微喷颗粒与气体混合过程的数值模拟研究

冲击波作用下金属与气体界面将发生微喷混合现象,即金属表面产生的微喷射物质在气体中的输运过程.提出采用散体颗粒分布代替微喷初始状态,基于气体-颗粒两相流模型对微喷混合现象进行了模拟研究.数值模拟给出了微喷混合的动力学演化过程,分析了初始气体压力和颗粒尺寸因素对混合层的影响规律;在数值模拟中发现了微喷颗粒的气动破碎现象,这可导致颗粒尺度明显减小,成为影响微喷混合演化性质的重要物理因素.本文模拟结果与相关实验结果取得一致,初步表明,气粒两相流模型是模拟微喷混合过程的一种有效方法.     

基于格子Boltzmann方法的Rayleigh-Taylor两相不稳定流动研究

Rayleigh-Taylor(RT)不稳定性现象是一种复杂的两相流动问题,对两相界面动力学和计算流体力学提出了很大挑战。本文发展了一种相场格子Boltzmann方法,并对RT不稳定性现象进行了数值模拟,重点分析了黏度和界面张力对两相失稳过程的影响。结果表明:黏度的增加会减慢RT现象的演化过程,降低所形成的涡结构的数目;界面张力会抑制RT现象的发展,本文所获得的临界韦伯数为17,当韦伯数小于临界值时,界面张力与重力的作用相抵消,重相流体不发生下沉,两相界面趋于稳定;反之,两相界面发生失稳。研究工作有助于加深对RT不稳定性现象的认识。     

移动网格与Level Set耦合方法在气-液两相流数值模拟中的应用

本文采用自适应移动网格与Level Set函数相耦合的方法来实现气-液两相流的数值模拟与计算.作为自适应网格方法的一种,移动网格方法主要是为了解决发展方程的计算问题而设计的方法.文中给出了移动网格的生成方程,并针对方程的非线性,给出了一种半隐式的离散方法用于进行求解.本文将移动网格方法与Level Set方法相耦合,将控制流体运动的Navier-Stokes方程以及追踪相界面的Level Set方程转换到曲线坐标下,应用一套曲线坐标方程组来同时描述气、液两相流的运动规律,成功实现了对气-液两相流问题的数值模拟.通过对顶盖驱动流的计算以及对液滴沉降现象的模拟计算,验证了本文方法的可靠性.本文对常重力与微重力下两气泡融合的发展规律进行了数值模拟,通过分析对比,得到了重力对两气泡融合变形的影响规律.     

ρ-VOF:一种可清晰模拟自由界面的两相流方法

文章通过对EFM(effective field modeling)模型进行简化, 消除了原模型的非守恒性项和非双曲性特性项, 发展了一种基于密度的气液两相流模拟方法: ρ-VOF方法.利用体积分数信息对控制单元内的自由界面进行重构, 得到了控制单元内流体的空间分布, 并采用AUSM+-up格式获得考虑气液流体接触间断信息的对流通量.新方法可统一处理激波间断和接触间断的相互作用, 保持自由界面的尖锐性, 并且其计算量与自由界面的空间复杂度无关.最后, 数值模拟了液体激波管气液激波管和气体激波跨二维液滴传播等问题, 并与文献结果进行对比, 验证了本方法在气液两相流模拟中的准确性.      

耦合界面力的两相流相场格子Boltzmann模型

提出了一种改进的基于相场理论的两相流格子Boltzmann模型.通过引入一种新的更加简化的外力项分布函数,使得此模型克服了前人工作中界面力尺度与理论分析不一致的问题,并且通过Chapman-Enskog多尺度分析表明,所提出的模型能够准确恢复到追踪界面的Cahn-Hilliard方程和不可压的Navier-Stokes方程,并且宏观速度的计算更为简化.利用所提模型对几个经典两相流问题,包括静态液滴测试、液滴合并问题、亚稳态分解以及瑞利-泰勒不稳定性进行了数值模拟,发现本模型可以获得量级为10^-9极小的虚假速度,并且这些算例获取的数值解与解析解或已有的文献结果相吻合,从而验证了模型的准确性和可行性.最后,利用所发展的两相流格子Boltzmann模型研究了随机扰动的瑞利-泰勒不稳定性问题,并着重分析了雷诺数对流体相界面的影响.发现对于高雷诺数情形,在演化前期,流体界面出现一排“蘑菇”形状,而在演化后期,流体界面呈现十分复杂的混沌拓扑结构.不同于高雷诺数情形,低雷诺数时流体界面变得相对光滑,在演化后期未观察到混沌拓扑结构.     

振荡流共轭换热格子-Boltzmann模拟

振荡流共轭换热现象广泛存在于热声热机等工程应用中.基于双分布格子-Boltzmann模型,对平行平板间振荡流共轭换热进行了数值模拟.通过假定共轭界面处流体和固体的未知内能分布函数均为对应的平衡态滑移修正格式,提出了一种处理共轭换热边界的新方法.模拟结果表明,该方法可以保证共轭界面上温度连续和热流连续.分析了不同流体与固体导热系数比情况下振荡流共轭换热的速度场、温度场以及热流分布的特点.     

