發(fā)布時間：2018-05-01 19:29

  本文選題：Richtmyer-Meshkov不穩(wěn)定性 + 極小曲面��； 參考：《中國科學技術(shù)大學》2016年博士論文

【摘要】：當具有初始擾動的物質(zhì)界面受到瞬時沖擊加載時,界面失去原有穩(wěn)定性,擾動不斷增長并最終演化成湍流流動的物理現(xiàn)象被稱為Richtmyer-Meshkov(RM)不穩(wěn)定性。RM不穩(wěn)定性在慣性約束核聚變、超燃沖壓發(fā)動機、天體物理中的超新星爆發(fā),以及流動穩(wěn)定性研究、漩渦和湍流形成機理方面等工程和學術(shù)領(lǐng)域具有非常重要的研究價值,自RM不穩(wěn)定性概念被提出以來的半個多世紀中,受到了國內(nèi)外廣泛的關(guān)注。在已有的RM不穩(wěn)定性現(xiàn)象研究中,大量的研究工作集中在對二維現(xiàn)象的討論并得到了頗為豐碩的研究成果。但是,在大量的自然現(xiàn)象和工程環(huán)境中,RM不穩(wěn)定性均以三維形式出現(xiàn)。三維問題的研究往往受到實驗技術(shù)的限制、計算資源不足、以及理論建模的復雜程度所制約,導致對三維RM不穩(wěn)定性現(xiàn)象的研究十分有限,界面的三維效應(yīng)亟需進行更為廣泛的研究。RM不穩(wěn)定性的界面發(fā)展受到界面初始形式的顯著影響,三維情況又與二維情況有很多不同之處。三維界面在其界面上的每個位置需由兩個主曲率進行描述,兩個界面主曲率的組合形式對RM不穩(wěn)定性界面的擾動增長速率具有非常重要的影響。本文基于課題組前期的實驗工作進行深入探討,利用實驗和數(shù)值相結(jié)合的手段對界面主曲率效應(yīng)進行研究,分析界面演化的內(nèi)在機制,驗證理論模型的可靠性。本文的主要內(nèi)容包括：1.在實驗研究方面,本文基于課題組前期的實驗基礎(chǔ),對試驗段中用于生成極小曲面單模界面的肥皂膜生成裝置進行了改進,從而可以對激波與界面相互作用的早期過程進行觀測,彌補了前期實驗方法的不足,從實驗結(jié)果可以得到更多激波與界面相互作用的信息。本文利用實驗手段對輕／重氣體界面和重／輕氣體界面進行了研究,得到了完整的流場演化過程,為數(shù)值方法提供了更為有效的參考。2.編制了數(shù)值方法對實驗過程進行了模擬,得到了實驗過程中更為詳盡的流場信息。數(shù)值程序采用level set結(jié)合真實虛擬流體(rGFM)的方法對物質(zhì)界面進行捕捉,五階WENO格式和三階TVD Runge-Kutta方法求解歐拉方程的空間項和時間項。并使用了OpenMP并行化處理來提高計算效率。計算結(jié)果清楚地重現(xiàn)了實驗過程中氣體界面的演化過程,給實驗圖像提供了更加直觀的三維波系形態(tài),加強了對極小曲面單模界面RM不穩(wěn)定性現(xiàn)象的理解。3.利用數(shù)值方法對具有相同方向的主曲率界面(三維單模界面)、具有相反方向的主曲率界面(極小曲面特征的三維單模界面)以及其中一個主曲率為零的單模界面(二維單模界面)進行了模擬,并對不同形式的界面中心對稱面上的擾動振幅曲線進行提取對比,發(fā)現(xiàn)相比于只有一個不為零主曲率的界面形式,相同方向的界面主曲率能夠促進擾動振幅的增長,而相反方向的界面主曲率能夠抑制擾動振幅的增長,甚至推遲擾動增長進入線性階段的時間。這與課題組早期的實驗結(jié)果相吻合,從數(shù)值角度驗證了實驗結(jié)果以及理論模型的有效性。對界面演化過程進行了波系分析和渦量分析,從而對影響界面擾動振幅的機制進行了解釋。4.以輕/重氣體界面為例,對多種不同主曲率組合形式的界面進行了討論,以便于對界面進行橫向比較和理論分析,對界面不同位置處的界面擾動振幅進行研究。從對比結(jié)果中發(fā)現(xiàn),界面主曲率效應(yīng)為一種局部效應(yīng),如果界面上同時存在主曲率方向相同區(qū)域和主曲率方向相反區(qū)域,則局部區(qū)域的振幅增長將分別呈現(xiàn)出不同的增長規(guī)律。從界面的整體來看,如果界面最大擾動振幅相等,則具有相反方向曲率的界面會比只有相同方向曲率的界面增長稍慢。從界面面積的增長速率來看,如果界面最大擾動振幅相等,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長更為緩慢,但是增長速率最為緩慢的仍然是二維單模界面,說明了最為穩(wěn)定的界面形式是二維界面,任何曲率組合形式的三維界面都將增強RM不穩(wěn)定性的擾動增長。本文通過實驗和數(shù)值手段系統(tǒng)地研究了RM不穩(wěn)定性問題中的三維效應(yīng),重點著眼于三維初始界面的主曲率效應(yīng)研究,初步得到了界面主曲率效應(yīng)對于界面擾動發(fā)展的影響規(guī)律,期望可以找到通過操控界面主曲率來調(diào)節(jié)界面擾動增長的方法,從而為實際應(yīng)用提供可能的解決方案。
[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.

【學位授予單位】：中國科學技術(shù)大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O354.5

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