Numerical Simulation of the Flow Field and Concentration Distribution in the Bulk Growth of Silicon Carbide Crystals

The physical vapor transport (PVT) method is being widely used to grow large-size single SiC crystals. The growth process is associated with heat and mass transport in the growth chamber, chemical reactions among multiple species as well as phase change at the crystal/gas interface. The current paper aims at studying and verifying the transport mechanism and growth kinetics model by demonstrating the flow field and species concentration distribution in the growth system. We have developed a coupled model, which takes into account the mass transport and growth kinetics. Numerical simulation is carried out by employing an in-house developed software based on finite volume method. The results calculated are in good agreement with the experimental observation.

槽道湍流的直接数值模拟

通过直接数值模拟(DNS)研究槽道湍流的性质和机理。包含五个部分：1）湍流直接数值模拟的差分方法研究。2）求解不可压N－S方程的高效算法和不可压槽道湍流的直接数值模拟。3）可压缩槽道湍流的直接数值模拟和压缩性机理分析。4）“二维湍流”的机理分析。5）槽道湍流的标度律分析。1．针对壁湍流计算网格变化剧烈的特点，构造了基于非等距网格的的迎风紧致格式。该方法直接针对计算网格构造格式中的系数，克服了传统方法采用 Jacobian 变换因网格变化剧烈而带来的误差。针对湍流场的多尺度特性分析了差分格式的精度、网格尺度与数值模拟能分辨的最小尺度的关系，给出不同差分格式对计算网格步长的限制。同时分析了计算中混淆误差的来源和控制方法，指出了迎风型紧致格式能很好地控制混淆误差。2．将上述格式与三阶精度的Adams半隐格式相结合，构造了不可压槽道湍流直接数值模拟的高效算法。该算法利用基于交错网格的离散形式的压力Poisson方程求解压力项，避免了压力边界条件处理的困难。利用FFT对方程中的隐式部分进行解耦，解耦后的方程采用追赶法（LU分解法）求解，大大减少了计算量。为了检验该方法，进行了三维不可压槽道湍流的直接数值模拟，得到了Re＝2800的充分发展不可压槽道湍流，并对该湍流场进行了统计分析。包括脉动速度偏斜因子在内的各阶统计量与实验结果及Kim等人的计算结果吻合十分理想，说明本方法是行之有效的。3．进行了三维充分发展的可压缩槽道湍流的直接数值模拟。得到了 Re=3300，Ma=0.8的充分发展可压槽道湍流的数据库。流场的统计特征（如等效平均速度分布，“半局部”尺度无量纲化的脉动速度均方根）和他人的数值计算结果吻合。得到了可压槽道湍流的各阶统计量，其中脉动速度的偏斜因子和平坦因子等高阶统计量尚未见其他文献报道。同时还分析了压缩性效应对壁湍流影响的机理，指出近壁处的压力－膨胀项将部分湍流脉动的动能转换成内能，使得可压湍流近壁速度条带结构更加平整。4．模拟了二维不可压槽道流动的饱和态（所谓“二维湍流”），分析了“二维槽道湍流”的非线性行为特征。分析了流场中的上抛－下扫和间歇现象，研究了“二维湍流”与三维湍流的区别。指出“二维湍流”反映了三维湍流的部分特征，同时指出了展向扰动对于湍流核心区发展的重要性。5．首次对可压缩槽道湍流及“二维槽道湍流”标度律进行了分析，得出了以下结论：a）槽道湍流中，在槽道中心线附近较宽的区域，存在标度律。b）该区域流场存在扩展自相似性（ESS）。c）在Mach数不是很高时，压缩性对标度指数影响不大。本文结果同SL标度律的理论值吻合较好，有效支持了该理论。对“二维槽道湍流”也有相似的结论，但与三维湍流不同的是，“二维槽道湍流”存在标度律的区域更宽，近壁处的标度指数比中心处有所升高。

Numerical simulation of a single fluid particle rising in non-Newtonian fluids

In this work, a level set method is developed for simulating the motion of a fluid particle rising in non-Newtonian fluids described by generalized Newtonian as well as viscoelastic model fluids. As the shear-thinning model we use a Carreau-Yasuda model, and the viscoelastic effect can be modeled with Oldroyd-B constitutive equations. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The level set method is implemented to compute the motion of a bubble in a Newtonian fluid as one of typical examples for validation, and the computational results are in good agreement with the reported experimental data．The level set method is also applied for simulating a Newtonian drop rising in Carreau-Yasuda and Oldroyd-B fluids．Numerical results including noticeably negative wake behind the drop and viscosity field are obtained, and compare satisfactorily with the known literature data.

