Remarks on the Rayleigh-Bénard Convection on Spherical Shells

The main objective of this article is to study the effect of spherical geometry on dynamic transitions and pattern formation for the Rayleigh-Bénard convection. The study is mainly motivated by the importance of spherical geometry and convection in geophysical flows. It is shown in particular that the system always undergoes a continuous (Type-I) transition to a 2l _c -dimensional sphere ${S^{2l_c}}$ , where l _c is the critical wave number corresponding to the critical Rayleigh number. Furthermore, it has shown in Ma and Wang (Physica D 239:3–4, 167–189, 2010) that it is critical to add nonisotropic turbulent friction terms in the momentum equation to capture the large-scale atmospheric and oceanic circulation patterns. We show in particular that the system with turbulent friction terms added undergoes the same type of dynamic transition, and obtain an explicit formula linking the critical wave number (pattern selection), the aspect ratio, and the ratio between the horizontal and vertical turbulent friction coefficients.     

Discussion on “Rectangular Plates with Free Edges on Elastic Foundations”

This paper points out the former work does not fulfill the boundary conditions that the concentrated force at the four corner points should not exist. Therefore, Ritz method adopted by the author concerned in the illustrative example will not be convergent in the best way. Moreover, Garlerkin method which is illustrated in this paper may carry out incorrect results if we apply its formulae. We have proved that the boundary conditions which govern the concentrated force equal to zero at the four corner points are indispensable if the problem is properly set.     

Discussion on“Rectangular Plates with Free Edges on Elastic Foundations”

This paper points out the former work does not fulfill the boundaryconditions that the concentrated force at the four corner points should notexist.Therefore,Ritz method adopted by the author concerned in the illus-trative example will not be convergent in the best way.Moreover,Garlerkinmethod which is illustrated in this paper may carry out incorrect results ifwe apply its formulae.We have proved that the boundary conditions whichgovern the concentrated force equal to zero at the four corner points areindispensable if the problem is properly set.     

Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both EulerBernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.     

Experimental study on the condensation of ethanol–water mixtures on vertical tube

The condensation heat transfer of the ethanol–water mixtures on the vertical tube over a wide range of ethanol concentrations was investigated. The condensation curves of the heat flux and the heat transfer coefficients revealed nonlinear characteristics and had peak values, with respect to the change of the vapor-to-surface temperature difference. This characteristic applies to all ethanol concentrations under all experimental conditions. With the decrease of the ethanol concentrations, the condensation heat transfer coefficient increased notably, especially when the ethanol concentration was very low. The maximum heat transfer coefficient of the vapor mixtures increased to 9 times as compared with that of pure steam at ethanol vapor mass concentration of 1%. With the increase of the ethanol concentrations, the condensation heat transfer coefficient decreased accordingly. When the ethanol concentration reached 50%, the heat transfer coefficient was smaller than that of the pure steam.     

Particles dispersion on fluid-liquid interfaces

This paper is concerned with the dispersion of particles on the fluid-liquid interface. In a previous study we have shown that when small particles, e.g., flour, pollen, glass beads, etc., contact an air-liquid interface, they disperse rapidly as if they were in an explosion. The rapid dispersion is due to the fact that the capillary force pulls particles into the interface causing them to accelerate to a large velocity. In this paper we show that motion of particles normal to the interface is inertia domin...     

X-ray measurements on the influence of optical probes on gas–solid fluidized beds

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Five Recent Books on Super-fine Powders

Professor Fengsheng Li of the Nanjing University of Science and Technology has been working in the field of superfine powders for many years, and at the turn of the century he started to write a series of monographs, now five, on the technology ofsuperfine powders including their preparation, measurement and application, andranging from catalysts through medicines and cosmetics to pyrotechnics.     

Fluid–structure interaction approaches on fixed grids based on two different domain decomposition ideas

This paper presents two domain decomposition techniques for fixed grid fluid–structure interaction simulations that can be applied to the interaction of general structures with incompressible flows. One approach is based on an overlapping domain decomposition idea while the other uses non-overlapping domains. The first technique combines a fixed grid Chimera approach with arbitrary Lagrangean Eulerian based methods, the second one is based on an eXtended Finite Element Method (XFEM) strategy. Both techniques are used in a partitioned and strong coupling fluid–structure framework. The usage of such fixed-grid methods considerably increases the range of possible applications. Several test examples demonstrate key features of both methods.     

Effect of structure parameters on forces acting on baffles used in gas–solids fluidized beds

Effects of some important structural parameters, i.e. slat pitch, and layout position, on dynamic forces acting on the baffles were examined in the fluidized bed of FCC particles operating under different superficial gas velocities. The experimental baffles were made of multiple inclined slats. We found that the forces acting on the baffles decreased significantly with reducing pitch between the slats. For the baffles with a small slat pitch, the forces acting on the baffles increased slightly and then decreased with increasing superficial gas velocity, which is very different from the measured results of a single slat or tube immersed in fluidized beds. The different results are greatly related to the appearance of the “gas cushion” beneath the baffles, whose height increases with increasing superficial gas velocity. On the other hand, a region with stronger particle circulation induced by the inclined slat array was observed in the experiments. The slat near the wall and located below the region of downward-flowing particles was found to be subjected to the severest forces. Therefore, the slats located in similar locations of industrial baffles are suggested to be reinforced to increase their structural strength.     

Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing

This paper is motivated by the works of Dickinson et al. (Science 284:1954–1960, 1999) and Sun and Tang (J Exp Biol 205:55–70, 2002) which provided two different perspectives on the influence of wing–wake interaction (or wake capture) on lift generation during flapping motion. Dickinson et al. (Science 284:1954–1960, 1999) hypothesize that wake capture is responsible for the additional lift generated at the early phase of each stroke, while Sun and Tang (J Exp Biol 205:55–70, 2002) believe otherwise. Here, we take a more fundamental approach to study the effect of wing–wake interaction on the aerodynamic force generation by carrying out simultaneous force and flow field measurements on a two-dimensional wing subjected to two different types of motion. In one of the motions, the wing at a fixed angle of attack was made to follow a motion profile described by “acceleration-constant velocity-deceleration”. Here, the wing was first linearly accelerated from rest to a predetermined maximum velocity and remains at that speed for set duration before linearly decelerating to a stop. The acceleration and deceleration phase each accounted for only 10% of the stroke, and the stroke covered a total distance of three chord lengths. In another motion, the wing was subjected to the same above-mentioned movement, but in a back and forth manner over twenty strokes. Results show that there are two possible outcomes of wing–wake interaction. The first outcome occurs when the wing encounters a pair of counter-rotating wake vortices on the reverse stroke, and the induced velocity of these vortices impinges directly on the windward side of the wing, resulting in a higher oncoming flow to the wing, which translates into a higher lift. Another outcome is when the wing encounters one vortex on the reverse stroke, and the close proximity of this vortex to the windward surface of the wing, coupled with the vortex suction effect (caused by low pressure region at the center of the vortex), causes the net force on the wing to decrease momentarily. These results suggest that wing–wake interaction does not always lead to lift enhancement, and it can also cause lift reduction. As to which outcome prevails depend very much on the flapping motion and the timing of the reverse stroke.     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = D . Combining the above relations, the steady flow curve was expressed by = D ^{1/2 +} + ₀ (1 – a D ^b/0.74)^–1.85 D, where ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the-potential, the flow behavior of the suspensions changed from Newtonian ( = = b = 0), slightly pseudoplastic ( = b = 0), pseudoplastic ( = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.     

Measurement on particle rotation speed in gas–solid flow based on identification of particle rotation axis

When a two-dimensional (2D) imaging system is used to visualize particle motion in a 3D gas–solid flow, the particle rotation speed was found extremely difficult to be accurately measured due to the fact that the direction of rotation axis was usually random and hard to be distinguished. The paper presents a method to calculate the particle rotation speed from particle images based on the identification of its rotation axis using two or more characteristic points on its surface. The idea was analyzed and realized in a mathematical way and based on which a calculation program was given. The measurement method was verified with an experiment using a small sphere with known rotation axis and rotation speed. The effects of several factors, including the direction of the particle rotation axis, the particle image resolution, the types and positions of characteristic points, etc., on the measurement error are discussed. The error is found to be acceptable for most cases. The measurement method was finally applied to those small glass beads in a real 3D gas–solid flow inside a cold circulating fluidized bed (CFB) riser, which indicates that the problems of 2D imaging system applying to 3D particulate system could be solved by using this mathematical method.     

Newtonian Mechanics on Kähler Manifold

In this paper we discuss Newtonian Mechanics on Kahler Manifold, and also givefoe complex mathematical aspects of Newton’s law, the law of kinetic energy, the lawof kinetic quantity,the equation of motion and the "general equation of dynamics",and so on.     

Coating metals on micropowders by magnetron sputtering

Magnetron sputtering was used to coat various metals on micropowder surfaces. By using this method, the fine particles are better dispersed and can therefore be coated more homogeneously. The micro-powders used include cenospheres from fly ash of coal-burning electric power plants （diameter 40-200 μm and particle density 0.7 ± 0.1 g/cm^3）, as well as carborundum particles of different sizes. Aluminum, silver, copper, cobalt and nickel were used as the coating metals. Tests showed that the coated metal film was compact adhering tightly on the base powders, and the coated powders possess adequate flow properties.     

Well-Posedness of the Multidimensional Fractional Stochastic Navier–Stokes Equations on the Torus and on Bounded Domains

In this work, we introduce and study the well-posedness of the multidimensional fractional stochastic Navier–Stokes equations on bounded domains and on the torus (briefly dD-FSNSE). For the subcritical regime, we establish thresholds for which a maximal local mild solution exists and satisfies required space and time regularities. We prove that under conditions of Beale–Kato–Majda type, these solutions are global and unique. These conditions are automatically satisfied for the 2D-FSNSE on the torus if the initial data has H ¹-regularity and the diffusion term satisfies growth and Lipschitz conditions corresponding to H ¹-spaces. The case of 2D-FSNSE on the torus is studied separately. In particular, we established thresholds for the global existence, uniqueness, space and time regularities of the weak (strong in probability) solutions in the subcritical regime. For the general regime, we prove the existence of a martingale solution and we establish the uniqueness under a condition of Serrin’s type on the fractional Sobolev spaces.     

Sino-German Workshop on Energy Utilization of Biomass

Need for Energy Utilization of Biomass in China China is on the way to be the most important energy market of the world. Economic growth and improvement in peo-ple抯 livelihood are leading to enormous increases in energy consumption. In view of the mainly coal dominated structure of the energy supply in China, however, this growth not only leads to increasing pressure on the available resources, but also possesses long-range effects on matters of the environment. At present, the national en…     

Some theoretical problems on variational data assimilation

Theoretical aspects of variational data assimilation (VDA) for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the validity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed.