A simple and effective approach for evaluating unconfined hydrogen/air cloud explosions
Introduction
Hydrogen is a promising energy carrier. Because of the flammability of hydrogen, its safety utilization has always been a key concern [1], [2], [3], [4]. Not only hydrogen, the leakage of combustible gas or liquefied combustible gas (with a low boiling point at ambient temperature), like methane, ethylene, propane etc., will form flammable cloud in the atmosphere [5]. Once the flammable cloud meets ignition source, the VCE (Vapor Cloud Explosions) accident may be occurs, which is a main hazardous issue in energy and chemical industries [6]. It is reported that approximately 174 VCE accidents occurred during 1940–2010 in the world [7], [8], which resulted in huge personal and property losses. The large overpressure load created by the flammable cloud explosion, could cause serious damage. Thus, it is necessary to investigate the pressure wave of potential accidents, for the safety assessment of existing and designed chemical plants and buildings [9]. And this topic has attracted much attention by researchers for several decades.
There are three categories models to predict the overpressure of VCE accidents [10], [11], [12]: empirical models (TNT equivalence model [13], TNO Multi-Energy model [14], [15], Baker-Strehlow model [16], CAM [17], etc.), phenomenological models (CLICHE model [18] and SCOPE model [19]) and CFD models. Compared with the first two models, an appropriate CFD model can obtain much accurate overpressure time history and more details of the flow field. However, the great demand for time and computer resource of CFD models makes it impractical for engineering applications, especially for complex geometries [10], [20], [21], [22], [23]. At this aspect, the empirical models and phenomenological models have their advantages, but these models also have their weaknesses. For empirical models, the weaknesses includes: the drawbacks of weak accuracy (TNT, Baker-Strehlow), only positive phase peak pressure can be solved (TNT, Multi-Energy), and not good realizability (Multi-Energy, CAM), etc. The sophistication of phenomenological models is between empirical models and complex CFD models, but few information of the flow field could be provided in phenomenological models [10], [11]. The detailed comments of the previous models can be seen in Ref. [10] and Ref. [12].
In addition, Deshaies [24] proposed an acoustic approximation model, in which the flow field outside the flame was divided into two zones, incompressible source flow (near the flame front) and acoustic approximation of source flow (far from the flame front). The overpressure time history at a distance of R from the ignition center was given as follows:near the flame front:and far from the flame front:
The acoustic approximation model can provide the pressure-time history with a varied distance R, and it has been checked by several deflagration experiments [25], [26]. As can be seen in Eqs. (1), (2), the flame radius history Rf(t) is necessary for overpressure calculation, but it is unknown before the experiment. Thus, this drawback restricts the practical use of the acoustic approximation model. Moreover, the acoustic approximation model can't obtain the pressure wave inside the flame sphere. However, the length of the flame may be hundreds of meters to several kilometers, and the affected zone is very broad in large scale VCE accidents.
Based on the discussions mentioned previously, the weaknesses of the models motivate the authors to develop a simple and effective model for engineering application of safety assessment. In the present study, a model on the basis of the acoustic approximation model is proposed, in which an independent flame history function improves the availability of the original model. In Section Theory hypothesis, the pressure wave shapes are classified with findings from hydrogen/air deflagration tests. The calculation model of overpressure is presented in Section Method, and in Section Result and discussion it will be validated.
Section snippets
Findings in gas deflagration experiments
In 1983, the Fraunhofer Institute for Propellants and Explosives (Germany) conducted a series of large scale unconfined vapor cloud explosion (UVCE) tests in open area, with H2/Air mixtures [27]. This program was part of the Prototype Plant Nuclear Process Heat project (PNP). Table 1 lists the experimental details of some tests in the series. The unconfined flammable clouds were considered as hemispherical shape, and were simulated by the balloons that made of thin polyethylene foil. The
Method
As Deshaies stated in Ref. [24], for the original acoustic approximation model, if the complete flame radius history Rf(t) is unknown, it is impossible to obtain the prediction of the pressure signal. In this section, we seek to develop a tentative solution that begins with the flame/piston speed history D(t), which is independent of experimental data. If D(t) is known, the flame/piston history Rf(t) can be solved by integrating. It should be noted that, the authors consider that the flow field
Validation of the method
To validate the method developed in Section Method, a large scale [28], [31], [32] and a series of small scale [30], [33] H2/Air deflagration experiments are employed. The calculated data of the former one are compared with both experimental and CFD predicted data, and the latter ones are contrasted with experimental data only. Note that, in these validations, the experimental data of average flame speed S′ are adopted (Eq. (5)).
Fig. 10 displays the comparison of experimental data, numerical
Conclusion
In this study, an improved acoustic approximation model for UVCE was proposed. For the large scale VCE accidents, a simplified scheme was also presented for overpressure evaluating of the area inside the flame cloud. The model could be used for engineering application of safety assessment on hydrogen energy, and has a high computational efficiency compared with CFD models, because there are no differential equations but only algebraic equations. The model appears good accuracy in the medium and
Acknowledgement
This research work was jointly supported by the National Natural Science Foundation of China (No. 51641608) and the State Key Laboratory of Technologies in Space Cryogenic Propellants of China (SKLTSCP1511, SKLTSCP1809).
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