Interaction d'un écoulement de thermosiphon avec un panache thermique à symétrie axiale: étude expérimentale

The present work reports an experimental study of a thermosiphon effect on an axisymmetric thermal plume. An experimental apparatus composed of a circular disc heated at constant temperature was set up. The disc is placed at the entrance to an open-ended vertical cylinder of larger diameter. Thermal radiation emitted by the hot disc heats the cylinder wall. The heating of fluid to the cylinder-inlet is the cause of the thermosiphon effect around the thermal plume. First, we studied the flow generated by the thermal plume. The analysis of the average fields of velocity and temperature shows that the structure of a thermal plume generated by a hot obstacle is affected by the characteristics of the main flow around this obstacle. Furthermore, these results allowed us to rediscover the two classical zones which constitute a thermal plume. Secondly, we studied the thermosiphon effect on the thermal plume development. The average fields evolution of velocity and temperature as well as the flow visualization show the existence of three different zones. The first zone of the plume air feeding is characterized by the dynamic and thermal profiles in three extrema structures. These extrema disappear in the second zone where the profiles present only one maximum. In the last zone, the profiles are flattened and self-similar. Thus, the turbulence is fully developed. However, one observes an improvement in the amount of energy absorbed by the fluid and an increase in the flow rate inside the cylinder. A flow visualization with laser plan allowed us to show that the position of the vertical cylinder around the hot disc affects the flow structure plume and causes the appearance of a new zone at the entrance to the system. However, the analysis of the fluctuating fields related to two studied cases shows that the thermosiphon effect has an important influence on the turbulent intensity structure of the flow evolution.     

Numerical simulation of the inner structure of a two-phase plume formed in a stratification environment

The inner structure of a two-phase plume, driven by air bubble buoyancy and formed in a stratification ambient fluid in a rectangular tank, is numerically simulated by means of two-phase flow theory and Large-eddy simulation technology. Focusing on the discrete nature of the buoyant dispersed phase and on the role of momentum exchange between two phases during plume formation, we investigated the phenomena of mass “entraining-in” and “peeling-out” that occurs inside the stratified ambient plume. These phenomena are thought to result from an intricate interplay among phase interaction, static stability of the stratification ambient fluid itself, and dynamic stability due to turbulence. Numerical simulations show that there exists an inner-out structure of the stratified ambient plume, while at the same time predicting that the re-entraining-in mass flux is on the same order of magnitude as that of the inner peeling-out mass flux within the annular region centered around the plume. This further explains the mechanism underlying the formation of multi-scale eddies at the edge of the air bubble plume, which also constitutes the boundary between the inner and outer zones of this inner-out stratified fluid plume. Within the inner part of the plume, the mass entraining-in and peeling-out appeared as a spatial discontinuity. The numerically visualized three-dimensional density fields are consistent with the two-phase plume characteristics.     

Instabilities of thermocapillary-buoyancy convection in open rectangular liquid layers

This article presents the experimental investigation on instabilities of thermocapillary-buoyancy convection in the transition process in an open rectangular liquid layer subject to a horizontal temperature gradient. In the experimental run,an infrared thermal imaging system was constructed to observe and record the surface wave of the rectangular liquid layer. It was found that there are distinct convection longitudinal rolls in the flow field in the thermocapillary-buoyancy convection transition process. There are different wave characterizations for liquid layers with different thicknesses. For sufficiently thin layers, oblique hydrothermal waves are observed, which was predicted by the linear-stability analysis of Smith Davis in 1983. For thicker layers, the surface flow is distinct and intensified, which is because the buoyancy convection plays a dominant role and bulk fluid flow from hot wall to cold wall in the free surface of liquid layers. In addition, the spatiotemporal evolution analysis has been carried out to conclude the rule of the temperature field destabilization in the transition process.     

