On the stability of plane parallel viscoelastic shear flows in the limit of infinite Weissenberg and Reynolds numbers

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. We study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet.The equation for stability is derived and solved numerically using the spectral Chebyshev collocation method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability.     

Pressure effects on viscosity and flow stability of polyethylene melts during extrusion

In the present work, the effects of pressure on the viscosity and flow stability of four commercial grade polyethylenes (PEs) have been studied: linear-low-density polyethylene copolymer, high-density polyethylene, metallocene polyethylenes with short-chain branches (mPE-SCB), and metallocene polyethylenes with long chain branching (mPE-LCB). The range of shear rates considered covers both stable and unstable flow regimes. “Enhanced exit-pressure” experiments have been performed attaining pressures of the order of 500×10⁵ Pa at the die exit. The necessary experimental conditions have been clearly defined so that dissipative heating can be neglected and pressure effects isolated. The results obtained show an exponential increase in both shear and entrance-flow pressure drop with mean pressure when shear rate is fixed and as long as flow is stable. These pressure effects are described by two pressure coefficients, β_S under shear and, β_E under elongation, that are calculated using time–pressure superposition and that are independent of mean pressure and flow rate. For three out of four PE, pressure coefficient values can be considered equal under shear and under elongation. However, for the mPE-LCB, the pressure coefficient under elongation is found to be about 30% lower than under shear. Flow instabilities in the form of oscillating flows or of upstream instabilities appear at lower shear rates as mean pressure increases. Nevertheless, the critical shear stress at which they are triggered remains independent of mean pressure. Moreover, it is found that the β_S values obtained for stable flows do not differ much from the values obtained during upstream instability regimes, and differ really from pressure effects observed under oscillating flow and slip conditions.     

THE RESEARCH PROGRESS OF LATTICE BOLTZMANN METHOD IN NON-NEWTONIAN FLUID FLOW

格子玻尔兹曼方法（lattice Boltzmann method,LBM）能够直接计算局部剪切速率并可以达到二次精度,因此在非牛顿流动数值模拟中展现出一定优势。尽管已证实LBM 对于非牛顿流动的适用性,但是LBM 需要通过即时调节BGK（Bhatnagar-Gross-Krook）碰撞项中的松弛时间来实时反映黏度改变,当松弛时间接近1/2 时,迭代会出现数值不稳定现象。该文对LBM 在非牛顿流体研究中的进展进行了总结,介绍了增加数值稳定性的方法并对结果的精度进行了比较,在此基础上对LBM 在非牛顿研究中的进一步发展进行了展望。     

Influence of elongational properties on the contraction flow of polyisobutylene in a mixed solvent

Over the last decade several international programmes have been developed around different standard fluids, one of which is the so-called S1 fluid. This is a solution of polyisobutylene in a mixed solvent and the aim of the programme has been to study the rheology of polymer solutions from the dilute solution to the melt. The focus of this paper will be on the flow visualisation of contraction flows of S1 through orifice dies and on the estimation of some of its extensional properties. The contraction ratios range from 24.4:1 and 124.3:1. The measured entry pressure drops will be correlated with contraction ratio and apparent wall shear rate. Experimental evidence will show that, when regarded as a function of wall shear rate, the entry pressure drops are independent of the contraction ratios. The flow fields for different contraction ratios, at any constant apparent wall shear rate, however, differ substantially. The evolution of the flow fields is monitored and it is shown that an initial increase in vortex size is followed by a slower decrease, this happening at a constant Weissenberg number. At the same Weissenberg number, small scale instabilities start occurring near the office. As the shear rate is increased further, these instabilities grow in size until, eventually, the flow structure is destroyed. An extensional viscosity is evaluated using a modified form of the Binding analysis for contraction flows and we show that the results are not only in qualitative agreement with those from other groups, but also that the analysis is able to predict exactly the onset of the aforementioned flow instabilities. Received: 20 March 1997 Accepted: 18 September 1997     

Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-layer flows that are linearly stable for Re = ∞. The basic methodology consists of two steps. First we eliminate interfacial instabilities by using a yield stress fluid in one fluid layer and ensuring that for the base flow configurations studied we maintain an unyielded plug region at the interface. Secondly we eliminate linear shear instabilities by ensuring a strong enough Couette component in the second fluid layer, imposed via the moving interface. We show that this technique can be applied to both shear-thinning and visco-elastic fluids.     

An error analysis of the dynamic mode decomposition

Dynamic mode decomposition (DMD) is a new diagnostic technique in fluid mechanics which is growing in popularity. A powerful analysis tool, it has great potential for measuring the spatial and temporal dynamics of coherent structures in experimental fluid flows. To aid interpretation of experimental data, error-bars on the measured growth rates are needed. In this article, we undertake a massively parallel error analysis of the DMD algorithm using synthetic waveforms that are shown to be representative of the canonical instabilities observed in shear flows. We show that the waveform of the instability has a marked impact on the error of the measured growth rate. Sawtooth and square waves may have an order of magnitude larger error than sine waves under the same conditions. We also show that the effects of data quantity and quality are of critical importance in determining the error in the growth or decay rate, and that the effect of the key parametric variables are modulated by the growth rate itself. We further demonstrate methods by which ensemble and orthogonal data may be introduced to improve the noise response. With regard for the important variables, precise measurement of the growth rates of instabilities may be supplemented with an accurately estimated uncertainty. This opens many new possibilities for the measurement of coherent structure in shear flows.     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Time–space characteristics of stratified shear layer from UVP measurements

The stratified shear layer flow pattern involves a fresh water layer flowing over a salted water one. The instabilities arising due to velocity gradients are mainly convective and thus evolve in time and space during their downstream propagation. This work was carried out within the framework of a study on the interaction between fresh water and seawater in the estuaries of rivers, where the main part of the physicochemical and biological phenomena occurs under the control of hydrodynamic conditions. The spatio-temporal velocity profile measurement by the ultrasonic Doppler method is well adapted to the stability analysis of such flows. It allows a comparison between the experimental wave properties and the theoretical results given by a linear temporal approach extended to the spatial point of view.     

Instabilities in shear and simple shear deformations of gold crystals

We use the tight-binding potential and molecular mechanics simulations to study local and global instabilities in shear and simple shear deformations of three initially defect-free finite cubes of gold single crystal containing 3480, 7813, and 58,825 atoms. Displacements on all bounding surfaces are prescribed while studying simple shear deformations, but displacements on only two opposite surfaces are assigned during simulations of shear deformations with the remaining four surfaces kept free of external forces. The criteria used to delineate local instabilities in the system include the following: (i) a component of the second-order spatial gradients of the displacement field having large values relative to its average value in the body, (ii) the minimum eigenvalue of the Hessian of the energy of an atom becoming non-positive, and (iii) structural changes represented by a high value of the common neighborhood parameter. It is found that these criteria are met essentially simultaneously at the same atomic position. Effects of free surfaces are evidenced by different deformation patterns for the same specimen deformed in shear and simple shear. The shear strength of a specimen deformed in simple shear is more than three times that of the same specimen deformed in shear. It is found that for each cubic specimen deformed in simple shear the evolution with the shear strain of the average shear stress, prior to the onset of instabilities, is almost identical to that in an equivalent hyperelastic material with strain energy density derived from the tight-binding potential and the assumption that it obeys the Cauchy-Born rule. Even though the material response of the hyperelastic body predicted from the strain energy density is stable over the range of the shear strain simulated in this work, the molecular mechanics simulations predict local and global instabilities in the three specimens.     

Espaces d'écoulements dits « universels », 3

Universal motions with uniform steady vorticity form a corolla of linear spaces derived from rigid body motions. Closely related to potential flows, they satisfy two extensions of Lagrange theorem, are investigated with the help of complex functions, as stand celebrated when be plane. They take place in hydrodynamics, aerodynamics, geophysics, astrophysics, turbulence, physics of plasmas and superfluid helium. In all the cases, arbitrary unsteady span-wise translations permit to generalise as well as to exhibit helical or 3D universal motions. Three misunderstood periodic flows illustrate our purpose, as they approach shear instabilities in numerous fluids. To cite this article: M. Bouthier, C. R. Mecanique 332 (2004).     

Electro-magnetic-field-induced flow and interfacial instabilities in confined stratified liquid layers

The electro-magneto-hydrodynamic (EMHD) flow and instabilities engendered by the Lorenz force arising from interaction between externally applied perpendicular electric and magnetic fields are investigated in layers of two immiscible liquids in a channel. A new finite wave-number EMHD instability mode is uncovered by the Orr–Sommerfeld analysis, in addition to the interfacial and shear modes which also arise in the pressure-driven flows. Thus, EMHD can be controlled for micro-channel transport, heat and mass transfer, mixing, micro-emulsion generation, etc.     

A rheological model for materials which support coexistent shear rates

In this work we study a version of the three constant differential-type Oldroyd constitutive relation which allows distinct objective time derivatives for the extra stress and the stretching. We integrate the constitutive equation and determine an equivalent history integral representation for this model for the general class of viscometric motions. For certain choices of the material parameters and initial conditions, we find that this model allows for the development of shear rate discontinuities in the flow domain as a steady viscometric flow is achieved. Correspondingly, we also give evidence that intense shear rate oscillations may occur during the transient period as an impulsively started viscometric flow in a channel tends to a steady state under a constant critical shear stress. This critical shear stress lies in an interval of values for which the material experiences the phenomenon of “flow yielding”. A qualitative comparison with experimental data is made for certain creams and greases. The material instabilities inherent in this constitutive theory for viscometric motions are suggestive of the instabilities that occur in many viscoelastic fluids such as sharkskin patterns, wavy fracture, and spurt flow.     

