在随气泡顶端运动的坐标系中，通过将理想流体模型推广到非理想流体的情况，研究了流体黏性和表面张力对Rayleigh-Taylor (RT)和Richtmyer-Meshkov (RM)不稳定性气泡速度的影响。首先得到了RT和RM不稳定性气泡运动的控制方程(自洽的微分方程组)；其次给出了二维平面坐标和三维柱坐标中气泡速度的数值解和渐近解，并定量分析了流体黏性和表面张力对RT和RM气泡速度和振幅的影响。结果表明：从线性阶段到非线性阶段的全过程中，非理想流体中的气泡速度和振幅小于理想流体中的气泡速度和振幅。也就是说，流体黏性和表面张力对RT和RM不稳定性的发展都具有致稳作用。

In a reference system moving with the bubble vertex we investigate the effects of fluid viscosity and surface tension on the bubble velocity in the nonlinear Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities, by extending the ideal fluid model [Goncharov V N, Phys. Rev. Lett. 88 134502 (2002)] to the non-ideal fluid case. First of all, the governing equation (i.e. self-consistent differential equations) describing the dynamic of the bubble front in RT and RM instabilities is obtained. Then, the numerical and asymptotic solutions of the bubble velocity in two-dimensional planar geometry and three-dimensional cylindrical geometry are obtained. Moreover, we quantitatively study the effects of fluid viscosity and surface tension on the RT and RM bubble velocities. It is found that in the fully nonlinear evolutions of RT and RM instabilities, the bubble velocity and amplitude in the non-ideal fluid are both less than those in its ideal fluid counterpart. That is to say, the effe

基于大涡模拟,结合五阶加权基本无振荡格式以及沉浸边界法对平面入射激波与两种SF_6梯形重气柱的相互作用过程进行了数值模拟,数值结果清晰地显示了激波诱导Richtmyer-Meshkov不稳定性所导致的两种梯形重气柱的变形过程,详细分析了入射激波在两种梯形重气柱界面发生反射、折射、绕射以及折射激波与透射激波在气柱内部来回反射的过程,并研究了该过程中所产生的复杂波系结构,对两种梯形气柱变形过程中与周围空气的混合过程进行了分析;通过记录气柱界面四个特征尺寸随时间的变化对两种梯形气柱界面的不同演化过程进行了定量分析。

Based on the large eddy simulation, combined with the 5th order weighted essentially non-oscillatory scheme and the immersed boundary method, the interaction between planar shock wave and two isosceles trapezoid SF6 cylinders is numerically simulated. Our numerical results clearly show that the deformations of isosceles trapezoid cylinders are induced by the Richtmyer-Meshkov instability due to the interaction of shock wave with them. The reflecting, refracting and diffracting process of incident shock are discussed in detail, and the complex wave structures induced during these processes are revealed. In addition, the mixing mechanism of SF6 gas and air is expatiated. Furthermore, the efforts are made to understand the difference in the evolution of the interface between these two isosceles trapezoid cylinders by analyzing the variation of four characteristic scales.

设计并加工了一套竖直环形同轴无膜激波管,可用于环形汇聚激波诱导下的Richtmyer-Meshkov不稳定性实验研究。与前人工作相比,本文在流体界面的形成以及流场的观测方法上做了较大的改进。通过实验和数值方法,对该竖直激波管产生的环形柱状汇聚激波的参数进行测量和分析,验证了同轴激波管形成柱状汇聚激波方法的可行性和可靠性。在界面形成方面,采用细丝约束肥皂膜技术形成正八边形气体界面,并利用数值方法考察了细丝对界面发展的影响。结果表明在界面发展的前期,细丝的影响几乎可以忽略。利用连续激光片光结合高速摄影相机对流场进行观测,获得了正八边形air/SF6气体界面在环形汇聚激波及其反射激波冲击下的演化过程,并与数值结果进行了对比,获得了较好的一致性,进一步验证了汇聚激波的对称性以及细丝约束肥皂膜技术用于形成多边形气体界面的可靠性。

A vertical annular coaxial diaphragm-less shock tube is designed based on the prin-cipal proposed by Hosseini and Takayama and modified in order to conveniently install the initial interface in the test section and visualize the flow field for the investigation of the Richtmyer-Meshkov (RM)instability.Parametric study is carried out both experimentally and numerically to explore the characteristics of the annular coaxial cylindrical converging shock wave.The varia-tion of pressure behind the shock shows the feasibility and reliability of this shock tube to generate the annular coaxial cylindrical converging shock wave.The pressure variations with time at differ-ent positions in the test section are acquired from the experiment and numerical simulation,and the converging effect of the shock wave is emphasized.After the validation of the converging shock wave,the experiment of RM instability induced by this converging shock wave is con-cerned.For this purpose,a regular octagon