Time-dependent modeling of oscillatory instability of three-dimensional natural convection of air in a laterally heated cubic box

Abstract

Transition from steady to oscillatory buoyancy convection of air in a laterally heated cubic box is studied numerically by straight-forward time integration of Boussinesq equations using a series of gradually refined finite volume grids. Horizontal and spanwise cube boundaries are assumed to be either perfectly thermally conducting or perfectly thermally insulated, which results in four different sets of thermal boundary conditions. Critical Grashof numbers are obtained by interpolation of numerically extracted growth/decay rates of oscillations amplitude to zero. Slightly supercritical flow regimes are described by timeaveraged flows, snapshots, and spatial distribution of oscillations amplitude. Possible similarities and dissimilarities with two-dimensional instabilities in laterally heated square cavities are discussed. Break of symmetries and sub-or super-critical character of bifurcations are examined. Three consequent transitions from steady to oscillatory regime, from oscillatory to steady, and finally to oscillatory flow, are found in the case of perfectly insulated horizontal and spanwise boundaries. Arguments for grid and time step independence of the results are given.

Computational modeling of magnetoconvection: Effects of discretization method, grid refinement and grid stretching

“…The method is based on the finite-volume discretization scheme described in [29,30]. The electromagnetic part of the scheme has been added for the present study.…”

“…The electromagnetic part of the scheme has been added for the present study. The method includes direct calculation of steady states done by Newton iterations as in [31] and integration of the governing equations in time as in [30] .…”

“…The semi-implicit projection algorithm is based on the second-order backward differentiation formula for the time derivative [29,30]. This requires solution of six elliptic (Poisson and Helmholtz) equations for the three velocity components, pressure, temperature, and electric potential.…”

Special issue on global flow instability and control

“…A unified perspective of instability in rotating Bödewadt, Ekman and von Kármán layers has been presented [7]. Instability of variable density flows in threedimensional containers has been analysed numerically [10,25] while a combined analytical and experimental effort discussed instability of compressible spanwise homogeneous cavity flow [31]. In the flow control theme, a linear feedback control approach was demonstrated to reduce the pressure drag of a D-shaped bluff body [6] and cluster-based control of a separating flow over a smoothly contoured ramp has been discussed [14].…”

Natural convection in a partially heated cylinder: A numerical study

“…Results show that the Nusselt number increases with the increasing heater size and the Rayleigh number (Cianfrini et al, 2013). Three-dimensional numerical studies reported multiple states and bifurcations on natural convection in a rectangular cavity with partially heated vertical walls (Gelfgat, 2017). The study of natural convection has been extended to nanofluids (Nascimento et al, 2019).…”