Numerical simulations of natural convection in a laterally-heated cylindrical reactor

Solvothermal crystal growth methods are of tremendous applied importance, but our level of fundamental understanding needs more investigations. Solvothermal crystal growth is driven thermodynamically and kinetically by a temperature gradient, which generates a higher concentration of dissolved species above a nutrient material relative to the seed crystals. Gallium-nitride (GaN)-based device technology has made remarkable progress during the past two decades, led by applications in light emitting diodes and laser diodes, with power switches now emerging as well. Numerical simulations are critical for the understanding of complex phenomena inside crystal growth reactors due to the inability to measure inside the harsh environments experimentally. The current study presents 2D numerical simulations of natural convection in a laterally-heated cylindrical reactor carried out using a commercial software ANSYS FLUENT. The definition of a characteristic length scale and hence the definition of the Rayleigh number (Ra) for such geometries that includes laterally heated walls has not been documented well enough in the literature. The main objective was to identify the critical Ra in such natural convection simulations in a laterally-heated cylindrical reactor. Towards this effort, a series of simulations, which solve the Navier-Stokes equations along with a Boussinesq approximation, were carried out at Ra ranging from 750-28000, calculated based on a length scale defined as the ratio of volume to area. Contours of time-averaged velocity and temperature and also their corresponding fluctuations and streamlines of instant velocity were analyzed to identify the transition from laminar to turbulent flow. The critical Ra was found to be 2800.