TITLE:
Blast Waves in Multi-Component Medium with Thermal Relaxation
AUTHORS:
Vyacheslav O. Vakhnenko
KEYWORDS:
Structured Medium, Asymptotic Model, Relaxation, Nonlinear Wave, Explosion
JOURNAL NAME:
Natural Science,
Vol.6 No.12,
August
28,
2014
ABSTRACT: The
mathematical models of relaxing media with a structure for describing nonlinear
long-wave processes are explored. The wave processes in non-equilibrium
heterogeneous media are studied in terms of the suggested asymptotic averaged
model. On the microstructure level of the medium, the dynamical behavior is
governed only by the laws of thermodynamics, while, on the macrolevel, the
motion of the medium can be described by the wave-dynamical laws. It is proved
rigorously that on the acoustic level, the propagation of long waves can be
properly described only in terms of dispersive dissipative properties of the
medium, and in this case, the dynamical behavior of the medium can be modeled
by a homogeneous relaxing medium. At the same time, the dynamical behavior of
the medium cannot be modeled by a homogeneous medium even for long waves, if
they are nonlinear. For a finite-amplitude wave, the structure of medium
produces nonlinear effects even if the individual components of the medium are
described by a linear law. The heterogeneity of the structure of medium always
introduces additional nonlinearity. It is shown that the solution of many
problems for multi-component media with incompressible phases can be obtained
through the known solution of a similar problem for a homogeneous compressible
medium by means of the suggested transformation. It is not necessary to solve
directly the problem for the medium with incompressible component, and it is
sufficient just to transform the known solution of the similar problem for a
homogeneous medium. The scope for the suggested transformation is demonstrated
by the reference to the strong explosion state in a two-phase medium. The
special attention is focused on the research of blast waves in multi-component
media with thermal relaxation. The dependence of the shock damping parameters
on the thermal relaxation time is analyzed in order to provide a deeper
understanding of the damping of shock waves in such media and to determine
their effectiveness as localizing media. This problem attracts the interest
also in view of the practical possibility to estimate the efficiency of medium
for damping the shock wave action. To find the nature of the relaxation
interaction between the components of medium and to estimate the attenuation of
shock waves generated by solid explosives, we have studied experimentally both
the velocity field of shock waves and the pressure at front in an air foam. The
comparison of experimental and theoretical investigations of the relaxation
phenomena which accompany the propagation of shock waves in foam indicates that
within the scope of relaxation hydrodynamics it is possible to explain the
observed phenomena and estimate the efficiency of medium as localizer of the shock
wave action.