Numerical Simulation Of KDP Crystal Growth Kinetics

Computational fluid mechanics (CFD) which is based on the classical hydrodynamics and numerical calculation method is a new independent discipline. And CFD, which is to combine computer numerical calculation and image display, is used to quantitative description of the numerical solution in time and space of the flow field and to achieve the research on physical problems. The CFD has dual characteristics of theory and practice. And many theories and methods have been set up by CFD which provides an efficient technology for complex problems about flow and heat transmission in modern science.Crystal materials occupy an important position in the national economy and science and technology. The improvement and breakthrough of crystal growth technique will bring new progress and leap for electronic technology, computer technology and laser technology. Crystal growth technique has close relationship with fluid mechanics due to the great part of the crystal material is generated by the melt or solution. The mass transfer, heat transfer and complex flow phenomenon in the process of crystal growth directly affect the quality of the generated crystals.Now the large-size KDP crystals can be grown by traditional cooling method and rapid growth method. The KDP crystals grown by traditional method have optical uniformity, but the process of the growth of KDP crystal takes a longer growth cycle, high risk, high cost, so on the premise of the optical quality, how to increase the growth rates of the crystal become one of the urgent needs to address the problem; While the rapid growth method using the "point seed" technology under high temperature and high supersaturation achieve a full range of crystal growth, so that the crystal growth rate increases10-15times, but the optical quality of the crystals is significantly lower than the crystals grown by raditional method. How to choose a suitable growth speed to ensure the optical quality of the crystals becomes one of the primary issues to be resolved. The growth process of KDP crystal experiences long time and is complex, so in the growing process a slightly disturbances may cause inclusions or avalanche appear which essentially caused by the stability of the growth solution. Therefore, improving the stability of the solution and preventing spontaneous nucleation in the growth process is particularly critical.In the growth process of KDP crystal, many factors affect their growth, such as temperature uniformity, the solution flow rate and the saturation distribution, etc. It is difficult for conventional experimental methods to measure the temperature distribution, the flow of the solution velocity and the degree of supersaturation. The use of numerical simulation can solve this problem. Therefore, this work uses a combination of experimental and numerical simulation explores the effects of rotation speeds on the growth morphology, growth kinetics of KDP crystal and the stability of the KDP solution. The main contents of this work are as follows:1. KDP crystals were grown by the conventional method at different rotation speeds.We studied the rotation speeds how to affect the caping of KDP crystal. The effects of rotation speeds on the distributions of temperature and velocities were simulated by the fluent software. When the speeds were low (9and15r/min), the temperature is more evenly distributed, so the crystal appears only one capping, but the temperature is higher, so the caping is very slow. When the rotation speeds were high (55and77r/min), the temperature distribution was relatively homogeneous and only one capping appeared. Moreover, the temperature is low which made the capping fast. When the speeds were between the speeds above, temperature disturbance occured, there were two or more cappings. Now the temperature was between the two which resulted in the speeds of capping in between. As the acceleration of rotation speeds, the relative velocity was increased. So the growth of the boundary layer thickness decreases which brought the capping faster. Within the simulated speed range, high speed77r/min was the optimum speed for the capping. By simulating the distribution of temperature in the vinicity of KDP crystal under the conditions of different positions of seed crystal, we found that when the seed crystal was away from the bottom1,2and3cm, the temperature distribution was uniform that was benefit for one capping. Otherwise, when the seed position away from the upper part of the solution1,2and3cm, temperature disturbance occurred. Then there were two or more cappings. When the seed position from the bottom of the solution2cm, the temperature was slightly lower than1and3cm and the degree of supercooling at this time was slightly larger which’ brought slightly faster crystal growth, so the best location for the seed was2cm away from the bottom of the solution.2. KDP crystals were grown by the conventional method at different rotation speeds. We investigated the influence of the speeds on crystal growth. The effects of rotation speeds on the temperature and velocity fields were numerical simulated. By combining experimental and numerical simulation we could draw the conclusions as follows. When the speed were low (9and15r/min), the temperature distribution was uniform, but the temperature was higher which resulted in the crystal growth slow that did not match cooling procedures. So it brought the accumulation of supersaturation which leaded to some spontaneous crystallization. When the rotation speeds was increased to the speeds (22-40r/min), temperature was low and crystals grew faster, but the forced convection was still not enough to eliminate the temperature disturbance caused by natural convection. So there was still some spontaneous crystallization. When the speeds continued to increase (55and77r/min), the stirring eliminated the uneven temperature caused by natural convection. While increasing the speed of crystal growth was match the cooling process better, spontaneous crystallization emerged occasionally. With the rotation speeds increased, velocity of solution flow of the crystal surface was getting bigger and the more substance was transported to the crystal surface which made the growth rates grow faster. So high speeds (55and77r/min) compared to the lower speeds (9.0-40r/min) were more conducive to crystal growth. When changing the crystal size from3to5cm, the temperature distribution in the radial lines more uniform as the crystal size increased. That was to say the temperature change of the crystal size in the horizontal direction is almost no effect. But the temperature differences in the axial line of the crystal