Showing papers on "Hele-Shaw flow published in 2000"

Elastic turbulence in a polymer solution flow

Abstract: Turbulence is a ubiquitous phenomenon that is not fully understood. It is known that the flow of a simple, newtonian fluid is likely to be turbulent when the Reynolds number is large (typically when the velocity is high, the viscosity is low and the size of the tank is large). In contrast, viscoelastic fluids such as solutions of flexible long-chain polymers have nonlinear mechanical properties and therefore may be expected to behave differently. Here we observe experimentally that the flow of a sufficiently elastic polymer solution can become irregular even at low velocity, high viscosity and in a small tank. The fluid motion is excited in a broad range of spatial and temporal scales, and we observe an increase in the flow resistance by a factor of about twenty. Although the Reynolds number may be arbitrarily low, the observed flow has all the main features of developed turbulence. A comparable state of turbulent flow for a newtonian fluid in a pipe would have a Reynolds number as high as 10(5) (refs 1, 2). The low Reynolds number or 'elastic' turbulence that we observe is accompanied by significant stretching of the polymer molecules, resulting in an increase in the elastic stresses of up to two orders of magnitude.

Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method

Abstract: A spherical drop, placed in a second liquid of the same density, is subjected to shearing between parallel plates. The subsequent flow is investigated numerically with a volume-of-fluid (VOF) method. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds number. Our simulations compare well with previous theoretical, numerical, and experimental results. For capillary numbers greater than the critical value, the drop deforms to a dumbbell shape and daughter drops detach via an end-pinching mechanism. The number of daughter drops increases with the capillary number. The breakup can also be initiated by increasing the Reynolds number.

Finite element simulation of an electroosmotic-driven flow division at a T-junction of microscale dimensions

Abstract: A finite element formulation is developed for the simulation of an electroosmotic flow in rectangular microscale channel networks. The distribution of the flow at a decoupling T-junction is investigated from a hydrodynamic standpoint in the case of a pressure-driven and an electroosmotically driven flow. The calculations are carried out in two steps: first solving the potential distribution arising from the external electric field and from the inherent zeta potential. These distributions are then injected in the Navier Stokes equation for the calculation of the velocity profile. The influence of the various parameters such as the zeta potential distribution, the Reynolds number, and the relative channel widths on the flow distribution is investigated.

Three-dimensional numerical simulation of thermocapillary flows in cylindrical liquid bridges

Abstract: The dynamics of thermocapillary flows in differentially heated cylindrical liquid bridges is investigated numerically using a mixed finite volume/pseudo-spectral method to solve the Navier–Stokes equations in the Boussinesq approximation. For large Prandtl numbers (Pr = 4 and 7) and sufficiently high Reynolds numbers, the axisymmetric basic flow is unstable to three-dimensional hydrothermal waves. Finite-amplitude azimuthally standing waves are found to decay to travelling waves. Close to the critical Reynolds number, the former may persist for long times. Representative results are explained by computing the coefficients in the Ginzburg–Landau equations for the nonlinear evolution of these waves for a specific set of parameters. We investigate the nonlinear phenomena characteristic of standing and pure travelling waves, including azimuthal mean flow and time-dependent convective heat transport. For Pr [Lt ] 1 the first transition from the two-dimensional basic flow to the three-dimensional stationary flow is inertial in nature. Particular attention is paid to the secondary transition leading to oscillatory three-dimensional flow, and this mechanism is likewise independent of Pr. The spatial and temporal structure of the perturbation flow is analysed in detail and an instability mechanism is proposed based on energy balance calculations and the vorticity distribution.

Navier-Stokes simulation with constraint forces: finite-difference method for particle-laden flows and complex geometries.

Abstract: Building on an idea of Fogelson and Peskin [J. Comput. Phys. 79, 50 (1988)] we describe the implementation and verification of a simulation technique for systems of non-Brownian particles in fluids at Reynolds numbers up to about 20 on the particle scale. This direct simulation technique fills a gap between simulations in the viscous regime and high-Reynolds-number modeling. It also combines sufficient computational accuracy with numerical efficiency and allows studies of several thousand, in principle arbitrarily shaped, extended and hydrodynamically interacting particles on regular work stations. We verify the algorithm in two and three dimensions for (i) single falling particles and (ii) a fluid flowing through a bed of fixed spheres. In the context of sedimentation we compute the volume fraction dependence of the mean sedimentation velocity. The results are compared with experimental and other numerical results both in the viscous and inertial regime and we find very satisfactory agreement.

