Nonlinear convection of a viscoelastic fluid with inclined temperature gradient

The energy method is used to analyze the viscoelastic fluid convection problem in a thin horizontal layer, subjected to an applied inclined temperature gradient. The boundaries are considered to be rigid and perfectly conducting. Both linear and nonlinear stability analyses are carried out. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and comparisons are reported between the results of the linear theory and energy stability theory.Received: 12 March 2004, Accepted: 19 April 2004, Published online: 17 September 2004PACS: 47.20 Ky, 47-27 Te, 83.60 Wc Correspondence to: P.N. Kaloni     

Asymptotic solutions of the axisymmetric moist Hadley circulation in a model with two vertical modes

A simplified model of the moist axisymmetric Hadley circulation is examined in the asymptotic limit in which surface drag is strong and the meridional wind is weak compared to the zonal wind. Our model consists of the quasi-equilibrium tropical circulation model (QTCM) equations on an axisymmetric aquaplanet equatorial beta-plane. This model includes two vertical momentum modes, one baroclinic and one barotropic. Prior studies use either continuous stratification, or a shallow water system best viewed as representing the upper troposphere. The analysis here focuses on the interaction of the baroclinic and barotropic modes, and the way in which this interaction allows the constraints on the circulation known from the fully stratified case to be satisfied in an approximate way. The dry equations, with temperature forced by Newtonian relaxation towards a prescribed radiative equilibrium, are solved first. To leading order, the resulting circulation has a zonal wind profile corresponding to uniform angular momentum at a level near the tropopause, and zero zonal surface wind, owing to the cancelation of the barotropic and baroclinic modes there. The weak surface winds are calculated from the first-order corrections. The broad features of these solutions are similar to those obtained in previous studies of the dry Hadley circulation. The moist equations are solved next, with a fixed sea surface temperature at the lower boundary and simple parameterizations of surface fluxes, deep convection, and radiative transfer. The solutions yield the structure of the barotropic and baroclinic winds, as well as the temperature and moisture fields. In addition, we derive expressions for the width and strength of the equatorial precipitating region (ITCZ) and the width of the entire Hadley circulation. The ITCZ width is on the order of a few degrees in the absence of any horizontal diffusion and is relatively insensitive to parameter variations.     

The boundary layer solutions of the interface problem considering the strain gradient

According to the classical elastic theory, there is always a discontinuity of rotation angle on the interface between different materials. This illogic result can be overcome by the strain gradient plasticity theory. In the light of this theory, there is a group of boundary layer solutions near the interface, which have made important adjustment of the classical results. This project is supported by National Natural Science Foundation of China (19891180).     

Comparative study of two corrective gradient models in the simulation of multiphase flows using moving particle semi-implicit method

In this study, two corrective gradient models (CGMs) are compared in the simulation of multiphase flows. Linear consistency of the gradient model of moving particle semi-implicit (MPS) method has been recovered by introducing corrective matrix. However, it is found that particles tend to disperse along the streamline while using the CGM proposed in a previous study. Particle shifting (PS) schemes are necessary to reduce the irregularity of particle distribution to stabilize the calculation. To enhance the accuracy and stability, another CGM with dummy particle (CGMD) was proposed in our previous study. This enhanced CGM is featured by linear consistency and purely repulsive pressure gradient force. In this study, this enhanced CGM is modified and applied to multiphase flow simulation. Comparative study suggests that the modified CGM with PS scheme is capable of calculating various multiphase flows and predicting the interface evolution both clearly and accurately.     

