Effects of Baffle Design on Fluid Flow and Heat Transfer in Ammonothermal Growth System of Nitrides

Efforts have been made in growing bulk single crystals of GaN front supercritical fluids using the ammonothermal method, which utilizes ammonia as fluid rather than water as in the hydrothermal process. Different mineralizers such as amide or azide and temperatures in the range of 200-600degreesC have been used to increase the solubility. The pressure is from 1 to 4 kbar. Modeling of the ammonothermal growth process has been used to identify factors which may affect the temperature distribution, fluid flow and nutrient transport. The GaN charge is considered as a porous media bed and the flow in the charge is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. The effects of baffle design and opening on flow pattern and temperature distribution in an autoclave are analyzed. Two cases are considered with baffle openings of 15% and 20% in cross-sectional area, respectively.

Progress In Modeling Of Fluid Flows In Crystal Growth Processes

Modeling of fluid flows in crystal growth processes has become an important research area in theoretical and applied mechanics. Most crystal growth processes involve fluid flows, such as flows in the melt, solution or vapor. Theoretical modeling has played an important role in developing technologies used for growing semiconductor crystals for high performance electronic and optoelectronic devices. The application of devices requires large diameter crystals with a high degree of crystallographic perfection, low defect density and uniform dopant distribution. In this article, the flow models developed in modeling of the crystal growth processes such as Czochralski, ammonothermal and physical vapor transport methods are reviewed. In the Czochralski growth modeling, the flow models for thermocapillary flow, turbulent flow and MHD flow have been developed. In the ammonothermal growth modeling, the buoyancy and porous media flow models have been developed based on a single-domain and continuum approach for the composite fluid-porous layer systems. In the physical vapor transport growth modeling, the Stefan flow model has been proposed based on the flow-kinetics theory for the vapor growth. In addition, perspectives for future studies on crystal growth modeling are proposed. (c) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

Designing Of Partial Similarity Models And Evaluation Method In Polymer Flooding Experiment

Based on the scaling criteria of polymer flooding reservoir obtained in our previous work in which the gravity and capillary forces, compressibility, non-Newtonian behavior, absorption, dispersion, and diffusion are considered, eight partial similarity models are designed. A new numerical approach of sensitivity analysis is suggested to quantify the dominance degree of relaxed dimensionless parameters for partial similarity model. The sensitivity factor quantifying the dominance degree of relaxed dimensionless parameter is defined. By solving the dimensionless governing equations including all dimensionless parameters, the sensitivity factor of each relaxed dimensionless parameter is calculated for each partial similarity model; thus, the dominance degree of the relaxed one is quantitatively determined. Based on the sensitivity analysis, the effect coefficient of partial similarity model is defined as the summation of product of sensitivity factor of relaxed dimensionless parameter and its relative relaxation quantity. The effect coefficient is used as a criterion to evaluate each partial similarity model. Then the partial similarity model with the smallest effect coefficient can be singled out to approximate to the prototype. Results show that the precision of partial similarity model is not only determined by the number of satisfied dimensionless parameters but also the relative relaxation quantity of the relaxed ones.

Stability Analysis Of The Moving Interface In Piston- And Non-Piston-Like Displacements

From the macroscopic point of view, expressions involving reservoir and operational parameters are established for investigating the stability of moving interface in piston- and non-piston-like displacements. In the case of axi-symmetrical piston-like displacement, the stability is related to the moving interface position and water to oil mobility ratio. The capillary effect on the stability of moving interface depends on whether or not the moving interface is already stable and correlates with the wettability of the reservoir rock. In the case of non-piston-like displacement, the stability of the front is governed by both the relative permeability and the mobility ratio.

