Three-dimensional mathematical simulation of two-phase detonation in the system of gaseous oxydizer with fuel droplets

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Abstract

The results of a three-dimensional numerical study of the propagation of detonation waves in a two-phase mixture of liquid iso-octane with air are presented. The detonation calculation technique is based on Navier-Stocks equations with the simulation of liquid phase evolution using the Lagrangian formalism. Numerical models consider droplet movement, evaporation and breakup as well as finite-rate mixing and chemical transformations. The reliability of the method is confirmed by the comparison of predicted and measured velocities of heterogeneous detonation in a vertical channel of square cross-section. The influence of the prehistory on the formation of a two-phase detonable mixture in the channel on the propagation velocity and structure of detonation waves is considered. The influence of droplet coagulation is also taken into account. New data on the spatiotemporal structure of a two-phase detonation wave have been obtained.

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About the authors

V. S. Ivanov

Semenov Federal Research Center for Chemical Physics of the Russian Academy of Sciences

Email: smfrol@chph.ras.ru
Russian Federation, Moscow

S. M. Frolov

Semenov Federal Research Center for Chemical Physics of the Russian Academy of Sciences; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)

Author for correspondence.
Email: smfrol@chph.ras.ru
Russian Federation, Moscow; Moscow

References

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Supplementary files

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2. Fig. 1. a – Schematic representation of the calculation area – a vertical channel with the gravity acceleration vector directed from top to bottom; b – mass distribution of isooctane droplets by size: curve 0 – experiment, curves 1–4 – calculation according to the droplet coagulation model for different channel sections, numbers 1–4 correspond to the distance from the beginning of the channel in meters.

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3. Fig. 2. Calculated change in the velocity of the detonation wave front along a vertical channel filled with a stoichiometric isooctane-air mixture. The calculation was performed for conditions obtained by blowing the channel with an initially monodisperse two-phase mixture with droplets 400 μm in diameter. The horizontal dashed line corresponds to the thermodynamic detonation velocity of the black liquid.

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4. Fig. 3. Calculated distributions of temperature, pressure and mass fraction of fuel vapor during propagation of heterogeneous detonation from bottom to top in a vertical channel with different initial mixture compositions: a – Ф = 0.7, b – Ф = 1.0, c – Ф = 1.8. The calculation was performed for conditions obtained by blowing the channel with an initially monodisperse two-phase mixture of air with isooctane droplets with a diameter of 400 μm. The reaction zone in the detonation wave, inside which the difference between the detonation and cocurrent flow velocities is less than the local speed of sound, is shown in white in the lower figures, and the ЧЖ condition is satisfied at the edges.

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5. Fig. 4. Comparison of calculated (curves) and measured (squares) dependences of the detonation velocity in a two-phase isooctane-air mixture on the total excess fuel coefficient. Calculations were performed for conditions obtained by blowing the channel with initially monodisperse two-phase mixtures with droplets of 150 (curve 1) and 400 μm (curve 2) diameters and for conditions with an initial polydisperse two-phase mixture, taking into account the coagulation of droplets during channel blowing (curve 3). The black dot corresponds to the thermodynamic detonation velocity of the BL.

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