‘Phase diagram’ of interfacial instabilities in a two-layer Couette flow and mechanism of the long-wave instability

Abstract: A unified view is given of the instabilities that may develop in two-layer Couette flows, as a ‘phase diagram’ in the parameter space. This view is obtained from a preliminary study of the single-fluid Couette flow over a wavy bottom, which reveals three flow regimes for the disturbances created at the bottom, each regime being characterized by a typical penetration depth of the vorticity disturbances and an effective Reynolds number. It appears that the two-layer flow exhibits the same flow regimes for the disturbances induced by the perturbed interface, and that each type of instability can be associated with a flow regime. Typical curves giving the growth rate versus wavenumber are deduced from this analysis, and favourably compared with the existing literature. In the second part of this study, we propose a mechanism for the long wavelength instability, and provide simple estimates of the wave velocity and growth rate, for channel flows and for semi-bounded flows. In particular, an explanation is given for the ‘thin-layer effect’, which is typical of multi-layer flows such as pressure driven flows or gravity driven flows, and according to which the flow is stable if the thinner layer is the less viscous, and unstable otherwise.

Steady flow separation patterns in a 45 degree junction

Abstract: Numerical and experimental techniques were used to study the physics of flow separation for steady internal flow in a 45° junction geometry, such as that observed between two pipes or between the downstream end of a bypass graft and an artery. The three-dimensional Navier–Stokes equations were solved using a validated finite element code, and complementary experiments were performed using the photochromic dye tracer technique. Inlet Reynolds numbers in the range 250 to 1650 were considered. An adaptive mesh refinement approach was adopted to ensure grid-independent solutions. Good agreement was observed between the numerical results and the experimentally measured velocity fields; however, the wall shear stress agreement was less satisfactory. Just distal to the ‘toe’ of the junction, axial flow separation was observed for all Reynolds numbers greater than 250. Further downstream (approximately 1.3 diameters from the toe), the axial flow again separated for Re [ges ] 450. The location and structure of axial flow separation in this geometry is controlled by secondary flows, which at sufficiently high Re create free stagnation points on the model symmetry plane. In fact, separation in this flow is best explained by a secondary flow boundary layer collision model, analogous to that proposed for flow in the entry region of a curved tube. Novel features of this flow include axial flow separation at modest Re (as compared to flow in a curved tube, where separation occurs only at much higher Re), and the existence and interaction of two distinct three-dimensional separation zones.

From Heat Transfer Principles to Shape and Structure in Nature: Constructal Theory

Abstract: This lecture reviews a relatively recent body of heat transfer work that bases on a deterministic (constructal) principle the occurrence of geometric form in systems with internal flows. The same principle of global optimization subject to constraints allow us to anticipate the natural (animate and inanimate) flow architectures that surround us. The lecture starts with the example of the optimal spatial distribution of material (e.g., heat exchanger equipment) in power plants. Similarly, void space can be allocated optimally to construct flow channels in the volume occupied by a heat generating system. The lecture continues with the optimization of the path for heat flow between a volume and one point. When the heat flow can choose between at least two paths, low conductivity versus high conductivity, the optimal flow structure for minimal global resistance in steady flow is a tree. Nearly the same tree is deduced by minimizing the time of discharge in the flow from a volume to one point. Analogous tree-shaped flows are constructed in pure fluid flows, and in flow through a heterogeneous porous medium. The optimization of trees that combine heat transfer and fluid flow is illustrated by means of two-dimensional trees of plate fins

Three-dimensional oscillatory flow over steep ripples

Abstract: The process which leads to the appearance of three-dimensional vortex structures in the oscillatory flow over two-dimensional ripples is investigated by means of direct numerical simulations of Navier–Stokes and continuity equations. The results by Hara & Mei (1990a), who considered ripples of small amplitude or weak fluid oscillations, are extended by considering ripples of larger amplitude and stronger flows respectively. Nonlinear effects, which were ignored in the analysis carried out by Hara & Mei (1990a), are found either to have a destabilizing effect or to delay the appearance of three-dimensional flow patterns, depending on the values of the parameters. An attempt to simulate the flow over actual ripples is made for moderate values of the Reynolds number. In this case the instability of the basic two-dimensional flow with respect to transverse perturbations makes the free shear layer generated by boundary layer separation become wavy as it leaves the ripple crest. Then the amplitude of the waviness increases and eventually complex three-dimensional vortex structures appear which are ejected in the irrotational region. Sometimes the formation of mushroom vortices is observed.

