界面曲率效应对Richtmyer-Meshkov不稳定性影响的研究

发布时间：2018-05-01 19:29

本文选题：Richtmyer-Meshkov不稳定性 + 极小曲面　；参考：《中国科学技术大学》2016年博士论文

【摘要】：当具有初始扰动的物质界面受到瞬时冲击加载时,界面失去原有稳定性,扰动不断增长并最终演化成湍流流动的物理现象被称为Richtmyer-Meshkov(RM)不稳定性。RM不稳定性在惯性约束核聚变、超燃冲压发动机、天体物理中的超新星爆发,以及流动稳定性研究、漩涡和湍流形成机理方面等工程和学术领域具有非常重要的研究价值,自RM不稳定性概念被提出以来的半个多世纪中,受到了国内外广泛的关注。在已有的RM不稳定性现象研究中,大量的研究工作集中在对二维现象的讨论并得到了颇为丰硕的研究成果。但是,在大量的自然现象和工程环境中,RM不稳定性均以三维形式出现。三维问题的研究往往受到实验技术的限制、计算资源不足、以及理论建模的复杂程度所制约,导致对三维RM不稳定性现象的研究十分有限,界面的三维效应亟需进行更为广泛的研究。RM不稳定性的界面发展受到界面初始形式的显著影响,三维情况又与二维情况有很多不同之处。三维界面在其界面上的每个位置需由两个主曲率进行描述,两个界面主曲率的组合形式对RM不稳定性界面的扰动增长速率具有非常重要的影响。本文基于课题组前期的实验工作进行深入探讨,利用实验和数值相结合的手段对界面主曲率效应进行研究,分析界面演化的内在机制,验证理论模型的可靠性。本文的主要内容包括：1.在实验研究方面,本文基于课题组前期的实验基础,对试验段中用于生成极小曲面单模界面的肥皂膜生成装置进行了改进,从而可以对激波与界面相互作用的早期过程进行观测,弥补了前期实验方法的不足,从实验结果可以得到更多激波与界面相互作用的信息。本文利用实验手段对轻／重气体界面和重／轻气体界面进行了研究,得到了完整的流场演化过程,为数值方法提供了更为有效的参考。2.编制了数值方法对实验过程进行了模拟,得到了实验过程中更为详尽的流场信息。数值程序采用level set结合真实虚拟流体(rGFM)的方法对物质界面进行捕捉,五阶WENO格式和三阶TVD Runge-Kutta方法求解欧拉方程的空间项和时间项。并使用了OpenMP并行化处理来提高计算效率。计算结果清楚地重现了实验过程中气体界面的演化过程,给实验图像提供了更加直观的三维波系形态,加强了对极小曲面单模界面RM不稳定性现象的理解。3.利用数值方法对具有相同方向的主曲率界面(三维单模界面)、具有相反方向的主曲率界面(极小曲面特征的三维单模界面)以及其中一个主曲率为零的单模界面(二维单模界面)进行了模拟,并对不同形式的界面中心对称面上的扰动振幅曲线进行提取对比,发现相比于只有一个不为零主曲率的界面形式,相同方向的界面主曲率能够促进扰动振幅的增长,而相反方向的界面主曲率能够抑制扰动振幅的增长,甚至推迟扰动增长进入线性阶段的时间。这与课题组早期的实验结果相吻合,从数值角度验证了实验结果以及理论模型的有效性。对界面演化过程进行了波系分析和涡量分析,从而对影响界面扰动振幅的机制进行了解释。4.以轻/重气体界面为例,对多种不同主曲率组合形式的界面进行了讨论,以便于对界面进行横向比较和理论分析,对界面不同位置处的界面扰动振幅进行研究。从对比结果中发现,界面主曲率效应为一种局部效应,如果界面上同时存在主曲率方向相同区域和主曲率方向相反区域,则局部区域的振幅增长将分别呈现出不同的增长规律。从界面的整体来看,如果界面最大扰动振幅相等,则具有相反方向曲率的界面会比只有相同方向曲率的界面增长稍慢。从界面面积的增长速率来看,如果界面最大扰动振幅相等,具有相反方向曲率的界面相比只有相同方向曲率的界面增长更为缓慢,但是增长速率最为缓慢的仍然是二维单模界面,说明了最为稳定的界面形式是二维界面,任何曲率组合形式的三维界面都将增强RM不稳定性的扰动增长。本文通过实验和数值手段系统地研究了RM不稳定性问题中的三维效应,重点着眼于三维初始界面的主曲率效应研究,初步得到了界面主曲率效应对于界面扰动发展的影响规律,期望可以找到通过操控界面主曲率来调节界面扰动增长的方法,从而为实际应用提供可能的解决方案。
[Abstract]:When the material interface with initial disturbance is loaded with instantaneous shock, the interface loses its original stability, and the physical phenomenon that the disturbance grows and eventually evolves into turbulent flow is called Richtmyer-Meshkov (RM) unstable.RM instability in inertial confinement fusion, supercomer, astrophysics and supernova explosion, and Flow stability research, vortex and turbulence formation mechanism have very important research value in engineering and academic fields. In the half century since the concept of RM instability is proposed, it has received extensive attention both at home and abroad. In the study of RM instability, a large amount of research work is focused on the two-dimensional phenomenon. However, in a large number of natural phenomena and engineering environments, RM instability appears in a three-dimensional form. The study of three-dimensional problems is often restricted by experimental techniques, insufficient computing resources and the complexity of theoretical modeling, resulting in the study of three-dimensional RM instability. Ten The three-dimensional effect of.RM instability is badly affected by the initial form of the interface. The three-dimensional situation is different from the two dimensional situation. The three-dimensional interface in each position of the interface needs to be described by two principal curvatures, and the combination of the main curvature of the two interfaces. It has a very important influence on the growth rate of the disturbance of the RM instability interface. This paper is based on the previous experimental work of the project group, and studies the main curvature effect of the interface by combining the experimental and numerical methods, analyzes the internal mechanism of the interface evolution, and verifies the reliability of the theoretical model. The main contents of this paper are the main contents of this paper. 