Validation and performance evaluation of C-SAT hydrogen jet flame length prediction model

doi:10.16265/j.cnki.issn1003-3033.2026.09.0320

Abstract

Abstract:

Conventional flame models are limited in addressing the buoyancy effects and low-density characteristics of hydrogen jet flames, which often lead to deviations in flame length prediction. In this study, the hydrogen jet flame length prediction model embedded in C-SAT is adopted to conduct model validation and performance evaluation. Based on multiple sets of publicly available experimental data for hydrogen jet flames, the prediction accuracies of the five virtual nozzle models (Y/O, Birch, Birch2, E/M, and Molkov) built into C-SAT are compared and screened, and the optimal model is further compared with the American Petroleum Institute(API) recommended model and the cone model in the Process Hazard Analysis Software Tool (PHAST). The results show that the Y/O model exhibits the best overall performance among the four nozzle models, with a safety factor of 1.077, a factor-of-two accuracy of 100%, a mean relative bias of -0.068, and a geometric mean bias of 0.934. In comparison with PHAST, C-SAT achieves a geometric mean bias of 0.934 and a mean relative bias of -0.068, both outperforming the API model (0.744, -0.292) and the cone model (1.132, 0.122).

Key words: safety assessment tool for carbon neutrality (C-SAT), hydrogen jet flames, flame length, prediction model, performance evaluation

CLC Number:

X932爆炸安全与防火、防爆

Zhu Kunlong, Hu Hui, Wang Zhi, Zhang Bin. Validation and performance evaluation of C-SAT hydrogen jet flame length prediction model[J]. China Safety Science Journal, 2026, 36(9): 210-216.

