1 Transmission of hydrogen detonation across a curtain of dilute inert particles Yong Xu1 Pikai Zhang12 Qingyang Meng2 Shangpeng Li1 and Huangwei Zhang1

2025-04-28 0 0 2.6MB 40 页 10玖币

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Transmission of hydrogen detonation across a curtain of

dilute inert particles

Yong Xu1, Pikai Zhang1,2, Qingyang Meng2, Shangpeng Li1, and Huangwei Zhang1,†

1 Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1,

Singapore, 117576, Republic of Singapore

2 National University of Singapore (Chongqing) Research Institute, Liangjiang New Area,

Chongqing 401123, People’s Republic of China

Abstract

Transmission of hydrogen detonation wave (DW) in an inert particle curtain is simulated using the

Eulerian─Lagrangian approach with gas-particle two-way coupling. A detailed chemical

mechanism is used for hydrogen detonative combustion and parametric studies are conducted based

on a two-dimensional computational domain. A detonation map of propagation and extinction

corresponding to various particle sizes, concentrations, and curtain thicknesses is plotted. It is

shown that the critical curtain thickness decreases considerably when the particle concentration is less

than the critical value. The effects of curtain thickness on the trajectories of peak pressure, shock

front speed, and heat release rate are examined. Three propagation modes of the DW in particle

curtain are found: detonation transmission, partial extinction and detonation re-initiation, and

detonation extinction. The chemical explosive mode analysis confirms that a detonation re-initiation

event is caused by a re-initiation point with high pressure and explosive propensity, resulting from

transverse shock focusing. The influence of particle dimeter/concentration, and curtain thickness on

the DW are also examined with peak pressure trajectories, shock speed, and interphase exchange rates

of energy and momentum. Furthermore, the evolutions of curtain morphologies are analyzed by the

particle velocity, volume fraction, Stokes drag and Archimedes force. This analysis confirms the

importance of the drag force in influencing the change of curtain morphologies. Different curtain

evolution regimes are found: quasi-stationary regime, shrinkage regime, constant-thickness regime,

and expansion regime. Finally, the influences of the curtain thickness on the characteristic time of

curtain evolutions are studied.

Key words: Hydrogen; detonation re-initiation; detonation extinction; inert particle; particle

concentration; curtain thickness

1. Introduction

Hydrogen is a promising fuel for decarbonization in energy sectors. Compared to other fuels (e.g.,

methane), hydrogen has lower ignition energy and wider flammability limit (Olmos &

Manousiouthakis 2013), and hence is prone to ignition and explosion. Therefore, safety measures to

inhibit the accidental explosion of hydrogen should be carefully implemented and evaluated.

Chemically inert fine particles are one of the promising explosion inhibitors considering that they can

be readily obtained, and are also cheap and safe to be used without additional damage (Olmos &

Manousiouthakis 2013; Fomin & Chen 2009; Liu, et al. 2013). According to the literature (Fomin &

Chen 2009; Liu, et al. 2013), by implementing a particle curtain (Fedorov, Tropin & Bedarev 2010;

Tropin & Fedorov 2014), the overpressure, propagation speed, and product gas temperature of

detonation and/or blast waves can be effectively reduced, thereby minimizing the damage to

surrounding infrastructure and personnel.

The influence of inert particle curtains on the detonation wave (DW) has been extensively studied.

Kratova and Fedorov (2014) found that the detonation speed is reduced in a two-phase oxygen/non-

reactive and aluminum particles mixture. Meanwhile, Khmel and Fedorov (2014) observed that

particle collisions have negligible effects on the detonation speed, cell size, and gas parameters. Liu et

al. (2016) confirmed that curtain concentration, particle material density, and particle size play key

roles in detonation inhibition. In addition to the above studies, Tahsini (2016) found that the residence

time of detonation wave in the curtain significantly affects detonation suppression.

Fedorov and Kratova (2015a, 2015b) observed that detonation propagation is more significantly

influenced by the composition and distribution of the particles than by particle size and volume fraction.

Fedorov and his co-authors (2010, 2018, 2019) also concluded that detonation speed deficit is a

function of particle size and concentration. Generally, smaller particle sizes and/or higher particle

concentrations tend to reduce the shock speed. These conclusions are also confirmed in Refs. (Fedorov

& Tropin 2013; Tropin & Fedorov 2014). Furthermore, some detonation suppression calculations

conducted by Tropin and Fedorov (2014) demonstrated that at smaller particle concentrations, particles

of 10 and 100 µm (diameter) have limited influences on the detonation velocity deficit, while the

influence becomes larger when critical concentrations are reached. They attributed this to the energy

exchanges between the gas and particles. Fomin and Chen (2009) proposed that mechanical and heat

equilibria are not achieved between the larger particles and shock, and their detonation suppression

efficiency is therefore generally lower than that of smaller particles. Although various effects on the

detonation propagation in particle curtains were investigated in these studies, the critical condition for

detonation inhibition has not been determined, which is of great importance for practical hydrogen

safety measures.

Existence of a particle curtain may induce unsteadiness in detonation propagation. For instance,

Pinaev et al. (2015) experimentally observed that the propagation speed of CH4/2O2/N2 detonation is

non-monotonically reduced in a silica sand curtain with three particle size ranges: 90─120, 120─250,

and 250─600 µm. They attributed it to the dual role of the sand particles in decelerating the shocked

flow and generating hot spots that induce secondary detonations behind the leading shock. More

interestingly, Fedorov and Tropin (2011) found that an increased concentration of silica particles,

beyond the critical value, will not result in more efficient detonation inhibition. Moreover, a reduction

in the particle volume fraction from the critical value to a certain smaller value leads to less detonation

speed deficit, compared with the constant limiting concentration.

