Blue sky catastrophe in double-diffusive convection

A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The catastrophe corresponds to the destruction of an orbit which, for a large range of Rayleigh numbers, is the only stable solution. This orbit is born in a global saddle-loop bifurcation and becomes chaotic in a period-doubling cascade just before its disappearance at the blue sky catastrophe.     

Bifurcations in a model of double-diffusive convection

A truncated fifth-order model has been solved numerically. In certain parameter regimes there is a bifurcation from symmetrical to asymmetrical oscillations, leading to a period-doubling cascade which is followed immediately by a period-halving cascade and a bifurcation back to symmetry.     

Acoustic scattering from double-diffusive microstructure

Laboratory measurements of high-frequency broadband acoustic backscattering (200-600 kHz) from the diffusive regime of double-diffusive microstructure have been performed. This type of microstructure, which was characterized using direct microstructure and optical shadowgraph techniques, is identified by sharp density and sound speed interfaces separating well-mixed layers. Vertical acoustic backscattering measurements were performed for a range of physical parameters controlling the double-diffusive microstructure. The echoes have been analyzed in both the frequency domain, providing information on the spectral response of the scattering, and in the time domain, using pulse compression techniques. High levels of variability were observed, associated with interface oscillations and turbulent plumes, with many echoes showing significant spectral structure. Acoustic estimates of interface thickness (1-3 cm), obtained for the echoes with exactly two peaks in the compressed pulse output, were in good agreement with estimates based on direct microstructure and optical shadowgraph measurements. Predictions based on a one-dimensional weak-scattering model that includes the actual density and sound speed profiles agree reasonably with the measured scattering. A remote-sensing tool for mapping oceanic microstructure, such as high-frequency broadband acoustic scattering, could lead to a better understanding of the extent and evolution of double-diffusive layering, and to the importance of double diffusion to oceanic mixing.     

温盐双扩散均衡场中的振荡现象

在一种简单的边界加密的坐标变换下,用高精度的差分法研究了温盐双扩散系统.为了保证求解的稳定性和精确性,对流项采用了四阶精度的迎风格式,扩散项和涡量方程的浮力项则采用四阶精度的中心差.首先针对温度占优(Rρ=032)和盐度占优(Rρ=168)的情形进行了计算,得到了与文献[2]和[12]一致的结果,从而验证方法的正确性.其次系统地给出了不同Lewis数下的流动形态,包括稳定的对称结构、周期性振荡结构和非周期非对称的随机运动形态 关键词： 温盐双扩散 高精度格式 周期性振荡结构     

Granular fingers on jammed systems: new fluidlike patterns arising in grain-grain invasion experiments

In this Letter we report spontaneous pattern formation in dense granular assemblies confined to a Hele-Shaw cell and quasistatic regime. Varied unexpected patterns, ranging from rounded to fingered, are observed due to the displacement of one granular material by another. Computer simulations reproduce the major features observed in these experiments. Two mechanisms are responsible for the pattern formation: crystallization of the injected grains and plastic deformation of the displaced grains. The experiment suggests analogies with viscous fingering and jamming transition experiments.     

Some properties of two-dimensional stochastic regimes of double-diffusive convection in plane layer

The existence of a two-dimensional attracting manifold is established for trajectories emanating from the vicinity of static solution. The structure of this manifold is studied with the help of succession map of points in intersection of trajectories with some coordinate plane. The structure of the attracting manifold varies depending on Rayleigh numbers of heat and salinity. With growth of Rayleigh numbers of heat and salinity the structure of one-dimensional curve becomes more irregular and sophisticated. The convergence of Bubnov-Galerkin approximation with a large number of basic functions was demonstrated in norms of kinetic energy, dissipation function, and directly by norm evaluation of the residual (noncompensated terms in substitution of Bubnov-Galerkin approximation to the initial double-diffusive convection system).     

Influence of thermal boundary conditions on the double-diffusive process in a binary mixture

This paper presents a precise numerical simulation of the transport processes in a rectangular cavity saturated with a binary liquid mixture. The full transient Navier-Stokes equations coupled with the mass and heat transfer equations are solved, numerically, using the finite-volume method. After validation against a proven commercial code comparing solutions on a benchmark natural convection problem, the newly developed code is used for a series of numerical experiments. Realistic thermal boundary conditions have been chosen, and the more drastic situation of power loss while conducting the experiment in microgravity is considered. The molecular and thermal diffusion coefficients are computed from theoretical models. Results reveal that, when vertical walls are held at constant but different temperatures, species separate in both the longitudinal and the transverse directions as radiation is allowed to take place along the horizontal walls. The numerical experiments performed clearly demonstrate that the kinetics of the mass transport in the mixture are conditioned by the ability to monitor the heat sources properly. Specifically, sudden temperature changes strongly disturb species separation in the experimental cells. This paper provides some trends for the accurate analysis of experiments involving mass transport inasmuch as the convective level is low enough to allow evaluation of the transport coefficients.     

