惰性颗粒抑爆过程的数值模拟

对高温火球诱导的爆炸及惰性颗粒的抑爆过程进行了数值研究。由于扰动特征时间 ,两相弛豫特征时间和化学平衡特征时间的差异 ,这种带激波的两相化学反应流守恒方程具有刚性。利用处理包括组元守恒方程的全耦合TVD格式和可处理方程源项的Lax Wendroff Rubin格式分别求解气相和颗粒相 ,并根据各特征时间的比值用分步法处理方程的刚性。计算结果反映了均温燃烧火球在可燃环境中形成加速火焰和激波 ,进而成长为爆轰波的过程 ,以及惰性颗粒对爆轰波的抑制过程 ,反映了激波、化学反应和惰性颗粒之间的相互作用和耦合。计算结果表明 ,仅当颗粒浓度大于某值时才能有效抑制爆轰 ,否则无论多大的颗粒散布区域 ,皆不能使爆轰波完全抑制 ,爆轰波或是在其中发展为两相爆轰波 ,或是穿越该区域后重新成长为气相爆轰。     

瞬态热传导问题的精细积分-双重互易边界元法

采用双重互易边界元法结合精细积分法求解二维含热源的瞬态热传导问题。针对边界积分方程中热源项和温度关于时间导数项引起的域积分,采用双重互易法处理,将域积分转换为边界积分。采用边界元法将边界积分方程离散后,得到关于时间的微分方程组,并利用精细积分法处理其中的指数型矩阵;对于微分方程组中由边界条件和热源项引起的非齐次项,采用解析的方法计算。为了比较精细积分-双重互易边界元法的计算效果,同时使用有限差分法计算温度对时间的导数项。通过数值算例验证了本文方法的有效性和精确性。计算结果表明:时间步长对于精细积分-双重互易边界元法的结果影响较小,而有限差分法对时间步长比较敏感且只在时间步长选取较小时有效;当选取较大时间步长时,精细积分-双重互易边界元法依然具有良好的计算精度。     

基于新型解耦算法的激波诱导燃烧过程数值模拟

对一种模拟化学非平衡流动的时间和空间二阶精度新型解耦算法进行两方面改进,流动算子采用基于Runge-Kutta方法的时间格式以后, 可以推广到更多的空间差分格式,化学反应源项求解算子可以采用梯形公式、拟稳态逼近法和变系数常微分方程求解器. 对H化学非平衡流动; 解耦算法; 计算方法对一种模拟化学非平衡流动的时间和空间二阶精度新型解耦算法进行两方面改进,流动算子采用基于Runge-Kutta方法的时间格式以后,可以推广到更多的空间差分格式,化学反应源项求解算子可以采用梯形公式、拟稳态逼近法和变系数常微分方程求解器.对H_2/Air预混气体中激波诱导振荡燃烧的Lehr试验进行模拟,考察了化学动力学模型、网格尺寸和差分格式耗散大小对计算结果的影响,同时对不同的化学反应源项算子求解算法的计算效率进行了比较.     

Wilson-θ法直接积分的运动约束和计算扰动

Wilson-θ法的积分过程一般不可能同时既符合计算假设规定的运动约束条件又满足动力平衡方程,时间步长内附加了一个计算扰动影响。由Wilson-θ法积分计算出的时间步长终点不平衡加速度和系统的动力平衡方程,本文导出了时间步长内计算扰动的确定方法,并进一步采用①同步计算消除计算扰动效应和②后续步计算消除计算扰动效应,两种途径抵消其不利影响。算例指出,本文方法有效减少Wilson-θ法直接积分结果的误差和超越现象,提高了计算稳定性。     

