激波和界面相互作用的数值研究

发布时间：2018-05-05 02:47

本文选题：界面追踪 + level-set　；参考：《中国科学技术大学》2017年硕士论文

【摘要】：本文研究运动激波和多物质界面相互作用问题。假设气体和水为无黏可压缩介质,采用Euler方程描述可压缩介质流场。将GFM方法拓展到多物质界面和计算域边界条件处理,采用level-set方法追踪气/气、气/水和气/固界面,界面边界条件处理同时考虑虚拟流体和当地真实流体的某些性质。气/气界面采用OGFM方法定义边界条件。气/水界面采用文献修正的rGFM方法定义边界条件,提高了 Riemann问题构造的精度。气/固界面基于GFM方法通过外推参数定义固壁边界条件。本文采用有限差分方法分别求解流场控制Euler方程(双曲守恒律方程)、界面level-set方程和重新初始化方程(Hamilton-Jacobi方程),结合方程特点,空间离散分别选用合适的五阶WENO格式,时间离散选用三阶TVD Runge-Kutta 方法。本文首先重复了文献中的算例,如Sod和Lax激波管问题、界面在旋转和剪切流场运动和变形、水下气泡膨胀以及激波和单个水/固体圆柱相互作用。给出了压力分布、界面位置等计算结果,表明本文与文献结果是符合的,也验证了本文数值方法和计算程序。在此基础上,本文对运动激波和双列水/固柱、单列水柱以及同时包含He气泡、气水和气固界面相互作用问题进行了计算,给出了不同时刻的流场密度纹影图和指定点的压力时间曲线。主要结论概述如下:(1)对于空气中激波分别和双列水柱/固体圆柱相互作用问题,计算结果表明:激波在水柱和固体圆柱表面间发生规则和Mach反射、透射等现象,相邻界面的反射激波还会进一步发生透射和反射,流场激波波系结构极为复杂。除了水柱的透射激波外,水柱和固体圆柱表面的反射激波及其相邻水柱/圆柱反射激波的相互透射和反射产生的激波波系结构几乎相同。原因是:水相对于空气密度和惯性都很大,在激波扫过柱体的短时间内,水柱运动和变形较为缓慢,与固体圆柱类似。空气和水声阻抗差异使得水柱吸收空气冲击波能量很小,而固体圆柱内部无能量吸收,两者表现较为一致。水柱和固体圆柱下游均出现旋涡。(2)对于空气激波与不同直径、不同数量单列水柱相互作用问题,计算结果表明:水柱直径越大或者数量越多,即孔隙率越小,激波传播过程中所受阻碍就越大,其受扰动程度也就越剧烈,导至相邻水牲或固体圆柱出现"泡状激波",类似喷管的喉道起动激波。(3)对于空气激波同时与He气泡、水柱和间体圆柱相互作用问题,计算结果表明:激波在不同物质界面产生了不同的激波波系结构。其中,水柱和固体圆柱表面的激波结构和强度相似,但He产气泡界面附近激波结构差异显著,界面形变剧烈,激波衰减程度较大。原因是:水和He气、空气声阻抗趋异巨大,水中透射激波能量低,因此,水和固体圆柱激波结构接近,但He气密度小于空气且He气与空气的声阻抗差异很小,He气泡惯性小,受激波冲击作用产生较大变形和明显运动,He气泡吸收能量较大,因而透射激波强度较大,导致入射激波衰减较快。(4)上述计算结果表明:本文采用的数值方法、界面边界条件处理是合适的,可以捕捉到激波和同类多个界面以及不同类多个界面相互作用的精细和复杂激波波系结构。本文将GFM方法由气/气和气/水界面推广到气/固界面和计算域边界处理,为复杂计算域和运动边界复杂流动计算提供了不同于坐标变换的一条新途径。
[Abstract]:This paper studies the interaction of motion shock wave and multi material interface. Assuming that gas and water are non viscous compressible media, the Euler equation is used to describe the flow field of compressible media. The GFM method is extended to the boundary conditions of the multi material interface and the computational domain, and the level-set method is used to trace gas / gas, gas / water and gas / solid interfaces and boundary condition treatment. At the same time, some properties of the virtual fluid and the local real fluid are considered. The gas / gas interface is defined by the OGFM method. The boundary conditions are defined by the revised rGFM method of the gas / water interface to improve the precision of the structure of the Riemann problem. The gas / solid interface is based on the GFM method to define the wall boundary conditions by the extrapolation parameter. The finite difference method is used to solve the Euler equation (hyperbolic conservation law equation), the interface level-set equation and the re initialization equation (Hamilton-Jacobi equation). In combination with the characteristic of the equation, the suitable five order WENO scheme is selected for spatial discretization and the three order TVD Runge-Kutta method is selected for time discretization. First, the examples in the literature are repeated in this paper. Such as Sod and Lax shock tube problems, the interface between the movement and deformation of the rotating and shear flow field, the expansion of the underwater bubble and the interaction between the shock wave and the single water / solid cylinder. The calculation results of pressure distribution and interface position are given. The results show that this paper is in accordance with the literature results, and the numerical method and calculation program are verified. Based on this, this paper is based on this method. The interaction of motion shock wave and double column water / solid column, single column water column, including He bubble, gas water and gas-solid interface is calculated. The