Turbulent structures in an optimal Taylor–Couette flow between concentric counter-rotating cylinders

The turbulent structures formed in a Taylor–Couette (TC) flow established between two concentric counter-rotating cylinders were explored numerically. The shear Reynolds number was set to Re_shear = 8000 and the radius ratio was set to r_i/r_o = 0.5. An optimal flow corresponding to the maximal angular velocity transport between the cylinders was selected for the TC flow. The mean velocity profile reached its steepest value near the cylinders in the optimal TC flow. The streamwise velocity correlations at the outer cylinder in the gap exceeded those at the inner cylinder. The large convective transport of angular velocity in the gap generated a maximal angular velocity flux to achieve the optimal flow. The angular velocity flux generated by the momentum source exceeded that generated by the momentum sink. The vorticity dispersion was larger near the inner cylinder than near the outer cylinder, but vorticity stretching near the outer cylinder exceeded than that near the inner cylinder. The skin friction coefficient budgets were plotted using the velocity–vorticity correlation. The vortex stretching contributions dominated the skin friction budgets. The area near the inner cylinder was populated by stronger vortices, but their population density was smaller than the population density of the vortices near the outer cylinder. The probability density functions of the wall-normal and streamwise velocity fluctuations delineated the presence of the large wall-normal velocity fluctuations near the outer cylinder.     

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent -?2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.     

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

This paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress is also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.     

Asymptotic Models of Diffusion Effects due to Nonlinear Resonant Interaction of Waves with Flows

We develop an asymptotic theory describing nonlocal effects caused by weak-diffusion processes in the case of resonant interaction of quasi-harmonic waves of small but finite amplitudes with flows of various physical nature in the case of an arbitrary relation between the nonlinearity and diffusion.We analyze the interaction of internal gravity waves with plane-parallel stratified shear flows in the nonlinearly-dissipative critical layer (CL) formed in the vicinity of the resonance level where the flow velocity is equal to the phase velocity of the wave. It is shown that the combined effect of the radiation force in the inner region of the CL and vorticity diffusion to the outer region results in the formation of a flow in which the asymptotic values of average vorticity at different sides of the CL are constant but different. If the criterion of the linear dynamic stability is satisfied (the Richardson number Ri>1/4), the resulting vorticity steps are comparable to the unperturbed vorticity. As a result, a wave reflected from the vorticity inhomogeneity in the CL is formed. As the amplitude of the incident wave increases, the average vorticity at the incidence side approaches the linear-stability threshold (Richardson number Ri > 1/4), and the reflection coefficient tends to -1.In the regime of nonlinear dissipative CL, we study the quasi-stationary asymptotic behavior of the flow formed by an internal gravity wave incident on a dynamically stable flow with velocity and density stratification, whose velocity at some level is equal to the phase velocity of the wave. It is shown that the vorticity diffusion results in the formation of a nonlocal transition region between the CL and the unperturbed flow, which we call the diffusive boundary layer (DBL). In this case, the CL is shifted toward the incident wave. We obtain a self-similar solution for the average fields, which is valid in the case of a constant vorticity step in the CL, and determine its parameters depending on the inner Reynolds number in the CL which describes the relation between the nonlinear and diffusive effects for the wave field in the resonance region. We determine the structure and temporal dynamics of the DBL formed by a rough surface streamlined by a stratified fluid whose velocity changes direction at some level.It is shown that in the case of the nonlinear resonance interaction of plasma electrons with a Langmuir wave, the electron diffusion in the velocity space leads to a significant nonlocal distortion of the electron distribution function outside the trapping region. We determine the distorted distribution function and calculate the rate of the nonlinear Landau damping of a finite-amplitude wave for an arbitrary ratio of the electron collision rate and the oscillation period of trapped electrons.     

Phase averaged velocity field in the near wake of a square cylinder obtained by a PIV method

Phase averaged velocity fields in the near wake region behind a square cylinder have been successfully obtained using randomly sampled PIV data sets. The Reynolds number based on the flow velocity and the model height was 3,900. To identify the phase information, we examined the magnitude of circulation and the center of peak vorticity. The center of vorticity was estimated from lowpass filtered vorticity contours adopting a sub-pixel searching algorithm. Due to the sinusoidal nature of circulation which is closely related to the instantaneous vorticity, the location of peak vorticity fits well with a sine curve of the circulation magnitude. Conditionally averaged velocity fields represent the Karman Vortex shedding phenomenon quite successfully within ±5° phase uncertainty. The oscillating nature of the separated shear layers and the separation bubble at the upper and lower surfaces are clearly observed. With the hot-wire measurement of Strouhal frequency, we found that the convection velocity changes its magnitude very rapidly from 25 to 75 percent of the free stream velocity along the streamwise direction when the flow passes the recirculation region.     

Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.     

Inline ultrasonic rheometry by pulsed Doppler

This will be a discussion of the non-invasive determination of the viscosity of a non-Newtonian fluid in laminar pipe flow over the range of shear rates present in the pipe. The procedure used requires knowledge of the flow profile in and the pressure drop along a long straight run of pipe. The profile is determined by using a pulsed ultrasonic Doppler velocimeter. This approach is ideal for making non-invasive, real-time measurements for monitoring and control. Rheograms of a shear thinning gel will be presented. The operating parameters and limitations of the Doppler-based instrument will be discussed. The most significant limitation is velocity gradient broadening of the Doppler spectra near the walls of the pipe. This limitation can be significant for strongly shear thinning fluids (depending also on the ratio of beam to pipe diameter and the transducer's insertion angle).     

Vortex shedding and vorticity fluxes in the wake of cylinders within a random array

This work investigates the impact of the background turbulence generated by randomly placed cylinders on the vortex shedding regime and the mechanisms associated to vorticity fluxes. The goals are achieved by exploring velocity databases acquired with a two-dimensional particle image velocimetry system in two types of turbulent flow experiments: flow around a single infinite cylinder and flow within random array of infinite cylinders. Formation lengths, power spectral density functions and vortex distributions are employed to discuss the vortex shedding regime. The effects of background turbulence and vorticity cancellation, due to opposite sign vorticity, on the vorticity fluxes are discussed. The results show that the background turbulence reduces the formation length and consequently increase the shedding frequency. The stronger decay of longitudinal vorticity flux in denser arrays is not accompanied by an increase of the lateral flux of vorticity. Furthermore, it was concluded that the decay of longitudinal vorticity flux is mainly caused by the vorticity cancellation due to the vorticity of opposite sign of close downstream cylinders.     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999     

串列双圆柱时均流场特性分析

对Re=12 000,间距比L/D=1.167,2.333,3.500和4.667的串列双圆柱后方速度场进行了实验测量,分析串列双圆柱后方不同剖面处的速度分布规律和湍流度分布规律.并通过流函数理论模型对小间距比串列双圆柱后方流场进行了分析,得出如下结论:与单圆柱相比,当串列双圆柱间距比较小时,后方圆柱的自由剪切层明显向内偏移.随着间距比的变大,由于前方圆柱的尾流对后方圆柱的干扰,后方圆柱的自由剪切层变得越来越模糊.对于间距比较大的串列双圆柱,其对后方流场的扰动较强,致使后方流场湍流强度和最大速度衰减量较大.通过流函数理论模型分析发现,在小间距比条件下,串列双圆柱由于两个圆柱的相互干扰,使得圆柱后方涡相互靠近,并且后方涡向外倾斜的角度也减小,从而导致了自由剪切层向内侧偏移.      

Direct visualization of continuous simple shear in non-Newtonian polymeric fluids

Using a particle tracking velocimetric technique, we show direct evidence of nonlinear velocity profiles during simple-shear flow of an entangled polymer solution, offering new insight into the origins of such characteristics as stress overshoot. Upon a startup shear by imposing a constant velocity on one of the two surfaces that confine the sample, the velocity field evolves from the initial linearity across the gap to a final state with a shear rate gradient. The unexpected deviation from the widely assumed linear variation of the velocity along the gap direction is most plausibly due to the entangled polymer's ability to disentangle in the presence of high shear that can orient the polymer chains leading to anisotropy in their mutual constraint.     

Ultrasound velocimetry in a shear-thickening wormlike micellar solution: Evidence for the coexistence of radial and vorticity shear bands

We carried out pointwise local velocity measurements on 40 mM cetylpyridinium chloride-sodium salicylate (CPyCl-NaSal) wormlike micellar solution using high-frequency ultrasound velocimetry in a Couette shear cell. The studied wormlike solution exhibits Newtonian, shear-thinning and shear-thickening rheological behavior in a stress-controlled environment. Previous rheology, flow visualization and small-angle light/neutron scattering experiments in the shear-thickening regime of this system showed the presence of stress-driven alternating transparent and turbid rings or vorticity bands along the axis of the Couette geometry. Through local velocity measurements we observe a homogeneous flow inside the 1mm gap of the Couette cell in the shear-thinning (stress-plateau) region. Only when the solution is sheared beyond the critical shear stress (shear-thickening regime) in a stress-controlled experiment, we observe inhomogeneous flow characterized by radial or velocity gradient shear bands with a highly sheared band near the rotor and a weakly sheared band near the stator of the Couette geometry. Furthermore, fast measurements performed in the shear-thickening regime to capture the temporal evolution of local velocities indicate coexistence of both radial and vorticity shear bands. However the same measurements carried out in shear rate controlled mode of the rheometer do not show such rheological complexity.     