Radiative effects on magnetohydrodynamic natural convection flows saturated in porous media

A boundary layer solution is presented to study the effects of joule heating on magnetohydrodynamic natural convection flow. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. Four different cases of flows have been studied namely an isothermal surface, a uniform heat flux surface, a plane plume and flow generated from—a horizontal line energy source a vertical adiabatic surface. Numerical results presented for the perturbation analysis four boundary conditions with various parameters are tabulated.     

Effects of variable thermal diffusivity on the structure of convection

The structure of multiscale convection in a thermally stratified plane horizontal fluid layer is investigated by means of numerical simulations. The thermal diffusivity is assumed to produce a thin boundary sublayer convectively much more unstable than the bulk of the layer. The simulated flow is a superposition of cellular structures with three different characteristic scales. In contrast to the largest convection cells, the smaller ones are localised in the upper portion of the layer. The smallest cells are advected by the larger-scale convective flows. The simulated flow pattern qualitatively resembles that observed on the Sun.     

Anisotropic geophysical vortices

A survey is made of many types of coherent vortices in the Earth's ocean and atmosphere. These vortices often occur with strong, environmentally induced anisotropy in their velocity and vorticity fields. We propose a definition of the essential characteristics of coherent vortices and formulate hypotheses concerning their dynamical role in complex, anisotropic fluid motions. Finally, we analyze numerical solutions both for uniformly rotating, stably stratified three-dimensional flow and for two-dimensional flow for the phenomena of enstrophy cascade and dissipation, intermittency, isotropy in the appropriate coordinate frame, coherent vortex emergence, vortex population dynamics, and approach to a nonturbulent end state.     

MHD Three-Dimensional Flow of Viscoelastic Fluid with Convective Surface Boundary Condition

This article reports the magnetohydrodynamic (MHD) three-dimensional flow of viscoelastic fluid over a stretching surface with heat transfer. Mathematical analysis is formulated using convective boundary conditions. Computations of dimensionless velocity and temperature fields are presented. The tabulated values show excellent agreement between present and previous limiting analysis. Graphical results show the impact of embedded parameters entering into the problem.     

Shearing of a stratified layer of amphiphilic (bio)molecules

With the goal to identify surface viscosity, this paper proposes the modelling of a shear flow within an annular channel whose floor is put in rotation while its two vertical cylindrical side walls are maintained stationary. The liquid surface at the top of the annular channel is covered by a layer of hydrophobic molecules. The flow is considered as permanent, axisymmetric and creeping. The ratio of the liquid depth to the outer radius is small enough (shallow flow) so that it is possible to develop a matched asymptotic model. In the rotating sub-phase, a core flow is therefore distinguished from the boundary layers along side walls. The modelling includes the possibility to take into account the impact of the radially-inwards molecular packing induced by centrifugation of the underlying bulk. More particularly, radial distribution of surface viscosity is taken into account via the transport equation for surface momentum. In this paper, the model by Mannheimer and Schechter [R.J. Mannheimer, R.S. Schechter, J. Colloid Interface Sci. 32 (2) (1970) 195] can be considered as revisited: a new integral formulation is made evident which enables a fair estimation of the Boussinesq number as well as a simple measurement of a stratified surface viscosity.     

Upper bounds on the convective heat transport in a rotating fluid layer of infinite Prandtl number: case of large Taylor numbers

By means of the Howard-Busse method of the optimum theory of turbulence we obtain upper bounds on the convective heat transport in a horizontal fluid layer heated from below and rotating about a vertical axis. We consider the interval of large Taylor numbers where the intermediate layers of the optimum fields expand in the direction of the corresponding internal layers. We consider the 1 - α-solution of the arising variational problem for the cases of rigid-stress-free, stress-free, and rigid boundary conditions. For each kind of boundary condition we discuss four cases: two cases where the boundary layers are thinner than the Ekman layers of the optimum field and two cases where the boundary layers are thicker than the Ekman layers. In most cases we use an improved solution of the Euler-Lagrange equations of the variational problem for the intermediate layers of the optimum fields. This solution leads to corrections of the thicknesses of the boundary layers of the optimum fields and to lower upper bounds on the convective heat transport in comparison to the bounds obtained by Chan [J. Fluid Mech. 64, 477 (1974)] and Hunter and Riahi [J. Fluid Mech. 72, 433 (1975)]. Compared to the existing experimental data for the case of a fluid layer with rigid boundaries the corresponding upper bounds on the convective heat transport is less than two times larger than the experimental results, the corresponding upper bound on the convective heat transport, obtained by Hunter and Riahi is about 10% higher than the bound obtained in this article. When Rayleigh number and Taylor number are high enough the upper bound on the convective heat transport ceases to depend on the boundary conditions. Received 30 January 2001 and Received in final form 28 May 2001     

Electromagnetic flow control in poor conductors

Lorentz force-based flow control in materials with low electrical conductivity has a long history back to the first half of the 19th century. This review will focus on developments during the last two decades, collecting results from numerical simulations and laboratory experiments. Typically, the actuators consist of permanent magnets and electrodes flush-mounted with the surface, generating Lorentz forces in the fluid layers adjacent to the wall. We will discuss the application of Lorentz forces to reduce friction drag in turbulent boundary layers and to delay boundary layer transition. The control of separated flows and shear layers is another key aspect of the review. Energetic efficiency, one of the main criteria for flow control, and its relation to typical operating conditions will be analyzed as well. Lorentz forces can be successfully used to control a broad range of flow phenomena and are a versatile tool for basic fluid dynamics research. However their current applicability in large scale systems is hampered by the low electrical to mechanical efficiency intrinsic to actuators based on the magnetic fields delivered by today’s permanent magnets.     

Symmetric heat and mass transfer in a rotating spherical layer

The general theory of heat and mass transfer maintaining rotation with slightly different velocities under conditions typical for cores of planets in the solar system is developed for the first time. The analytic solution is obtained for thermal and diffusion equations without nonlinear terms responsible for the convective transfer. This spherically symmetric basic solution is applicable when the thermal flux from a planet core is weaker than or comparable to the adiabatic (radiative) flux. In the general case, by subtracting the basic solution, we simplified the inhomogeneous system of convective equations to obtain a completely homogeneous and dimensionless system. The latter system is controlled by two asymptotically small parameters: the Rossby number ε<10^?5, which characterizes the relative value of differential rotation, and the generalized Eckman number E<10^?12, which characterizes the relative role of viscosity-diffusion effects during rapid rotation. The principal order of the solution for ε →0 and then for \(\sqrt E \to 0\), for the transfer coefficients close to molecular coefficients, results in the basic flow, which is symmetric with respect to the rotation axis and directed predominantly along the azimuth. The basic-flow liquid ascends from a solid core along spirals inside an axial cylinder in contact with the equator of the solid core and descends in a narrow layer along the cylinder walls. The moment of viscous forces in the inner boundary Eckman layer provides a faster rotation of the inner solid core of terrestrial planets compared to a massive outer mantle due to the growth of the solid core at the expense of a low-density liquid core.     

Stability of Large Amplitude Ekman-Hartmann Boundary Layers in MHD : The Case of Ill-Prepared Data

In this paper, we study an incompressible highly rotating fluid submitted to a high magnetic field between two planes with a Dirichlet boundary condition. We investigate the nonlinear stability of Ekman-Hartmann boundary layers under a spectral assumption for general initial data; this means that the data can be chosen as an arbitrary (but smooth enough) three-dimensional divergence free vector field independent of the small parameter.     