基于SIMPLE求解对流-扩散方程的一种新方法

针对SIMPLE系列算法,通过分别求解控制容积界面和节点两个位置的对流-扩散方程来提高数值计算精度,提出了一种流动与传热数值模拟的新方法。采用新的数值方法对顶盖驱动流与正方腔自然对流进行了数值模拟。数值模拟结果表明,在相同网格划分时,新的数值方法相对迎风格式、乘方格式、QUICK格式SIMLE算法的计算精度高;而在计算精度基本相同时,新方法有较高的计算效率。     

数值模拟两相汽蚀流动的新模型和算法

提出了数值模拟两相汽蚀流动现象的新汽蚀模型和算法.提出的汽蚀模型和算法耦合了考虑紊流粘性效应的Reynolds-Averaged Navier-Stokes方程求解方法,可以自动模拟空泡起始点、空泡长度和汽蚀空泡形状.在流场计算和界面修正的迭代计算过程中,跟踪并得到液相/气相界面.数值模拟了圆锥形圆柱体和半球形圆柱体在不同汽蚀系数下的汽蚀流动现象,得到了与实验值完全吻合的数值模拟结果,并且与已发表的数值研究结果进行了比较.计算结果表明提出的汽蚀模型和算法能够有效地模拟汽蚀流动中的气泡界面和气泡长度,汽蚀模型和算法的正确性和实用性得到了相应的验证.     

改进粒子水平集法及其应用

针对传统粒子水平集方法的缺陷提出一种虚拟粒子对距离函数的修正方法.改进算法针对虚拟粒子与待修正网格点的各种相对位置进行误差修正,可以避免虚拟粒子在非界面法线方向移动而产生的误差.数值求解涡旋流场问题显示:改进算法的界面捕捉性能得到显著提高.在此基础上,结合投影法求解Navier-Stokes方程组,数值模拟存在高密度比(10³量级)及粘性比(10²量级)的不可压缩两相流问题(气泡上升及自由面不稳定性问题).计算结果与已有结果吻合良好,详细分析主要控制参数对瑞利-泰勒不稳定性现象的影响.     

气液两相流的间断有限元模拟

基于非结构网格,给出模拟两相流的统一间断有限元框架.其中,不可压Navier-Stokes方程采用IPDG(Interior penalty discontinuous Galerkin)方法求解;Level Set方程采用RKDG(Runge-Kutta discontinuous Galerkin)方法求解.方腔驱动流在不同Re数时的数值结果验证了该方法在单相流动中的有效性.气泡上升过程的模拟结果表明:该方法避免了重新初始化,且计算量小、实施简单,可有效求解具有运动界面的不可压两相流问题.     

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, is studied. Then, the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore, based on the established relation between the effective velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm, the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data. Supported by the National Natural Science Foundation of China (Grant Nos. 10672019 and 10272003)     

液面位置对流-固交界面上伪瑞利波幅度影响的数值模拟

研究了流体半空间中存在气-液交界面并且其位置发生改变时,流-固交界面上伪瑞利波的传播特性和幅度响应特征。借助有限差分的方法,实现了对不同气-液交界面位置时振动方向垂直于流-固交界面的脉冲面源所激发表面波声场的数值模拟,分别讨论了气-液交界面自身的散射作用与伪瑞利波传播过程中的能量泄漏对伪瑞利波幅度的影响。数值模拟结果表明:气-液交界面自身对伪瑞利波的散射作用对伪瑞利波幅度仅有极微小的影响,而能量泄漏才是引起伪瑞利波衰减的决定性因素;随着气-液交界面位置的升高,脉冲伪瑞利波幅度呈指数规律下降,与此同时主频向低频偏移。所得研究结果可以发展为一种利用伪瑞利波幅度进行液位检测的可靠方法。      

Z变换在磁化等离子体电磁脉冲传播时域分析中的应用

 通过Z变换的方法,将与频率有关的磁化等离子体的介电常数由频域变换到Z域,推导了Z变换形式的时域有限差分法计算式,模拟了电磁脉冲在磁化等离子体中的传播。经过离散傅里叶变换,给出了电磁波通过磁化等离子体后的反射系数和透射系数与频率的关系。还给出了模拟结果和理论值的对比。结果表明,Z变换算法的模拟结果比卷积分更接近理论值。     

A numerical approach for the computation of dispersion relations for plate structures using the Scaled Boundary Finite Element Method

In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.     

固-固界面退化特性的超声反射评价方法

提出了一种基于有限宽超声束反射的固-固界面退化特性评价方法,从理论和数值仿真角度进行了分析和计算。将两固体界面间的薄层简化为界面弹簧模型,以界面法向和切向劲度系数表征界面的退化程度。通过数值计算求得有限宽超声纵波束在不同入射角和界面不同退化程度下的反射横波、反射纵波的镜面反射系数。进一步地,通过建立二维有限元模型,仿真研究了有限宽超声纵波束在给定入射角及界面不同退化程度下镜面反射系数的变化规律。结果表明,反射纵波和反射横波的镜面反射系数随有限宽超声纵波束的入射角及界面劲度系数的改变而变化,且存在镜面反射系数随界面劲度系数单调且敏感变化的入射角,据此可准确评价界面的退化程度。     

Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for two-fluid computations

We extend the direct numerical simulation (DNS) capability developed in [D. Yang, L. Shen, Simulation of viscous flows with undulatory boundaries: Part I. Basic solver, J. Comput. Phys. (submitted for publication) ] to the simulation of two-fluid interaction with deformable interface. Two approaches are used to couple the DNS of one fluid with the simulation of another fluid. In the first, the DNS is coupled with a potential-flow based wave solver that uses a high-order spectral (HOS) method. This coupled method is applied to simulate the interaction of turbulent wind with surface waves, including single wave train and broadband wavefield. Validation with previous theoretical and experimental studies shows the accuracy and efficiency of this coupled DNS-HOS method for capturing the essential physics of wind–wave interaction. In the second approach, both of the fluids are simulated by the DNS and are coupled by an efficient iterative scheme, in which the continuity of velocity and the balance of stress are enforced at the interface. The performance of this coupled DNS–DNS method is demonstrated and validated by several test cases including: interfacial wave between two viscous fluids, water surface wave over highly viscous mud flow with interfacial wave, and interaction of two-phase vortex pairs with a deformable interface. Comparison with existing theoretical and numerical results confirms the accuracy of this coupled DNS–DNS method. Finally, this method is applied to study the interaction of air and water turbulence. The nonlinear development of interfacial wave by the excitation of the air and water turbulence, and the wave effect on the instantaneous and statistical characteristics of the turbulence are elucidated.     

管道后传声数值模拟的不稳定波抑制

在管道后传声的数值模拟中,必须考虑平均流剪切层的散射效应,然而在非均匀剪切流动下时域求解线化欧拉方程会面临Kelvin-Helmholtz不稳定波产生和放大的难题。已有的不稳定波抑制技术通常很难获得令人满意的结果。本文采用一种混合方法,首先引入有限时段的宽频声源波包将声波和不稳定波分离,进而采用声源滤波器技术对不稳定波进行抑制。数值验证算例选择半无限长轴对称环形硬壁直管道,采用计算气动声学方法时域求解2.5维线化欧拉方程,无背景流动的数值解与解析解符合很好,验证了程序的精度与可靠性,非均匀流动算例则表明所采用波包加声源滤波器混合方法对不稳定波抑制效果明显,对声场影响很小,充分显示了该方法的精度与可行性。     

Fractional optimal control problem of a distributed system in cylindrical coordinates

In this work, Fractional Optimal Control Problem (FOCP) of a Distributed system is investigated in cylindrical coordinates. Axis-symmetry naturally arises in the problem formulation. The fractional time derivative is described in the Riemann-Liouville (RL) sense. The performance index of a FOCP is considered as a function of state and control variables and system dynamics are given as a Partial Fractional Differential Equation (PFDE). The method of separation of variables is used to find the solution of the problem. Eigenfunctions are used to eliminate the terms containing space parameters and to define the problem in terms of a set of generalized state and control variables. For numerical computations, Grünwald-Letnikov (GL) approach is used. A time-invariant example is considered to demonstrate the effectiveness of the formulation. The comparison of analytical and numerical solutions is given using simulation results and also it can be seen that analytical and numerical results converge each other. In addition, simulation results for different values of order of derivative, time discretizations and eigenfunctions are analyzed.     

Improved CE/SE scheme with particle level set method for numerical simulation of spall fracture due to high-velocity impact

In the present paper, an Eulerian scheme combined with the hybrid particle level set method for numerical simulation of spall fracture due to high-velocity impact is proposed. An axisymmetric framework is established, based on an improved CE/SE scheme, to solve the high-velocity impact problems with large deformations, high strain rates and spall fractures. The hybrid particle level set method is adopted for tracking material interfaces and describing the formation and propagation of a crack. A novel representation of crack by level set is proposed. Numerical simulations are carried out and compared to the corresponding experimental results. The numerical results are in good agreement with the experimental data. The edge effects are reproduced and the decrease of scab thickness with increase in impact velocity is observed owing to the numerical analysis. It is proved that our computational technique is feasible and reliable for analyzing the spall fracture.     

Wave Simulation in Frozen Porous Media

We propose a numerical algorithm for simulation of wave propagation in frozen porous media, where the pore space is filled with ice and water. The model, based on a Biot-type three-phase theory, predicts three compressional waves and two shear waves and models the attenuation level observed in rocks. Attenuation is modeled with exponential relaxation functions which allow a differential formulation based on memory variables. The wavefield is obtained using a grid method based on the Fourier differential operator and a Runge–Kutta time-integration algorithm. Since the presence of slow quasistatic modes makes the differential equations stiff, a time-splitting integration algorithm is used to solve the stiff part analytically. The modeling is second-order accurate in the time discretization and has spectral accuracy in the calculation of the spatial derivatives.