Figures/Tables 9

Fig.1

Table 1

Table 2

Fig.2

Fig.3

Fig.4

Table 3

Fig.5

Table 4

References 25

[1]	池立勋, 苏文龙, 杨坤, 等. 氢能在工业领域的脱碳利用现状及发展策略[J]. 石油科技论坛, 2025, 44(3):83-89.
	Chi Lixun, Su Wenlong, Yang Kun, et al. The application and strategies of hydrogen energy in industrial decarbonization[J]. Petroleum Science and Technology Forum, 2025, 44(3): 83-89.
[2]	赵钦新, 王宗一, 邓世丰, 等. 氢气燃烧技术及其进展[J]. 科学技术与工程, 2022, 22(36):15870-15 880.
	Zhao Qinxin, Wang Zongyi, Deng Shifeng, et al. Hydrogen combustion technology and progress[J]. Science Technology and Engineering, 2022, 22(36): 15 870-15 880.
[3]	李润之, 刘明帅, 黄子超, 等. 可燃气体泄爆特性研究现状及发展趋势[J]. 爆炸与冲击, 2025, 45(11):44-61.
	Li Runzhi, Liu Mingshuai, Huang Zichao, et al. Research status and development trend about combustible gas explosion venting[J]. Explosion and Shock Waves, 2025, 45(11): 44-61.
[4]	汪志雷, 潘旭海, 蒋军成. 高压氢气泄漏自燃研究进展[J]. 南京工业大学学报(自然科学版), 2019, 41(5):656-663.
	Wang Zhilei, Pan Xuhai, Jiang Juncheng. Research challenges in high-pressure hydrogen spontaneous ignition[J]. Journal of Nanjing University of Technology (Natural Science Edition), 2019, 41(5): 656-663.
[5]	Mogi T, Nishida H, Horiguchi S. Flame characteristics of high-pressure hydrogen gas jet[C]. Proceedings of the 1^st International Conference on Hydrogen Safety (ICHS 2005). Pisa, Italy, 2005: 425-434.
[6]	Mogi T, Horiguchi S. Experimental study on the hazards of high-pressure hydrogen jet diffusion flames[J]. Journal of Loss Prevention in the Process Industries, 2009, 22(1): 45-51. doi: 10.1016/j.jlp.2008.08.006
[7]	Iwasaka M, Urano Y, Hashiguchi Y. Fire hazard of compressed hydrogen by rapid leak[J]. Koatsu Gas (Journal of the High Pressure Gas Safety Institute of Japan), 1979, 16(7): 333-338.
[8]	Imamura T, Hamada S, Mogi T, et al. Experimental investigation on the thermal properties of hydrogen jet flame and hot currents in the downstream region[J]. International Journal of Hydrogen Energy, 2008, 33(13): 3 426-3 435.
[9]	Schefer R W, Houf W G, Bourne B, et al. Spatial and radiative properties of an open-flame hydrogen plume[J]. International Journal of Hydrogen Energy, 2006, 31(10): 1 332-1 340.
[10]	Schefer R W, Houf W G, Williams T C, et al. Characterization of high-pressure, under expanded hydrogen-jet flames[J]. International Journal of Hydrogen Energy, 2007, 32(12): 2 081-2 093.
[11]	Ekoto I W, Ruggles A J, Creitz L W, et al. Updated jet flame radiation modeling with buoyancy corrections[J]. International Journal of Hydrogen Energy, 2014, 39(35): 20 570-20 577.
[12]	Ekoto I W, Houf W G, Ruggles A J, et al. Large-scale hydrogen jet flame radiant fraction measurements and modeling[C]. International Pipeline Conference. American Society of Mechanical Engineers, 2012: 713-724.
[13]	Proust C, Jamois D, Studer E. High pressure hydrogen fires[J]. International Journal of Hydrogen Energy, 2011, 36(3): 2 367-2 373.
[14]	Cirrone D, Makarov D, Kuznetsov M, et al. Effect of heat transfer through the release pipe on simulations of cryogenic hydrogen jet fires and hazard distances[J]. International Journal of Hydrogen Energy, 2022, 47(50): 21 596-21 611.
[15]	Cirrone D M C, Makarov D, Molkov V. Thermal radiation from cryogenic hydrogen jet fires[J]. International Journal of Hydrogen Energy, 2019, 44(17): 8 874-8 885.
[16]	Cirrone D M C, Makarov D, Molkov V. Simulation of thermal hazards from hydrogen under-expanded jet fire[J]. International Journal of Hydrogen Energy, 2019, 44(17): 8 886-8 892.
[17]	Wang Jianpeng, Luan Xiaoyang, Huo Jiali, et al. Numerical study on the effect of complex structural barrier walls on high-pressure hydrogen horizontal jet flames[J]. Process Safety and Environmental Protection, 2023, 175: 632-643. doi: 10.1016/j.psep.2023.05.080
[18]	Carboni M, Pio G, Mocellin P, et al. Experimental and numerical characterization of hydrogen jet fires[J]. International Journal of Hydrogen Energy, 2022, 47(51): 21 883-21 896.
[19]	Houf W, Schefer R. Predicting radiative heat fluxes and flammability envelopes from unintended releases of hydrogen[J]. International Journal of Hydrogen Energy, 2007, 32(1): 136-151. doi: 10.1016/j.ijhydene.2006.04.009
[20]	Choudhuri A R, Gollahalli S R. Combustion characteristics of hydrogen-hydrocarbon hybrid fuels[J]. International Journal of Hydrogen Energy, 2000, 25(5): 451-462. doi: 10.1016/S0360-3199(99)00027-0
[21]	Hu Hui, Xu Rongcen, Hou Shuya, et al. Study on the effect of forced convection and thermal radiation on foam stability[J]. Journal of Loss Prevention in the Process Industries, 2024, 87: DOI:10.1016/j.jlp.2023.105231.
[22]	Wang Zhi, Hou Shuya, Zhang Muchen, et al. Assessment of the mass burning rate of LNG pool fires by a validated CFD model[J]. Process Safety and Environmental Protection, 2022, 168: 642-653. doi: 10.1016/j.psep.2022.10.019
[23]	Baraldi D, Melideo D, Kotchourko A, et al. Development of a model evaluation protocol for CFD analysis of hydrogen safety issues the SUSANA project[J]. International Journal of Hydrogen Energy, 2017, 42(11): 7 633-7 643.
[24]	Molkov V, Saffers J B. The correlation for non-premixed hydrogen jet flame length in still air[C]. 10^th International Symposium on Fire Safety Science. International Association for Fire Safety Science, 2011: 933-943.
[25]	Delichatsios M A. Transition from momentum to buoyancy-controlled turbulent jet diffusion flames and flame height relationships[J]. Combustion and Flame, 1993, 92(4): 349-364. doi: 10.1016/0010-2180(93)90148-V

