湍流中大尺度结构对小尺度结构的影响

发布时间：2018-01-07 00:00

本文关键词：湍流中大尺度结构对小尺度结构的影响　出处：《哈尔滨工业大学》2016年博士论文　论文类型：学位论文

【摘要】：湍流的复杂性在于它由相当广泛的湍流尺度组成。这种复杂性使得湍流的预测变得极其困难。因此,在实际中,往往引入一些合理的假设,比如流场的局部各向同性(local isotropy)和自相似性(self-preservation)等。这些假设大大简化湍流的研究,使得湍流中一些重要理论的形成得以实现。本文首先对尾流(wake)远场区域流动中心线上的湍流结构进行自相似分析。关于平均动量输运方程的自相似分析以及逐个尺度能量平衡方程的自相似分析表明后者是对前者的重要补充。通过逐个尺度能量平衡方程的自相似分析可知,不同的长度尺度(比如泰勒微尺度和Kolmogorov长度尺度)和不同的速度尺度(比如速度波动的均方根值和Kolmogorov速度尺度)有相似的指数演化特性,即:所有速度尺度按指数规律x-1/2减少,而所有长度尺度按指数规律x1/2增加。这些指数演化特性与尾流远场区域流动中心线上的测量数据吻合得很好。同时,该流场中能谱和速度结构函数在所有波数或所有分离距离都重合得很好。这些结果表明远场区域流动中心线上的流场是完全自相似的。这种完全自相似的特性将大大简化平均湍能耗散率输运方程的推导。本文随后分析了圆柱尾流远场区域中心线上和完全发展槽道流中心线上的各向同性形式湍能耗散率?iso的输运方程,并与格栅湍流,外力作用下的均匀各向同性湍流,和圆管射流远场区域流动中心线上的输运方程进行对比。结果表明由于涡拉伸和粘性引起的?iso的产生和耗散之间的不平衡在不同的流场中不同。例如,圆柱尾流远场区的流动中心线上,这种不平衡由大尺度的顺流输运项和沿着侧向的扩散共同决定;在格栅湍流中,不平衡由大尺度顺流输运项决定;然而槽道流流动中心线上的流动由大尺度的侧向扩散决定。更重要的是,这种差异决定了顺流方向速度偏导数偏斜因子S和熵耗散系数G之间有不同的约束关系。进而导致随着湍流微尺度雷诺数Rλ的增加,S将沿着不同的路径接近一个“普适的”常数。例如,在圆柱尾流远场区的流动中心线上,当(Rλ≤40)时,S随着Rλ的增加而减少。当Rλ40时,S随着Rλ的增加然后逐渐接近“普适的”常数。对于本论文中研究的所有的湍流速度场,实验和仿真数据均为S将沿着不同的路径接近一个“普适的”常数的结论供不容质疑的支撑。值得注意的是,当Rλ足够大时S接近一个“普适的”常数验证了Kolmogorov在1941年出相似性假设(通常被称为K41理论),与Kolmogorov在1962年修正的相似性假设(通常被称为K62理论)相悖。本文理论推导得到的S和熵耗散系数之间的解析关系被用来改进标准的k-ˉ?湍流模型。文献和计算流体力学商业软件给出的该湍流模型中的常数C?2≈1.92。本文推导了以上几种流场中标准k-ˉ?湍流模型中C?2的解析表达式。结果发现这些表达式不相同。即使是在同一流场中,C?2也可能在不同的区域取不同的值。在使用严谨方式证明C?2不是一个普适的常数的同时,研究亦发现,尽管C?2的取值依赖于具体的流场,但是对于一给定的自相似流场,那么C?2的取值将不随雷诺数的改变而改变。以上关于速度场的研究被进一步拓展到湍流中的被动标量场(turbulent passive scalar field)。从广义的Yaglom方程出发推导了平均温度耗散率?θ的输运方程,得到了速度-温度混合偏导数偏斜因子-ST和?θ的耗散系数之间的解析表达式。实验和数值模拟数据与解析表达式的预测高度吻合。在格栅湍流中,随着雷诺数的增加,-ST逐渐接近一个常数。在外力作用下的均匀各向同性湍流中,-ST是独立于雷诺数的。最后,本文研究了尾流中的大尺度结构。流场中的大尺度结构一般可用本征正交分解POD(proper orthogonal decomposition)来取。传统的POD方法需要流场中多点相关信息,因此只能用于PIV数据,DNS数据,或多点同时测量的热线(往往需要几十只热线同时测量)数据。本文出一新的POD方法,使其可以用于单点湍流信号数据的分析。在大幅简化对试验数据需求的同时,该方法的优势更体现在能识别不同POD分量对应的主导频率,并由此首次发现了圆柱尾流近场流向肋条结构(rib structures)对湍动能贡献的百分比。在剪切流中,由于平均速度梯度的存在,流场是偏离局部各向同性的。偏离的程度可以用顺流速度沿着侧向偏导数的偏斜因子量化。大剪切率条件下的Lumley使用量纲分析得到该因子随着雷诺数的增加按指数规律R-1λ减少(通常被称为Lumley定律)。该定律表征剪切流中流场趋于局部各向同性的速率。本文从基于Navier-Stokes方程的逐个尺度的能量平衡方程出发,更严谨地推导了相同条件下的Lumley定律。
[Abstract]:The complexity of turbulence is composed of turbulence scale widely. This complexity makes the prediction of turbulent flows has become extremely difficult. Therefore, in practice, often introduce some reasonable assumptions, such as the flow of local isotropy (local isotropy) and self similarity (self-preservation). These assumptions greatly simplify the turbulence of the the formation of some important theory of turbulence is realized. Firstly, wake (wake) self similarity analysis of far-field flow turbulent region center line structure. The average momentum transport equation of self similar analysis and one scale energy balance equation of self similar analysis shows that the latter is an important supplement to the former. Through the self similar scale analysis one by one energy balance equation, different length scales (such as the Taylor micro scale and Kolmogorov length scale) and different scales (speed ratio Such as RMS velocity fluctuation and Kolmogorov velocity scale) have similar evolution characteristics, namely: all index velocity scale exponentially decreased x-1/2, while all the length scales exponentially increase. The x1/2 index evolution characteristics and wake far field flow the center line of the measured data are in good agreement. At the same time, the the flow field in the energy spectrum and the function of velocity structure in all wavenumber or all separation distance coincides well. These results indicate that the far field flow the center line of the flow field is completely self similarity. The self similarity will greatly simplify the average turbulent kinetic energy transport equation is derived. The paper then analyzes the dissipation rate of turbulence the form of isotropic cylindrical wake flow far field center line and the center line of the fully developed channel flow dissipation rate? ISO transport equation, and grid turbulence, uniform loads of the same Turbulent round jet, and the far field flow of the center line of the transmission were compared. The results show that the vorticity transport equation and the viscous tension caused? Imbalance between the generation and dissipation of ISO in different field. For example, the far field flow of the center line of the wake flow, which is not balanced by the downstream large