摘要
计算流体力学(Computational Fluid Dynamics, CFD)是建立在经典流体力学与数值计算方法基础之上的一门新型独立学科,通过计算机数值计算和图像显示的方法,在时间和空间定量描述流场的数值解,从而达到对物理问题研究的目的。它兼有理论性和实践性的双重特点,建立了许多理论和方法,为现代科学中许多复杂流动与传热问题提供了有效的计算技术。
晶体材料在国民经济和科学技术中占有重要的地位,晶体生长技术的改进和突破,意味着给电子技术、计算机技术和激光技术等领域带来新的进步和飞跃。由于大部分晶体材料是由熔体或溶液生成的,因此晶体生长技术与流体力学有着密切的关系。在晶体生长过程中伴随的传质、传热及复杂的流动现象直接影响所生成的晶体的质量。目前国内生长大尺寸KDP晶体的方法有传统降温法和快速生长法。传统法生长的晶体光学质量好,但是生长周期较长,风险大,成本高,所以在保证光学质量的基础上如何提高晶体的生长速度成为迫切需要解决的问题之一；快速生长法采用“点籽晶”技术在高温高过饱和度下实现全方位的晶体生长,使晶体的生长速度增大10-15倍,但是晶体的光学质量明显低于传统法生长的晶体,如何选择一个合适的生长速度保证晶体的顺利生长,提高晶体的光学质量成为首要解决的问题之一。
KDP晶体在生长过程中,影响其生长的因素很多,比如温度均匀性,晶体表面的溶液流动状态、过饱和度分布、边界层厚度以及溶液稳定性等,通过传统的实验方法很难测得晶体附近的温度分布、溶液的流动状态、过饱和度分布以及边界层厚度等。而利用数值模拟可以很好的解决这个问题。所以本论文采用实验与数值模拟相结合的方式研究了动力学因素对传统法和快速生长KDP晶体生长动力学和溶液的稳定性的研究。本论文的主要内容如下：
1.用传统降温法在不同转速下生长了KDP晶体,主要观察了转速的改变所带来的晶体成帽情况的改变,同时也利用Fluent软件对晶体生长过程中的温度场和速度场进行了数值模拟计算,研究转速对晶体成帽的影响。晶体转速较低为9和15转/min,温度分布比较均匀,所以晶体只出现一个帽区,但温度较高,成帽较慢；晶体转速较高为55和77转/min时,温度分布也比较均匀,相应的晶体也只有一个帽区,此时温度较低,成帽较快；晶体转速介于两者之间时,温度分布出现扰动,晶体出现两个或多个帽区,温度介于两者之间,成帽速度也介于两者之间。随着晶体转速的加快,晶体表面晶体与溶液的相对速度增大,生长边界层厚度减小,晶体成帽速度加快。所模拟的晶体转速范围内,较高转速77转/min是晶体帽区恢复的最优转速。通过数值计算不同籽晶位置时晶体表面的温度分布,发现籽晶位置距离溶液底部1、2和3cm时温度分布都比较均匀,有利于晶体成帽有一个帽区；而籽晶位置距离溶液上部1、2和3cm时,温度分布出现扰动,晶体成帽容易出现两个或多个帽区。当籽晶位置距溶液底部2cm时温度比1和3cm时稍低,此时过冷度稍大,晶体生长稍快,所以籽晶的最佳位置为距离溶液底部2cm处。
2.用传统降温法在不同转速下生长了KDP晶体,考察转速对晶体生长的影响。运用流体力学软件对晶体生长过程中的温度场和速度场进行了数值模拟,结合实验与数值计算结果可知,晶体转速较低时(9和15转/min)时,温度分布比较均匀,但温度较高,晶体生长稍慢,与降温程序不匹配造成过饱和度积累,晶体生长过程中出现较多杂晶；当晶体转速增大至(22-40转/min),温度较低,晶体生长较快,但是强迫对流还不能足以消除自然对流带来的温度扰动,仍有杂晶出现；当晶体转速继续增大时(55和77转/min),搅拌消除了自然对流带来的温度不均匀性,同时转速的增大带来的晶体生长加快与降温程序匹配较好,杂晶偶尔出现。随着晶体转速的增大,晶体表面的溶液流速愈来愈大,往晶体表面输运的物质越多,晶体生长越来越快。所以较高转速(55和77r/min)较于较低转速(9.0-40r/min)更有利于晶体生长。保持晶体转速77转/min不变时：晶体尺寸由3变化到5cm时,径向线上的温度分布比较均匀,即晶体尺寸的改变对水平方向上的温度分布几乎没有影响；但是轴向线上的温差由晶体3cm时的0.179K逐步增大到5cm时的0.204K。改变晶体尺寸由3到4.5cm时,槽内温差随晶体尺寸的增大逐步减小；而晶体尺寸由4.5到5cm时槽内温差有小幅增大,即随着晶体尺寸的增加,晶体转速应适当调低。
