# Simulations of Blast Wave and Fireball Occurring Due to Rupture of High-Pressure Hydrogen Tank

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Model

_{i}, x

_{j}and x

_{k}are the Cartesian coordinates; u

_{i}, u

_{j}and u

_{k}are the velocity components; p is the pressure; g

_{i}is the gravity acceleration in direction i; μ

_{t}is the turbulent dynamic viscosity; δ

_{ij}is the Kronecker symbol; E is the total energy; T is the temperature; Y

_{H2}is the hydrogen mass fraction; c

_{p}is the specific heat at constant pressure; Sc

_{t}is the turbulent Schmidt number; Pr

_{t}is the turbulent Prandtl number; D

_{H2}is the hydrogen molecular diffusivity; and S

_{E}and S

_{H2}are the source terms in the equations of energy conservation and hydrogen conservation during combustion [11].

_{k}is the generation of turbulent kinetic energy by the mean velocity gradients; G

_{b}is the generation of turbulent kinetic energy by buoyancy; Y

_{M}is the contribution of the fluctuating dilatation in compressible turbulence flow to the dissipation rate; C

_{2}, C

_{1ε}and C

_{3ε}are constants; and σ

_{k}and σ

_{ε}are the turbulent Prandtl numbers for k and ε, respectively. In this simulation, the initial values of both k and ε are assumed to be 1.

_{i,r}is expressed by:

_{w,i}, M

_{w,j}are the molecular weights of species i and j; Y

_{p}and Y

_{R}are the mass fractions of the product and reactant, respectively; and A = 4.0 and B = 0.5 are empirical constants. The chemical reaction is regulated by the large-eddy mixing time scale. Combustion occurs whenever turbulence is present, i.e., k/ε > 0, and an ignition source is not required to initiate combustion [14]. In this simulation, the one-step chemical reaction mechanism of hydrogen combustion in the air is applied, i.e., 2H

_{2}+ (O

_{2}+ 3.76N

_{2}) → 2H

_{2}O + 3.76N

_{2}, and the model is therefore incapable of predicting kinetics of intermediate species.

## 3. Numerical Details

_{H}

_{2}= 1.0 and the initial pressure was set to p = 35 MPa. The ground was modeled as a non-slip impermeable adiabatic boundary. A far-field non-reflective boundary was set as the interface with the ambient atmosphere. ANSYS Fluent software was used as the computational fluid dynamics (CFD) platform. A coupled compressible solver with an explicit time stepping was used in the simulations with the Courant-Friedrichs-Lewy (CFL) number equal to 0.8. Convective terms were discretized using a second-order upwind scheme and diffusive terms were discretized using a second-order central difference scheme. Tank rupture was modeled as the instantaneous disappearance of the tank wall.

## 4. Results and Discussion

#### 4.1. Blast Wave

^{−4}, 9.1 × 10

^{−4}, and 1.5 × 10

^{−3}s). This is possibly owing to the stagnation conditions. Figure 2 (instance t = 3.1 × 10

^{−4}s) also illustrates the formation of a secondary pressure wave, which, being reflected from the ground, provides the largest overpressure of approximately 47 bar at this instant. This wave continues to travel back and forth between the ground and hydrogen-air interface, providing high pressure at the focal point on the ground, e.g., approximately 5 bar overpressure at t = 2.1 × 10

^{−3}s, which generates the next oscillation in the pressure wave propagating through hydrogen to approach the initial blast wave propagating through the air with a slower velocity.

^{−4}s. It can be observed that although the high-temperature profile coincides with the blast wave propagation and is generally hemispherical, the low temperature area of the expanding hydrogen envelope is not hemispherical. The low temperature area exhibits preferential propagation direction along the longitudinal and transverse tank axes, and the authors consider that this is, to a certain extent, the result of the cylindrical shape of the high-pressure hydrogen charge and the effect of buoyancy.

^{−5}s and t = 3.1 × 10

^{−4}s. At t = 5.1 × 10

^{−4}s, the velocity profile is affected by the reflection wave travelling through hydrogen between the interface with the heavier air and the ground. The maximum velocity of 1780 m/s is observed as anticipated at the beginning of the process (t = 7.5 × 10

^{−4}s in Figure 4), when the pressure in the blast wave is maximum (starting shock).

#### 4.2. Fireball

^{−3}s, combustion practically has negligible effect, and its role becomes apparent later at approximately t = 5.0 × 10

^{−3}s. Hydrogen concentration starts to decrease owing to combustion, beginning with the area of intensive hydrogen-air mixing at the hydrogen-air interface, while it remains unchanged at the ground (see t = 0.1–0.3 s in Figure 6). Once the reacting hydrogen cloud (fireball) is affected by the buoyancy force, mixing with air and combustion start to occur in the vicinity of the ground as well (t = 0.3–0.5 s). The fireball development progresses, and it assumes the shape characteristic of a thermic attached to the ground by a narrow “leg” (t = 0.5–0.8 s). Then, the “leg” burns completely, and the mushroom-shaped fireball continues to burn in the air and rise upward (t = 1.0–1.2 s).

## 5. Concluding Remarks

^{−4}s. Hydrogen expansion was considered to be affected by the cylindrical shape of the hydrogen tank, with preferential expansion directions along the main and transversal tank axes.

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Computational domain and numerical mesh: (

**a**) central cross-section; (

**b**) side view of the domain boundary, fireball resolution area, and tank location; and (

**c**) tank boundary mesh.

**Figure 2.**Pressure wave in the surroundings of the tank due to the rupture of the high pressure hydrogen tank.

**Figure 3.**Temperature in the surroundings of the tank due to the rupture of the high pressure hydrogen tank.

**Figure 4.**Velocity magnitude in the surroundings of the tank due to the rupture of the high pressure hydrogen tank.

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**MDPI and ACS Style**

Kim, W.; Shentsov, V.; Makarov, D.; Molkov, V.
Simulations of Blast Wave and Fireball Occurring Due to Rupture of High-Pressure Hydrogen Tank. *Safety* **2017**, *3*, 16.
https://doi.org/10.3390/safety3020016

**AMA Style**

Kim W, Shentsov V, Makarov D, Molkov V.
Simulations of Blast Wave and Fireball Occurring Due to Rupture of High-Pressure Hydrogen Tank. *Safety*. 2017; 3(2):16.
https://doi.org/10.3390/safety3020016

**Chicago/Turabian Style**

Kim, Wookyung, Volodymyr Shentsov, Dmitriy Makarov, and Vladimir Molkov.
2017. "Simulations of Blast Wave and Fireball Occurring Due to Rupture of High-Pressure Hydrogen Tank" *Safety* 3, no. 2: 16.
https://doi.org/10.3390/safety3020016