On the effect of temperature gradient on the stability of circular tubes made of hyperelastic entropic material

Rubber-like materials are very applicable in almost all fields of industries, but due to their large deformation characteristic, they can exhibit a variety of instabilities. Accordingly, many researchers have been motivated to investigate the effects of different parameters on the stability of hyperelastic cylindrical tubes under finite deformation, while the effects of temperature gradient have not been considered. In this paper, the effects of temperature variation on the stability and thermo-mechanical behavior of the cylindrical tubes made of the entropic materials such as rubber-like materials and elastomers are investigated via an effective strain energy density function. To this purpose, an Ogden-type strain energy density with only integer powers is applied in order to determine an analytical solution, not involving the integral form, for the stress distribution through the wall thickness of cylindrical tubes at finite deformation thermoelasticity. This problem is examined in two cases including (i) a thick-walled cylindrical tube under internal pressure and uniform variation of temperature and (ii) a thick-walled cylindrical tube under internal pressure and temperature gradient, simultaneously. It was observed that the positive temperature gradients in comparison with environment temperatures improve the stability of the circular tubes made of the entropic materials.     

On the homogenization of metal matrix composites using strain gradient plasticity

The homogenized response of metal matrix composites（MMC） is studied using strain gradient plasticity.The material model employed is a rate independent formulation of energetic strain gradient plasticity at the micro scale and conventional rate independent plasticity at the macro scale. Free energy inside the micro structure is included due to the elastic strains and plastic strain gradients. A unit cell containing a circular elastic fiber is analyzed under macroscopic simple shear in addition to transverse and longitudinal loading. The analyses are carried out under generalized plane strain condition. Micro-macro homogenization is performed observing the Hill-Mandel energy condition,and overall loading is considered such that the homogenized higher order terms vanish. The results highlight the intrinsic size-effects as well as the effect of fiber volume fraction on the overall response curves, plastic strain distributions and homogenized yield surfaces under different loading conditions. It is concluded that composites with smaller reinforcement size have larger initial yield surfaces and furthermore,they exhibit more kinematic hardening.     

Determination of the yield properties of thin films using enhanced coherent gradient sensing

This paper describes coherent gradient sensing (CGS) as an optical, full-field, real-time, nonintrusive, noncontact technique for measurement of curvature and curvature changes in single-layered and multilayered thin films deposited on substrates. The sensitivity of the basic CGS technique is enhanced using optical fringe multiplication to map curvature in very flat specimens (k0.001 m^–1). Subsequently, this curvature measurement technique is applied to the determination of the yield properties of thin films subjected to cyclic thermomechanical loading.     

A note on the two temperature theory with dual-phase-lag delay: Some exact solutions

In this note we present exact solutions of two initial-boundary value problems (IBVP)s in the setting of a recently-introduced theory of heat conduction, wherein the two temperature theory of the late 1960s is merged with Tzou’s dual-phase-lag flux relation. First, we solve a one-dimensional problem on a finite interval for a simple, parabolic initial condition. We then describe how to extend the analysis to the general three-dimensional case. In particular, it is demonstrated that the instability which generally arises in connection with the dual-phase-lag model can be avoided under this hybrid formulation.     

基于应变梯度理论的微尺度蜂窝等效模量计算方法

本文提出了一种新的能够计及尺度效应的微纳米蜂窝等效模量的计算方法。将一种单参数应变梯度理论引入到本构方程当中,并基于能量等效原理推导了蜂窝面内等效模量地计算公式。算例分析表明,本文方法能够有效地计及尺度效应对蜂窝等效模量的影响。尺度效应与胞壁厚度和长度的值都有关,当胞壁厚度较小时,尺度效应显著,本文方法预测的模量会明显高于传统方法;而当胞壁厚度较大时,尺度效应变得微弱乃至可以忽略不计。但如果胞壁的长度/厚度比很大,则面内等效模量会趋近于0,此时是否考虑尺度效应意义不大。     

Numerical study of adverse pressure gradient generation over a flat plate using a rotating cylinder

Generating an adverse pressure gradient (APG), using a rotating cylinder in the proximity of a plane wall under a laminar freestream flow, is studied numerically in this work. The magnitude of the generated APG is a function of the gap, G, between the cylinder and the wall, and the rotational speed of the cylinder, Ω. The flow in such a configuration is characterized by periodic transient vortex shedding at high Reynolds number. A numerical model for the computation of the transient flow for this configuration is developed using the ANSYS CFD simulation tool. The model is validated against published experimental and numerical data for similar flow configurations and excellent agreement is observed. A parametric study is carried out for different combinations of G and Ω for two different Reynolds numbers of 200 and 1000 to examine the development of the resulting separation bubble due to the generated APG. The mechanism of the boundary layer separation over the plane wall and the corresponding wake dynamics is investigated. Results are presented in terms of the distribution of the pressure coefficient as well as skin friction coefficient along the wall and flow patterns around and downstream of the cylinder in the proximity of the wall. The results of these computations confirm that using a rotating cylinder over a plane wall in a freestream flow is an effective technique to generate a controlled range of adverse pressure gradients.     