爆轰波平掠惰性气体界面及其解耦现象的数值研究

采用基元化学反应模型和迎风TVD格式,数值研究了爆轰波平掠惰性气体界面时的物理现象及其作用机制,并用点隐方法克服化学反应源项引起的计算刚性。数值结果显示,当爆轰波平掠过惰性气体界面时,形成了爆轰波、界面、透射激波以及稀疏波相互作用的现象。在高N2比例稀释的可燃混合气体情况下,当爆轰波平掠过特定惰性气体界面时,它与惰性气体界面相互作用产生的稀疏波可以导致爆轰波的解耦。     

配点型区间有限元法

在分析Taylor展开``点逼近'区间有限元法不足的基础上, 提出了基于Chebyshev第一类正交多项式全局逼近目标函数的配点型区间有限元法. 该方法不需要计算目标函数对不确定性变量的灵敏度, 不要求不确定性变量的变化范围为小区间, 并适合求解目标函数为不确定变量非线性函数的情形. 目标函数正交展开式的系数采用Gauss-Chebyshev求积公式得到,故需要在不确定性变量所在区间内配置高斯积分点. 计算目标函数在高斯点的取值是该方法的主要工作量, 当不确定性变量数为m, 并选用高斯十点法进行积分时, 需要对系统进行12$m$次分析. 算例表明, 在其他区间有限元法失效的情况下, 配点型区间有限元法依然能够得到几乎精确的区间界限.      

高温激波管化学非平衡流动数值模拟研究

为了预测氢氧定容燃烧驱动的高温激波管性能,需要准确分析激波管非定常化学非平衡流动过程.本文在破膜前的驱动段定容燃烧以及破膜后的化学非平衡流动数值模拟中,引入双时间步长方法,发展高温激波管化学非平衡流动数值模拟方法,该方法在时间上具有二阶精度.计算结果与目前存在的激波管流动解析解以及零维化学反应系统的数值解进行了比较,吻合较好.对于典型高温激波管状态,采用有限体积方法离散准一维流动Euler控制方程,并通过将流动过程和化学反应动力学过程耦合求解,获得了激波管内部的化学非平衡流动特征.     

非线性度对修正双步长显式法及常用逐步积分法的影响

为了掌握非线性度对逐步积分法的影响,研究了几种积分算法在不同非线性度振动系统中的响应。通过3个典型非线性算例,对修正双步长显式法、蛙跳式中心差分法、Newmark法、广义α法和精细积分法的计算精度和稳定性能等进行了比较。结果表明:非线性度对广义α法、精细积分法和Newmark法的稳定性有影响;高非线性度对Newmark法的计算稳定性影响最大;时间步长越小,算法精度和计算量越高;相同小步长情况下,精细积分法的精度最高,而修正双步长显式法的计算量最小;在时间步长较大时,低非线性度会引起精细积分法不稳定,修正双步长显式法的精度最高,修正双步长显式法在非线性系统中具有很强的鲁棒性。     

浅水波方程的高精度隐式WCNS格式

设计了高精度隐式WCNS格式,用于数值求解浅水波方程。方程通量导数采用四阶隐式紧致差分格式计算;半节点通量采用五阶非线性加权插值方法计算。对于含源项浅水波方程,采用特殊的源项处理,使得隐式WCNS格式具有和谐性,即在静水条件下保持流速为零,水位为常数。通过线性算例及几个经典的无源项和含源项数值算例对WCNS格式进行测试,结果表明:该格式在光滑区具有四阶精度,在间断处具有良好的捕捉激波能力,同时对于含源项问题具有保持静水条件下定常解的和谐性。     

