Strain localization in an oscillating Maxwell viscoelastic cylinder

The transient rotation responses of simple, axisymmetric, viscoelastic structures are of interest for interpretation of experiments designed to characterize materials and closed structures such as the brain using magnetic resonance techniques. Here, we studied the response of a Maxwell viscoelastic cylinder to small, sinusoidal displacement of its outer boundary. The transient strain field can be calculated in closed form using any of several conventional approaches. The solution is surprising: the strain field develops a singularity that appears when the wavefront leaves the center of the cylinder, and persists as the wavefront reflects to the outer boundary and back to the center of the cylinder. The singularity is alternately annihilated and re-initiated upon subsequent departures of the wavefront from the center of the cylinder until it disappears in the limit of steady state oscillations. We present the solution for this strain field, characterize the nature of this singularity, and discuss its potential role in the mechanical response and evolved morphology of the brain.     

A nonlinear model of vortex-induced forces on an oscillating cylinder in a fluid flow

A nonlinear model relating the imposed motion of a circular cylinder, submerged in a fluid flow, to the transverse force coefficient is presented. The nonlinear fluid system, featuring vortex shedding patterns, limit cycle oscillations and synchronisation, is studied both for swept sine and multisine excitation. A nonparametric nonlinear distortion analysis (FAST) is used to distinguish odd from even nonlinear behaviour. The information which is obtained from the nonlinear analysis is explicitly used in constructing a nonlinear model of the polynomial nonlinear state-space (PNLSS) type. The latter results in a reduction of the number of parameters and an increased accuracy compared to the generic modelling approach where typically no such information of the nonlinearity is used. The obtained model is able to accurately simulate time series of the transverse force coefficient over a wide range of the frequency–amplitude plane of imposed cylinder motion.     

Wavy mode of the streaked flow around an oscillating cylinder in a stratified fluid at rest

The structures of the flow induced by a vertical circular cylinder performing transverse oscillations in a linearly stratified fluid at rest are investigated. The density gradient inhibits the onset of the three-dimensional instability. The instability appears as regularly spaced streaked flows along the cylinder axis. Each streaked flow follows a wavy path in the horizontal plane in a certain range of amplitude and frequency of the oscillations.     

基于格子Boltzmann方法的粘弹性流体圆柱绕流分析

将光滑界面法引入到格子Boltzmann方法中分析粘弹性流体绕流问题,分别采用单松弛模型和对流扩散模型求解运动方程和Oldroyd-B本构方程,针对圆形和椭圆内部边界条件,给出连续界面插值函数,在此基础上,运用光滑界面法将内部边界转换为作用力项施加到演化方程中。首先分析圆柱绕流问题,给出不同材料参数情况下的流场分布和阻力系数计算结果,比较发现与宏观数值模拟结果相吻合。将模型拓展到绕椭圆流动中,分析椭圆形状和材料参数对粘弹性流体绕柱流的影响,发现随着椭圆长轴与短轴比值的增加和维森伯格数的增加,阻力系数逐渐下降,并且长短轴比对迭代收敛有较大影响。     

Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Mixed convection from a cylinder oscillating vertically in a quiescent fluid

 The problem of heat convection from a vertically oscillating cylinder in a quiescent fluid is investigated. The governing equations of motion and energy are solved numerically in a non-inertial frame of references to determine the flow field and heat transfer characteristics under different conditions. The main dominating parameters are Keulegan–Carpenter number, KC, frequency parameter, β, Grashof number, Gr and Prandtl number, Pr. The ranges considered for these parameters are KC ≤ 10, β≤40 and Gr ≤ 10⁵ while Prandtl number is kept constant. The study revealed that the effect of amplitude and frequency of oscillation on heat transfer is strongly influenced by the Grashof number range. In the forced convection regime (Gr = 0), the increase of KC creates extensive vortex motion at all cylinder positions that leads to a significant increase in heat transfer. A similar trend, but with a lesser extent, is also observed for the increase of β. However, at high Grashof numbers, the effect of oscillation on heat convection is only significant at large values of KC. Received on 5 June 2000 / Published online: 29 November 2001     

Quantitative interpretation of vortices from a cylinder oscillating in quiescent fluid

 The instantaneous, quantitative patterns of vortices arising from sinusoidal oscillation of a cylinder in quiescent fluid are experimentally characterized for the first time using high-image-density particle image velocimetry. The near-wake does not indicate a separated layer of distributed vorticity leading to a single, large-scale vortex. Rather, for sufficiently high Reynolds number, a sequence of small-scale vorticity concentrations is formed. Agglomeration of only a fraction of the adjacent concentrations forms a larger-scale vortex. Simultaneously, vorticity concentrations of opposite sense are formed along the base (rear) of the cylinder. Streamline patterns typically indicate, however, only the larger-scale vortex; it has a circulation smaller than the total circulation of all vorticity concentrations that are not revealed by the streamlines. These observations are interpreted in the context of the effective resolution of the flow images. Received: 27 October 1995 / Accepted: 27 August 1996     

