Instability results related to compressible Korteweg system

This paper presents the study of surface tension effects in compressible mixtures in the framework of diffuse interface models. In the first part, we describe results previously obtained on the so-called compressible Korteweg and shallow water models and we present nonlinear stability using energy estimates and a new entropy equality recently discovered. These diffuse interface models also allow to take account of capillarity effects in turbulent mixtures and plasma flows subject to Rayleigh–Taylor instabilities. The aim of the last part is to study the influence of surface tension on this instability phenomena. More precisely we look at the expression of the growth rate under a small perturbation of wave number k. We prove that for an appropriate choice of the capillary number σ in terms on the surface tension coefficient T _s (that means particular pressure laws), we find the same expression as for the two incompressible fluids model with surface tension coefficient on a sharp interface studied for instance by Chandrasekhar (Hydrodynamic and hydromagnetic stability. Dover Publications, Inc. New York, 1981). The first author would like to thank the CEA/DAM (Bruyères le Chatel, France) for its financial support through the contract no. 4600052302/P6H28. He is also partially supported by the IDOPT project in Grenoble and the “ACI jeunes chercheurs 2004” du ministère de la Recherche “études mathématiques de paramétrisations en océanographie”.     

流体可压缩性对Rayleigh-Taylor不稳定性影响机理分析

在等熵方程为压力是密度的任意单值函数形式情况下 ,分析了R T(Rayleigh Taylor)不稳定性中流体可压缩性的作用。在没有边界效应的条件下所作的分析表明 :在重力场作用下流体可压缩性形成的密度分布是R T不稳定性中的致稳因素 ,而扰动流体的膨胀 (收缩 )效应助长R T不稳定性的发展 ;上层重流体的可压缩性是稳定因素 ,而下层轻流体的可压缩性是失稳因素。从扰动发展驱动力和扰动带动的等效质量两个方面对该结论的物理机制进行了分析。     

关于无振荡、无自由参数有限元格式的研究

利用双曲守恒律方程的Ｔａｙｌｏｒ弱解表达式，建立了有限元法修正方程，选择合适的展开式系数能得到一系列数值格式．通过稳定性分析研究了格式的稳定性、色散误差与有限元修正方程导数项系数之间的关系，该关系与差分法的ＮＮＤ格式一致．在选定格式下，通过ＣＦＬ数可控制有限元离散解的振荡而使格式不含自由参数．最后，用数值算例验证了这一关系，并在二、三维欧拉方程作了推广应用．     

On the dynamics and instability of bubbles formed during underwater explosions

Dynamics of explosion bubbles formed during underwater detonations are studied experimentally by exploding fuel (hydrogen and/or carbon monoxide)–oxygen mixture in a laboratory water tank. Sub-scale explosions are instrumented to provide detailed histories of bubble shape and pressure. Using geometric and dynamic scaling analyses it has been shown that these sub-scale bubbles are reasonable approximations of bubbles formed during deep sea underwater explosions. The explosion bubble undergoes pulsation and loses energy in each oscillation cycle. The observed energy loss, which cannot be fully explained by acoustic losses, is shown here to be partly due to the excitation of instability at the interface between the gaseous bubble and the surrounding water. Various possible mechanisms for the dissipation of bubble energy are addressed. The analysis of the experimental data gives quantitative evidence (confirmed by recent numerical studies) that the Rayleigh–Taylor instability is excited near the bubble minimum. The dynamics of the bubble oscillation observed in these experiments are in good agreement with experimental data obtained from deep sea explosions     

HC轧机辊间接触与辊系变形的Taylor级数多极边界元数学规划解析

分析HC轧机辊间接触分布和辊系弹性变形对于改善辊间压力分布状态,减少轧故褂檬倜案纳瓢逍畏浅Ｖ匾?醯捎诩扑懔亢艽?使用传统数值方法(有限元法或边界元法)分析辊间接触和辊系变形是非常困难的.本文描述了一种基于点-面接触模型的三维弹性接触Taylor级数多极边界元法,给出了数学规划解析方法,适合大规模弹性接触问题的求解....     

JOB-9003的动态性能实验

对JOB-9003进行了SHPB压杆实验和逆向Taylor柱实验,研究其在冲击载荷下的动态特性,为进行JOB-9003的本构模型研究提供实验数据基础。通过对SHPB实验获得的应力应变曲线分析得出:在中低应变率范围,JOB-9003应变率对应力的影响成线性关系。通过对逆向Taylor柱实验获得的变形照片分析,发现破坏损伤对材料的力学性能影响显著,不可忽略。利用Taylor实验的结果对SHPB实验中获得的本构模型进行校核,发现该本构模型并不能准确描述处于高应变率下的材料压缩变形。     

Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall

Periodic wall oscillations in the spanwise or circumferential direction can greatly reduce the friction drag in turbulent channel and pipe flows. In a concentric annulus, the constant rotation of the inner cylinder can intensify turbulence fluctuations and enhance skin friction due to centrifugal instabilities. In the present study, the effects of the periodic oscillation of the inner wall on turbulent flows through concentric annulus are investigated by the direct numerical simulation (DNS). The radius ratio of the inner to the outer cylinders is 0.1, and the Reynolds number is 2 225 based on the bulk mean velocity U_m and the half annulus gap H. The influence of oscillation period is considered. It is found that for short-period oscillations, the Stokes layer formed by the circumferential wall movement can effectively inhibit the near-wall coherent motions and lead to skin friction reduction, while for long-period oscillations, the centrifugal instability has enough time to develop and generate new vortices, resulting in the enhancement of turbulence intensity and skin friction.     

On the time development of dispersion in electroosmotic flow through a rectangular channel

This is an analytical study on the time development of hydrodynamic dispersion of an inert species in electroosmotic flow through a rectangular channel.The objective is to determine how the channel side walls may affectthe dispersion coefficient at different instants of time.Tothis end,the generalized dispersion model,which is valid forshort and long times,is employed in the present study.Analytical expressions are derived for the convection and dispersion coefficients as functions of time,the aspect ratio ofthe channel,and the Debye-Hu¨ckel parameter representingthe thickness of the electric double layer.For transport ina channel of large aspect ratio,the dispersion may undergoseveral stages of transience.The initial,fast time development is controlled by molecular diffusion across the narrowchannel height,while the later,slower time development isgoverned by diffusion across the wider channel breadth.Fora sufficiently large aspect ratio,there can be an interludebetween these two periods during which the coefficient isnearly steady,signifying the resemblance of the transportto that in a parallel-plate channel.Given a sufficiently longtime,the dispersion coefficient will reach a fully-developedsteady value that may be several times higher than that without the side wall effects.The time scales for these periods oftransience are identified in this paper.     

Wave angle for oblique detonation waves

The flow field associated with a steady, planar, oblique detonation wave is discussed. A revision is provided for- diagrams, where is the wave angle and is the ramp angle. A new solution is proposed for weak underdriven detonation waves that does not violate the second law. A Taylor wave, encountered in unsteady detonation waves, is required. Uniqueness and hysteresis effects are also discussed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

The distribution of values of taylor series

Clarify some classical results and their proofs on the distribution of values of simple Taylor series and extend them to multiple Taylor series.