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Shock waves in sprays: numerical study of secondary atomization and experimental comparison

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Abstract

Numerical modeling of the interaction between a cloud of water droplets and a planar shock wave is compared with experimental data. The mathematical model relies on an Eulerian description of the dispersed phase with the assumption of dilute flows. It is shown that the secondary atomization of the droplets strongly influences the structure of both the shock wave and the induced flow. After shock loading, the individual liquid components generate daughter droplets, and the overall interphase surface per unit volume undergoes strong variations which modify the pressure relaxation process towards a dynamic and thermal equilibrium state. The experimental data enable one to determine the best analytical formulation of the droplet number production rate. Models of droplet number production rate are compared in order to highlight this feature. The model based on the assumption of linear variation of droplet diameter with time gives the best agreement between the numerical results and the experimental data.

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Acknowledgments

The authors would like to thank DGA-Tn for supporting this study and Robert Tosello for valuable discussions.

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Authors and Affiliations

  1. Aix-Marseille Université, CNRS, UMR IUSTI 7343, 5 rue E. Fermi, 13013, Marseille, France

    A. Chauvin, E. Daniel, J. Massoni & G. Jourdan

  2. ENSMA, CNRS, Institut PRIME, UPR 3346, 1, Av. Clément Ader, 86961, Futuroscope, France

    A. Chinnayya

Authors
  1. A. Chauvin
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  2. E. Daniel
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  3. A. Chinnayya
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  4. J. Massoni
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  5. G. Jourdan
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Corresponding author

Correspondence to E. Daniel.

Additional information

Communicated by A. Hadjadj.

Appendix

Appendix

Although the numerical method is detailed in [16], it is important for this specific unsteady application to verify the grid independence of the solutions. Various meshes are tested on the simulations presented in Sect. 7. Mesh 1 corresponds to the one used in the present study (\(\mathrm{d}x =1\) mm), the cell is then divided by two (Mesh 2), and the third mesh \(\mathrm{d}x = 0.25\) mm (Mesh 3). The pressure evolution along the shock tube axis is plotted at time \(t=4.5\) ms for these different meshes. This pressure evolution shows that each wave pattern (expansion fan, shock wave, interaction with the droplet cloud) is computed in the same way regardless of the mesh used. The differences are quite negligible and cannot be seen on this figure (Fig. 15), and one can state that the results are independent of the grid.

Fig. 15
figure 15

Influence of the mesh size on the pressure evolution along the shock tube axis

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Chauvin, A., Daniel, E., Chinnayya, A. et al. Shock waves in sprays: numerical study of secondary atomization and experimental comparison. Shock Waves 26, 403–415 (2016). https://doi.org/10.1007/s00193-015-0593-0

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  • DOI: https://doi.org/10.1007/s00193-015-0593-0

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