Influence of temperature on the slip velocity of semidilute xanthan gum solutions

We obtain experimental evidence of the influence of temperature in the range 12-32°C on the slip phenomena of two different 0.3% xanthan solutions in a glass capillary rheometer. Enhancement of the slip velocity was observed for both samples around the corresponding thermally induced order-disorder transition temperature. Intrinsic viscosity measurements were performed to find the conformation change of both samples. Concentrations of 0.15% and 0.2% were analyzed for one sample, showing absence of slip at 0.15%.Slip velocity measurements were determined with the traditional Mooney method for a L/D ratio of the capillaries (640) enough to neglect entry head losses. Comparisons were done with the method developed by Piau et al. (1990) and with the one developed by Hatzikiriakos and Dealy (1992). The resulting behavior of the slip velocity with the capillary diameters, calculated with the method of Hatzikiriakos and Dealy, was contrary to the behavior experimentally found by other authors. The observed differences in the slip velocity, measured with the other two methods, were proportional and nearly independent of temperature and diameter of the capillaries.     

Analysis of iterative methods for the viscous/inviscid coupled problem via a spectral element approximation

Based on a new global variational formulation, a spectral element approximation of the incompressible Navier–Stokes/Euler coupled problem gives rise to a global discrete saddle problem. The classical Uzawa algorithm decouples the original saddle problem into two positive definite symmetric systems. Iterative solutions of such systems are feasible and attractive for large problems. It is shown that, provided an appropriate pre‐conditioner is chosen for the pressure system, the nested conjugate gradient methods can be applied to obtain rapid convergence rates. Detailed numerical examples are given to prove the quality of the pre‐conditioner. Thanks to the rapid iterative convergence, the global Uzawa algorithm takes advantage of this as compared with the classical iteration by sub‐domain procedures. Furthermore, a generalization of the pre‐conditioned iterative algorithm to flow simulation is carried out. Comparisons of computational complexity between the Navier–Stokes/Euler coupled solution and the full Navier–Stokes solution are made. It is shown that the gain obtained by using the Navier–Stokes/Euler coupled solution is generally considerable. Copyright © 2000 John Wiley & Sons, Ltd.     

Exact closed-form solutions for the static analysis of multi-cracked gradient-elastic beams in bending

Cracks and other forms of concentrated damage can significantly affect the performance of slender beams under static and dynamic loads. The computational model for such defects often consists of a localised reduction in the flexural stiffness, which is macroscopically equivalent to a beam where the undamaged parts are hinged at the position of the crack, with a rotational spring taking into account the residual stiffness (“discrete spring” model). It has been recently demonstrated that this model is equivalent to an inhomogeneous Euler–Bernoulli beam in which a Dirac’s delta is added to the bending flexibility at the position of each damage (“flexibility crack” model). Since these models concentrate the increased curvature at a single abscissa, a jump discontinuity appears in the field of rotations. This study presents an improved representation of cracked slender beams, based on a general class of gradient elasticity with both stress and strain gradient, which allows smoothing the singularities in the flexibility crack model. Exact closed-form solutions are derived for the static response of slender gradient-elastic beams in flexure with multiple cracks, and the numerical examples demonstrate the effects of the nonlocal mechanical parameters (i.e. length scales of the gradient elasticity) in this context.     