Entropy production in the flow over a swirling stretchable cylinder

In the present work, the entropy generation due to the heat transfer and fluid friction irreversibility is investigated numerically for a three-dimensional flow induced by rotating and stretching motion of a cylinder. The isothermal boundary conditions are taken into account for the heat transfer analysis. The similarity transformations are utilized to convert the governing partial differential equations to ordinary differential equations. Resulting nonlinear differential equations are solved using a numerical scheme. Expressions for the entropy generation number, the Nusselt number and the Bejan number are obtained and discussed through graphs for various physical parameters. An analysis has been made to compare the heat transfer irreversibility with fluid friction irreversibility using the expression of the Bejan number. It is found that the surface is a durable source of irreversibility and the curvature of cylinder is to enhance the fluid friction irreversibility.     

On calculating the oscillations of a viscous liquid layer over a solid spherical core in terms of the boundary layer theory

The theory of a boundary layer near the periodically oscillating free surface of a spherical viscous liquid layer over a solid core (bottom) is modified. Two boundary layers are considered to adequately describe a liquid viscous flow in the system: one at the free surface of the liquid and the other at the solid bottom. The thicknesses of the boundary layers are estimated, which provide any given discrepancy between an exact solution to the model problem and a solution obtained in the small viscosity approximation. Taking into account the boundary layer near the solid bottom is shown to be significant only for lower oscillation modes. For higher modes, the flow near the core can be considered potential. In the case of lower modes and shallow liquid, the surface and bottom boundary layers overlap and an eddy flow occupies the entire volume of the liquid.     

热可压缩流体的流动和传热

本文把由温度引起密度变化的运动流体称为热可压流，并由无因次加热数来度量其压缩程度。它有别于气体动力学中以马赫数度量压缩性的由速度（因而压力）变化导致密度变化的可压缩流。列举和讨论了热可压流流动和传热的一些特征现象，它可望用于发展一些新的热控制技术。     

Soret效应对具有自由表面的圆柱形浅池内双组分溶液热对流影响的实验研究

为了探究Soret效应对具有自由表面的圆柱形浅液池内双组分溶液热对流过程的影响, 通过实验观察了质量分数为50%的正癸烷/正己烷混合溶液在不同深宽比的液池内流动失稳后的自由表面耗散结构及液池内的温度波动. 结果表明, 双组分溶液流动失稳的临界热毛细Reynolds数小于纯工质的值, 且其随液层深宽比的变化规律与纯工质相同. 当深宽比小于0.0848时, 流动失稳后在自由表面观察到热流体波, 监测点处温度波动主频随热毛细Reynolds数增大而增加; 当深宽比大于0.0848时, 随热毛细Reynolds数的增大, 流动失稳后自由表面依次呈现轮辐状、花苞状、分离-合并-分离交替变化的条纹状结构.     

Mixed boundary value problems for the stationary magnetohydrodynamics model of a viscous heat-conducting fluid

The boundary value problem for the stationary magnetohydrodynamics model of a viscous heatconducting fluid considered under inhomogeneous mixed boundary conditions for an electromagnetic field and the temperature and Dirichlet condition for the velocity is investigated. This problem describes the flow of an electricaland heat-conducting liquid in a bounded three-dimensional domain the boundary of which consists of several parts with different thermoand electrophysical properties. Sufficient conditions imposed on the initial data to provide for global solvability of the problem and local uniqueness of its solution are established.     

单转子压气机设计状态和近失速状态出口三维紊流流场

用单斜丝详细测量了单转子压气机设计状态和近失速状态转子出口的三维素流流场。结果表明，设计状态叶尖泄漏涡和端壁附面层的掺混是造成尖部流动损失、气流阻塞和亲流脉动的主要原因。近失速状态流动三维性和非定常性较强；尖部吸力面角区轴向速度最低、相对动能损失最大；吸力面附面层径向潜移、叶尖吸力面角区低能团周向潜移及其输运的低能物质在尖部通道中部与叶尖泄漏流、泄漏涡、刮削涡发生掺混，造成尖部大范围的高损失区；根部和尖部吸力面阻面层局部发生分离。     

On the Existence of Traveling Waves in the 3D Boussinesq System

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.