Sensitivity Analysis Of The Dimensionless Parameters In Scaling A Polymer Flooding Reservoir

A set of scaling criteria of a polymer flooding reservoir is derived from the governing equations, which involve gravity and capillary force, compressibility of water, oil, and rock, non-Newtonian behavior of the polymer solution, absorption, dispersion, and diffusion, etc. A numerical approach to quantify the dominance degree of each dimensionless parameter is proposed. With this approach, the sensitivity factor of each dimensionless parameter is evaluated. The results show that in polymer flooding, the order of the sensitivity factor ranges from 10(-5) to 10(0) and the dominant dimensionless parameters are generally the ratio of the oil permeability under the condition of the irreducible water saturation to water permeability under the condition of residual oil saturation, density, and viscosity ratios between water and oil, the reduced initial oleic phase saturation and the shear rate exponent of the polymer solution. It is also revealed that the dominant dimensionless parameters may be different from case to case. The effect of some physical variables, such as oil viscosity, injection rate, and permeability, on the dominance degree of the dimensionless parameters is analyzed and the dominant ones are determined for different cases.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.

渗流力学研究的现状和发展趋势

简述了水利、环境、能源工程和生物学中的渗流力学问题,扼要概括了渗流力学理论研究的现状,并指出渗流力学在多孔介质描述、裂缝型介质渗流、多相多组分渗流、物理化学渗流、非线性渗流、非饱和渗流、微观渗流、渗流模拟等理论及相关方法和测试技术等方面的发展趋势.

纵向非均匀多孔介质Marangoni对流不稳定性

理论研究了纵向非均匀多孔介质中流体表面张力驱动的对流不稳定性、充满液体的多孔介质层从下方加热，上方自由表面冷却，形成可引起多孔介质液层Marangoni—Benard对流流动的纵向温度梯度．采用线性化的Brinkman．Forchheimier方程作为控制方程组，对孔隙率分别为线性函数、正弦三角函数分布的非均匀多孔介质液层的Marangoni—Benard问题进行了线性稳定性分析、通过采用Chebyshev-Tau谱方法求解广义特征值问题，得到了系统临界Marangoni数随无量纲波数变化的中性稳定性曲线，分析和比较了孔隙率的变化对液层对流稳定性和流场结构的影响，获得了纵向非均匀多孔介质液层不稳定性现象的新特征．

Modeling of Ammonothermal Growth of Gallium Nitride Single Crystals

Ammonothermal growth of GaN crystals with a retrograde solubility has been modeled and simulated here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow in the porous charge is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. For the case of retrograde solubility, the charge is put above the baffle. The temperature difference between the dissolving zone and growth zone is found smaller than that applied on the sidewall of autoclave. The baffle opening has a strong effect on the nutrient transport and supersaturation of GaN species in the growth zone.

Transport Phenomena in Ammonothermal Growth of Gallium Nitride

GaN can be used to fabricate blue/green/UV LEDs and high temperature, high power electronic devices. Ideal substrates are needed for high quality III-nitride epitaxy, which is an essential step for the manufacture of LEDs. GaN substrates are ideal to be lattice matched and isomorphic to nitride-based films. Bulk single crystals of GaN can be grown from supercritical fluids using the ammonothermal method, which utilizes ammonia as fluid rather than water as in the hydrothermal process. In this process, a mineralizer such as amide, imide or azide is used to attack a bulk nitride feedstock at temperatures from 200 - 500癈 and pressures from 1 - 4 kbar. Baffle design is essential for successful growth of GaN crystals. Baffle is used to separate the dissolving zone from the growth zone, and to maintain a temperature difference between the two zones. For solubility curve with a positive coefficient with respect to temperature, the growth zone is maintained at a lower temperature than that in the dissolving zone, thus the nutrient becomes supersaturated in the growth zone. The baffle opening is used to control the mixing of nutrients in the two zones, thus the transfer of nutrient from the lower part to the upper part. Ammonothermal systems have been modeled here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. We investigated the effects of baffle opening and position on the transport phenomena of nutrient from dissolving zone to the growth zone. Simulation data have been compared qualitatively with experimental data.