1. in the experimental research, based on the experimental basis of the project group, this paper improves the soap film generation device used to generate the single mode interface of the minimal surface in the test section, so that the early process of the interaction between the shock wave and the interface can be observed, and the deficiency of the previous experimental method is made up, and the results can be obtained from the experimental results. In this paper, the interface of the light / heavy gas and the heavy / light gas interface is studied by experimental means, and the complete flow field evolution process is obtained. The numerical method is provided with a more effective reference.2. to simulate the experimental process. Detailed flow field information. The numerical program uses the level set combined with real virtual fluid (rGFM) to capture the material interface, the five order WENO scheme and the three order TVD Runge-Kutta method to solve the space term and time term of the Euler equation, and use the OpenMP parallelization to improve the calculation efficiency. The calculation results clearly reproduce the experiment. The evolution of the gas interface in the process provides a more intuitive three-dimensional wave form to the experimental image, and strengthens the understanding of the RM instability in the single mode interface of the minimal surface..3. uses the numerical method for the main curvature interface with the same direction (the three-dimensional single mode interface) with the opposite direction of the principal curvature interface (three of the minimum surface characteristics). A single mode interface (a single mode interface) and a single mode interface (two-dimensional single mode interface) with zero principal curvature are simulated and the perturbation amplitude curves of different forms of the interface center symmetry are extracted and compared. It is found that the main curvature of the interface in the same direction can promote the disturbed vibration compared with only one interface with no zero principal curvature. The increase of amplitude, and the main curvature of the interface in the opposite direction can restrain the increase of the amplitude of the disturbance and even delay the time of the perturbation growth into the linear phase. This is in agreement with the experimental results of the early research group. The results of the experiment and the validity of the theoretical model are verified from the numerical point of view. An explanation of the mechanism that affects the amplitude of the interfacial disturbance is explained. The interface of a variety of different principal curvatures is discussed in the light / heavy gas interface as an example, in order to facilitate the transverse comparison and theoretical analysis of the interface, and to study the amplitude of the interface disturbance at different interfaces at the interface. It is found that the interface is main from the contrast results. The curvature effect is a local effect. If there is the same region of the main curvature and the opposite region of the main curvature in the interface, the amplitude growth of the local region will show different growth laws. The interface growth of the same direction curvature is slightly slower. From the growth rate of the interface area, the interface with the opposite direction curvature is slower than the same direction curvature if the maximum perturbation amplitude of the interface is equal, but the slowmost growth rate is still the two-dimensional single mode interface, indicating the most stable interface shape. The three dimensional interface of any curvature combination will enhance the disturbance growth of RM instability. In this paper, the three-dimensional effect in the RM instability problem is systematically studied by experimental and numerical methods. The main curvature effect of the three-dimensional initial interface is focused on, and the interfacial principal curvature effect is preliminarily obtained for the interface disturbance. The influence law of dynamic development is expected to find a way to adjust the growth of interface disturbance by controlling the main curvature of the interface, so as to provide a possible solution for the practical application.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O354.5

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