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

TL;DR

This paper numerically investigates the transition from steady to oscillatory natural convection in a cubic box with various thermal boundary conditions, identifying critical parameters and flow regimes through detailed simulations.

Contribution

It provides a comprehensive time-dependent analysis of oscillatory instability in three-dimensional natural convection with different boundary conditions, including bifurcation behavior and flow transitions.

Findings

Critical Grashof numbers for instability are determined.

Multiple flow regimes and transitions are identified.

Effects of boundary conditions on oscillatory behavior are analyzed.

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 time-averaged 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.