肝脏中生物流体流动的多重介质渗流模型和数值模拟

本文采用生物渗流理论，建立了肝脏内不同生物流体流动的多重介质渗流模型，采用有限元法求解这种特殊的渗流问题，根据数值计算结果揭示了肝内血液、组织液以及胆汁等的流动规律，并探讨了肝脏血流动力学的一些问题。论文将肝脏内部与生物代谢功能有关的肝血窦和窦周间隙当作两重并存的多孔介质，血液在肝血窦中，以及组织液在窦周间隙中的流动均当作渗流处理，通过Starling公式考虑了两重介质之间的流量交换，从而建立了肝血窦-窦周间隙的双重介质模型。针对肝脏胆汁分泌功能，将肝脏内密布的毛血肝管网当作多孔介质，以受静压及渗透压驱动的流体跨壁流动表示肝汁从肝细胞向毛细肝管的分泌，肝汁在毛细胆管网中的流动作为渗流处理，从而建立了肝汁分泌与输运的双重介质模型。采用有限元法求解了生物流体的双重介质渗流问题，针对非牛顿渗流和两重介质的相互作用，本文发展了一种嵌套迭代方法，即采用直接迭代求解血液在肝血窦中的非线性渗流，采用交替迭代解决双重介质渗流中由跨壁流支引起的相互流体交换，直接迭代嵌套于交替迭代中。这种算法比较有效的解决了包含非牛顿渗流的双重介质渗流问题。根据生物多孔介质中微细管系统的构筑方式以及不同微细管系统之间的联系方式，论文提出将生物多孔介质划分为分级多孔介质和多重多孔介质两种主要类型。基于多相混合物的平均化的理论，论文推导了双重多孔介质中的动量守恒方程、质量守恒方程以及相应的渗流方程，建立了双重多孔介质渗流的平均化模型。基于分级多孔介质渗流的理论，论文将脏器中的血管树按管径分为不同级别的多孔介质，各级血管中和血液流动均作为渗流处理，从而提出了计算脏器整体血流的一种渗流方法。采用这种方法，在论文提出的肝血窦 - 窦周间隙双重介质渗流流模型的基础之上，初步研究了肝脏门静脉系统的血液动力学规律。采用本文提出的肝血窦 - 窦周间隙双重介质模型和胆汁分泌 - 流动的双重介质模型，得到了血液、组织液和胆汁在肝小叶中的压力分布和速度分布，并分析了肝血窦壁的跨壁流动模式，胆汁流量的影响因素，以及窦周间隙中组织液流量与肝血窦中血液流动及肝血窦壁渗透系数等因素的关系，揭示了肝脏内血液、组织液及胆汁等生物流体流动的一般规律。

Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

考虑介质微观非均质特征的乳状液渗流模型

油水乳化渗流是三元复合驱和热力采油过程中常见的现象,地层介质的微观孔隙结构特征对乳状液流动有着重要影响.现有描述乳状液渗流的理论模型都属于确定性方法,只能反映出介质孔隙结构的体积平均效果.当介质内部微观非均质性相比其尺寸不能被忽略时,采用确定性方法描述会与实验结果存在偏差.基于连续时间随机游走理论建立了描述乳状液渗流的随机理论模型.该模型引入反映液滴微观运动特征的跃迁时间和跃迁位移两个概率分布函数来反映多孔介质微观非均质特征.研究结果表明该模型能很好地刻画实验曲线中出现的与介质尺度相关的拖尾现象,可作为更一般的过滤模型.

The Experimental and Numerical Studies on Gas Production from Hydrate Reservoir by Depressurization

A set of experimental system to study hydrate dissociation in porous media is built and some experiments on hydrate dissociation by depressurization are carried out. A mathematical model is developed to simulate the hydrate dissociation by depressurization in hydrate-bearing porous media. The model can be used to analyze the effects of the flow of multiphase fluids, the kinetic process and endothermic process of hydrate dissociation, ice-water phase equilibrium, the variation of permeability, convection and conduction on the hydrate dissociation, and gas and water productions. The numerical results agree well with the experimental results, which validate our mathematical model. For a 3-D hydrate reservoir of Class 3, the evolutions of pressure, temperature, and saturations are elucidated and the effects of some main parameters on gas and water rates are analyzed. Numerical results show that gas can be produced effectively from hydrate reservoir in the first stage of depressurization. Then, methods such as thermal stimulation or inhibitor injection should be considered due to the energy deficiency of formation energy. The numerical results for 3-D hydrate reservoir of Class 1 show that the overlying gas hydrate zone can apparently enhance gas rate and prolong life span of gas reservoir.