钝头体激波诱导振荡燃烧现象的数值模拟

采用一种改进的化学非平衡流解耦方法对轴对称Euler反应流方程解耦处理,对流项采用五阶WENO格式离散,化学反应源项的刚性采用简化的隐式方法处理,时间步进采用二阶精度的Runge-Kutta方法,对H₂/Air预混气在来流Ma=4.48和Ma=4.79时的激波诱导振荡燃烧现象进行了数值研究. 对比分析了网格尺度的影响,发现计算结果对法向网格尺度比较敏感,流向网格密度的变化对结果影响不大;Ma=4.48时,采用敏感性分析方法对各反应模型进行了对比分析,J和B-W模型在实验所处的温度和压力范围内能够比较准确的预测诱导时间,所得的振荡频率与实验结果相符,所揭示的振荡机理与McVey和Toong振荡机理吻合,而JM模型预测的诱导时间偏长,其振荡频率低于实验观测值;Ma=4.79时,J模型所得的振荡频率与实验值吻合,而B-W模型释热时间短,且对流场波动比较敏感,流场扰动引起了瞬时局部爆震现象,破坏了振荡的规律性;五阶WENO空间离散格式的应用使计算结果精度较好.      

High‐order implicit Runge–Kutta time integrators for fluid‐structure interactions

This paper presents an approach to develop high‐order, temporally accurate, finite element approximations of fluid‐structure interaction (FSI) problems. The proposed numerical method uses an implicit monolithic formulation in which the same implicit Runge–Kutta (IRK) temporal integrator is used for the incompressible flow, the structural equations undergoing large displacements, and the coupling terms at the fluid‐solid interface. In this context of stiff interaction problems, the fully implicit one‐step approach presented is an original alternative to traditional multistep or explicit one‐step finite element approaches. The numerical scheme takes advantage of an arbitrary Lagrangian–Eulerian formulation of the equations designed to satisfy the geometric conservation law and to guarantee that the high‐order temporal accuracy of the IRK time integrators observed on fixed meshes is preserved on arbitrary Lagrangian–Eulerian deforming meshes. A thorough review of the literature reveals that in most previous works, high‐order time accuracy (higher than second order) is seldom achieved for FSI problems. We present thorough time‐step refinement studies for a rigid oscillating‐airfoil on deforming meshes to confirm the time accuracy on the extracted aerodynamics reactions of IRK time integrators up to fifth order. Efficiency of the proposed approach is then tested on a stiff FSI problem of flow‐induced vibrations of a flexible strip. The time‐step refinement studies indicate the following: stability of the proposed approach is always observed even with large time step and spurious oscillations on the structure are avoided without added damping. While higher order IRK schemes require more memory than classical schemes (implicit Euler), they are faster for a given level of temporal accuracy in two dimensions. Copyright © 2015 John Wiley & Sons, Ltd.     

Method of relaxed streamline upwinding for hyperbolic conservation laws

In this work a new finite element based Method of Relaxed Streamline Upwinding is proposed to solve hyperbolic conservation laws. Formulation of the proposed scheme is based on relaxation system which replaces hyperbolic conservation laws by semi-linear system with stiff source term also called as relaxation term. The advantage of the semi-linear system is that the nonlinearity in the convection term is pushed towards the source term on right hand side which can be handled with ease. Six symmetric discrete velocity models are introduced in two dimensions which symmetrically spread foot of the characteristics in all four quadrants thereby taking information symmetrically from all directions. Proposed scheme gives exact diffusion vectors which are very simple. Moreover, the formulation is easily extendable from scalar to vector conservation laws. Various test cases are solved for Burgers equation (with convex and non-convex flux functions), Euler equations and shallow water equations in one and two dimensions which demonstrate the robustness and accuracy of the proposed scheme. New test cases are proposed for Burgers equation, Euler and shallow water equations. Exact solution is given for two-dimensional Burgers test case which involves normal discontinuity and series of oblique discontinuities. Error analysis of the proposed scheme shows optimal convergence rate. Moreover, spectral stability analysis gives implicit expression of critical time step.     

