Symmetric Sheet Research Articles

Thermally induced van der Waals rupture of thin viscous fluid sheets

We consider the dynamics of a thin symmetric fluid sheet subject to an initial temperature profile, where inertia, viscous stresses, disjoining pressures, capillarity, and thermocapillarity are important. We apply a long-wave analysis in the limit where deviations from the mean sheet velocity are small, but thermocapillary stresses and heat transfer from the sheet to the environment are significant and find a coupled system of partial differential equations that describe the sheet thickness, the mean sheet velocity, and the mean sheet temperature. From a linear stability analysis, we find that a stable thermal mode couples the velocity to the interfacial dynamics. This coupling can be utilized to delay the onset of rupture or to promote an earlier rupture event. In particular, rupture can be induced thermally even in cases when the heat transfer to the surrounding environment is significant, provided that the initial phase shift between the initial velocity and temperature disturbances is close to ϕ = π/2. These effects suggest a strategy that uses phase modulation in the initial temperature perturbation related to the initial velocity perturbation that assigns priority of the rupture events at particular sites over several spatial periods.

A two-phase approach to wave-induced sediment transport under sheet flow conditions

A numerical model for the general description of the sediment transport under oscillatory sheet flow conditions is developed based on a two-fluid representation of the two-phase turbulent flows. The governing equations of the model are the Reynolds averaged continuity equations and equations of motion for both the fluid and the sediment phases. The two phases are coupled by the interphase forces including the resistance force, the inertia force, and the lift force. Turbulence closure of the fluid phase is based on a slightly modified k– ε model while an algebraic particle-turbulence model is applied to the sediment phase. The numerical method is based on the modified SIMPLE scheme and an improved time stepping technique. The model is validated by the published data for the symmetrical oscillatory sheet flows generated in an oscillatory flow tunnel at the University of Tokyo and for both the symmetrical and the asymmetrical oscillatory sheet flows generated in an oscillatory flow tunnel at University of Aberdeen. The numerical results on the temporal and spacial variation of the sediment concentration, the horizontal velocities of the two phases, the horizontal and vertical fluxes of the sediment phase, as well as the thickness of the sheet flow layer all show satisfactory agreement with the laboratory data. The model is also shown to predict the net sediment transport rate with a reasonably good accuracy.

Symmetrical Facing Wrinkling of Composite Sandwich Panels

The article presents the solution of symmetrical face sheet wrinkling problem for sandwich panel with composite facings and an orthotropic core. The new model is proposed for elastic core that takes into account compressive and shear stiffnesses as well as nonlinear change of transverse displacement over the core thickness at wrinkling. The governing buckling equation is derived using energy method. Analysis of cylindrical face wrinkling is performed for sandwich strips subjected to compressive loads applied to the two opposite simply supported edges. The effects of elastic and geometric parameters on the critical buckling stresses and wrinkling waves' formation are examined.

A two-phase numerical model for sediment transport prediction under oscillatory sheet flows

To predict sediment transport under oscillatory sheet flow condition, especially for fine sand, is still a challenging research subject in coastal engineering. This paper describes a newly-developed numerical model based on two-phase theory with the use of a one-equation turbulence closure, and its applications in predicting fine sediment suspension in near-prototype oscillatory sheet flow conditions. Model results were compared with comprehensive laboratory measurements of flow velocity and sediment concentration under both symmetrical and asymmetrical oscillatory sheet flows from a large-scale water tunnel. Good agreements between the model results and measurements were achieved and the results demonstrated that the model is capable of reproducing detailed characteristics of sediment entrainment process in the sheet flow regime. The comparisons also revealed the fact that the concentration peaks at flow reversal is associated with the strong vertical sediment transport flux in the pickup layer, which has been widely observed in many laboratory experiments. The effects of flow reversal events on total sediment transport were also discussed.

