Prof.  Igor  Palymskiy
Siberian State University of Telecommunications and Information Sciences,  Russia

Title: Study of the stability of a compressible gas layer in a gravity field.

Abstract:

The stability of the equilibrium of a compressible gas layer in a gravity field is investigated. The same temperature is maintained on all boundaries of the computational domain. The stability of the static equilibrium solution is analyzed in the linear approximation. In the linear approximation, it is shown that at a sufficiently large height of the domain, the equilibrium static solution becomes unstable. The obtained data are supplemented by the results of solving a system of complete nonlinear equations describing the flows of compressible gas. The features of the obtained non-stationary solution are discussed.

Biography:

Let us briefly describe the main areas of scientific activity and scientific interests of the professor Dr Sc Igor B. Palymskiy. These include direct numerical modeling (DNS) of unsteady two-dimensional and three-dimensional turbulent convective flows in a layer heated from below without using semi-empirical relations. Numerical modeling was performed using the author's pseudospectral method and allows modeling for Rayleigh numbers 34,000 times greater than the critical value (for two-dimensional models) and 1000 times greater than the critical value (for three-dimensional models). Using a parallel version of the pseudospectral method, we investigated the role of boundary conditions - free from tangential stresses - rigid horizontal boundaries, studied the dynamics of spatial spectra in turbulent flows, and also investigated the direct and reverse (red) energy cascades. As a practical application, convective flows in the upper mantle of the Earth were modeled.

We are currently studying convection in a compressible viscous gas. Modeling convection based on gas dynamics equations is much more complicated than modeling incompressible fluid convection in the Boussinesq approximation. This is due to the high rigidity of the system of equations caused by the coexistence of two different motions: slow convective and fast in the form of thermoacoustic waves. It is shown that the characteristics of convection in a compressible medium differ radically from the characteristics of incompressible fluid convection at a height of the convection region exceeding the critical one. The critical height for air under normal conditions is 17.3 cm. Of course, the compression of the medium (relative increase in density) at such a height of the region is extremely insignificant, and this leads to the widespread erroneous conclusion about the possibility of considering the medium incompressible. However, at a region height greater than the critical one, a sufficient change in hydrostatic pressure makes it possible to develop adiabatic processes, which leads to a significant intensification of convective processes and a change in the convection regime, in which the isobaric convection regime is replaced by an adiabatic one, and at a sufficiently large temperature difference - by a superadiabatic one. It is shown that due to adiabatic processes, convection in a compressible medium can develop even at neutral or stable density stratification!!!

The latter is fundamentally impossible during convection of an incompressible fluid in the Boussinesq approximation. Of particular practical and theoretical interest is the study of the stability of a compressible gas layer in a gravity field, in the absence of specified temperature gradients. Thus, in numerical modeling, the same temperature is specified at all boundaries of the region. As the results of linear analysis show, the static equilibrium state here becomes unstable at a sufficiently large height of the gas layer, which is due to the variation in pressure height and the compressibility of the medium. The conclusion about instability is confirmed by the results of numerical modeling based on a complete nonlinear system of equations. These studies are of interest in solving the issues of explosion safety of hydrocarbon storage in tanks. In fact, when emptying the tank, the evaporation of fuel residues during air movement in the tank leads to mixing of the medium with the formation of an explosive vapor-gas mixture.