Visual observations of the flow around a half-submerged oscillating circular cylinder

Visual observations are made on the flow around a horizontal circular cylinder which is half-submerged in still water and forced to oscillate vertically. The ends of the cylinder have great influence on the wave pattern and flow field. Progressive plane waves are generated at small forcing amplitudes, but cross-waves are superimposed on the progressive plane waves at large forcing amplitudes. The wavelength of the cross-waves in the direction parallel to the cylinder axis increases with the forcing amplitude. The crests of the cross-waves are in parallel lines which are oblique to the cylinder axis. The angle at which the parallel lines meet the cylinder axis decreases as the forcing amplitude is increased. Three kinds of steady flows are induced in the water: surface flow, undersurface flow, and vertical jet.     

The squeeze-film flow of a viscoelastic fluid

We report on the use of a numerical method to solve the (inertia-less) squeeze-film flow problem for a viscoelastic fluid. The method is based on a Boundary Element formulation and relies on a time-marching scheme. The viscoelastic fluid is modelled by a constitutive law that allows for a shear stress overshoot mechanism in a suddenly started shear flow. The results show convincingly that the load enhancement sometimes observed experimentally is due to stress overshoot. A simple explanation for the enhancement is suggested; the stress overshoot appears quickly and takes a long time to die away, so that steady-state viscous behaviour is not very relevant.     

Stability of a viscoelastic plate in fluid flow

The stability of an infinite viscoelastic plate on an elastic foundation in a viscous incompressible flow is studied. The Navier-Stokes system is linearized for an exponential velocity profile. The problem is reduced by a Fourier-Laplace transform to a system of ordinary differential equations, whose solution is found in the form of convergent series. The roots of the dispersion relation that characterize the stability of the system are found numerically. The effect of the viscosities of the fluid and the plate on the stability of the waves propagating upstream and downstream is studied. The results are compared with available data on the stability of a viscoelastic plate in an ideal fluid flow. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 66–74, July–August, 2006.     

Secondary flow structures in developing viscoelastic fluid flow through curved ducts with square cross section

Meccanica - The present paper numerically investigates viscoelastic fluid flow in the developing flow regime through both straight and 90-degree curve ducts. The aim is to investigate the effects...     

Hydroelastic instabilities in viscoelastic flow past a cylinder confined in a channel

Experimental investigation of viscoelastic flow past a cylinder is conducted for a polyisobutylene-based polymer solution. High-image-density particle image velocimetry is utilized to quantitatively determine the spatial features of elastic wake instabilities. The viscoelastic flow bifurcates from steady two-dimensional flow to steady three-dimensional flow for values of the Deborah number (dimensionless flow rate) greater than a critical value. These hydroelastic flow transitions are manifested in the form of three-dimensional cells spaced periodically along the axis of the cylinder. The elastic flow structures do not exist in the Newtonian counterpart of creeping flow past a cylinder. Received: 7 October 1998 / Accepted: 22 April 1999     

Three-dimensional instability of an oscillating viscous flow past a circular cylinder

IntroductionTheunsteadyflowpastacircularcylinderhasreceivedagreatdealofattentionowingmainlytoitstheoreticalandpracticalsignificance .Theflowgeneratedbytheoscillationofthecylinder,oroscillatingflowsaroundthecylinder,canbecharacterizedbytwoparameters.OneistheKeulegan_Carpenternumber,definedasKC =UmT/D ,andtheotheristheReynoldsnumberRe=UmD/ν,orafrequencyparameter,definedasβ=D2 / (νT) =Re/KC) ,whichisoftenusedtoreplacetheReynoldsnumberasthesecondparameter.Here,Umisthemaximumvelocityofth…     

Uniform flow of viscoelastic fluids past a confined falling cylinder

Uniform steady flow of viscoelastic fluids past a cylinder placed between two moving parallel plates is investigated numerically with a finite-volume method. This configuration is equivalent to the steady settling of a cylinder in a viscoelastic fluid, and here, a 50% blockage ratio is considered. Five constitutive models are employed (UCM, Oldroyd-B, FENE-CR, PTT and Giesekus) to assess the effect of rheological properties on the flow kinematics and wake patterns. Simulations were carried out under creeping flow conditions, using very fine meshes, especially in the wake of the cylinder where large normal stresses are observed at high Deborah numbers. Some of the results are compared with numerical data from the literature, mainly in terms of a drag coefficient, and significant discrepancies are found, especially for the constant-viscosity constitutive models. Accurate solutions could be obtained up to maximum Deborah numbers clearly in excess of those reported in the literature, especially with the PTT and FENE-CR models. The existence or not of a negative wake is identified for each set of model parameters.     

Resonance in flow past oscillating cylinder under subcritical conditions

Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method(LBM). The effects of the Reynolds number,oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime(VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime(VSR II)occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle,and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately.