Modeling Dynamics of Shock Impact on Aqueous Foams with Account for Viscoelastic Properties and Syneresis Phenomena
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ling Dynamics of Shock Impact on Aqueous Foams with Account for Viscoelastic Properties and Syneresis Phenomena R. Kh. Bolotnovaa,* and E. F. Gainullinaa,** aMavlyutov
Institute of Mechanics, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa, 450054 Russia *e-mail: [email protected] **e-mail: [email protected] Received March 1, 2020; revised March 12, 2020; accepted March 12, 2020
Abstract—A two-phase model of aqueous foam is proposed. It is based on the laws of conservation of mass, momentum, and energy of the phases in accordance with the single-pressure, two-velocity, and two-temperature approximations in the axisymmetric formulation, with account of the interphase drag forces, contact heat transfer, viscoelastic properties, and foam syneresis. The thermodynamic properties of the water and the air are described by the Mie—Grüneisen and Peng—Robinson equations of state, respectively. The model is numerically realized in the OpenFOAM software. The results obtained are in reasonable agreement with the experimental data on the spherical explosion in aqueous foam. The evolution of a spherical shock wave propagating in the aqueous foam is analyzed. Keywords: spherical shock wave, aqueous foam, OpenFOAM software, numerical simulation DOI: 10.1134/S001546282005002X
The importance of studying the damping properties of aqueous foams under dynamic loading is due to the possible use of foam barriers as effective protections against the devastating impact of shock waves. In [1–4] the properties of aqueous foams, which make it possible to reduce the main shock wave parameters, are described. The interaction of a spherical shock pulse with a foam screen was studied in [1, 2] using the method of movable Lagrangian meshes [1] and the OpenFOAM software [2, 5] in the two-dimensional axisymmetric formulation. The numerical simulation of the shock wave evolution initiated by an explosion in aqueous foam for the conditions of experiments [3] was performed in [4] in the one-dimensional approximation using the shock-capturing technique with an analysis of the effect of the interphase contact heat transfer on the shock-wave energy dissipation level. In this study, the mathematical and numerical simulation of the spherical explosion dynamics in aqueous foam is performed in accordance with experiments [3], taking account for the interphase drag forces, the contact heat transfer, the viscoelasic properties, and the foam syneresis with realistic equations of state of its components, in more detail, than it was done in [4]. The proposed aqueous foam model is numerically realized in a new solver developed by the authors in the OpenFOAM software. 1. BASIC EQUATIONS The system of model equations includes the laws of conservation [6] of mass, momentum, and energy of the phases
∂(αi ρi ) + div(αi ρi vi ) = 0, ∂t
∂(αi ρi vi ) + div(αi ρi vi vi ) = −αi ∇p + div(αi τi ) + Fi,drag + Fi,vm , ∂t 604
(1.1) (1.2)
MODELING DYNAMICS OF SHOCK IMPACT ON AQUEOUS FOAMS
∂(αi ρi (ei + K i )) + div(αi ρi (ei + K i )vi ) ∂t c
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