Diffusion of Na and Cs in montmorillonite

AbstractThe state and dynamics of water and cations in pure and mixed Na-Cs-montmorillonite as a function of the interlayer water content were investigated in the present study, using Monte Carlo and classical, molecular-dynamics methods. While highly idealized, the simulations showed that the swelling behavior of hetero-ionic Na-Cs-montmorillonite is comparable to the swelling of a homo-ionic Na- or Cs-montmorillonite. The mixed Na-Cs-montmorillonite is characterized by intermediate interlayer distances compared to homo-ionic Na- and Cs-montmorillonites. Dry, hetero-ionic Na-Cs-montmorillonite is characterized by a symmetric sheet configuration, as is homo-ionic Cs-montmorillonite.We found that at low degrees of hydration the absolute diffusion coefficient of Cs+ is less than for Na+, whereas at greater hydration states the diffusion coefficient of Cs+ is greaterthan for Na+. An analysis of the relative diffusion coefficients (the ratio between the diffusion coefficient of an ion in the interlayer and its diffusion coefficient in bulk water) revealed that water and Na+ are always less retarded than Cs+. With large interlayer water contents, tetralayer or more, Na+ ions preferentially form outer-sphere complexes. The mobility perpendicular to the clay surface is limited and the diffusion is equivalent to two-dimensional diffusion in bulk water. In contrast, Cs+ ions preferentially form ‘inner-sphere complexes’ at all hydration states and their two-dimensional diffusion coefficient is less than in bulk water.The question remains unanswered as to why experimentally derived relative diffusion coefficients of Cs+ in the interlayer of clays are about 20 times less than those we obtained by classical molecular dynamics studies.

MIXED-POTENTIAL GREEN'S FUNCTION OF AN AXIALLY SYMMETRIC SHEET MAGNETIC CURRENT ON A CIRCULAR CYLINDRICAL METAL SURFACE

An effective approach is suggested for calculating the Green's function of an axially symmetric sheet magnetic current placed on a circular cylindrical metal surface. Upon improving convergence of the available Fourier transform, it has been possible to explicitly develop the Green's function logarithmic singularity at the source. Also, the Green's function behavior at the branch point in the spectral domain has been considered, ending up with the singularity extraction in the space domain. It is shown that this branch point singularity (pole) corresponds to the cylindrical quasi-TEM mode of the cylinder exterior. Finally, the rest of the Green's function is effectively numerically calculated.

Active Material Flow Control during High-Pressure Sheet Metal Forming

During forming of non-rotationally symmetric sheet metal parts at high pressures nonuniform deformation conditions arise in the flange area. These deformations vary in height and consequently lead to heterogeneous sheet thickness distributions. When using semi-rigid tools, high clamping forces are necessary in order to compensate for the developing sheet thickness variations in the flange area and to avoid leakages of the system or wrinkling. Moreover, the heterogeneous distribution of the clamping force is strengthened by press inaccuracies. This results in a higher surface pressure distribution on one side of the flange and finally in a non-uniform material flow out of the flange area. The development of a segmented active-elastic blank holder enables an active material flow control of the flange movement during sheet metal forming at high pressures. The local elasticity of the active-elastic blank holder is based on an optimized layout of the local tool rigidity. For this purpose, different grooves were integrated below the blank holder surface. This paper provides an overview of the developed technology, advantages with regard to the part’s quality, and recent results comparing the production of non-rotationally symmetric parts with segmented active-elastic tools vs. semi-rigid tools.

高速新聞抄紙機のウエットパート

MHI High Speed Newsprint Machines have been developed to produce paper of the highest quality using 'state of the art' technology verified by the data from our field operations. Focussing on the 'Wet End' of the machine, the main features and resulting performance are hereby outlined.The “Concept IV-MH” Headbox has been developed and designed to deliver a uniform and stable jet at high speed. It has achieved an excellent dry basis weight profile (2 sigma= 0.13 g/m2) and uniform fiber orientation profile (less than +-2 degrees) by combining the latest technology such as “Dual Temperature Controlled Water Re-circulation”, “Edge Flow Control” and “Consistency Profile Control (CP)” system.The “MH Former +CB” can produce paper of superior quality in comparison with the “Roll Blade” type former due to the following unique features it offers.(1) Small diameter of the Forming & Breast roll makes for easy jet impingement adjustment.(2) The large radius Forming Board and alternative drainage equipment's arrangement in both wires perfects symmetrical sheet structure.(3) Location adjustable “Serrated Shoe” together with “Counter Blades” enables optimum dewatering conditions over a wide range of operational speeds.Results to date have realized and confirmed our goal of the “MH Former +CB” which produces paper of even sided sheet with excellent formation. In addition to the Head Box and Former developments, our latest Newsprint Machines are further equipped with new technology such as.-Enclosed type Shoe Press (ENP-C) -Anti-blowing boxes in the Dryer section-Center Wind Assisted Reel (TNT-C) All the above features are operating with great success in our latest High Speed Newsprint Machines, both in “Oji Paper Tomakomai mill N-6 M/C” and Iwaki-Daio Paper # 2 machine.