Competition between anisotropic viscous fingers

We consider viscous fingers created by injection of low viscosity fluid into the network of capillaries initially filled with a more viscous fluid (motor oil). Due to the anisotropy of the system and its geometry, such a setup promotes the formation of long-and-thin fingers which then grow and compete for the available flow, interacting through the pressure field. The interaction between the fingers is analyzed using the branched growth formalism of Halsey and Leibig (Phys. Rev. A 46, 7723, 1992) using a number of simple, analytically tractable models. It is shown that as soon as the fingers are allowed to capture the flow from one another, the fixed point appears in the phase space, corresponding to the asymptotic state in which the growth of one of the fingers in hindered by the other. The properties of phase space flows in such systems are shown to be remarkably insensitive to the details of the dynamics.     

Mesoscopic analysis of heatline and massline during double-diffusive MHD natural convection in an inclined cavity

Double-diffusive natural convection in an inclined cavity with the presence of magnetic field is studied numerically via heatline and massline approach. The governing equations are discretized using the Lattice Boltzmann Method (LBM). In this investigation, the controlling parameters involved are Rayleigh number (10³ ≤ Ra ≤ 10⁵), buoyancy ratio (−5 ≤ N ≤ 5), cavity inclination angle (0° ≤ Ø ≤ 180°), Lewis number (2 ≤ Le ≤ 10), Prandtl number (Pr = 5.0) and Hartmann number (0 ≤ Ha ≤ 50). The numerical results obtained by the effect of parameters mentioned above are reported as contours of streamlines, isotherms, isoconcentrations, heatlines, and masslines. The obtained results are compared with the existing literature to validate the coding. The heat and mass transfer rate decrease with increasing the magnetic field and increase with an increase in Rayleigh number. The impact of Ø is maximum for higher Ra and negligible for lower Ra (10³). Increasing Le influences the mass transfer rate to increase and heat transfer to reduce for both opposing and aiding flow.     

Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below

Linear stability analysis of Maxwell fluid in the Bénard problem for a double-diffusive mixture in a porous medium is studied based on the Darcy-Maxwell model. The critical Rayleigh number and the corresponding wave number for the exchange of stability are obtained. On the other hand, the effect of the relaxation time of Maxwell fluid on the critical Rayleigh number is discussed. In limiting cases, some results published previously are recovered from our results.     

A nonlinear stability analysis of a double-diffusive magnetized ferrofluid with magnetic field-dependent viscosity

A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic field-dependent (MFD) viscosity, for stress-free boundaries. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter, M₃, solute gradient, S₁ and MFD viscosity parameter, δ, on the subcritical instability region have also been analyzed.     

Periodic adhesive fingers between contacting cells

We study in detail the properties of fingers, a particular type of cell-cell adhesive structures appearing in adherens junctions. These periodic patterns break the symmetry of cell-cell contacts. We show that finger formation is driven by cadherin interactions and actin growth. A theoretical model is introduced in which the growth of fingers is limited by membrane tension. The steady shape and formation kinetics of fingers are experimentally measured and compared with the theoretical predictions.     

Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media

A model for double-diffusive convection in a heterogeneous porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source using the Brinkman model. In particular, we analyse the effect of slip boundary conditions on the stability of the model. Because of the many applications in micro-electro-mechanical systems (MEMS) and other microfluidic devices, a study of this problem is necessary. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient.     

Radially interrupted viscous fingers in a lifting Hele-Shaw cell

Viscous fingers have been produced in the lifting Hele-Shaw cell (LHSC), with concentric circular grooves etched onto the lower plate. The invading fluid (air) enters the defending newtonian fluid-olive oil, as fingers proceeding radially inwards towards the centre. The fingers are interrupted at the circular groove, and reform as secondary fingers. The effect of the grooves is to speed up the fingering process considerably and the fingers now reach the centre much faster. We explain this by comparing the variation with time, in velocity of the fingers in the normal LHSC and the grooved cells. In the normal lifting HS cell the fingers move fastest on initial formation and slow down later. Since in case of the grooved plate, the fingers reform and receive a boost in their speed each time they encounter a groove, the fingers proceed to the centre faster.Received: 14 August 2003, Published online: 23 December 2003PACS: 47.20.Gv Viscous instability - 47.54. + r Pattern selection; pattern formation - 68.03.-g Gas-liquid and vacuum-liquid interfaces     

多喷嘴氦冷偏滤器的优化与分析

利用ANSYS/CFX对聚变堆氦冷多喷嘴冷却偏滤器模块在相同高热负荷条件但不同冷却条件下进行了有限元数值分析,得到了偏滤器冷却单元的温度和换热系数分布图,将该温度场作为结构力学分析的加载条件,利用ANSYS/Mechanical对冷却模块进行了稳态条件下的结构应力分析,得到了具有不同结构参数的偏滤器模块的应力分布。通过分析各结构参数对偏滤器模型的热应力的影响,对结构参数进行筛选,得到内应力相对较低的结构设计,从而优化多喷嘴氦冷偏滤器结构。     

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利用ANSYS/CFX对聚变堆氦冷多喷嘴冷却偏滤器模块在相同高热负荷条件但不同冷却条件下进行了有限元数值分析,得到了偏滤器冷却单元的温度和换热系数分布图,将该温度场作为结构力学分析的加载条件,利用ANSYS/Mechanical对冷却模块进行了稳态条件下的结构应力分析,得到了具有不同结构参数的偏滤器模块的应力分布.通过分析各结构参数对偏滤器模型的热应力的影响,对结构参数进行筛选,得到内应力相对较低的结构设计,从而优化多喷嘴氦冷偏滤器结构.