模型名称	模型简介	模型特点
Y/O	阻塞条件法:将其简化为一个简单的阻塞喷嘴问题,忽略出口后的所有复杂波系	结果稳定、逻辑简单,处理较为简化,可能不适用于射流近场结构有极高精度要求的理论研究
Birch	有效面积法:为射流创建一个出口压力等于环境压力的虚拟出口	能够较好地预测射流的宏观扩散状态,但计算的出口速度可能过高,导致下游流场预测出现偏差
Birch2	改进的有效面积法:基于该面积重新计算质量流率	其改进并不总是能带来更精确的结果,取决于具体案例。使用Birch模型的基本假设,同样存在物理清晰度的问题
E/M	经验驱动法:通过指定一个经验性的高马赫数作为出口条件,拟合试验观测到的射流核心区	如果马赫数较为合适,预测结果可能较好。但过于依赖于经验参数且该参数缺乏普适性,物理机制不透明,可解释性差
Molkov	物理精细法:试图模拟射流中的马赫盘结构,将虚拟喷嘴出口定义在马赫盘位置	精度高,但计算复杂且稳定性相对较差,对物性参数和边界条件非常敏感,容易导致模拟发散或结果异常

试验	试验条件			火焰长度/m	喷射方向
试验	压力/MPa	孔径/mm	流体温度/℃	火焰长度/m	喷射方向
Mogi等^[5]	10 ~ 35	1 ~4	25	1.7~ 6.5	水平
Imamur等^[8]	0.23~3.26	1~ 4	25	0.35 ~ 1.82	水平
Schefer等^[10]	41.3	5.08	25	11.3	垂直
Ekoto等^[11]	5.98、6.21	20.9、52.5	35.55、14.65	17.4、48.5	水平
Proust等^[13]	10~ 70	1 ~ 3	-62~42	1.3 ~6.2	水平
Cirrone等^[14]	0.3~2	2、4	-163.15~-123.15	1.48、1.68、1.73、1.90	水平

统计性能指标	表达式	理想值	Y/O 模型	Birch 模型	E/M 模型	Molkov 模型
安全因子	$0.5\le \frac{{\mathit{c}}_{\mathit{P}}}{{\mathit{c}}_{\mathit{m}}}\le 2.0$	1	1.077	1.319	1.368	1.367
二因子比例/%	$\sum \left(0.5\le \frac{{\mathit{c}}_{\mathit{p}}}{{\mathit{c}}_{\mathit{m}}}\le 2.0\right)\ge 50$	100	100	100	96	100
平均相对偏差	$-0.4\le \frac{{\mathit{c}}_{\mathit{m}}-{\mathit{c}}_{\mathit{p}}}{0.5·({\mathit{c}}_{\mathit{p}}+{\mathit{c}}_{\mathit{m}})}\le 0.4$	0	-0.068	-0.264	-0.301	-0.300
几何平均偏差	$0.5\le \mathit{e}\mathit{x}\mathit{p}\mathit{l}\mathit{n}\frac{{\mathit{c}}_{\mathit{m}}}{{\mathit{c}}_{\mathit{p}}}\le 2$	1	0.934	0.765	0.737	0.738

统计性能指标	表达式	理想值	C-SAT	PHAST
统计性能指标	表达式	理想值	C-SAT	API模型	锥模型
安全因子	$0.5\le \frac{{\mathit{c}}_{\mathit{P}}}{{\mathit{c}}_{\mathit{m}}}\le 2.0$	1	1.077	1.358	0.897
二因子比例/%	$\sum \left(0.5\le \frac{{\mathit{c}}_{\mathit{p}}}{{\mathit{c}}_{\mathit{m}}}\le 2.0\right)\ge 50$	100	100	100	100
平均相对偏差	$-0.4\le \frac{{\mathit{c}}_{\mathit{m}}-{\mathit{c}}_{\mathit{p}}}{0.5·({\mathit{c}}_{\mathit{p}}+{\mathit{c}}_{\mathit{m}})}\le 0.4$	0	-0.068	-0.292	0.122
几何平均偏差	$0.5\le \mathit{e}\mathit{x}\mathit{p}\mathit{l}\mathit{n}\frac{{\mathit{c}}_{\mathit{m}}}{{\mathit{c}}_{\mathit{p}}}\le 2$	1	0.934	0.744	1.132