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Direct simulations of outdoor blast wave propagation from source to receiver

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Abstract

Outdoor blast waves generated by impulsive sources are deeply affected by numerous physical conditions such as source shape or height of burst in the near field, as well as topography, ground nature, or atmospheric conditions at larger distances. Application of classical linear acoustic methods may result in poor estimates of peak overpressures at intermediate ranges in the presence of these conditions. Here, we show, for the first time, that converged direct fully nonlinear simulations can be produced at a reasonable CPU cost in two-dimensional axisymmetric geometry from source location to more than \(500\,\hbox {m/kg}^{1/3}\). The numerical procedure is based on a high-order finite-volume method with adaptive mesh refinement for solving the nonlinear Euler equations with a detonation model. It is applied to a real outdoor pyrotechnic site. A digital terrain model is built, micro-meteorological conditions are included through an effective sound speed, and a ground roughness model is proposed in order to account for the effects of vegetation and unresolved scales. Two-dimensional axisymmetric simulations are performed for several azimuths, and a comparison is made with experimental pressure signals recorded at scaled distances from 36 to \(504\,\hbox {m/kg}^{1/3}\). The relative importance of the main physical effects is discussed.

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Acknowledgements

This work is part of the Prolonge project supported by the French Agence Nationale de la Recherche (ANR) under reference ANR-12-ASTR-0026. A. Llor and the HERA team are acknowledged for valuable discussions. INERIS is acknowledged for providing us access to their measurements. We also thank the Managing Editor for his meticulous work which helped us to improve the English version of this paper.

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Authors and Affiliations

  1. CEA, DAM, DIF, 91297, Arpajon Cedex, France

    M. Nguyen-Dinh, N. Lardjane, C. Duchenne & O. Gainville

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  1. M. Nguyen-Dinh
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  2. N. Lardjane
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  3. C. Duchenne
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Correspondence to N. Lardjane.

Additional information

Communicated by C. Needham and A. Higgins.

Appendix: Validation of the 1D roughness model

Appendix: Validation of the 1D roughness model

The drag force formulation of the roughness model described in Sect. 3.6.1 has been successfully validated in comparison to 2D and 3D simulations of an experimental configuration proposed by Suzuki et al. [41]. These authors considered plane shocks interacting with different arrays of cylindrical obstacles perpendicular to the flow in a shock tube. The shock tube cross section is a square of side 46.7 mm. We retained the regular arrangement configuration of \(4 \times 4\) cylinders of diameter 4 mm spaced by 10 mm (code 4444-R of Table 1 in [41]) with a shock Mach number of 1.36.

Reference simulations are performed with the HERA software, with a cell size of 0.2 mm, and with an immersed boundary method [46] to accurately model the cylinders within the cartesian grid. Figure 20 presents snapshots of both the 2D and 3D simulations. The shock moves from the left to the right. When the shock front has passed the matrix, its strength is reduced and complex flow patterns develop as also pointed out in [47].

Fig. 20
figure 20

Instantaneous pressure field from our 2D simulation (top) and 3D simulation (bottom) of a plane shock at Mach number 1.36 interacting with a regular array of cylindrical obstacles in a shock tube. Configuration proposed by Suzuki et al. [41]. The shock moves from the left to the right. At t = 2.2 ms the shock has left the matrix. Pressure iso-surfaces 90, 125, 160, 195, and 230 kPa are drawn. In 3D, half of the computational domain is presented with the pressure field at the bottom of the shock tube and the second half part using pressure iso-surfaces

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Fig. 21
figure 21

Pressure signals recorded at a station located 25 cm after the matrix of cylindrical obstacles. Both 2D (magenta curve) and 3D (cyan curve) reference simulations are presented as well as 1D simulations with roughness model and several drag coefficients. The dashed line corresponds to the signal without the array of obstacles. The Jones and Krier drag coefficient relation (red curve) provides solutions that are in good agreement with reference simulations and Suzuki et al. experiments (blue curve)

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The HERA hydrocode is also applied in 1D, without the cylindrical array zone, but with the drag model active, as in Suzuki et al. The mesh size is 5 mm which leads to a mean porosity parameter of 0.11. The spatial roughness length scale \(\varDelta \) is set to the cylinder diameter. Figure 21 shows the pressure signals recorded with this 1D model and the 2D and 3D reference simulations at a station located 25 cm after the matrix (pressure port #8 in [41]). As a comparison, 1D results from the well-established Ergun model [48] are also displayed. Obviously, the roughness model cannot reproduce the complex flow behaviour from the high-resolution reference simulations with the cylinders. Nevertheless, the shock strength is well estimated by the Jones and Krier relation, in agreement with the results of Suzuki et al. Moreover, not shown here, a reflected wave is generated in the downstream of the matrix of obstacles. Both the amplitude and the time of arrival of this reflected wave are well estimated by the roughness model. These results confirm the efficiency of the model to reproduce the main ground roughness effect on a shock wave.

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Nguyen-Dinh, M., Lardjane, N., Duchenne, C. et al. Direct simulations of outdoor blast wave propagation from source to receiver. Shock Waves 27, 593–614 (2017). https://doi.org/10.1007/s00193-017-0711-2

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