Determination of Outside Heating Distribution Using an Inverse Algorithm for an Industry Hydrothermal Autoclave With Three-Dimensional Flows

Hydrothermal growth is the industry method of preference to obtain high quality single crystals. Due to the high pressure and high temperature growth conditions, growth process is carried out in closed containers. During a growth run, the only flow and heat transfer that control crystal growers have is the outside heating. An inverse algorithm, used to obtain the heating distribution for an autoclave with a two-dimensional flow, is further developed and used to determine the heating distribution for an industry autoclave with three-dimensional flows. A cross-section area average temperature distribution is set as a target. With the three steps, including CFD simulation of the fluid flow, heat conduction in the metal wall, and heat conduction in the insulation layer, the heater heat flux distribution is determined. The distributions appear close to linear from the median height to the top/bottom with small magnitude deviation in the circumferential direction. Linearly distributed heaters, based on the determined heat flux distribution, are then used and heat transfer and fluid flow is numerically simulated with a conjugate model. The achieved temperature agrees well with the targeted one. The distribution and heating rates of linearly distributed heaters can be applied to industry autoclaves.