Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang     

Rod–coil block copolymers: An iterative synthetic approach via living free-radical procedures

A modular approach has been developed for the synthesis of rod–coil block copolymers involving the initial preparation of a macroinitiator based on the rod block followed by the growth of the coil segment with living free-radical procedures. The key feature of this strategy is the utilization of an alkoxyamine group from the beginning of the synthesis, which serves as a solubilizing group and ensures that each rod block contains a single initiating fragment. Using this approach permits block copolymers based on insoluble biphenyl ester oligomers to be conveniently prepared with coil segments that range from styrenes to acrylates to 1,3-dienes. The tendency of the rod segments to crystallize is strongly dependent on the weight fraction of the rod segment and the chemical nature of the coil segment. Rod–coil molecules containing at least 25–35 wt % polystyrene or poly(n-butyl acrylate) coil segments show a two-dimensional hexagonal arrangement of rod aggregates, as characterized by transmission electron microscopy and small-angle X-ray scattering. Polyisoprene block copolymers exhibit a lamellar microstructure with short rigid domains in which the rod units lie in an interdigitated smectic C arrangement. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3640–3656, 2003     

Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.     

Effects of the H-bond donor structure on the properties of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane)s and stilbazoles

Supramolecular side chain liquid crystalline polymers (SCLCPs) based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane) (PSIX, X=100, 76, 60, 41 or 23, denoting the mole percentage of 3-carboxypropylmethylsiloxane unit in the polymer) and stilbazole derivatives have been obtained through intermolecular hydrogen bonding (H-bonding) interactions between the carboxylic acid and the pyridyl moieties. The formation of H-bonding and self-assembly results in the formation of new mesogenic units, in which H-bonds function as molecular connectors. FTIR shows the existence of H-bonding in the complexes. The polymeric complexes behave as single component liquid crystalline polymers and exhibit stable and enantiotropic mesophases. The liquid crystalline properties of the supramolecular SCLCPs were studied using differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction, and were found to exhibit smectic A phases with focal-conic textures. The thermal stability of the SCLCP increases on increasing the carboxylic acid content in the polysiloxane and the concentration of the stilbazole derivative in the complex. However, the thermal stability decreases on increasing the chain length of the stilbazole derivative. The crystal phase was not formed even on cooling to the glass transition temperature of the polymeric complex.     

The Spectrum of a Linearized 2D Euler Operator

We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two-dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator.     

A minimal pair joining to a plus cupping Turing degree

A computably enumerable (c.e.) degree a is called nonbounding, if it bounds no minimal pair, and plus cupping, if every nonzero c.e. degree x below a is cuppable. Let NB and PC be the sets of all nonbounding and plus cupping c.e. degrees, respectively. Both NB and PC are well understood, but it has not been possible so far to distinguish between the two classes. In the present paper, we investigate the relationship between the classes NB and PC , and show that there exists a minimal pair which join to a plus cupping degree, so that PC ? NB . This gives a first known difference between NB and PC . (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear rheological behavior of silica filled solution‐polymerized styrene butadiene rubber

The reinforcement and nonlinear viscoelastic behavior have been investigated for silica (SiO₂) filled solution‐polymerized styrene butadiene rubber (SSBR). Experimental results reveal that the nonlinear viscoelastic behavior of the filled rubber is similar to that of unfilled SSBR, which is inconsistent with the general concept that this characteristic comes from the breakdown and reformation of the filler network. It is interesting that the curves of either dynamic storage modulus (G′) or loss tangent (tan δ) versus strain amplitude (γ) for the filled rubber can be superposed, respectively, on those for the unfilled one, suggesting that the primary mechanism for the Payne effect is mainly involved in the nature of the entanglement network in rubbery matrix. It is believed there exists a cooperation between the breakdown and reformation of the filler network and the molecular disentanglement, resulting in enhancing the Payne effect and improving the mechanical hysteresis at high strain amplitudes. Moreover, the vertical and the horizontal shift factors for constructing the master curves could be well understood on the basis of the reinforcement factor f(φ) and the strain amplification factor A(φ), respectively. The surface modification of SiO₂ causes a decrease in f(φ), which is ascribed to weakeness of the filler–filler interaction and improvement of the filler dispersion. However, the surface nature of SiO₂ hardly affects A(φ). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2594‐2602, 2007