Processing the Couette viscometry data using a Bingham approximation in shear rate calculation

This paper presents an approach to computing the shear flow curve from torque–rotational velocity data in a Couette rheometer. The approximation techniques in shear rate calculation are generally dictated by the radius ratio between coaxial cylinders and the rheological behaviour of fluid tested. Here, the approach consists in analysing the sheared material as a Bingham fluid and computing an average shear rate when the fluid in the cylindrical gap is partially and fully sheared. We focus in particular on the applicability of the Bingham approximation in shear rate calculation. First, the approach is assessed by examining synthetic data generated with Newtonian, non-Newtonian and yield stress materials with known properties, varying the gap radius ratio. The results, which are compared with commonly used techniques in shear rate calculation, prove the relevance of the proposed approach. Finally, its efficiency is examined by applying it to process Couette data of yield stress fluids taken from published works.     

初始和边界不同恒温时二维梯度板瞬态温度场

为了研究二维功能梯度板的平面瞬态温度场及影响因素,假设热导率和容积比热容在板的高和宽方向为同一类型指数函数分布,基于该板的瞬态热传导基本方程,采用分离变量法,导出在初始和边界不同恒温时该板平面瞬态温度场的级数解析解.通过两种方法的对比,验证了论文研究结果的正确性.结果表明:方板内的等温线,在梯度参数α=β时,对称于板的45°对角线分布,在α=β=0时,对称于板的中心分布;在α≠β时,板的等温线不具对称性;随着冷却时间的增加,非均匀板的等温线向左下(或右上)角移动,右上(或左下)角等温线间距变宽,左下(或右上)角等温线间距变窄,且矩形板的冷却过程比方板更快.因此,可选择适合的梯度参数和几何形状来满足设计、应用和热应力分析的需要,该解析解可作为检验其他近似方法的参考标准.     

Fracture of bicrystal metal/ceramic interfaces: A study via the mechanism-based strain gradient crystal plasticity theory

Two continuum mechanical models of crystal plasticity theory namely, conventional crystal plasticity theory and mechanism-based crystal plasticity theory, are used to perform a comparative study of stresses that are reached at and ahead of the crack tip of a bicrystal niobium/alumina specimen. Finite element analyses are done for a stationary crack tip and growing cracks using a cohesive modelling approach. Using mechanism-based strain gradient crystal plasticity theory the stresses reached ahead of the crack tip are found to be two times larger than the stresses obtained from conventional crystal plasticity theory. Results also show that strain gradient effects strongly depend on the intrinsic material length to the size of plastic zone ratio (l/R₀). It is found that the larger the (l/R₀) ratio, the higher the stresses reached using mechanism-based strain gradient crystal plasticity theory. An insight into the role of cohesive strength and work of adhesion in macroscopic fracture is also presented which can be used by experimentalists to design better bimaterials by varying cohesive strength and work of adhesion.     

Fully coupled finite volume solutions of the incompressible Navier–Stokes and energy equations using an inexact Newton method

An inexact Newton method is used to solve the steady, incompressible Navier–Stokes and energy equation. Finite volume differencing is employed on a staggered grid using the power law scheme of Patankar. Natural convection in an enclosed cavity is studied as the model problem. Two conjugate-gradient -like algorithms based upon the Lanczos biorthogonalization procedure are used to solve the linear systems arising on each Newton iteration. The first conjugate-gradient-like algorithm is the transpose-free quasi-minimal residual algorithm (TFQMR) and the second is the conjugate gradients squared algorithm (CGS). Incomplete lower-upper (ILU) factorization of the Jacobian matrix is used as a right preconditioner. The performance of the Newton- TFQMR algorithm is studied with regard to different choices for the TFQMR convergence criteria and the amount of fill-in allowed in the ILU factorization. Performance data are compared with results using the Newton-CGS algorithm and previous results using LINPACK banded Gaussian elimination (direct-Newton). The inexact Newton algorithms were found to be CPU competetive with the direct-Newton algorithm for the model problem considered. Among the inexact Newton algorithms, Newton-CGS outperformed Newton- TFQMR with regard to CPU time but was less robust because of the sometimes erratic CGS convergence behaviour.