Two different DW propagation modes in particle curtains modes were observed, i.e., detonation

extinction and transmission (Gottiparthi & Menon 2012; Fedorov & Kratova 2013; Kratovaa &

Fedorova 2014; Tropin & Fedorov 2018; Tropin & Fedorov 2019; Tropin & Bedarev 2021). In the

detonation extinction mode, the reaction front decouples with the leading shock, and their distance is

gradually increased. In the latter mode, the reaction zone is still coupled with the SF, but typically with

various degrees of speed reduction. In addition, propagation modes of instantaneous extinction

followed by detonation re-initiation (Gottiparthi & Menon 2012; Fedorov & Kratova 2013; Fedorov

& Tropin 2013; Tropin & Fedorov 2014; Pinaev, Vasilev & Pinaev 2015) and a galloping detonation

near the flammability limit (Tropin & Fedorov 2018; Tropin & Fedorov 2019; Tropin & Bedarev 2021)

are also observed, which is caused by “explosion in the explosion” (Tropin & Bedarev 2021). The

detonation is re-ignited by hot spots due to gas-particles interactions (Pinaev, Vasilev & Pinaev 2015),

whilst a galloping mode is a regularly repeated process with a pulsation phenomenon (Tropin &

Bedarev 2021). However, the underlying mechanisms behind these transient detonation dynamics have

not been clarified, particularly in terms of the interactions between the detonation wave and solid

particles.

In this work, detailed simulations with the Eulerian─Lagrangian method and two-way gas-

particle coupling are conducted to simulate the transmission of hydrogen detonation in a curtain of

dilute inert particles. A two-dimensional configuration is considered and a detailed chemical

mechanism is used for hydrogen combustion in our simulations. The objectives of this paper include:

(1) critical curtain conditions for quenching detonation; (2) transient detonation phenomena with

various particle sizes, concentrations, and curtain thickness; (3) interactions between gas and particles;

and (4) evolution of curtain morphology in detonated flows. This paper is structured as follows. The

physical model and the mathematical model are introduced in Section 2 and Section 3, respectively.

The results and discussion are presented in Section 4, followed by the main conclusions given in

Section 5.

Figure 1 Schematic of the computational domain. Curtain thicknesses  is varied from 0 to 0.1 m.

The blue dots represent particles. Domain and particle sizes not to scale. UF and DF:

upstream/downstream fronts of the curtain.

00.3

0.2

0.1

Detonation

wave

Two-phase section:

∆ = 0.02 mm

Development section: ∆ = 0.16 mm

Hot spots:

T= 2,000 K

p= 5 MPa

0.0125

─0.0125

y[m]

x[m]

2.5≤ ≤10μm

0 < L ≤ 0.1 m

UF DF

2. Physical problem

Transmission of a hydrogen detonation wave across a curtain of chemically inert solid particles

is simulated with a two-dimensional configuration in Fig. 1. The computational domain is 0.3 m ×

0.025 m, which includes a detonation development section (0 ≤ x < 0.2 m) and a two-phase section

(0.2 ≤ x ≤ 0.3 m). The domain is initially filled with stoichiometric H2/air mixture. The initial

temperature and pressure are  = 300 K and  = 0.05 MPa, respectively. For the left boundary (x

= 0), a non-reflective condition is enforced for the pressure, while a zero-gradient condition for other

quantities. Zero-gradient condition is applied at x = 0.3 m and the upper and lower boundaries are set

to be periodic.

The two sections are respectively discretized by uniform Cartesian cells of 0.16×0.16 and

0.02×0.02 mm2. The total mesh number is about 8 million. Based on the ZND structure of the particle-

free stoichiometric H2/air detonation, the Half-Reaction Length (HRL)  is approximately 382

µm. Therefore, in the two-phase section, at least 19 cells exist within , given that the particle

heating behind the lead shock would delay the ignition of shocked gas and hence increase the HRL.

Halving the mesh resolution almost does not change the detonation propagation speed and average

detonation cell size; see the analysis in Section A of supplementary document.

Monodispersed and static ( ) solid particles are uniformly distributed in the two-phase

section (i.e., x = 0.2 m ─ 0.2+L m; 0 < L ≤ 0.1 m). The left and right fronts are termed as upstream

front (UF) and downstream front (DF), respectively (see the annotation in Fig. 1). In this study, 

corresponds to the instant when the detonation reaches the curtain UF. In our simulations, each CFD

cell in the curtain area initially has one parcel, and particle concentration variation is achieved by

changing the particle number in a parcel. The initial particle concertation of c = 0.1 ─ 2.5 kg/m3 and

particle sizes of  = 2.5, 5, and 10 µm will be considered. The size does not change throughout the

simulations because of inert particles without any swelling. The two-phase flow is considered to be

dilute since the particle concentration does not exceed 0.1% (Crowe et al. 2011). The initial

temperature, material density and isobaric heat capacity of the particles are 300 K, 2,500 kg/m3 and

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1TransmissionofhydrogendetonationacrossacurtainofdiluteinertparticlesYongXu1,PikaiZhang1,2,QingyangMeng2,ShangpengLi1,andHuangweiZhang1,†1DepartmentofMechanicalEngineering,NationalUniversityofSingapore,9EngineeringDrive1,Singapore,117576,RepublicofSingapore2NationalUniversityofSingapore(Chongqing)Re...

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1 Transmission of hydrogen detonation across a curtain of dilute inert particles Yong Xu1 Pikai Zhang12 Qingyang Meng2 Shangpeng Li1 and Huangwei Zhang1

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