density schlieren diagram and pressure time curve of the specified point at different time are given. The main conclusions are as follows: (1) in the air, the shock wave and the double column / solid cylinder phase are respectively in the air. The interaction problem, the results show that the shock wave between the water column and the surface of the solid cylinder has rules and Mach reflection, transmission and so on. The reflection shock wave in the adjacent interface will be further transmitted and reflected. The structure of the shock wave system is very complex. Besides the transmission shock of the water column, the reflection shock and its phase of the water column and the solid cylinder surface are reflected. The shock wave system structure of the adjacent water column / cylindrical reflection shock wave is almost the same. The reason is: the water phase is very strong for air density and inertia. In the short time of shock sweep through the column, the movement and deformation of the water column are slow, similar to the solid cylinder. The difference of air and water acoustic impedance makes the water column absorb air shock wave The energy is very small, and there is no energy absorption inside the solid cylinder. The two performances are consistent. (2) the interaction of air shock and different diameter, different number of single column water column. The results show that the larger the diameter of the column or the more the number of water column, that is, the smaller the porosity, the shock wave propagation process. The greater the hindrance, the greater the degree of disturbance, and the degree of disturbance is more intense, which leads to the emergence of "bubble shock" to adjacent water or solid cylinders, similar to the throat starting shock of the nozzle. (3) the interaction of air shock waves with He bubbles, water column and interbody cylinder shows that the shock wave produces different excitation waves at different material interfaces. The shock structure and strength of the surface of the water column and the solid cylinder are similar, but the shock wave structure near the He bubble interface is distinct, the interface deformation is intense and the shock wave attenuation is great. The reason is: water and He gas, the acoustic impedance of the air is different and the energy of the shock wave in the water is low. Therefore, the water and the solid cylindrical shock wave structure is close, but the He gas density is close. The difference of the acoustic impedance of He gas and air is small. The He bubble has a small inertia, and the shock effect of the shock wave produces larger deformation and obvious motion. The He bubble absorbs more energy, so the intensity of the transmission shock wave is larger and the incident shock wave attenuates faster. (4) the numerical results mentioned above show that the numerical method adopted in this paper is to deal with boundary conditions. It is suitable to capture the fine and complex excitation wave structure of the shock wave and the similar interfaces and the interaction of different kinds of interfaces. This paper extends the GFM method from gas / gas and gas / water interfaces to the gas / solid interface and the boundary processing of the computational domain, which provides different coordinates for complex computation domain and motion boundary complex flow calculation. A new way of changing.

【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O354.5

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