Flow pattern in a polymer coil placed into a stationary longitudinal flow

The flow pattern of solvent in a polymer coil placed into a stationary flow is examined. In contrast to the previous works, the flow of solvent at large distances from the macromolecule has a constant longitudinal gradient. The calculations are based on a simple model of macromolecule dynamics in flowing solutions proposed earlier. An analysis of the results shows that, in the first-order approximation in the longitudinal velocity at a certain threshold value of the parameter of hydrodynamic interactions P, the coil acquires a hydrodynamic boundary at which the radial component of the flow velocity is zero. The threshold value of P coincides with that for a stationary shear flow, determined earlier. At large P, i.e., large molecular mass, the hydrodynamic boundary of the coil encompasses a major part of the macromolecule, while the longitudinal intrinsic viscosity takes a form analogous to that characteristic of a suspension of solid balls with a radius equal to the radius of inertia of the polymer coil. In the second-order approximation in the flow velocity, the radial component of the flow velocity is nonzero. As a result, the mass transfer of solvent between the regions separated by the hydrodynamic boundary only slows down, without hindering the speedup of reactions by mixing the reagents and macromolecules.     

High Pressure High Temperature Dynamic Rheometry of Sulfonated Polyacrylamide Solutions in Electrolyte Media as Used for Oil Recovery Applications

Sulfonated polyacrylamide (SPAA) solutions were prepared and the effects of pressure, polymer concentration, and water temperature, pH and salinity on their rheological behavior were investigated using a concentric cylinder dynamic rheometer equipped with a high pressure cell. According to the rheological flow curves the shear stress of SPAA solutions increased less than in proportion to their shear rates; that is, a shear thinning effect occurred. For polymer solutions containing 15,000 ppm of SPAA, shear viscosity, and stress were nearly insensitive to pressure. However, the shear viscosity and stress of SPAA solutions were affected by temperature and this effect was more evident at lower pressure. The flow curves indicated the shear viscosity and stress of the samples increased with increasing SPAA concentration and pH of the water, but were decreased with increasing water salinity and temperature.     

锥体后速度场与压力场的测量与分析

利用全流向十七孔压力探针,测量了Re=1.5×105与Re=3.0×105（基于锥体底面直径）,攻角为0°,锥角为60°的圆锥体后流场速度与压力分布,并用烟线法进行了流场显示对比,得到了所述两种来流条件下锥体后流动速度场与压力场的详细实验测量数据.对速度与压力分布特征进行相关分析后,得到了两种来流条件下流场涡量ω与耗散熵产S_f云图.同时发现在两种来流条件下,锥体后流场可明显划分为3个区域.轴向速度V_z沿锥体轴线分布规律非常相似,均存在3个低速极值点,且锥体后流动驻点位置静压力均基本等于环境静压力.      

On Symmetric Water Waves with Constant Vorticity

We prove that a solution to the gravity water wave problem with constant vorticity, whose wave profile as well as its horizontal velocity component at the free surface are symmetric at any instant of time, is given by a traveling wave. The proof is based on maximum principles and structural properties of the governing equations.     

Unstable Surface Waves in Running Water

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that the free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves is demonstrated at all wave numbers. We show the linear instability of small nontrivial waves that appear after bifurcation at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of free-surface water waves.     

An investigation of strong backflow events at the interface of air–water systems using large-eddy simulation

A large-eddy simulation of a counter-current gas–liquid flow is performed. At the flat interface where the different fluids meet, continuity of momentum and momentum fluxes are enforced following the work of Lombardi et al. [Direct numerical simulation of near-interface turbulence in coupled gas-liquid flow. Phys Fluids. 1996;8(6):1643–1665]. The increase in vertical vorticity fluctuations near the interface increases mixing, reducing the thickness of the inner region of the boundary layer. Such increase reduces shear while allowing for more frequent backflow motions in the inner region, being this phenomenon stronger on water. Due to the higher inertia of water these backflow motions are ultimately responsible for the streaky structure of shear stresses seen along the interface. The present study shows that such bimodality in the streamwise velocities is also seen in the angle distribution of vorticity relative to the interface, where such angles are linked to the presence of interface-connected and quasi-streamwise vortex cores. Finally, it is shown that backflow events on the interface shear stresses correlate with coupled ‘strong’ ejections in the near interface region despite the disparagingly different near-interface streamwise velocity distributions on the near interface boundary layers.     

PIV method for research of the structure of pulsating flow in a smooth duct

The system for Particle Image Velocimetry (PIV) measurements in the flow with superimposed pulsations of the fluid (air) has been developed. Measurements of velocity and vorticity fields in a smooth duct in certain phases of superimposed pulsations have been performed. Statistics of a turbulent pulsating flow: velocity profiles, turbulent pulsations, and Reynolds stresses has been obtained.     

Flow of wet granular materials

The transition from frictional to lubricated flows of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number Le=eta(s)gamma / sigma, the ratio of lubrication to frictional forces. Le defines a critical shear rate below which no steady flow without localization exists. In the frictional regime the shear flow is localized. The lubricated regime is not simply viscous: the ratio of shear to normal stresses remains constant and the velocity profile has a universal form in both frictional and lubricated regimes. Finally, a discrepancy between local and global measurements of viscosity is identified, which suggests inhomogeneity of the material under flow.