The morphology of ice-structure in a planar nozzle subjected to forced internal convection flow

The present paper deals with the ice-formation in a planar nozzle with various convergence angles. Experiments have been carried out for different wall cooling parameters B in the range between 4 and 25 and for different flow rate Reynolds numbers in the range of 5,000 < Re _4h  < 50,000 for two different convergence angles of the nozzle. For all experiments with the larger convergence angle of the nozzle (2.5°), only smooth ice-layers could be observed. However, for the nozzle with the smaller convergence angle (1.25°), also wavy ice-layers could be detected. This interesting result is a justification for the hypothesis that the formation of wavy ice-layers is caused by flow laminarisation (due to the rapid growth in ice-layer thickness with increasing axial position from the inlet) and retransition to the fully turbulent state (after the acceleration falls below a certain critical value). Thus, this paper proves for the first time, that wavy ice-layers are suppressed by superimposed strong flow acceleration.     

Transient freezing of liquids in forced laminar flow inside a parallel plate channel

A simple analytical approximative solution was given for calculating the time dependent development of the ice-layers at the cooled walls inside a parallel plate channel. By ignoring the effect of acceleration, resulting from converging ice-layers in the axial direction, an analytical solution for the variation of the ice-layer thickness with time and axial position could be obtained. The approximative solution was checked by numerical calculations and good agreement was found.Es wurde ein analytisches Näherungsverfahren entwickelt, das es ermöglicht, die zeitliche Entwicklung der Erstarrungsfronten im gekühlten, ebenen Kanal zu bestimmen. Die Methode liefert unter Vernachlässigung der Beschleunigungsterme durch die konvergenten Eisschichten eine exakte Lösung der Phasengrenzbeziehung. Das Näherungsverfahren wurde mittels numerischer Berechnungen überprüft und stimmt bis zu Wandunterkühlungsverhältnissen vonB=10 sehr gut mit der numerischen Lösung überein.     

Heat transfer and solidification of a laminar liquid flow in a cooled parallel plate channel: The stationary case

A simple numerical model is presented to predict the steady-state ice layers on the cooled walls inside a parallel plate channel for arbitrary entrance velocity profiles. The effect of two different entrance velocity distributions (a parabolic velocity distribution and a slug flow) on the shape of the ice-layers are examined. The quality of an approximative solution given in literature was checked by comparing with the numerical results. For the case of a fully developed parabolic velocity distribution at the entrance of the cooled channel the results are compared with experimental findings of Kikuchi [8]. A generally good agreement was found.Es wurde ein einfaches numerisches Modell entwickelt, das es ermöglicht, die stationären Erstarrungsfronten an den Kanalwänden für beliebige Verteilungen des Eintrittsgeschwindigkeitsprofils zu berechnen. Als Beispiele wurden ein voll ausgebildetes Parabelprofil und ein Pfropfenprofil am Eintritt in die Kühlstrecke untersucht. Mit Hilfe der numerischen Lösung konnte die Güte einer aus der Literatur bekannten Näherungslösung zur Berechnung der Erstarrungsfronten überprüft werden. Für den Fall des Parabelprofils am Kanaleintritt wurde die Rechnung mit Meßwerten von Kikuchi [8] verglichen. Es zeigte sich eine gute Übereinstimmung zwischen Theorie und Experiment.     

Single-exposure neutron tomography of two-phase flow

A method is presented for measuring the phase density distribution at a cross-section of a gas-liquid flow system. The method utilizes the information carried by measured fluences of scattered fast neutrons. Reconstruction of the local density distribution is viewed as an inverse problem and a numerical method is developed for solving this problem. The physical and practical aspects of the problem are considered and some numerical and experimental results are presented.     

关于变分不等式问题近似解的数值证明

基于文献[1]给出了一种数值证明变分不等式解的存在性方法。通过Hilbert空间中的Riesz表示定理,首先将变分不等式问题的迭代过程转化为一种不动点形式,再利用Schauder不动点定理构造了一个高效率的数值证明过程,即通过数值计算产生一个包含近似解的有界闭凸子集。非线性Helmholtz方程的算例说明这一方法的可行性和高效性。     

An efficient Legendre-Galerkin spectral method for the natural convection in two-dimensional cavities

An efficient numerical method is developed for solving the natural convection in two-dimensional cavities. The numerical scheme is proposed by using second-order projection scheme in time direction and Legendre-spectral in spatial variable of the incompressible flow. Finally, a series of numerical examples are presented to demonstrate the efficiency of our algorithm. The numerical strategies developed in this article could be readily applied to study other incompressible fluid problems.     

Falkner-Skan方程的近似解析解

研究了粘性流体绕流楔型物体的Falkner-Skan边界层方程求解问题.利用Adomian拆分方法,通过引入Crocco变量变换将无穷区间的边界值问题转为初值问题并利用Padé逼近技巧确定初值,给出了一种有效的解析分解方法.进一步,本文设计了一种数值解法,将本文得到的近似解析解及数值结果与早期研究者Hartree等人的结果进行了比较,证明了本文提出的解法的有效性和可靠性.     

On TVD difference schemes for the three-dimensional Euler equations in general co-ordinates

An improved treatment for the Harten–Yee and Chakravarthy–Osher TVD numerical flux functions in general co-ordinates is presented. The proposed formulation is demonstrated by a series of numerical experiments for three-dimensional flows around the ONERA-M6 wing. The numerical results indicate that it is important to use a suitable artificial compression parameter in order to obtain more accurate solutions around the leading edge of the wing. The two TVD numerical fluxes give excellent results: they capture the shock wave without numerical oscillations, they capture the rapid expansion around the leading edge sharply, they have self-adjusting mechanisms regarding numerical viscosity and they also have robustness.     

Investigation of flux formulae in transonic shock wave/turbulent boundary layer interaction

The aim of the present study is to examine the accuracy and improvement of various numerical methods in the solution of the transonic shock/turbulent boundary layer interaction problem and to show that a significant source of numerical inaccuracies in turbulent flows is not only the inadequacy of the turbulence model but also the numerical discretization. Comparisons between a Riemann solver and a flux-vector-splitting method as well as between various numerical high-order extrapolation schemes with corresponding experimental results are presented.     

Simulation of Three-Dimensional Bluff-Body Flows Using the Vortex Particle and Boundary Element Methods

Recent contributions to the 3-D vortex method for bluff-body flows are presented. The numerical method--a vortex method combined with a boundary element method--is briefy reviewed. It is applied to direct numerical simulation (DNS) of the flow past a sphere (Re= 300, 500 and 1000). The on-going work to extend the method towards vortex-based large-eddy simulation (LES) for high Reynolds number flows is also presented. Preliminary results for the flow past a hemisphere are discussed.     

Engineering Models for Numerical Analysis of Composite Bending Members∗

Abstract

ABSTRACT The two-step numerical analysis of a composite beam structure is presented in this paper. The first step, based on the idea of dividing the cross section into laminas, leads to the estimation of the moment-curvature relation for different types of cross sections used in composite beams. The second step adopts this constitutive relation, which is expressed in the space of generalized stresses and strains, into finite element nonlinear code. Some numerical examples are given, to show the agreement of numerical calculations with results of the authors' experiments, when the shrinkage of a concrete encasement and stresses due to welding processes in steel beams are considered. In addition, the numerical concept presented here seems to reduce the sensitivity of the final results obtained to finite element discretization error.     

Covariant principal axis formulation of associated coupled thermoplasticity at finite strains and its numerical implementation

In this work we discuss a covariant formulation of the finite strain viscoplasticity in a fully coupled thermomechanical setting. The formulation is presented within the framework of the principal axis methodology, which leads to a very efficient numerical implementation. Several numerical simulations, dealing with fully coupled thermomechanical response at large viscoplastic strains and including both strain localization and cyclic loading cases, are presented in order to illustrate a very satisfying performance of the proposed methodology.     

Flux difference splitting for open-channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.     

带源参数的二维热传导反问题的无网格方法

利用无网格有限点法求解带源参数的二维热传导反问题,推导了相应的离散方程. 与 其它基于网格的方法相比,有限点法采用移动最小二乘法构造形函数,只需要节点信息,不 需要划分网格,用配点法离散控制方程,可以直接施加边界条件,不需要在区域内部求积分. 用有限点法求解二维热传导反问题具有数值实现简单、计算量小、可以任意布置节点等优点. 最后通过算例验证了该方法的有效性.     

The numerical solution of a singularly perturbed problem for quasilinear parabolic differential equation

We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L~2 norm is proved and numerical examples are presented.     

On dual-grid level-set method for contact line modeling during impact of a droplet on hydrophobic and superhydrophobic surfaces

In this paper, a numerical methodology for modeling contact line motion in a dual-grid level-set method (DGLSM) – solved on a uniform grid for interface which is twice that for the flow equations – is presented. A quasi-dynamic contact angle model – based on experimental inputs – is implemented to model the dynamic wetting of a droplet, impacting on a hydrophobic or a superhydrophobic surface. High-speed visualization experiments are also presented for the impact of a water droplet on hydrophobic surfaces, with non-bouncing at smaller and bouncing at larger impact velocity. The experimental results for temporal variation of the droplet shapes, wetted-diameter and maximum height of the droplet match very well with the DGLSM based numerical results. The validation of the numerical results is also presented with already published experimental results, for the non-bouncing on a hydrophobic and bouncing on a superhydrophobic surface, at a constant impact velocity. Finally, a qualitative as well as quantitative performance of the DGLSM as compared to the traditional level set method (LSM) is presented by considering our experimental results. The accuracy of the partially refined DGLSM is close to that of the fine-grid based LSM, at a computation cost which is close to that of the coarse-grid based LSM. The DGLSM is demonstrated as an improved LSM for the computational multi-fluid dynamics (CMFD) simulations involving contact line motion.     

Numerical and experimental investigations of micromechanical processes during wire sawing

In the following paper the mechanisms of the slurry-based wire sawing process at micro level are studied by numerical simulations. For the simulation a new approach in simulating the wire sawing process is presented. A discrete element method (DEM) with polyhedral particles is used to simulate the movement of the abrasive particles as well as the wire during the process. The results are verified by direct observations of the sawing channel of an experimental setup. The presented numerical model is applied for a detailed study of the influence of different process parameters.     

施工期混凝土浇筑块的脆弹性徐变应力分析

本文将线性徐变理论和脆弹性破坏模型相结合,推导出计算混凝土浇筑块温度徐变应力的非线性有限元递推公式,并编制了计算机程序。最后以东江拱坝基础部分浇筑块为例进行了分析计算。     

流形Trefftz直接法

基于数值流形方法,结合广义节点的概念,构造了一类节点位移用任意阶多项式展开的流形Trefftz直接法。这种方法融合了数值流形方法和Trefftz直接法的优点。计算结果表明,流形Trefftz直接法与Trefftz直接法以及其他计算方法相比有较高的精度。     

跨音叶栅流场中Euler方程的对角化隐式算法

本文在非因式分解隐式通量分裂有限面积法的基础81提出了一种单向隐式对角化算法,并给出了相应的固壁边界条件的一种精确的隐式处理方法.数值结果表明,这种方法是高效率的。