【作者】 李宁；

【导师】 罗纪生；

【作者基本信息】 天津大学 ， 流体力学， 2007， 博士

【摘要】 本文基于空间模式的角度,采用直接数值模拟(DNS)的方法,应用MPI并行技术,模拟了不可压缩平板边界层层流到湍流转捩的过程,继续研究了转捩过程中“breakdown”过程的内在机理,重点考察了平均流剖面修正在层流转捩的“breakdown”过程中所起的作用。流动的雷诺数选定为732,基本流为层流Blasius相似性解,计算域入口扰动形式为一个二维T-S波和一对对称的三维T-S波。控制方程为直角坐标系下无量纲化的扰动形式Navier-Stokes方程,时间离散采用三阶精度混合显隐相结合的分裂格式,空间离散则采用高精度紧致有限差分逼近与Fourier伪谱方法相结合的方法。法向采用非等距网格坐标变换,出口边界条件采用嵌边函数法。应用具体算例,验证了本文并行程序不仅符合线性理论,而且与串行计算结果一致。按照扰动幅值的大小,本文计算了亚谐转捩的三种情况,随后从壁面摩擦系数、平均脉动动能、谱空间扰动演化、y-z平面速度矢量分布、平均速度剖面的演化、流动稳定性分析、边界层的各种厚度及形状因子的演化等方面对计算结果进行了分析,得出以下结论:1.不同的初始扰动幅值,转捩发生在下游不同的位置。如果三维扰动的幅值较小,只有在“breakdown”前的大约一、两个二维流向波长的范围内有明显三维扰动,且展向尺度基本上与入口处的三维波的展向尺度一致。转捩后更高的高次谐波被快速激发,扰动的展向尺度变得更小,同时平均流修正也增大的很快。2.在“breakdown”的前期,用当地层流边界层排移厚度无量纲化的壁面摩擦系数是相同的。在“breakdown”的后期,壁面摩擦系数基本上增大到同样的大小。“breakdown”的过程为120个计算域入口处层流边界层排移厚度。3.平均脉动动能随空间演化的规律与壁面摩擦系数类似,但先于壁面摩擦系数开始快速增长。总的脉动能量可以达到0.05左右,其中流向脉动能量占五分之三,法向和展向脉动能量各占五分之一。另外,初始扰动越小,转捩越靠下游,各个方向的平均脉动能量都越大,但平均脉动能量快速增长区间的大小是基本一致的。4.不同初始扰动引起转捩,直至“breakdown”前,二维波的幅值都是不一样的,但平均流修正开始快速增长的位置是相同的,平均流修正快速增长的过程也是大致相同的。平均流修正开始快速增长的位置与二维波开始不规则的位置是一致的。在这个位置有规则的三维波达到最大,约为0.05左右,然后三维波开始变得无规则。这一期间三维波增长很快,也许是流动稳定性的二次稳定性在起作用。在转捩前,二维扰动幅值的演化与流动稳定性线性理论的预测基本符合,波长也与入口处二维波的波长近似相等,从某种意义上讲,这也许为转捩预测中的EN方法提供了理论依据。5.对沿流向不同位置的平均流速度进行的稳定性分析表明,沿着流动方向,不稳定区域先逐渐减小,缩小到很小以后,再逐渐的增大到最大范围,然后再一次逐渐减小,趋于很小。不稳定区域开始逐渐增大的位置对应于壁面摩擦系数开始快速增长的位置,不稳定区域达到最大的位置大致位于壁面摩擦系数曲线快速增长段的1/3处,不稳定区域再一次逐渐减小,趋于零的位置对应于壁面摩擦系数达到最大的位置。当层流中的扰动幅值增大后,由于非线性作用将修正平均流剖面。当平均流剖面被修正到一定程度,不稳定性区域会扩得很大,这将导致更多的谐波被快速激发并增长,开始了“breakdown”过程。在“breakdown”过程中,由于大量谐波快速增长,导致扰动能量快速增长。扰动能量的快速增长又进一步加速了平均流剖面的快速修正。这样相互的快速增长使得流动快速地转变为湍流。这里的结论与其他流动中的研究结果是一致的。6.在转捩过程中,排移厚度的增长比相应的层流排移厚度的增长要慢。更多还原