Implicit solution of harmonic balance equation system using the LU-SGS method and one-step Jacobi/Gauss-Seidel iteration

ABSTRACT

This paper presents efficient alternative numerical methods for an implicit solution of the harmonic balance equation system for analysing temporal periodic unsteady flows. The proposed method employs approximate factorisation to decouple the common residual term and the time spectral source term of a harmonic balance equation system when it is discretised implicitly. With this approximate factorisation, the complexity of implicit solution of the discrete system is greatly reduced. The common residual term can be dealt with using a lower-upper symmetric-Gauss-Seidel (LU-SGS) method and the time spectral source term is integrated using a Jacobi iteration (JI) or one step Gauss-Seidel (GS) iteration, leading to the LU-SGS/JI method or LU-SGS/GS method. The NASA stage 35 compressor and the 1.5 stage Aachen turbine were used to demonstrate the effectiveness of the proposed methods in stabilising solution and its advantages in comparison with the existing lower-upper symmetric-Gauss-Seidel/block Jacobi (LU-SGS/BJ) method. The LU-SGS/GS method and the LU-SGS/JI method are more robust than the LU-SGS/BJ method in stabilising solution. The LU-SGS/GS method also has faster and tighter convergence and lower memory consumption in comparison with the LU-SGS/BJ method.     

Study of a Filtered Flamelet Formulation for Large Eddy Simulation of Premixed Turbulent Flames

Despite significant advances in the understanding and modelling of turbulent combustion, no general model has been proposed for simulating flames in industrial combustion devices. Recently, the increase in computational possibilities has raised the hope of directly solving the large turbulent scales using large eddy simulation (LES) and capturing the important time-dependant phenomena. However, the chemical reactions involved in combustion occur at very small scales and the modelling of turbulent combustion processes is still required within the LES framework. In the present paper, a recently presented model for the LES of turbulent premixed flames is presented, analysed and discussed. The flamelet hypothesis is used to derive a filtered source term for the filtered progress variable equation. The model ensures proper flame propagation. The effect of subgrid scale (SGS) turbulence on the flame is modelled through the flame-wrinkling factor. The present modelling of the source term is successfully tested against filtered direct numerical simulation (DNS) data of a V-shape flame. Further, a premixed turbulent flame, stabilised behind an expansion, is simulated. The predictions agree well with the available experimental data, showing the capabilities of the model for performing accurate simulations of unsteady premixed flames.     

条件矩模型模拟湍流扩散燃烧

对条件矩模型模拟湍流扩散燃烧进行了初步的研究.在条件矩模型中,标量的统计是以混合分数为条件的,条件平均使得非线性化学反应源项可以在一阶条件下被封闭.模拟结果和美国Sandia国家实验室的实验结果对比表明:对温度、主要组分浓度的预报结果是令人满意的,NO浓度的预报在趋势上也符合实验结果.误差分析表明,提高标量耗散率的预报精度和二阶条件矩模型都将有助于推动条件矩模型的发展.     

基于2D网格的轴对称浸没边界法

浸没边界法是处理颗粒两相流中运动边界问题的一种常用数值模拟方法. 当研究的物理问题的无量纲参数满足一定要求时, 该流场结构呈现轴对称状态. 为此本文提出了一种基于2D笛卡尔网格和柱坐标系的轴对称浸没边界法. 该算法采用有限体积法(FVM)对动量方程进行空间离散, 并通过阶梯状锐利界面替代真实的固体浸没边界来封闭控制方程. 为了提高计算效率, 本文采用自适应网格加密技术提高浸没边界附近网格分辨率. 由于柱坐标系的使用, 使得动量方程中的黏性项产生多余的源项, 我们对其作隐式处理. 此外, 在对小球匀速近壁运动进行直接数值模拟时, 由于球壁间隙很小, 间隙内的压力变化比较剧烈. 因此想要精确地解析流场需要很高的网格分辨率. 此时, 需要在一个时间步内多次实施投影步来保证计算的稳定性. 而在小球自由碰壁运动中, 我们通过引入一个润滑力模型使得低网格分辨率下也能模拟小球近壁处的运动. 最后通过小球和圆盘绕流、Stokes流小球近壁运动以及小球自由下落碰壁弹跳算例验证本算法对于轴对称流的静边界和动边界问题均是适用和准确的.      

