【作者】 张斌；

【导师】 谷传纲； 王彤；

【作者基本信息】 上海交通大学 ， 流体机械及工程， 2011， 博士

【摘要】 随着对湍流研究的不断发展和深入,工程界对于自然环境和工程流动的分析预报提出了更多、更高的要求。大涡模拟方法是现阶段计算机水平下,对复杂流动进行较精确预测的最有效途径之一。滤波网格尺度是大涡模拟方程中的关键参数,大涡模拟数值计算中滤波网格尺度多通过计算网格尺寸的某种函数式获得,这便使得大涡模拟计算结果从根本上受到计算网格尺寸和空间疏密分布的直接影响。而基于湍流能谱分布,适宜的滤波网格尺度应位于湍流惯性副区内。计算网格的不合理控制或划分将会导致滤波网格尺度的计算值和适宜值不相匹配,进而影响着大涡模拟计算结果的合理性、可靠性和经济性。因此,本文将主要研究焦点定位于开展大涡模拟中适宜滤波网格尺度的深入理论研究,尝试解决基于湍流物理意义上的适宜滤波网格尺度确定的基础问题;并致力于从物理意义层面上来建立合理、可行的针对大涡模拟方法的计算网格控制机制。本文深入开展了大涡模拟适宜滤波网格尺度的理论研究,首次提出了湍流流动结构中的“能量比系数”概念,依据湍流理论和大涡模拟方法思想,从惯性副区的能谱分布规律出发,合理导出了适宜滤波网格尺度的计算表达式;基于大涡模拟控制方程,并结合Karman-Howarth方程推导思路,从另一角度建立了适宜滤波网格尺度的又一等量计算表达式;确定了反映适宜滤波网格尺度的湍流参数(包含湍动能、湍流耗散率和“能量比系数”)。基于湍流不同分区特征,给出了适宜滤波网格尺度计算式中“能量比系数”的合理取值范围;借助小波分析多尺度方法,并结合不同流动实验的数据采集和信号分析,进一步得出了“能量比系数”的综合推荐方程。为实现本文所提的大涡模拟适宜滤波网格尺度计算,开展了相应的支撑性研究工作。为给大涡模拟适宜滤波网格计算中分析信号样本数的设定提供理论依据,结合小波分析和统计检测理论,提出了一种相对合理的确定湍流采样数据量尺度的方法;为给大涡模拟适宜滤波网格计算中提供优选的小波基函数,基于湍流时频特性和信息熵理论,建立了以品质因数和特征谱熵值为评价指标的小波基选取流程;为给大涡模拟适宜滤波网格计算中提供可靠的湍流采样信号数据,提出了一种改进的小波阈值消噪方法,以尽可能地消除湍流数据采集中的干扰噪声污染。为有效辨识区分湍流不同流动尺度特征,提出了一种基于小波和双谱分析的辨识相干结构的方法,建立了基于小波分析辨识湍流含能尺度的能量最大准则。本文基于“滤波网格尺度计算值(计算网格尺寸的函数)与适宜滤波网格尺度相匹配”的思路,提出了具备一定物理意义的大涡模拟网格自适应控制新方法。该方法能通过自适应优化调整网格划分和疏密分布,建立与适宜滤波网格尺度相匹配的计算网格分布。首次定义了新的针对大涡模拟计算网格的自适应调整指标—“网格比系数”,并给出了自适应网格控制中近壁面计算网格处理的合理方法。通过网格自适应指标的不断调整,使得计算网格分布和适宜滤波网格尺度相适应,并可以在雷诺时均计算网格的基础上逐步调整出适于大涡模拟的计算网格。本文成功应用新方法实现了雷诺数Re=5147后台阶流动、雷诺数Re=37500后台阶流动和雷诺数Re=5730经典槽道流动的大涡模拟网格自适应控制,进行了三个流动应用实例的自适应网格大涡模拟结果、精细网格(其网格数约为自适应网格数的3倍)大涡模拟结果、直接数值模拟数据或实验数据的对比分析。结果表明,自适应网格的大涡模拟数据与实验数据和直接数值模拟数据符合良好;自适应网格可以在网格总数相对少的情况可以通过自适应控制网格分布取得与精细计算网格几乎相近的流动数据。通过自适应控制可改进大涡模拟计算网格尺寸和网格分布的质量,并能有效降低数值计算代价。结论有效验证了本文所提的适宜滤波网格尺度和新方法的合理性、可靠性和经济性等特点。本文首次应用新方法更深入地开展了等宽离心风机叶轮流道大涡模拟计算网格的网格指标分布以及自适应调整、大涡模拟和实验数据对比分析等工作。开展了可视化低速等宽离心风机叶轮性能测试和内部流道PIV测量的实验研究,有效获取了三种不同风机叶片的内部流速分布和性能数据。本文实现了三种不同风机叶片的离心叶轮流道的大涡模拟网格自适应控制调整,所得适于离心叶轮流道的计算网格分布与旋转流道流动特征有着较好的适应性,能合理反映流动结构的分布和计算网格尺度要求。以相对流速分布和叶轮进出口总压升为主要指标,进行了大涡模拟数值和实验数据的研究对比。结果显示,自适应网格的大涡模拟数据与PIV实验数据、性能数据均取得了较好的符合,这也进一步验证了本文所提的适宜滤波网格尺度和新方法是合理、可行的以及能同样应用于复杂旋转流动分析的良好发展前景。更多还原