Numerical experiments on stability and transition in plane channel flow

Various secondary and tertiary instabilities in plane channel flow are explored via time-dependent numerical simulations using the incompressible Navier-Stokes equations. Comparisons are made between transitional flows at Reynolds numbers 1500, 5000, and 8000. The lambda vortex, detached shear layer, and inverted vortex regions are identified and the origin of the latter is explained. The laminar breakdown of the Re=1500 flow is computed with high resolution and the nature of its ensuing hairpin eddies is clarified by numerical particle paths. The potential of center-mode rather than wall-mode transitions is proposed and the resulting flow structure is described.     

Active Control of Wave Instabilities in Three-Dimensional Compressible Flows

In many fluid flows of practical importance transition is caused by the linear growth of wave instabilities, such as Tollmien–Schlichting waves, which eventually grow to a finite size at which stage secondary instabilities come into play. If transition is to be delayed or even avoided in such flows, then the linear growth of the disturbances must be prevented since control in the nonlinear regime would be a considerably more difficult task. Here a strategy for active control of two-dimensional incompressible and compressible Tollmien–Schlichting waves and its use in controlling the more practically relevant problem of crossflow instability which arises in swept-wing flows is discussed. The control is through an active suction/blowing distribution at the wall though the same result could be achieved by variable wall heating. In order to control the instability it is assumed that the wall shear stress and pressure are known from measurements. It is shown that, certainly at finite Reynolds numbers, it is sufficient to know the flow properties at a finite number of points along the wall. The cases of high and finite Reynolds numbers are discussed using asymptotic and numerical methods respectively. It is shown that a control strategy can be developed to stop the growth of all two-dimensional Tollmien–Schlichting waves at finite and large Reynolds numbers. Some discussion of nonlinear effects in the presence of active control is given and the possible control of other instability mechanisms investigated. Received 1 May 1998 and accepted 24 September 1998     

Turbulence measurements in a rectangular mesoscale confined impinging jets reactor

Mesoscale chemical reactors capable of operating in the turbulent flow regime, such as confined impinging jets reactors (CIJR), offer many advantages for rapid chemical processing at the microscale. One application where these reactors are used is flash nanoprecipitation, a method for producing functional nanoparticles. Because these reactors often operate in a flow regime just beyond transition to turbulence, modeling flows in these reactors can be problematic. Moreover, validation of computational fluid dynamics models requires detailed and accurate experimental data, the availability of which has been very limited for turbulent microscale flows. In this work, microscopic particle image velocimetry (microPIV) was performed in a mesoscale CIJR at inlet jet Reynolds numbers of 200, 1,000, and 1,500. Pointwise and spacial turbulence statistics were calculated from the microPIV data. The flow was observed to be laminar and steady in the entire reactor at a Reynolds number of 200. However, at jets Reynolds numbers of 1,000 and 1,500, instabilities as a result of the jets impinging along the centerline of the reactor lead to a highly turbulent impingement region. The peak magnitude of the normalized Reynolds normal and shear stresses within this region were approximately the same for the Reynolds numbers of 1,000 and 1,500. The Reynolds shear stress was found to exhibit a butterfly shape, consistent with a flow field dominated by an oblique rocking of the impingement zone about the center of the reactor. Finally, the spatial auto- and cross-correlations velocity fluctuations were calculated and analyzed to obtain an understanding of size of the coherent structures.     

Shear banding and interfacial instability in planar Poiseuille flow

Motivated by the need for a theoretical study in a planar geometry that can easily be implemented experimentally, we study the pressure driven Poiseuille flow of a shear banding fluid. After discussing the “basic states” predicted by a one-dimensional calculation that assumes a flat interface between the bands, we proceed to demonstrate such an interface to be unstable with respect to the growth of undulations along it. We give results for the growth rate and wavevector of the most unstable mode that grows initially, as well as for the ultimate flow patterns to which the instability leads. We discuss the relevance of our predictions to the present state of the experimental literature concerning interfacial instabilities of shear banded flows, in both conventional rheometers and microfluidic channels.     

