Influence of buoyancy on floating-zone convection of small bond number

Gravity may influence the velocity and temperature distributions, bouyancy may induce Rayleigh instability and the instability may be excited due to the change of free surface shape associating with gravity in the thermocapillary convection. These effects have been studied in the present paper. The results show that gravity may have an important effect in thermocapillary oscillatory convection even for the cases of small Bond number experiments either on the ground or in space.

Micromechanics of elastic solids weakened by a large number of cracks

This paper presents a micromechanics analysis of the elastic solids weakened by a large number of microcracks in a plane problem. A new cell model is proposed. Each cell is an ellipse subregion and contains a microcrack. The effective moduli and the stress intensity factors for an ellipse cell are obtained. The analytic closed formulas of concentration factor tensor for an isotropic matrix containing an anisotropic inclusion are derived. Based on a self-consistent method, the effective elastic moduli of the solids weakened by randomly oriented microcracks are obtained.

Approximate theory of natural-convection with small grashof number

To gain some insight into the behaviour of low-gravity flows in the material processing in space, an approximate theory has been developed for the convective motion of fluids with a small Grashof number Gr. The expansion of the variables into a series of Gr reduces the Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.

The influence of buoyancy on the oscillatory thermocapillary convection with small bond number

This work is an experimental study of unidirectional bamboo-epoxy laminates of varying laminae number, in which tensile, compressive, flexural and interlaminar shear properties are evaluated. Further, the disposition of bamboo fibre, the parenchymatous tissue, and the resin matrix under different loading conditions are examined. Our results show that the specific strength and specific modulus of bamboo-epoxy laminates are adequate, the former being 3 to 4 times that of mild steel. Its mechanical properties are generally comparable to those of ordinary glass-fibre composites. The fracture behaviour of bamboo-epoxy under different loading conditions were observed using both acoustic emission techniques and scanning electron microscopy. The fracture mode varied with load, the fracture mechanism being similar to glass and carbon reinforced composites. Microstructural analyses revealed that natural bamboo is eligibly a fibre composite in itself; its inclusion in a plastic matrix will help solve the problems of cracking due to desiccation and bioerosion caused by insect pests. Furthermore, the thickness and shape of the composite can be tailored during fabrication to meet specific requirements, thereby enabling a wide spectrum of applications.

Turbulent passive scalar field of a small prandtl number

The statistical-mechanics theory of the passive scalar field convected by turbulence, developed in an earlier paper [Phys. Fluids 28, 1299 (1985)], is extended to the case of a small molecular Prandtl number. The set of governing integral equations is solved by the equation-error method. The resultant scalar-variance spectrum for the inertial range is F(k)~x−5/3/[1+1.21x1.67(1+0.353x2.32)], where x is the wavenumber scaled by Corrsin's dissipation wavenumber. This result reduces to the − (5)/(3) law in the inertial-convective range. It also approximately reduces to the − (17)/(3) law in the inertial-diffusive range, but the proportionality constant differs from Batchelor's by a factor of 3.6.

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<numbers RDxi between different cells in Navier-Stokes (NS) equations computations for high Reynolds number flows, an idea of solving the conservation equations for discrete cells was proposed and named the discrete fluid dynamics (DFD) algorithm. Analysis shows that the basic conservative equations for discrete cells are the Euler equations, NS- and diffusion parabolized (DP) NS equations. In this paper, a new multiscale-domain decomposition method is developed for the high Reynolds number flow. First, the whole domain is decomposed to different sub-domains with the different characteristic scales. Then the different dominant equation of all sub-domains is defined according to the diffusion parabolized (DP) theory of viscous flow. Finally these different equations are solved simultaneously in whole computational region. For numerical tests of high Reynolds numerical flows, two-dimensional supersonic flows over rearward and frontward steps as well as an interaction flow between shock wave and boundary layer were solved numerically. The pressure distributions and local coefficients of skin friction on the wall are given. The numerical results obtained by the multiscale-domain decomposition algorithm are well agreement with those by NS equations. Comparing with the usual method of solving the Navier-Stokes equations in the whole flow, under the same numerical accuracy, the present multiscale domain decomposition method decreases CPU consuming about 20% and reflects the physical mechanism of practical flow more accurately.

Smaller Deborah number inducing more serrated plastic flow of metallic glass

Spherical nano-indentations of Cu46Zr54 bulk metallic glass (BMG) model systems were performed using molecular dynamics (MD) computer simulations, focusing specifically on the physical origin of serrated plastic flow. The results demonstrate that there is a direct correlation between macroscopic flow serration and underlying irreversible rearrangement of atoms, which is strongly dependent on the loading (strain) rate and the temperature. The serrated plastic flow is, therefore, determined by the magnitude of such irreversible rearrangement that is inhomogeneous temporally. A dimensionless Deborah number is introduced to characterize the effects of strain rate and temperature on serrations. Our simulations are shown to compare favorably with the available experimental observations.

A universal Biot number determining the susceptibility of ceramics to quenching

A universal Biot number of ceramics, which not only determines the susceptibility of the ceramics to quenching but also indicates the duration that the ceramics fail during thermal shock, is theoretically obtained. The present analysis shows that the thermal shock failure of the ceramics with a Biot number greater than this universal value is a very rapid process that just occurs in the initial regime of the heat conduction of the ceramics. This universal Biot number provides a guide to the selection of the ceramics applying to the thermostructural engineering including thermal shock.

Number of phase levels of a Talbot array illuminator

The number of phase levels of a Talbot array illuminator is an important factor in the estimation of practical fabrication complexity and cost. We show that the number it) of phase levels of a Talbot array illuminator has a simple relationship to the prime number. When there is an alternative pi -phase modulation in the output array, the relations are similar. (C) 2001 Optical Society of America OCIS codes: 070.6760, 050.1950, 050.1980.

A New theory for evaluating the number density of inclusions in films

A new formulation derived from thermal characters of inclusions and host films for estimating laser induced damage threshold has been deduced. This formulation is applicable for dielectric films when they are irradiated by laser beam with pulse width longer than tens picoseconds. This formulation can interpret the relationship between pulse-width and damage threshold energy density of laser pulse obtained experimentally. Using this formulation, we can analyze which kind of inclusion is the most harmful inclusion. Combining it with fractal distribution of inclusions, we have obtained an equation which describes relationship between number density of inclusions and damage probability. Using this equation, according to damage probability and corresponding laser energy density, we can evaluate the number density and distribution in size dimension of the most harmful inclusions. (c) 2005 Elsevier B.V. All rights reserved.