 0.015 ρ l

表1 分布参数和加权滑移速度计算公式

Table 1 Calculation formula for distribution parameters and weighted slip velocity

含气率

分布参数C₀

加权滑移速度

V d j

$α g$ <0.4

0.4< $α g$ <0.6

0.6< $α g$ <0.8

1.2 - 0.2 ρ g ρ l

$2 σ g ρ l - ρ g ρ l 2 1 / 4 1 - α g 1.75$

$0.35 g D ρ l - ρ g ρ l$

$2 σ g ρ l - ρ g ρ l 2 1 / 4$

α g

>0.8

1 + 1 - α g α g + 4 ρ g ρ l

1 - α g α g + 4 ρ g ρ l ρ l - ρ g g D 1 - α g 0.015 ρ l

表2 流体与管壁换热计算公式

Table 2 Calculation formula for heat transfer between fluid and pipe wall

临界点和换热工况	模型	关联式	误差
膜态沸腾起始温度T_LFP	Jin关联式^[12]	$T L F P = T c r - T s a t 76.46 μ l (1 + β) + T s a t, β = (k ρ c p) l (k ρ c p) w$	±5%
临界热通量q_CHF	修正Katto公式^[27]	$q C H F = 0.486 G l h f g ρ g ρ l 0.6353 ρ l σ l G l 2 L 0.4987 L D 0.3112$	±30%
临界热流温度T_CHF	Kalinin^[28]	$T C H F - T s a t T c r - T f = 0.1 + 1.5 β + 0.6 β 2$	—
核态沸腾起始点T_ONB	Darr^[28]	$T O N B = T s a t (p) + 0.0071 p + 5$	—
膜态沸腾区	Darr^[2]	$h f b = h b + h t c + h d w h b = 0.06 ρ g (ρ l - ρ g) g h f g k g 3 4 L μ g (T w - T s a t) 1 / 4 h t c = 0.112 1 + D L + 0.1 D 0.7 k g D (1 - x e) - 0.8 R e g 0.58 P r g 0.4, x e = h f - h l h f g h d w = 0.00007 k l D e x p - L D 0.55 W e 2 c p l (T w - T s a t) h f g - 1$	30%以内
过渡沸腾区	线性插值	根据临界热流壁温T_CHF与最低膜态沸腾温度T_LFP插值计算	—
核态沸腾区	线性插值	根据临界热流壁温T_CHF与核态沸腾起始温度T_ONB插值计算	—
液/气相强制对流区	Dittus-Boelter公式^[29]	$h = 0.023 R e 0.8 P r 0.4$ , $h = 0.023 R e f 0.8 P r f 0.4 T f T w 0.5 k f D$	—

表2 流体与管壁换热计算公式

Table 2 Calculation formula for heat transfer between fluid and pipe wall

临界点和换热工况	模型	关联式	误差
膜态沸腾起始温度T_LFP	Jin关联式^[12]	$T L F P = T c r - T s a t 76.46 μ l (1 + β) + T s a t, β = (k ρ c p) l (k ρ c p) w$	±5%
临界热通量q_CHF	修正Katto公式^[27]	$q C H F = 0.486 G l h f g ρ g ρ l 0.6353 ρ l σ l G l 2 L 0.4987 L D 0.3112$	±30%
临界热流温度T_CHF	Kalinin^[28]	$T C H F - T s a t T c r - T f = 0.1 + 1.5 β + 0.6 β 2$	—
核态沸腾起始点T_ONB	Darr^[28]	$T O N B = T s a t (p) + 0.0071 p + 5$	—
膜态沸腾区	Darr^[2]	$h f b = h b + h t c + h d w h b = 0.06 ρ g (ρ l - ρ g) g h f g k g 3 4 L μ g (T w - T s a t) 1 / 4 h t c = 0.112 1 + D L + 0.1 D 0.7 k g D (1 - x e) - 0.8 R e g 0.58 P r g 0.4, x e = h f - h l h f g h d w = 0.00007 k l D e x p - L D 0.55 W e 2 c p l (T w - T s a t) h f g - 1$	30%以内
过渡沸腾区	线性插值	根据临界热流壁温T_CHF与最低膜态沸腾温度T_LFP插值计算	—
核态沸腾区	线性插值	根据临界热流壁温T_CHF与核态沸腾起始温度T_ONB插值计算	—
液/气相强制对流区	Dittus-Boelter公式^[29]	$h = 0.023 R e 0.8 P r 0.4$ , $h = 0.023 R e f 0.8 P r f 0.4 T f T w 0.5 k f D$	—

图1 流体域交错网格离散示意图

Fig.1 Schematic diagram of fluid domain staggered grid discretization

图2 固体域离散划分示意图

Fig.2 Schematic diagram of discrete division of solid domain

图3 无关性验证

Fig.3 Independence verification

表3 模型验证所用实验工况

Table 3 Experimental conditions used for model validation

D_out=12.70 mm

D=11.68 mm

L =572 mm

液氮

真空绝热

竖直向上

126

220

324

饱和温度

0.18

0.25

0.42

图4 模型验证计算结果对比

Fig.4 Comparison of model validation calculation results

图5 预冷过程全时态壁面温降特性

Fig.5 Full time wall temperature drop characteristics during pre cooling process

图6 特征位置处平均气相速度和体积通量的关系

Fig.6 The relationship between average gas-phase velocity and volumetric flux at characteristic positions

图7 20 s时含气率、热通量和气液相速度沿管路分布

Fig.7 Distribution of gas content, heat flux density and gas-liquid phase velocity along the pipeline at 20 s

图8 40 s时含气率、热通量和气液相速度沿管路分布

Fig.8 Distribution of gas content, heat flux density and gas-liquid phase velocity along the pipeline at 40 s

图9 预冷后期不同时刻平均速度、密度与质量流速的变化规律

Fig.9 The variation law of average velocity, density and mass flow rate at different times

图10 相同相对位置处质量流速随时间的变化

Fig.10 The variation of mass flow velocity with time at the same relative position

图11 不同位置处质量流速的变化与波动幅度

Fig.11 Changes and fluctuation amplitude of mass flow velocity at different positions

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