Instabilities of micellar systems under homogeneous and non-homogeneous flow conditions

The rheological behavior of a cetylpyridinium chloride 100 mmol l^–1/sodium salicylate 60 mmol l^–1 aqueous solution was studied in this work under homogeneous (cone and plate) and non-homogeneous flow conditions (vane-bob and capillary rheometers), respectively. Instabilities consistent with non-monotonic flow curves were observed in all cases and the solution exhibited similar behavior under the different flow conditions. Hysteresis and the sigmoidal flow curve suggested as characteristic of systems that show constitutive instabilities were observed when running cycles of increasing and decreasing stress or shear rate, respectively. This information, together with a detailed determination of steady states at shear stresses close to the onset of the instabilities, allowed one to show unequivocally that "top and bottom jumping" are the mechanisms to trigger the instabilities in this micellar system. It is shown in addition that there is not a true plateau region in between the "top and bottom jumping". Finally, the flow behavior beyond the upturn seemed to be unstable and was found accompanied by an apparent violation of the no-slip boundary condition.     

A shear flow instability in cylindrical geometry

Conclusion The results show, that this model experiment is useful for studying the interaction between two parallel shear layers in a rotating system. The structures of the observed instabilities exhibit some similarities with the wake flow behind cylindrical obstacles. Additional investigations in analyzing the dynamical behaviour of the shear instabilities are necessary to get a deeper insight into the physical mechanism. Up to that it is an open question, whether the physical effects described by Meiburg (1987), play an important role in these shear layer instabilities.     

Simulations of Spatially Developing Two-Dimensional Shear Layers and Jets

A computational study of spatially evolving two-dimensional free shear flows has been performed using direct numerical simulation of the Navier–Stokes equations in order to investigate the ability of these two-dimensional simulations to predict the overall flow-field quantities of the corresponding three-dimensional “real” turbulent flows. The effects of inflow forcing on these two-dimensional flows has also been studied. Simulations were performed of shear layers, as well as weak (large co-flow and relatively weak shear) and strong (small co-flow and relatively strong shear) jets. Several combinations of discrete forcing with and without a broadband background spectrum were used. Although spatially evolving direct simulations of shear layers have been performed in the past, no such simulations of the plane jet have been performed to the best of our knowledge. It was found that, in the two-dimensional shear layers, external forcing led to a strong increase in the initial growth of the shear-layer thickness, followed by a region of decreased growth as in physical experiments. The final downstream growth rate was essentially unaffected by forcing. The mean velocity profile and the naturally evolving growth rate of the shear layer in the case of broadband forcing compare well with experimental data. However, the total and transverse fluctuation intensities are larger in the two-dimensional simulations with respect to experimental data. In the weak-jet simulations it was found that symmetric forcing completely overwhelms the natural tendency to transition to the asymmetric jet column mode downstream. It was observed that two-dimensional simulations of “strong” jets with a low speed co-flow led to a fundamentally different flow with large differences even in mean velocity profiles with respect to experimental data for planar jets. This was a result of the dominance of the two-dimensional mechanism of vortex dipole ejection in the flow due to the lack of spanwise instabilities. Experimental studies of planar jets do not show vortex dipole formation and ejection. A three-dimensional “strong”-jet simulation showed the rapid evolution of three-dimensionality effectively preventing this two-dimensional mechanism, as expected from experimental results. Received: 25 November 1996 and accepted 17 April 1997     

Two-phase flow instabilities in a silicon microchannels heat sink

Two-phase flow instabilities are highly undesirable in microchannels-based heat sinks as they can lead to temperature oscillations with high amplitudes, premature critical heat flux and mechanical vibrations. This work is an experimental study of boiling instabilities in a microchannel silicon heat sink with 40 parallel rectangular microchannels, having a length of 15 mm and a hydraulic diameter of 194 μm. A series of experiments have been carried out to investigate pressure and temperature oscillations during the flow boiling instabilities under uniform heating, using water as a cooling liquid. Thin nickel film thermometers, integrated on the back side of a heat sink with microchannels, were used in order to obtain a better insight related to temperature fluctuations caused by two-phase flow instabilities. Flow regime maps are presented for two inlet water temperatures, showing stable and unstable flow regimes. It was observed that boiling leads to asymmetrical flow distribution within microchannels that result in high temperature non-uniformity and the simultaneously existence of different flow regimes along the transverse direction. Two types of two-phase flow instabilities with appreciable pressure and temperature fluctuations were observed, that depended on the heat to mass flux ratio and inlet water temperature. These were high amplitude/low frequency and low amplitude/high frequency instabilities. High speed camera imaging, performed simultaneously with pressure and temperature measurements, showed that inlet/outlet pressure and the temperature fluctuations existed due to alternation between liquid/two-phase/vapour flows. It was also determined that the inlet water subcooling condition affects the magnitudes of the temperature oscillations in two-phase flow instabilities and flow distribution within the microchannels.