Radially symmetric ice sheet flow

The evolution equations for a radially symmetric grounded ice sheet flowing under gravity are formulated on the basis that the ice is an incompressible nonlinearly viscous heat conducting fluid with temperature–dependent rate factor. The reduced model, which comprises the leading order balances when longitudinal gradients are small compared with gradients through the sheet thickness, is derived. Steady flow is analysed when the temperature field is prescribed, uncoupled from the energy balance or satisfying energy balance with the addition of an appropriate heat source. The problem reduces to a second–order differential equation for the thickness with boundary conditions at the divide (axis of symmetry) and margin, with the margin radius unknown. Asymptotic analysis yields an expression for the surface slope at the margin. Numerical algorithms for both non–slip and sliding at the base are constructed and tested against solutions of special cases. A variety of examples are solved to demonstrate the influence of the viscous law, surface accumulation distribution, sliding and the bed form for different prescribed temperature fields; including evaluation of the heat source distribution necessary to maintain the temperature field.

Analysis of plastic instability during sandwich sheet rolling

In this study, plastic instability occurring in the hard inner layer during symmetrical sandwich sheet rolling was investigated. Two criteria for diffusion necking and local necking under a tri-axial stress state were developed to predict the occurrence of plastic instability in the hard inner layer during sandwich sheet rolling. Stress states in the inner hard layer at the exit of the roll-gap, where plastic instability is most likely to occur, were employed to formulate the plastic instability criteria. The effects of various rolling conditions such as the thickness ratio of sheets, yield shear stress ratio of sheets, etc. upon the critical thickness reduction, under which plastic instability can be avoided, were discussed systematically. Furthermore, experiments on sandwich sheet rolling were also conducted by employing aluminum and mild steel as layers of sandwich sheets. It was found that the theoretical predictions of the critical reduction were in good agreement with the experimental measurements. Throughout the study, it is clear that the proposed plastic instability criteria are able to offer useful knowledge in designing the pass-schedule of sandwich sheet rolling processes.

Analysis of sandwich sheet rolling by stream function method

A mathematical model for symmetrical sandwich sheet rolling is proposed by using the stream function method and the upper bound theorem to investigate the plastic deformation behavior of sheets at the roll-gap. The velocity fields derived from the newly proposed stream functions can automatically satisfy the volume constancy and the velocity boundary conditions within the roll-gap. Effects of various rolling conditions such as the thickness ratio and flow stress ratio of sheets, total thickness reduction, friction factor between the sheet and roll, etc., upon the thickness ratio of the rolled product, the relative length of the plastic region in each layer, rolling force and rolling power are discussed systematically. Furthermore, experiments on sandwich sheet rolling are also conducted by employing aluminium, mild steel and stainless steel as layers of sandwich sheets. It is found that the theoretical predictions of the thickness ratio of the rolled products and rolling force are in good agreement with the experimental measurements. Through the study, it becomes clear that the proposed analytical method is applicable for simulating the sandwich sheet rolling processes and is able to offer useful knowledge in manufacturing sandwich sheets.

Fabrication of a CuAkNiMn shape memory alloy

In the development of an optimized hot-rolling process for a CuAlNiMn alloy, the effects of the recrystallized and transformed texture on ductility and shape memory recovery were examined. The sheet texture of samples rolled in the β-phase region (750°C) was characterized by martensitic (128) poles along the normal direction and (0 0 18) pole inclined 60° from the normal to the rolling direction. The samples rolled in the α + β region (600°C) exhibited a slightly stronger but less symmetrical sheet texture. The shape memory recovery is more or less isotropic in the rolling plane, relatively independent of the rolling conditions. However, an improved bending ductility of 9.5% was observed along the rolling direction in specimens rolled at 750°C with a reduction per pass of 27%.

An analysis of the axisymmetric and nonaxisymmetric sheet stretching by a hemispherical punch

An incremental elasto-plastic finite element method is used to analyze the deformation of the axially symmetric sheet and nonsymmetric rectangular strip sheet stretch formed by a hemispherical punch. In order to simplify the 3-D axially nonsymmetric problem to a 2-D analysis of plane stress with neglect of bending stress, the membrane element is adopted. Three coordinates, i.e., global coordinate ( X, Y, Z), element transformation coordinate ( x, y, z), and nodal local surface coordinate (ξ, η, ζ) are incorporated, and the entire processing simulation is formulated according to an updated Lagrangian formulation. The computer program determines the thickness distribution, the strain distribution, the final deformed profile and the springback behavior.

