G.-X. Wang

Flow of Solution in Hydrothermal Autoclaves with Various Aspect Ratios

A good understanding of the natural convective flow in hydrothermal autoclaves is essential for the control of the growth rate and the quality of the grown crystals. This paper presents a numerical simulation of turbulent natural convection in industry-size autoclaves with various aspect ratios. A simplified 2D axisymmetric model was developed. Numerical results were obtained for autoclaves with aspect ratios ranging from 2 to 20. Results show typical two counter-flow cells in both the bottom and upper chambers. Heat conduction through the baffle is negligible. Detailed analyses and discussions are presented to characterize the bulk flows in the upper chamber under various aspect ratios, and their effect on crystal growth. As the aspect ratio increases the gradients in flow velocity and temperature decrease making uniform growth possible in larger autoclaves.

Flow and Heat Transfer Study in an Autoclave for Hydrothermal Crystal Growth With a Three-Dimensional Conjugate Heat Transfer Model

Numerical modeling becomes an important technique to study hydrothermal crystal growth since experimental measurements in hydrothermal autoclaves are extremely difficult due to the high pressure and high temperature growth conditions. In all existing models for hydrothermal growth, isothermal boundary conditions are assumed, although electric heaters are employed around the outside surface of the thick autoclave wall in practice. In this paper, a conjugate heat transfer model based on an industry size autoclave is developed to investigate the validity of such an assumption. The model includes not only turbulent fluid flow and heat transfer of the solution but also the heat conduction in the thick wall. The outside surfaces of the wall are under constant heat flux conditions, simulating electric resistance heating used in practice. Non-uniformity of the heat flux in the circumferential direction is also introduced in the model. The results indicate that the temperature at the solution/wall interface is far away from uniform. The isothermal wall boundary condition in previous efforts is questionable. Predictions of the isothermal wall model are analyzed. Parametric studies with the conjugate model show that total heat supply rate does not affect vertical uniformity dramatically. Heat loss can be lowered without affecting the flow and temperature fields if heaters are put half diameter or further away from the middle height (baffle) plane.Copyright

Determination of Surface Heating Condition for a Desired Thermal Growth Environment in an Industry-Size Hydrothermal Autoclave

Hydrothermal growth is the most common technique to grow piezoelectric single crystals such as quartz. Due to a high-temperature and high-pressure growth condition, hydrothermal autoclaves are designed to operate as a closed system. During operation, the only control mechanism that crystal growers have is adjusting the power input of the heaters, based on the temperature readings obtained by the thermocouples along the centerline inside the autoclaves. The power adjusting process, however, is purely experience dependent, and, normally, uniform heating conditions from electric heaters are employed along the autoclave wall. This study develops an inverse algorithm, with which the required heat flux distributions from the heaters can be obtained for a desired growth environment inside an autoclave. The algorithm involves solving three sub-models step by step. The first step is to solve a two-dimensional axisymmetric model of solution in the autoclave to obtain the temperature and heat flux on the solution/wall interface. Using these temperature and heat flux conditions as thermal boundary conditions, the second step solves an inverse heat conduction problem in the metal wall. The solution provides the heat flux and temperature on the outer surface of the metal wall. The final step is to solve a heat conduction problem in the insulation layer to obtain the heat flux on the inner surface of the insulation layer. The heat flux distributions for heaters are then determined by the heat flux on the outer surface of the metal wall and heat flux on the inner surface of the insulation layer. The paper describes the details of each model. As an example, the method is used to find the required heat flux distributions of heaters for the growth environment predicted by a 2-D isothermal wall model. The result is then used to develop a two-patch heater for industry autoclaves.© 2003 ASME

Transport Through Single-Hole Baffles in Industry Hydrothermal Autoclaves With Three-Dimensional Flows

Hydrothermal growth is the industrial preference to obtain high quality piezoelectric crystals. The industry growth process is carried out in autoclaves, cylindrical containers filled with an aqueous solution. The solution flows in industry autoclaves during growth are usually three-dimensional. A baffle is normally used to partition an autoclave into two chambers and reduce flow strength. In this paper transport through single-hole baffles of various are a openings in the three-dimensional flow is investigated systematically. It was found that a single-hole baffle is effective in controlling the fluid exchange and heat transfer between the two chambers. A smaller baffle opening leads to a more uniform thermal environment for growth. Flow structure and heat transfer data show that there is a pair of steady flow streams between the two chambers. However the heat exchange carried by this pair of streams, as well as heat exchange through molecular diffusion, is negligibly small. Transport through baffle opening is dominated by turbulence diffusion. Heat transfer analysis shows that heat flow rate depends on both the baffle opening area and the area of the chamber walls.Copyright

Steady Laminar Flows in Lower Half Heated Upper Half Cooled Rectangular and Cylindrical Enclosures: Comparison of the Transport Mechanism

Flows in enclosures have been studied for various applications. Transport in lower half heated upper half cooled enclosures becomes a focus of research recently due to its application on hydrothermal crystal growth. Natural convection flows in hydrothermal autoclaves are driven by the temperature differential on the enclosure walls; lower half hot and upper half cooled. Due to the difficulties associated with visualization of flow in cylindrical enclosures, flows were experimentally visualized in a rectangular model autoclave. In this study, flows and transport mechanisms in rectangular and cylindrical enclosures are studied numerically in the steady laminar flow regime. Flow structures and transport mechanisms are analyzed and compared. Parametric studies on aspect ratios are carried out for both enclosures. Results show that flows in rectangular and cylindrical enclosures have the same transports mechanism. Fluid in the wall layers in one half form streams that feed into the center of the other half. However, for two kinds of enclosures quantitative differences exist on the stream formation.Copyright

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.Copyright

Flow and Heat Transfer in an Upper Half Cooled Lower Half Heated Enclosure With Horizontal Temperature Deviations

The nature and patterns of solution flow in hydrothermal autoclaves are critical to the quality, growth uniformity, and growth rates of synthetic single crystals. Small horizontal temperature deviations, which exist in industrial practice, were found to be critical in establishing flow patterns. However, the mechanism that determines how temperature deviations affect flow pattern is not well understood. In this study, an experimental system is set-up to study the flow in a model reactor (an enclosure). Temperature in the enclosure is visualized using liquid crystals. With the experimental results, a numerical model is validated and then used to simulate flows in enclosures that are subjected to similar thermal condition as industrial autoclaves. Flow patterns are obtained with various temperature deviations, for various aspect ratios and various Rayleigh (Ra) number between 4.05E8 to 3.24E9. Flows studied are unsteady in nature. Without temperature deviations, the overall flow pattern is anti-symmetric. With a temperature deviation, the wall layers are un-balanced. The impingement of streams on the wall layers does not affect the wall layer flow at low Ra numbers. At high Ra number, wall layers are broken by the impinging streams. The dominant heat transfer mechanism in the enclosure changes significantly as the aspect ratio of the enclosure changes. In enclosures of high aspect ratios that heat transfer resistance is mainly at the fluid exchange between the two halves, temperature deviations significantly affect heat transfer by stabilizing the direction of the streams.Copyright

Interface Shape and Melt Flow Near the Solid-Liquid Interface During Horizontal Unidirectional Solidification

Generally, unindirectional solidification experiments of transparent alloys are conducted using thin film samples sandwiched between two glass slides with a small channel height[1]. In such systems, natural convection and melt flow can be assumed negligible and the solification process is diffusive in nature [2,3]; these physical realities allow fundamental simplifications in theoretical/numerical modeling, without losing physical significance. However, natural convection and melt flow do exist in all actual solidification processes and have a significant effect on interface morphology and microstructure formation and development. Recognizing the latter, a great deal of effort went in recent years towards the investigation of the effect of melt flow on interface dynamics and morphology [3–5]. The objective of this paper is to study the natural convection and melt flow near the solid-liquid interface during horizontal unidirectional solidification. In particular, the authors are interested in the melt flow and solid-liquid interface under various channel heights (H) and temperature differences across the hot and cold ends (ΔT) of the samples. A horizontal unindirectional solidification experimental system was constructed. The samples used here are rectangular ampoules made of borosilicate glass that is 3.2 mm thick (on bottom and top sides) and 2.3 mm thick (on the vertical sides). The channel formed in the sample is 75 mm long and 50 mm wide. Three ampoules with channel heights of 1, 3.2 and 5 mm, respectively, are used in these experiments. The ampoules are filled with succinonitrile (99% pure) seeded with polyamide tracer particles (5 μm in diameter, density ρ=1030 kg/m3 ); the latter are used to resolve and visualize the fluid velocity in the melt. Surface temperatures of the sample on the hot end and cold end are measured with J-type thermocouples. The unidirectional solifification setup is mounted on a microscope stage so that the interface can be observed from the top with the regular microscope. A long distance microscope (LDM) affixed either to a photo- or video- camera is used to observe the vertical shape of the interface, as well as to qualitatively and quantitatively assess the flow. During experiments, the sample is allowed to reach both thermally and flow-wise a steady state situation. The heating and cooling systems are adjusted to make the solid-liquid interface stay at the center of the gap between the heating and cooling chambers for case of observation. The density of polymide particle being close to that of succinonitrile melt allows an almost neutrally buoyant behavior of the tracing particles and thus minimizes the error in flow velocity calculations as well as enhances confidence in the observed qualitative flow patterns. With the help of proprietary computer software, the flow velocity is obtained by evaluating the difference in successive two images of the same particle at time intervals consistent with the sampling speed of video-camera (0.033 sec).Copyright

A Numerical Study of Heat Transfer and Fluid Flow in a Hydrothermal Autoclave With a Single- or Multi-Hole Baffle

Hydrothermal solution growth is an important technique to grow high quality piezoelectric single crystals. In industry hydrothermal crystal growth, an autoclave is divided into two chambers by a baffle located in the middle height. Industrial practice found that better quality crystals could be grown under certain baffle hole openings or using a multi-hole baffle. This paper presents a numerical study of the effects of the baffle opening, as well as the arrangement of holes on the baffle, on the fluid flow and temperature fields in an industry-size autoclave. A wide range of baffle hole openings from 2% to 25%, together with five hole-arrangements, is investigated. Computational results indicate that changing the baffle hole opening and number of holes on the baffle are effective ways to control the temperature uniformity in the upper growing chamber. With a single-hole baffle, a smaller hole-opening leads to a weaker flow field and more uniform temperature in the growing chamber. With the same opening area, a multi-hole baffle will perform better than a single-hole baffle. The number of holes in a multi-hole baffle shows a strong effect on thermal condition in the upper chamber with 8-hole baffles working better than both baffles with 4 and 16 holes. The hole-arrangement, however, does have significant effect on thermal condition in the growing chamber.Copyright