【Abstract】 With the development of turbulence research, more and higher requirements are put forward for the flow analysis of natural environment and engineering turbulence. Under the present computational level, large eddy simulation (LES) is one of the most effective approachs to predict complex turbulent flow relatively accurately. LES equations of the resolved turbulent scale are established by the low-pass filtering of Navier-Stokes equations, so the filtering grid scale of the spatial filter plays a decisive role for LES. Based on turbulence theory, the proper filtering grid scale should be within or close to the inertial sub-range of turbulence. However, present filtering grid scale solutions for numerical computation and sub-grid stress model are mostly built up by the local computational mesh. Because of the improper LES mesh, the employed filtering grid scale solution will not match with the theoretical proper filtering grid scale. It may lead to lose some useful small-scale fluctuations, economical cost advantage and the rationality of LES results. Therefore, this work focus on the deep research on the proper filtering grid scale of LES and trys to establish a rational adaptive control strategy for proper LES mesh from the views of the physical significance.On the basis of turbulence theory and LES method, a new formula for proper filtering grid scale was derived from the energy spectrum distribution law of the inertial sub-range. By incorporating LES control equation with Karman-Howarth equation thoughts, anther equal formula for proper filtering grid scale was established as well. In this work, a new concept defined energy ratio coefficient in turbulent flow structure was proposed firstly to associate turbulent energy spectrum with the filtering grid scale and the key turbulent parameters was determined to reflect the proper filtering grid scale. Based on different turbulent characteristic scale and multi-scale wavelet method, the rational value range and commended equations of the energy ratio coefficient were set up firstly.In order to relize the above mentioned computational method, the relevant researches were carried out. Based on wavelet method and statistic theory, a new approach for proper sampled data scale was put forward to offer the support for the sample size in the analysis of the proper filtering grid scale. An improved wavelet threshold de-noising method was set up to remove the noise signals and get the relatively reliable data for the turbulent signal post-processing. According to wavelet and bi-spectrum analysis, a reasonable method to indentify the coherent structures and a new identification criterion of energy-containing scale were established. In terms of time-frequency characteristics and information entropy theory, an integrated method was put forward to determine the proper wavelet function in the analysis for the energy ratio coefficient.Based on the view that the computational mesh distribution should match with the proper filtering grid scale, a new physical strategy for LES mesh adaptive-control was put forward firstly to get optimized meshing size and distribution. The new index named grid ratio coefficient for mesh adjustment and the realizable method for near wall meshing treatment were offered respectively. Through the abovel strategy, the proper mesh of LES could be built directly from the adjustment of RANS mesh. This work applied the novel strategy to achieve LES mesh adaptive-control and data comparative analysis among LAM (LES of Adaptive-control Mesh), LFM (LES of Fine Mesh), DNS (Direct Numerical Simulation) and experiments for three typical flow cases, including Re=5147 backward facing step flow, Re=37500 backward facing step flow and Re=5147 turbulent channel flow. The results showed that the grid numbers of LAM were less than those of LFM evidently and the data of LAM were in a good agreement with those of DNS and experiments. It was revealed that results of LAM were very close to those of LFM. The conclusions provided positive evidences for the rationality, reliability and economy of the novel strategy.This work used the novel strategy to carry out LES grid index analysis, LES mesh adative control and data comparative analysis for the centrigugal blower with the equal width blade. The visual centrigugal blower experiments were set up to get the inner velocity distribution and performance data of three different blades by PIV and performance tests. It was shown that the adjusted LES mesh distribution could well reflect the inner flow structure characteristics and local mesh size requirements. The results indicated that the data of adaptive control LES mesh were in a good agreement with those of PIV experiment and performance test. The conclusions offered further confidence in the rationality, realizability and good prospect for complex turbulent flow of the novel strategy.更多还原