On the instability of a full non‐parallel flow—Kovasznay flow

AbstractThe local instability of a full non‐parallel flow is investigated. The basic flow is a horizontal uniform flow about a vertical array of periodic bound eddies. This flow was found by Kovasznay as an exact solution to the Navier–Stokes equations. The problem is formulated as an initial value problem with two sets of complete orthogonal functions. A new approach to the problem with semi‐infinite domain is given computationally with a new modified rational Chebyshev function. The linear stability analysis of the Kovasznay flow is performed with respect to the odd–rational Chebyshev mode and the even–rational Chebyshev mode for the evolution of disturbances. While symmetrical vortex sheets appeared through the process of big eddies breaking into small eddies in the odd–rational Chebyshev mode, the von Kármán vortex street phenomena is found in the even–rational Chebyshev mode. The mode corresponding to antisymmetric velocity perturbation is found to be far more unstable than symmetric disturbance. An organized structure is developed after the onset of instability. Several general characteristics of non‐parallel flow stability are discussed.

Growth behavior and structures of carbon nanotubes

Recent discovery of the novel hollow graphitic tubules of nanometer dimensions, so called carbon nanotubes, has greatly stimulated the studies in the field of carbon fiber growth. Their potential applications in electronic and materials industries have been suggested. In the present study, carbon nanotubes were fabricated by an arc-discharge method. The microstructures of nanotubes thus obtained were examined with a JEM-2000FX high-resolution transmission electron microscopy (HRTEM) and with an electron nanodiffraction technique in a VG HB-5 scanning transmission electron microscopy (STEM).HRTEM images show that nanotubes, consisting of 3 to 30 carbon sheets, have a length up to 1 μm and a diameter of 6 to 26 nm. Some nanotubes have a symmetric uniform sheet spacing of 0.34 nm. Others show non-symmetric uneven fringes (Fig. 1), indicating that they may have a polyhedral cross section. Most nanotubes are closed by cone-like or polyhedral shaped caps (Figs. 2 and 3). The closure angle varies from 17 to 40° and the internal sheets have a tendency to be closed in pairs. Fig. 4 shows the image of a growing tubes.

A topological approach to the strain-rate pattern of ice sheets

AbstractThe pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

A topological approach to the strain-rate pattern of ice sheets

AbstractThe pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

Slender Jets and Thin Sheets with Surface Tension

Simplified equations governing the potential flow and the shape of slender jets and thin sheets of liquid are derived, taking into account surface tension. Families of similarity solutions of these equations are introduced. For jets and for symmetrical sheets they satisfy ordinary differential equations. The properties of these similarity solutions are examined analytically and numerically. They can be used to describe the motion of a liquid sheet on a solid, the thickening and flow following the breaking of jets, the merging of two jets, the formation or closing of holes or slits in sheets, etc. Some applications to such problems are given.

Robotic range sensor with projection of bright ring pattern

AbstractA new type of optical range sensor is being proposed as a robotic sensor. The range sensor consists of the projection subsystem of an axially symmetrical light sheet and the detection subsystem for monitoring the focussing process of a lens. The projection subsystem produces a bright ring pattern through an objective lens on the surface of an object. Next, the distance from the range sensor to the surface of an object is calculated from the position of the lens. The prototype range sensor is able to measure the distance in the range of 430 to 570 mm with an accuracy of 0.3 mm. As the position of the objective lens is controlled so that the ring pattern projected on the surface of an object becomes a fine spot, the detection subsystem finds the position of the objective lens on which the output of photodiode comes to be maximum.

New type of miniaturized optical range‐sensing methods RORS and RORST

AbstractTwo types of miniaturized optical range‐sensing methods have been developed. The first is called RORS (Riken Optical Range‐Sensing Scheme). In this method, a mirror tunnel is first placed between an objective lens and an object to be measured; a bright spot is then projected onto the object through the objective lens. This spot is observed through the objective lens after reflection with the mirror tunnel, and range information is determined by the triangulation. The width of an optical system can be reduced remarkably smaller than the effective base line length of the triangulation. Therefore, it is suitable to miniaturize a range‐sensing system such as an optical stylus and a proximity sensor. The second method, RORST (Riken Optical Range Sensing Method for Surface Tracing), projects an axially symmetrical light sheet onto an object and a ring pattern is produced. The ring pattern image is then projected onto the observation plane by the objective lens, radii of the ring pattern image for different azimuths are detected, distances corresponding to the specified azimuths are determined by the triangulation, and thus the information of partial inclination can be obtained.