可压平面混合层稳定性分析及数值模拟

IMECH-IR > 力学所知识产出(1956-2008)

	可压平面混合层稳定性分析及数值模拟
	王强
导师	傅德薰
	1999
学位授予单位	中国科学院研究生院
学位授予地点	北京
学位类别	博士
学位专业	流体力学
关键词	可压平面混合层稳定性分析直接数值模拟数值行为分析紧致格式 Compressible Planar Mixing Layer Stability Analysis Direct Numerical Simulation Numerical Behaviour Analysis Compact Difference Scheme
英文摘要	可压平面混合层是包含复杂多时空尺度运动的非定常流体力学部问题，具有深刻的理论意义和广泛的应用背景。针对该问题所涉及内容的多面性，本文的目的是，基于高精度、高分辨率数值算法的构造、发展和数值行为分析，采用线性稳定性分析和直接数值模拟方法。从理论和计算两方面集中研究压缩性效应、粘性效应、初值效应以及燃烧反应放热效应等对可压平面混合层早期稳定性行为和大尺度拟序涡结构非线性演化的影响。以混合层已有研究成果的分析和综述为开端，论文主体共包括四部分：第一部分是可压平面混合层时间/空间模式数值线性稳定性分析。实现了高精度对称紧致差分格式（SCD）对可压粘性扰动线性稳定性边值问题的求解，对导出的线性和非线性离散特征值问题，提出了两个高效局部解法。研究涉及二维/三维扰动波、无粘/粘性扰动波、特征函数和特征值谱、第一/第二模态、超声速快/慢模态、速度比和密度比等。验证了对流Mach数Mc为一个合理的压缩性参数。指出压缩性效应和粘性效应对最不稳定扰动波的波数（频率）和增长率呈相拟的抑制作用，且时间模式稳定性分析结果在许多方面是可信的。从随机和线性扰动场出发，采用高精度五阶迎风紧致和六阶对称紧致混合差分算法（UCD5/SCD6）对可压平面混合层的稳定性特征进行了直接数值模拟，揭示了初始主导线性扰动与一些实际涡结构非线性作用形态间的内在关联，印证了线性稳定性分析方法的合理性和有效性。第二部分是高精度迎风紧致差分格式（UCD）时空全离散数值行为分析。导出了其一维/二维一般色散表达式。研究表明，UCD格式在高波数区具有内在的全离散耗散和色散特性；其数值群速度的快/慢特征可因CFL数不同而改变；在稳定CFL数下简单附加人工粘性可强化UCD格式在高波数区的耗散量；提高时间精度可放宽稳定CFL数限制；UCD格式的二维全离散色散介质中存在三个不同性质的数值波，其全离散稳定性由数值声波主控。第三部分实现了高精度UCD5/SCD6差分算法对空间发展可压平面混合层的直接数值模拟。通过亚谐扰动波的个数和扰动频率的控制，捕捉到了基频涡的饱和、一次和二次对并等现象，显示了大尺度涡结构与入中初始扰动方式之间的内在联系。利用参数Mc观察了压缩性效应对大尺度涡空间演化及其相互作用的影响。第四部分实现了高精度UCD5/SCD6差分算法对非预混扩散火焰化学反应平面混合层的直接数值模拟。研究指出，放热效应可抑制和延迟涡的形成，使基频涡卷拉伸甚至丧失，混合层Reynolds 应力ρu'v'和流向速度波动关联项u'v'下降，以致涡结构与外流动量交换和标量输运减少，脉动输运能力被削弱，从而混合效率、产物生成率和混合层增长率下降，放热主要通过膨胀效应和斜压效应来抑制大尺度涡的演化。; The compressible planar mixing layer (CPML) is unsteady and complicated, including many time/space scales, so it is important to both fluid mechanics and its applications. Taking notice of its intricacy, the present thesis is aimed at studying many effects on the stability and large-scale vortex structures of CPML, such as, compressibility, viscosity, initial disturbances and heat release, by using linear stability analysis and direct numerical analysis (DNS) related to the theory and the computation, respectively. The construction, improvement, and behavior analysis of the high-accuracy and high-resolution numerical algorithms are firstly carried out. Based on the review of materials about CPML, the main body of the present thesis can be divided into four parts: The first part is related to the numerical linear stability analysis of temporally/spatially developing CPML. The high accuracy symmetric compact difference scheme (SCD) is introduced to solve the boundary-value problem about the compressible viscous linear stability analysis, and two high-efficient local methods are developed for the derived linear and nonlinear discrete eigenvalue problems. The research has dealt with the two-/three-dimensional waves, inviscid/viscous waves, eigenfunction and eigenvalue spectra, first/second modes, supersonic fast/slow modes, ratios of velocity or density. The compressibility parameter of convetive Mach number (Mc) is observed. The effects of compressibility and viscosity can damp similarly the most unstable wavenumber (frequency) and its growth, and at many aspects the results of temporally mode are reliable. The DNS of the stability characteristics of CPML using UCD5/SCD6 method with random and linear initial fields shows that there is a relation of initial prominent linear disturbance and real vortex structure, and manifest the reasonability and effectiveness of the linear stability analysis method. The second part is about the numerical behaviour analysis of the high-accurate upwind compact difference scheme (UCD) being fully-discretized. The one- and two-dimensional dispersion closed-forms are derived. The fully-discretized dissipation and dispersion errors are mainly in the high wavenumber region. The fast/slow characteristics of the numerical group velocity can vary with the variation of CFL number. The simple artificial-dissipation at stability CFL number can increase the dissipation error in the high wavenumber region. Increasing time accuracy can enlarge the stability limitation. There are three different numerical waves in the two-dimensional numerical dispersion media, and the numerical acoustic wave controls the stability of UCD scheme. In the third part, UCD5/SCD6 method is successfully implemented on DNS of the spatially-developing CPML. Through controlling the number of subharmonic disturbance and its frequency, the phenomena of the primary vortex saturation, the primary and secondary vortex pairing are displayed. The result an inherent relation of the large-scale vortex structure and the inlet initial disturbance manner. Using the parameter Mc, the effect of compressibility on the development and interaction of the large-scale vortex structures is observed. In the fourth part, UCD5/SCD6 method is successfully implemented on DNS of chemically reactive CPML with non-premixed diffused flame. Heat release can delay and damp the vortex forming, and make the primary vortex stretched or disappeared. Because the Reynolds stress ρu'v' and the correlation of disturbed velocity u'v' decrease, the momentum and scalar transport measure between vortex and outer fluid is also decrease, and the transport ability of disturbance is weaken. So the mixing efficiency, product rate and growth rate of mixing layer drop. Through the dilatation and baroclinic effects, heat release damps the large-scale vortex.
索取号	29874
语种	中文
文献类型	学位论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/23850
专题	力学所知识产出(1956-2008)
推荐引用方式 GB/T 7714	王强. 可压平面混合层稳定性分析及数值模拟[D]. 北京. 中国科学院研究生院,1999.

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