scale transport and along the lateral diffusion is determined; in grid turbulence, is not balanced by large scale downstream transport decision; however, the center line of the flow channel flow by lateral diffusion of large scale decision. More importantly, this difference determines the relationship between the different constrained direction of flow velocity the partial derivative deviation factor S and entropy dissipation coefficient G. With the increase of turbulence resulting in micro scale Reynolds number R, S will be along a different path to a "universal" constant. For example, in the wake of a circular cylinder flow in the far field region When the heart line (R = 40, lambda) S decreases with the increase of R. When the R lambda lambda 40, lambda R S with constant increase and then gradually close to the "universal". For all of the turbulent velocity field in this paper, the experimental and simulation data are S will follow different paths to a "universal" constant conclusion can not be questioned for support. It is worth noting that, when the R lambda is large enough S to a "universal" constant validation of the Kolmogorov similarity hypothesis in 1941 (commonly known as K41 and Kolmogorov in theory), similarity that amendment in 1962 (commonly known as K62 theory). Contrary to the analytic relationship between the theoretical derivation of S and entropy dissipation coefficient are used to improve the standard of k- -? Turbulence model. The turbulence model of literature and the commercial CFD software are in constant C? 2 = 1.92. is derived by several flow In the field of standard k- - turbulence model in C?? 2. The analytical expressions of these expressions are not the same. Even in the same field, C? 2 may take different values in different regions. In the use of rigorous proof of C? 2 is a universal constant at the same time, research also found that although C? 2 of the value depends on the specific field, but for the self similar flow field, then a given C? 2 of the value of the Reynolds number will not change. On the velocity field of the study was to further expand the passive scalar in turbulent flow (turbulent passive scalar field). The generalized Yaglom equation was deduced based on the average temperature dissipation rate? Theta transport equation, the velocity temperature deviation factor -ST and mixed partial derivative? Analytical expression of dissipation coefficient theta. Prediction of experimental and numerical simulation data and the analytical expressions in the lattice is highly consistent. Grid turbulence, with the increase of Reynolds number, -ST gradually close to a constant. In homogeneous isotropic turbulence under external force, -ST is independent of the Reynolds number. Finally, this paper studies the large scale structures in the wake flow. The large scale structure of the proper orthogonal decomposition generally available (POD proper orthogonal decomposition) to take. The traditional method of POD flow should be more relevant information, so can only be used for PIV data, DNS data, or multi-point measurement hotline (often require dozens of simultaneous measurement data. In this paper, the hotline) a new POD method, which can be used to analyze the single point turbulence signal data in greatly simplified test data of demand at the same time, the advantage of this method is more reflected in the dominant frequency can identify different components corresponding to the POD, which was first discovered near field to the rib structure of cylinder wake flow (rib structures) of turbulence The percentage contribution in shear flow, the mean velocity gradient has deviated from the local flow field is isotropic. The degree of deviation can be used downstream along the speed deviation factor quantitative lateral partial derivative. The shear rate of Lumley under the conditions of using dimensional analysis to obtain the factor increases with Reynolds number decreased exponentially R-1 lambda (commonly known as Lumley's law). The rate of shear flow field characterization law tends to local isotropy. From the energy balance equation by Navier-Stokes scale based on the equation of more rigorous derivation of Lumley's law under the same conditions.

【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O357.5

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