【Abstract】 In this paper, direct numerical simulation (DNS) was adopted for the laminar-turbulent transition of an incompressible boundary layer on a flat plate based on the spatial model with MPI technology. Studies on breakdown mechanism of laminar-turbulent transition was carried on sequentially. The priority was given to the effects of the modification of the mean flow profile on the process of breakdown in laminar-turbulent transition.The Reynolds number was taken as 732. The laminar Blasius similarity solution was taken as the basic flow. One two-dimensional T-S wave and two symmetrical three-dimensional T-S waves were taken as the disturbers at the entrance. Under Cartesian coordinate, the non-dimensional perturbation equations were taken as the governing equations. A third-order precision mixed explicit-implicit scheme was employed for time discretization and a combination method of high precision compact finite difference with the Fourier pseudo-spectral expansion was implemented for spatial discretization. The method of non-uniform meshes was applied in normal direction and the fringe method was applied in dealing with outlet boundary condition. By a simple case, the parallel programs were not only validated to be consistent with the linear theory, but also the results got by one computer.According to the magnitude of amplification, we simulated three cases of subharmonic transition. Then we anaylized the results from the following aspects: skin friction coefficient、mean fluctuation kinetic energy、disturbance velocity evolution in Fourier space、velocity vector at y-z plane、evolution of mean velocity profile、stability analysis、thicknesses of boundary and shape factor. From the analysis, we drew the following conclusions:1. Disturbance with different initial amplitude led to different transition positions at backward position. If the amplitudes of three-dimensional disturbers were smaller, obvious three-dimensional disturbances only began to exist at a length of one or two two-dimensional wavelengths in front of the breakdown, and the magnitudes of waves in z-direction approximate to the length of three-dimensional waves which were added at the entrance. Some higher frequency harmonic waves came into exist rapidly after the process of transition, the magnitudes of waves in z-direction became smaller, meanwhile, the modification of mean flow increased rapidly.2. In the prophase of breakdown, The skin friction coefficient non-dimensionized by local laminar boundary layer displacement thickness was equal at every point along x-direction. In the anaphase of breakdown, skin friction coefficient increased to the same value for the cases considered, the length of breakdown process was about 120 laminar boundary layer displacement thickness of the entrance.3. The evolution of mean fluctuation kinetic energy along x-direction was analogous with the one of skin friction coefficient, but it started to increase before the skin friction coefficient did. The total fluctuation kinetic energy could reach about 0.05, of which 0.03 was contributed by u, and the other 0.02 was contributed by v and w equally. In addition, the smaller the initial disturbers were, the longer distance from the entrance transition started and the bigger the mean fluctuation kinetic energy was along every direction, but the lengths of the regions that the mean fluctuation kinetic energy increased rapidly were almost the same.4. Different initial disturbers all caused transition, the amplitudes of two-dimensional waves were not the same until the breakdown, but the positions where mean flow was modified rapidly were the same, the processes that the modification of mean flow increased rapidly were almost the same. The position that modification of mean flow increased rapidly agreed with the one that two-dimensional wave began to be ruleless. At that position, the regular three-dimensional waves reached their maximum values of about 0.05, then the three-dimensional waves began to be ruleless. During this process, the three-dimensional waves increased rapidly, it may because the second stability of stability began to work. Before the transition, the amplitude evolution of two-dimensional disturber agreed with the linear stability theory, and the wavelength approximated to the one of the two-dimensional wave added at the entrance, to some extent, this might offer theory basis for EN method in transition forecasting.5. We analysised mean flow velocity stability for different positions along x direction,it indicated that the instability zone became smaller and smaller along x direction at first, when being very small, it began to increase to the maximum range, then smaller it became again, and to be very small. The position where instability zone began to increase corresponded to the one that skin friction coefficient began to increase rapidly, the position where instability zone reached it’s maximum located at the 1/3 station of skin friction coefficient increased rapidly. The instability zone decreased again, the position that it was to be zero corresponded to the one where skin friction coefficient reached the maximum. When the disturber’s amplitude increased in laminar flow, the nonlinear effect would modify the mean flow profile. When the mean flow profile was modified to certain extent, the instability zone would enlarge to be of great magnitude, more harmonic waves came into exist and they increased rapidly, then breakdown started. In the process of breakdown, because of the rapid increase of many harmonic waves, disturber’s energy increased rapidly. In return, the rapidly increased energy accelerated the mean flow profile modification rapidly. All of these mutually rapid increases made the flow turn into turbulent rapidly. The results of this thesis were consistent with other investigations.6. In the process of transiton, the increase of displace thickness was slower than the one of the corresponding laminar displace thickness.更多还原