Rayleigh–Benard convection in a chemical equilibrium gas (simulation of surface detonation wave initiation)

Abstract

The problem of the Rayleigh-Benard convection for a chemical equilibrium gas is solved numerically. The gas is assumed to be incompressible, and the layer boundaries are assumed to be flat, isothermal, and free from shear stress. The Boussinesq model with the coefficient at the buoyancy term depending on the transverse coordinate is used. The resultant nonlinear system of equations is solved by a previously developed numerical method based on the spectral representation of vorticity and temperature fields. According to the idea of splitting, analytical formulas are first used to take into account the linear increase in disturbances, and then the nonlinear convective transfer is calculated by the finite-difference method. Various convection modes are obtained: stationary, periodic, quasi-periodic, and stochastic convection.The model of convection of a chemical equilibrium gas, presented here, can be useful for the understanding of the transition of a cellular combustion of surface systems into an explosion (initiation of surface detonation) and for the calculation of operating regimes of chemical reactors.

About control of convection intensity in chemical reacting equilibrium gas

“…Then, the gas density ρ, as is seen from system (1), depends on the absolute temperature T only. Note that the molar mass and density have monotonic dependence from absolute temperature [8,9]. The more detail description of used kinetic model may be found in [10].…”

“…In the case of a chemically equilibrium gas, the dependence of this coefficient on temperature changes considerably and becomes non-monotonic with a noticeable local maximum [5][6][7]. Authors in [8,9] were the first to formulate and solve numerically a two-dimensional problem for Rayleigh-Benard convection in a chemically equilibrium gas, as well as considered linear and nonlinear regimes. The molar mass and thermodynamic parameters of the gas were calculated according to a high accuracy model of chemical equilibrium [5][6][7].…”

“…Following [8][9][10], we consider a convective two-dimensional and non-stationary flow of a viscous incompressible fluid in the horizontal layer heated from below in the Boussinesq approximation. The boundaries of the layer are assumed isothermal and free from shearing stresses.…”

“…The molar mass and thermodynamic parameters of the gas were calculated according to a high accuracy model of chemical equilibrium [5][6][7]. Nevertheless, the physical and mathematical model provided in [8,9] is quite complicated and inconvenient. Some development of this physical and mathematical model may be found in [10].…”