甲烷气体的冲击化学反应流研究

用二级轻气炮加载技术将W89Mo9Ni1Fe1飞片加速到约5.0km/s,撞击封装有接近常态的甲烷气体的LY12铝靶。利用六通道高温计和示波器记录到冲击压缩的甲烷气体的光辐射历史曲线,并获得甲烷气体的冲击波速度与温度。利用一维Euler方程与化学反应方程的全流场耦合,采用甲烷体系的13组元40反应步的化学反应模型,并用3阶WENO数值格式对空间进行离散。为避免刚性过强,化学反应源项用点隐方法处理。由此得到了甲烷的冲击反应流场和波后热力学参数。通过比较,数值结果与实验结果符合较好。最后,解释了甲烷用作电探针保护气体的物理机制。     

On unconditionally positive implicit time integration for the DG scheme applied to shallow water flows

We present a new unconditionally positivity‐preserving (PP) implicit time integration method for the DG scheme applied to shallow water flows. This novel time discretization enhances the currently used PP DG schemes, because in the majority of previous work, explicit time stepping is implemented to deal with wetting and drying. However, for explicit time integration, linear stability requires very small time steps. Especially for locally refined grids, the stiff system resulting from space discretization makes implicit or partially implicit time stepping absolutely necessary. As implicit schemes require a lot of computational time solving large systems of nonlinear equations, a much larger time step is necessary to beat explicit time stepping in terms of CPU time. Unfortunately, the current PP implicit schemes are subject to time step restrictions due to a so‐called strong stability preserving constraint. In this work, we hence give a novel approach to positivity preservation including its theoretical background. The new technique is based on the so‐called Patankar trick and guarantees non‐negativity of the water height for any time step size while still preserving conservativity. In the DG context, we prove consistency of the discretization as well as a truncation error of the third order away from the wet–dry transition. Because of the proposed modification, the implicit scheme can take full advantage of larger time steps and is able to beat explicit time stepping in terms of CPU time. The performance and accuracy of this new method are studied for several classical test cases. Copyright © 2014 John Wiley & Sons, Ltd.     

Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations

This investigation is concerned with the use of an implicit integration method with adjustable numerical damping properties in the simulation of flexible multibody systems. The flexible bodies in the system are modeled using the finite element absolute nodal coordinate formulation (ANCF), which can be used in the simulation of large deformations and rotations of flexible bodies. This formulation, when used with the general continuum mechanics theory, leads to displacement modes, such as Poisson modes, that couple the cross section deformations, and bending and extension of structural elements such as beams. While these modes can be significant in the case of large deformations, and they have no significant effect on the CPU time for very flexible bodies; in the case of thin and stiff structures, the ANCF coupled deformation modes can be associated with very high frequencies that can be a source of numerical problems when explicit integration methods are used. The implicit integration method used in this investigation is the Hilber–Hughes–Taylor method applied in the context of Index 3 differential-algebraic equations (HHT-I3). The results obtained using this integration method are compared with the results obtained using an explicit Adams-predictor-corrector method, which has no adjustable numerical damping. Numerical examples that include bodies with different degrees of flexibility are solved in order to examine the performance of the HHT-I3 implicit integration method when the finite element absolute nodal coordinate formulation is used. The results obtained in this study show that for very flexible structures there is no significant difference in accuracy and CPU time between the solutions obtained using the implicit and explicit integrators. As the stiffness increases, the effect of some ANCF coupled deformation modes becomes more significant, leading to a stiff system of equations. The resulting high frequencies are filtered out when the HHT-I3 integrator is used due to its numerical damping properties. The results of this study also show that the CPU time associated with the HHT-I3 integrator does not change significantly when the stiffness of the bodies increases, while in the case of the explicit Adams method the CPU time increases exponentially. The fundamental differences between the solution procedures used with the implicit and explicit integrations are also discussed in this paper.