Delayed Equilibrium Modeling for Cryogen Throttling and Experimental Validation in Liquid Nitrogen

Xu Jieai; Gao Xiangyu; Huang Yonghua; Miao Ruijiao

doi:10.12465/issn.0253-4339.20260821002

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Delayed Equilibrium Modeling for Cryogen Throttling and Experimental Validation in Liquid Nitrogen

更新时间：2026-10-24

- Delayed Equilibrium Modeling for Cryogen Throttling and Experimental Validation in Liquid Nitrogen
- Journal of Refrigeration Pages: 1-9(2026)
- 作者机构：
  
  1.上海交通大学制冷与低温工程研究所上海 200240
  2. 上海交通大学四川研究院成都 610213
- 作者简介：
  
  Miao Ruijiao， female， associate professor， School of Mechanical Engineering， Shanghai Jiao Tong University， 86-13327193398， E-mail： miaorj@sjtu.edu.cn. Research fields： thermophysical properties of cryogenic fluids and micro-/nanoscale heat transfer.
- 基金信息：
- DOI：10.12465/issn.0253-4339.20260821002
  CLC： TB61⁺1;O359⁺.1
- Received：21 August 2026，
  
  Revised：2026-09-01，
  
  Accepted：22 September 2026，
  
  Online First：23 October 2026，
- 稿件说明：
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徐杰艾，高翔宇，黄永华，等. 低温流体节流的延迟平衡模型与液氮实验验证［J］. 制冷学报，XXXX，XX（XX）：1-9.

Xu Jieai，Gao Xiangyu，Huang Yonghua，et al. Delayed Equilibrium Modeling for Cryogen Throttling and Experimental Validation in Liquid Nitrogen［J］. Journal of Refrigeration，XXXX，XX（XX）：1-9.
徐杰艾，高翔宇，黄永华，等. 低温流体节流的延迟平衡模型与液氮实验验证［J］. 制冷学报，XXXX，XX（XX）：1-9. DOI： 10.12465/issn.0253-4339.20260821002.

Xu Jieai，Gao Xiangyu，Huang Yonghua，et al. Delayed Equilibrium Modeling for Cryogen Throttling and Experimental Validation in Liquid Nitrogen［J］. Journal of Refrigeration，XXXX，XX（XX）：1-9. DOI： 10.12465/issn.0253-4339.20260821002.

摘要

为提高低温流体节流过程中质量流率、沿程压力及非平衡闪蒸特性的预测能力，本文建立了一维真实低温流体延迟平衡模型，并采用文丘里管、收缩—扩张喷嘴、厚孔板及搭建的孔板实验数据进行验证。结果表明：相较均相平衡模型，延迟平衡模型在文丘里测压点的压力均方根误差从0.616 kPa降为0.232 kPa；对喷嘴轴向压力和质量流率的预测平均绝对百分比误差分别为5.10%和6.94%；针对厚孔板质量流率预测的平均绝对百分比误差和相对均方根误差分别为11.81%和14.40%。研究发现，非平衡相变影响程度与节流几何及流动时间尺度密切相关，连续变截面喷嘴中2类模型差异较小，而锐边短尺度孔板中延迟气化效应更为显著。进一步开展0.5～2.0 mm孔径液氮节流实验，结果表明：质量流率随入口压力、入口过冷度和喉径增加而增大，在0.5～2.0 mm区间内近似满足

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10.92199993

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，低温节流特性由入口热力状态、几何尺度及非平衡相变共同控制，所建模型可为低温节流元件的流量预测、压力评估及结构设计提供计算依据。

Abstract

A one-dimensional real-fluid delayed equilibrium model （DEM） was developed to improve the prediction of mass flow rate， axial pressure， and nonequilibrium flashing in cryogenic throttling flows. The model was validated against the data from Venturis， converging-diverging nozzles， thick orifices， and a self-built orifice test rig. Compared with the homogeneous equilibrium model （HEM）， DEM reduced the root mean squared error of pressure （RMSE） at the Venturi pressure taps from 0.616 to 0.232 kPa. For the nozzle cases， the mean absolute percentage error （MAPE） values of axial pressure and mass flow rate were 5.10% and 6.94%， respectively， while the mass-flow MAPE and RMSE for thick orifices were 11.81% and 14.40%， respectively. The results show that nonequilibrium effects depend strongly on the throttling geometry and flow time scale and are more pronounced in sharp-edged short orifices than in smoothly varying nozzles. Further liquid-nitrogen experiments with 0.5-2.0 mm orifices showed that the mass flow rate increased with the inlet pressure， inlet subcooling， and orifice diameter， approximately following

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10.92199993

2.53999996

. These results indicate that cryogenic throttling is jointly governed by the inlet thermodynamic state， geometric scale， and nonequilibrium phase change， and the proposed model can support the flow prediction， pressure evaluation， and design of cryogenic throttling components.

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references

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