gradually increased from0.179K to0.204K when changes in crystal size from3to4.5cm. The tank temperature differences with the increases of crystal size from3to4.5cm gradually decreased. While the crystal size from4.5to5cm, temperature difference in the tank slightly increased. So with the increase of the size of KDP crystal, the rotation speed should appropriate to reduce. The conclusions achieved on the basis of the crystal rotation77r/min the same.3. KDP crystals were grown by the rapid growth method at different rotation speeds. Meanwhile, the dependence of velocity distributions and flow state on rotation speeds during KDP crystal growth process was numerical simulated. Combining experimental and calculation results showed that the rotation speeds were at9to100r/min range, the growth rates increased with the acceleration of rotation speeds and no spontaneous crystallization appeared. While the speed at100-120r/min, due to the state of the fluid flow from laminar flow to turbulent, it caused instability of the solution and then there were spontaneous crystallization appeared. When the speed at120-300r/min, solution flow rate was too fast, turbulence occured, the solution stability deteriorated and spontaneous crystallization and "avalanche" phenomenon appeared which could not continue to crystal growth. The maximum speed suitable for crystal growth is100r/min. As the crystal size increased, the Reynolds number increased and the probability of spontaneous crystallization increased. So the rotation speed should be appropriately reduced. Meanwhile two seed rack structure changes brought velocity field was simulated. The results showed that under the same stirring speed, the solution flow rate brought by two pillars of the seed rack was slightly bigger than that brought by the four pillars of the seed rack which resulted that two pillars of the seed rack could bring more substance to the surface of the crystal. In such circumstances, the seed rack consisted of two pillars was beneficial to the rapid growth of KDP crystal.4. KDP crystals were grown by the rapid growth method at different rotation speeds.We studied the effects of rotation speeds on the crystal growth rates, the formation of defects and the stability of the solution. We established a geometric model based on experimental equipment used for the growth KDP System. The transport of substance and the flow of solution during KDP crystal growth process were numerical simulated. Remaining the solution supersaturation4%the same, we explored the rotation speeds how to affect the crystal growth of the KDP crystal. When the rotation speeds were between9and100r/min, the degree of supersaturation began to increase with the increase of the rotational speeds and the crystal growth rate increased accordingly. At the same time the inclusions never appeared. When the rotation speeds were low (9and15r/min), the natural convection had’ an advantage in the flow of the solution which resulted in the nonuniformity of the supply of the substance, so occlusions occured during the crystal growth. With the rotation speed increaseed, the forced convection enhanced to eliminate the nonuniformity, the growth of the crystal can be transparent. When the rotation speeds reached to120and300r/min, with the increase of the degree of supersaturation, the critical radius that was required for the formation of crystal nucleus reduced. Moreover, the more proportion the quantity of crystal nucleus was in the total quantity of crystal nucleus. The crystal nucleus larger than the critical radius could form a new crystal nucleus which was stability in the solution. The new crystal nucleus can grow to form the stable inclusions. And as the solution supersaturation increased, the greater the driving force crystal growth, the more likely these crystal nucleus grew into spontaneous crystallization, which resulted in a decline in the growth solution stability, so spontaneous crystallization and "avalanche" were easy to appeared. When the crystal rotation speeds were between9and120r/min, the boundary layer thickness is reduced and the reduced rate is relatively slow. Meanwhile, the crystal growth rate was also a corresponding increase and the stability of the solution was better, so there was no spontaneous crystallization. When the crystal rotation speeds were between120and300r/min, the boundary layer thickness was reduced and the decrease was in linear format. Now the crystal growth rate did not match with the supply of subtances, which caused an overflow of supersaturation which leaded to the emergence of spontaneous crystallization and the pnenomenon of "avalanche". Keeping the rotation speed constant, we researched the effects of bulk degree of supersaturation (4-10%) on crystal growth. When the bulk Supersaturation degree was lower (4%), the solution was relatively stable, no spontaneous crystallization occurred. With the bulk degree of supersaturation increased, the crystal surface and the degree of supersaturation in the solution increased, but the solution stability is decreased. The changes of bulk saturation degree on the boundary layer thickness at the center of the crystal surface had little effects, that meaned the boundary layer thickness was closely related with the stirring speed.5. Experimental study on the effects of different rotation speed and seed crystal on the stability of KDP solution was developed. While the solution flows under different speeds were numerically simulated. Experimental results indicated with the increase of rotation speeds from9to300r/min temperature of spontaneous crystallization was gradually increased that meaned the metastable zone width was narrowed and solution stability was deteriorated. When the speeds were from200to300r/min, the "avalanche" phenomenon was easy to emerge. Further, with or without the seed crystal, the width of the metastable region had no alteration, indicating that the seed was introduced no significant effect on the crystallization temperature of the solution spontaneously. Namely the presence of inclusions was not because of the secondary nucleation by adding the seed crystal. The results by numerical simulation were as follows. When the stirring speeds (9and15r/min), the state of the solution flow was the laminar which had more stability for the solution. While the rotation speeds increased to (22-120r/min), the solution flow was transition from laminar to turbulent. As the speed increased, the solution stability was getting worse. When the speeds increased to200and300r/min, the solution flow was turbulent which lowered the solution stability that was sensitive to the emergence of spontaneous crystallization and the pnenomenon of "avalanche".