A VORTICITY–STREAMFUNCTION FORMULATION FOR STEADY INCOMPRESSIBLE TWO-DIMENSIONAL FLOWS

A vorticity–streamfunction formulation for incompressible planar viscous flows is presented. The standard kinematic field equations are discretized using centred finite difference schemes and solved in a coupled way via a Newton-like linearization scheme. The linearized system of partial differential equations is handled through the restarting linear GMRES algorithm, preconditioned by means of an incomplete LU approximate factorization. The proposed solution technique constitutes a fast and robust algorithm for treating laminar flows at high Reynolds numbers. The pressure field is obtained at a subsequent step by solving a convection– diffusion equation in terms of the stagnation pressure, which presents certain advantages compared with the widely used static pressure Poisson equation. Results are shown for a wide variety of applications including internal and external flows.     

Prediction of resolvent mode shapes in supersonic turbulent boundary layers

This work applies resolvent analysis to compressible zero-pressure-gradient turbulent boundary layers with freestream Mach numbers between 2 and 4, focusing exclusively on large scale motions in the outer region of the boundary layer. We investigate the effects of Mach number on predicted flow structures, and in particular, look at how such effects may be attributed to changes in mean properties. By leveraging the similarity between the compressible and incompressible resolvent operators, we show that the shape of the streamwise velocity and temperature components of resolvent response modes in the compressible regime can be approximated by applying ideas from wavepacket pseudospectral theory to a simple scalar operator. This gives a means of predicting the shape of resolvent mode components for compressible flows without requiring the singular value decompositions of discretized operators. At a Mach number of 2, we find that accurate results are obtained from this approximation when using the compressible mean velocity profile. At Mach numbers of 3 and 4, the quantitative accuracy of these predictions is improved by also considering a local effective Reynolds number based on the local mean density and viscosity.     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

颗粒流的动力学模型和实验研究进展

首先叙述了颗粒流研究的背景和基本概念,接着概述了颗粒流动力学研究的三种基本数学力学模型:颗粒动理论(kinetic theory)模型、摩擦塑性模型和离散元模拟模型.介绍了它们的基本原理,并分析了各个模型的优缺点和适用范围.随之,对颗粒流的实验研究情况作了简要的介绍,列举了研究中几种常用的试验方法和观测手段,以及观测到的一些典型现象.最后,我们简述了颗粒流研究的主要困难,并提出了某些有待解决的研究课题.      

5.12汶川大地震诱发大型崩滑灾害动力特征初探

对乙炔氧气混合气体中爆轰波与激波的正面对撞现象的实验研究是以高速摄影获 取两波对撞的x-t纹影图,以烟迹板记录对撞中的爆轰胞格图案,并基于激波 理论和经典CJ爆轰理论求解了两波对撞的稳态解并探寻其规律. 研究发现透射波系包括一道激波和爆轰波, 以及紧随爆轰波后的稀疏波区,这一结果对应于一维理论分析中的CJ解. 透射波系基本不受 初始压强影响;初始温度也只成比例地改变流场整体速度,温度越高,速度越快;对波系起 实质影响作用的是入射激波强度,激波越强,则整个透射流场呈现偏向激波的趋势;理论分 析还指出,稀疏波区的出现不可避免,当激波强度趋于声波稀疏波区趋于消失,激波越强则 疏波区趋于扩大. 两波对撞存在一个有限的转变阶段,透射爆轰首先减缓,接着迅速迸发为 过驱爆轰,然后再逐渐平衡为CJ爆轰. 对于强不稳定的燃气,对撞后爆轰波在空间上的发展 极不均衡,一些区域发生火焰面与诱导激波的严重脱离,随后的火焰面失稳发展为诱导激波 区内的爆轰波,实验观察到了这种爆轰在烟迹板上留下的极为精细的迹线.     

各向异性浮力紊流的显式代数应力模型及其验证

在Wallin & Johansson的显式代数雷诺应力模型(EARSM)基础上,引入浮力的紊动效应,使该模型能够反映浮力对紊流运动的影响.利用同位网格上的SIMPLEC算法,模拟了T-型连接管内的温度混合流动.与实验资料和DNS计算结果比较表明,提出的模型能够反映各向异性的浮力紊流特征,而且模型在计算进程中显示出良好的数值收敛性能,与涡粘性两方程模型的计算花费相当.     

Numerical analysis of conservative unstructured discretisations for low Mach flows

Unstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell‐centred velocity reconstructions, the standard first‐order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd–even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable‐density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy‐preserving scheme is applied to the momentum equations, namely, the symmetry‐preserving scheme. Furthermore, a new approach to define the far‐neighbouring nodes of the quadratic upstream interpolation for convective kinematics scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self‐igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable‐density flows. Furthermore, the quadratic upstream interpolation for convective kinematics scheme shows close to second‐order behaviour on unstructured meshes, and the symmetry‐preserving is reliably used in all computations. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite element and sensitivity analysis of thermally induced flow instabilities

This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.