槽道湍流的直接数值模拟
文献类型：学位论文
| 作者 | 李新亮
|
| 学位类别 | 博士 |
| 答辩日期 | 2000 |
| 授予单位 | 中国科学院研究生院 |
| 授予地点 | 北京 |
| 导师 | 马延文 |
| 关键词 | 槽道湍流 直接数值模拟 基于非等距网格的紧致差分格式 压缩性效应 “二维湍流” 标度律 turbulent channel flow direct numerical simulation upwind compact difference schemes on non-uniform meshes compressibility effect two-dimensional turbulence scaling law |
| 学位专业 | 流体力学 |
| 中文摘要 | 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。 |
| 索取号 | 29911 |
| 英文摘要 | Direct numerical simulation (DNS) is applied to study channel turbulence. There are five parts in this paper: a) Finite difference methods for DNS of turbulence. b) High efficient method for the incompressible N-S equations and DNS of incompressible turbulent channel flow. c) DNS of compressible turbulent channel flow and analysis of compressibility effects. d) "Two-dimensional turbulence". e) Analysis of the scaling law of turbulent channel flow. 1. Upwind compact difference schemes on non-uniform meshes are developed to suit rapidly varying of grid spacing near the channel wall. In these schemes, the coefficients in those schemes are varying with meshes, which eliminate large errors of Jacobian transformation near the wall. The errors of approximation and aliasing error are also studied. 2. A high-efficient method for incompressible N-S equations is developed. Non-linear terms of the N-S equations are approximated by using upwind compact difference schemes on non-uniform meshes, and the discrete pressure equation on staggered grid is used to approximate the pressure equation, then difficulties of pressure boundary treatments can be avoided. Finally, Fourier transformation is used to decouple the implicit terms, and LU method is used to solve the decoupled equations. The method has very high efficiency. To test method, a fully developed channel flow is simulated. The turbulence statistics (include mean velocity, mean-square-root and skewness factor of velocity fluctuations, Reynolds shear stress, energy spectrums) agree well with the experiment data or computational data of Kim et al (1987). 3. Fully developed compressible turbulent channel flow (Ma = 0.8, Re = 3300) is simulated. The data base of compressible turbulent channel flow is developed. Density-weighted mean-stream velocity (by using Van Driest transformation) and RMS velocity fluctuation (in "semi-local" coordinates) are very close to those of computed data for incompressible flow (Kim et al 1987) and compressible flow (Ma = 1.5, Ma = 3, Coleman et al 1995). The skewness and flatness factors of velocity fluctuation in compressible turbulence are given, which are not seen in other literatures. Compressibility effects are also studied. According to analysis, a part of kinetic energy are absorbed by pressure-dilatation and turned into inner energy, which makes streamwise velocity streaks more smooth. 4. Fully developed "two-dimensional turbulent channel flow" is simulated. The difference and similarity between "two-dimensional turbulence" and three-dimensional turbulence are also discussed in this paper. 5. Scaling laws of 3-D channel turbulence and "2-D channel turbulence" are studied, and the conclusions are: a) Scaling law is found in the center area of the channel. b) In this area, ESS is also found. c) When Mach number is not very high, compressibility has little effect on scaling exponents. |
| 学科主题 | 流体力学 |
| 语种 | 中文 |
| 公开日期 | 2009-04-13 ; 2009-08-25 |
| 出处 | [博士论文].北京.中国科学院力学研究所,2000 |
| 源URL | [http://dspace.imech.ac.cn/handle/311007/23354]  |
| 专题 | 力学研究所_力学所知识产出(1956-2008) |
| 推荐引用方式 GB/T 7714 | 李新亮. 槽道湍流的直接数值模拟[D]. 北京. 中国科学院研究生院. 2000. |
入库方式： OAI收割
来源：力学研究所
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