An Improved CE/SE Scheme for Numerical Simulation of Gaseous and Two-Phase Detonations

A new structure of solution elements and conservation elements based on rectangular mesh was pro- posed and an improved space-time conservation element and solution element (CE/SE) scheme with sec- ond-order accuracy was constructed. Furthermore, the application of improved CE/SE scheme was extended to detonation simulation. Three models were used for chemical reaction in gaseous detonation. And a two-fluid model was used for two-phase (gas–droplet) detonation. Shock reflections were simu- lated by the improved CE/SE scheme and the numerical results were compared with those obtained by other different numerical schemes. Gaseous and gas–droplet planar detonations were simulated and the numerical results were carefully compared with the experimental data and theoretical results based on C–J theory. Mach reflection of a cellular detonation was also simulated, and the numerical cellular pat- terns were compared with experimental ones. Comparisons show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for above-mentioned problems.

Numerical simulation of condensation of bubbles under microgravity conditions by moving mesh method in the double-staggered grid

A numerical 2D method for simulation of two-phase flows including phase change under microgravity conditions is presented in this paper, with a level set method being coupled with the moving mesh method in the double-staggered grid systems. When the grid lines bend very much in a curvilinear grid, great errors may be generated by using the collocated grid or the staggered grid. So the double-staggered grid was adopted in this paper. The level set method is used to track the liquid-vapor interface. The numerical analysis is fulfilled by solving the Navier-Stokes equations using the SIMPLER method, and the surface tension force is modeled by a continuum surface force approximation. A comparison of the numerical results obtained with different numerical strategies shows that the double-staggered grid moving-mesh method presented in this paper is more accurate than that used previously in the collocated grid system. Based on the method presented in this paper, the condensation of a single bubble in the cold water under different level of gravity is simulated. The results show that the condensation process under the normal gravity condition is different from the condensation process under microgravity conditions. The whole condensation time is much longer under the normal gravity than under the microgravity conditions.

Numerical Simulation of Liquefaction Deformation of Sand Layer around Bucket Foundations under Dynamic Loadings

Bucket Foundations under Dynamic Loadings The liquefaction deformation of sand layer around a bucket foundation is simulated under equivalent dynamic ice-induced loadings. A simplified numerical model is presented by taking the bucket-soil interaction into consideration. The development of vertical and horizontal liquefaction deformations are computed under equivalent dynamic ice-induced loadings. Firstly, the numerical model and results are proved to be reliable by comparing them with the centrifuge testing results. Secondly, the factors and the development characteristics of liquefaction deformation are analyzed. Finally, the following numerical simulation results are obtained: the liquefaction deformation of sand layer increases with the increase of loading amplitude and with the decrease of loading frequency and sand skeleton’s strength. The maximum vertical deformation is located on the sand layer surface and 1/4 times of the bucket’s height apart from the bucket’s side wall (loading boundary). The maximum horizontal deformation occurs at the loading boundary. When the dynamic loadings is applied for more than 5 hours, the vertical deformation on the sand layer surface reaches 3 times that at the bottom, and the horizontal deformation at 2.0 times of the bucket height apart from the loading boundary is 3.3% of which on the loading boundary.

Characterization and modeling of premixed turbulent n-heptane flames in the thin reaction zone regime

n-heptane/air premixed turbulent flames in the high-Karlovitz portion of the thin reaction zone regime are characterized and modeled in this thesis using Direct Numerical Simulations (DNS) with detailed chemistry. In order to perform these simulations, a time-integration scheme that can efficiently handle the stiffness of the equations solved is developed first. A first simulation with unity Lewis number is considered in order to assess the effect of turbulence on the flame in the absence of differential diffusion. A second simulation with non-unity Lewis numbers is considered to study how turbulence affects differential diffusion. In the absence of differential diffusion, minimal departure from the 1D unstretched flame structure (species vs. temperature profiles) is observed. In the non-unity Lewis number case, the flame structure lies between that of 1D unstretched flames with "laminar" non-unity Lewis numbers and unity Lewis number. This is attributed to effective Lewis numbers resulting from intense turbulent mixing and a first model is proposed. The reaction zone is shown to be thin for both flames, yet large chemical source term fluctuations are observed. The fuel consumption rate is found to be only weakly correlated with stretch, although local extinctions in the non-unity Lewis number case are well correlated with high curvature. These results explain the apparent turbulent flame speeds. Other variables that better correlate with this fuel burning rate are identified through a coordinate transformation. It is shown that the unity Lewis number turbulent flames can be accurately described by a set of 1D (in progress variable space) flamelet equations parameterized by the dissipation rate of the progress variable. In the non-unity Lewis number flames, the flamelet equations suggest a dependence on a second parameter, the diffusion of the progress variable. A new tabulation approach is proposed for the simulation of such flames with these dimensionally-reduced manifolds.

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures. (c) 2006 Published by Elsevier GmbH.