3.用“点籽晶”快速生长技术生长了不同转速下的KDP晶体,同时对晶体生长过程中的速度场分布和流动状态的改变进行了数值计算,结合实验现象与计算结果表明,晶体转速在9到100转/min范围,晶体生长速度随转速提高而加快,无杂晶出现；转速在100到120转/min时,溶液的流动状态由层流到湍流的过渡,造成溶液的不稳定性,进而有杂晶出现；转速在200到300转/min时,溶液流速太快,由更多的层流转变成湍流,溶液稳定性更差,溶液中容易出现杂晶进而发生“雪崩”现象,无法继续晶体的生长。所以初始阶段适于晶体生长的最大转速是100转/min。保持晶体转速100转/min不变,考察晶体尺寸的改变对晶体生长的影响。随着晶体尺寸的增加,雷诺数增大,过渡段湍流成分较高,溶液稳定性较差,杂晶出现几率增大,晶体转速应适当调低。同时对两种籽晶架结构所带来的速度场的变化进行了数值模拟计算,相同搅拌速度下,两根柱子的籽晶架带来的溶液流动速度相比四根柱子时稍大,往晶体表面输运的物质较多,这种情况下边界层厚度较薄,越有利于晶体的快速生长。
4.用“点籽晶”快速生长技术在不同转速下生长了一系列KDP晶体,研究了动力学参数对晶体生长速度和晶体生长的影响。同时采取数值模拟计算的手段,根据实验室所用实验装置建立几何模型,对KDP晶体生长过程中的对过饱和度和边界层厚度进行了数值计算。晶体转速在9-100转/min范围时,晶体表面的过饱和度随着晶体转速的增大而增大,生长速度也随着相应的增大,生长过程中无杂晶出现；晶体转速较低时(9和15转/min),自然对流占优势,由于重力的作用,晶体底部溶质浓度高,上部溶质浓度低,晶体晶面出现溶质供应不均匀,晶体生长过程中容易出现包藏。随着晶体转速的增大,强迫对流增强,能够消除自然对流带来的晶面溶质供应不均匀,晶体能够透明生长；晶体转速继续增大至(120-300转/min)时,过饱和度的梯度增大,生长溶液稳定性的下降,溶液中易出现杂晶或者“雪崩”。晶体转速由9变化到300转/min时,随着晶体转速的增大生长边界层的厚度δ减小。体过饱和度的改变对晶体表面中心处的边界层厚度影响不大,边界层厚度只与搅拌速度密切相关的。5.实验研究了不同转速和有无籽晶对KDP快速生长溶液的稳定性的影响,实验结果表明,搅拌速度由9至300转/min时,自发结晶的温度逐渐升高,表明亚稳区的宽度变窄、溶液稳定性变差；转速达到200-300转/min时,溶液稳定性极差,溶液极易出现杂晶进而发生“雪崩”。此外,溶液中加入籽晶后,亚稳区的宽度与未加入籽晶时基本一致,这表明引入籽晶对溶液中自发结晶的温度没有明显的影响,即溶液中出现的杂晶并不是由于加入籽晶可能导致的二次成核引起的而是由于引入籽晶操作程序影响了溶液稳定性所致。同时对不同转速下的溶液流动情况进行了数值模拟计算。发现：(1)搅拌速度较低时(9和15转/min)溶液流动为层流,溶液稳定性较好；(2)转速继续增大至(22-106转/mmin),溶液流动为层流到湍流的过度,随着转速的增大,溶液稳定性越来越差；转速增至(120和300转/min)时,溶液流动为完全湍流,溶液稳定性显著降低,溶液中极易出现杂晶进而“雪崩”。溶液稳定性变差的机理可能与转速升高引起的湍流动能耗散率和涡量的大小有关,即溶液流体的旋转动能更多地转化为热运动能,为溶液跨过成核势垒提供了更多的可能；(3)要保持溶液稳定性,晶体生长过程应当在层流或湍流成分较低的过渡段进行。
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".
引文
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