Shear flow over a self-similar expanding pulmonary alveolus during rhythmical breathing

Abstract: Alternating shear flow over a self-similar, rhythmically expanding hemispherical depression is investigated. It provides a fluid-mechanical model for an alveolated respiratory unit, by means of which the effect of lung rhythmical expansion on gas mixing as well as aerosol dispersion and deposition can be studied. The flow is assumed to be very slow and governed by the quasi-steady linear Stokes equations. Consequently, superposition of the following two cases provides an easy route toward characterizing the aforementioned flow field. The first case treats the flow field that is generated by a rhythmically expanding spherical cap (the alveolus). The cap is attached at its rim to a circular opening in an expanding unbounded plane bounding a semi-infinite fluid region. The rate of expansion of the cap and the plane are chosen such as to maintain the system's configurational self-similarity. The second case addresses the flow disturbance that is generated by an alternating shear flow encountering a rigid hemispherical cavity in a plane bounding a semi-infinite fluid domain. For the first case, a stream-function representation employing toroidal coordinates furnishes an analytical solution, whereas the second case was solved numerically by Pozrikidis (1994). Linear superposition of the two flow cases results in particularly rich streamline maps. In the symmetry plane (bisecting the cap and parallel to the mean shear flow), for a certain range of shear to expansion-rate ratios, the streamline maps are self-similar and display closed orbits and two internal stagnation points. One of the stagnation points is a'centre' surrounded by closed streamlines whereas the other constitutes a 'saddle point'. For other planes, no stagnation points exist in the field, but the streamlines associated with the saddle point display complex looping patterns. These unique flow structures, when subjected to a small perturbation (e.g. a small asynchrony between ductal and alveolar entering flows) cause highly complex stochastic particle trajectories even in the quasi-static Stokes alveolar flow. The observed irreversible flow phenomena in a rhythmically expanding alveolus may be partially responsible for the 'stretch-and-fold' flow mixing patterns found in our recent flow visualization studies performed in excised animal lung acini.

Spontaneous growth of fluctuations in the viscous flow of a fluid past a soft interface

Abstract: The flow induced instability in the flow past a soft material is studied in the limit of low Reynolds number where inertial effects are insignificant. A transition from laminar flow to a more complicated flow profile is observed when the strain rate of the base flow increases beyond a critical value; the transition is found to be reproducible. The experimental results are compared with theoretical predictions and quantitative agreement is found with no adjustable parameters.

Surface water-groundwater interaction near shallow circular lakes: Flow geometry in three dimensions

Abstract: Steady flow regimes for three-dimensional lake-aquifer systems are studied via idealized mathematical models that are extensions of earlier simplified vertical section models of interaction between shallow lakes and underlying aquifers. The present models apply to a shallow circular lake at the surface of a rectangular aquifer of finite depth, yielding a truly three-dimensional representation of the resulting flow system. Flux boundary conditions are applied at the ends of the aquifer, with net vertical recharge or evapotranspiration at the water table. The lake is defined by a region with constant head. By determining and visualizing solutions to the discretized saturated flow equations, a range of possible flow regimes is identified, and their topological properties are studied. Tools for analyzing flow regimes are described, including a method for locating and mapping three-dimensional dividing surfaces within steady flow fields. Results show strong similarities between two- and three-dimensional systems, including a large number of flow-through, recharge, and discharge regimes and reverse flow cells. Flow lines calculated on a vertical plane through the middle of a lake resemble but are not identical to two-dimensional streamlines for a range of aquifer flow and recharge conditions. Estimates of the widths and depths of capture and release zones for various lake-aquifer geometries are asymptotic to earlier results for two-dimensional systems. Numerical predictions are compared with analytical results for certain limiting flow regimes.

Symmetry breaking of the flow in a cylinder driven by a rotating end wall

Abstract: The flow driven by a rotating end wall in a cylindrical container with aspect ratio H/R=2.5 is time dependent for Reynolds numbers Re=ΩR2/ν>2700. For Reynolds numbers up to 4000 three solution branches have been identified, and we examine a solution on each one. At Re=3000, the flow is axisymmetric and time periodic. At Re=3500, the flow is quasiperiodic with a low-frequency modulation and supports a modulated rotating wave with azimuthal wave number k=5. At Re=4000, the flow is time periodic with a qualitatively different mode of oscillation to that at Re=3500. It also supports a modulated rotating wave, with k=6. The peak kinetic energy of the nonaxisymmetric modes is associated with the jet-like azimuthal flow in the interior.

Large-eddy simulations of turbulent flow in a rotating square duct

Abstract: The turbulent flow at low Reynolds numbers in a rotating straight square duct was simulated using the large-eddy simulation technique. The rotation axis is parallel to two opposite walls of the duct, and the pressure-driven flow is assumed to be fully developed, isothermal and incompressible. The Reynolds number based on the friction velocity (Reτ=300) was kept constant in the range of the rotational numbers studied (0⩽Roτ⩽1.5) Computations were carried out using a second-order finite volume code with a localized one-equation dynamic subgrid scale model. Simulations of rotating channel flows were initially carried out and were seen to be in agreement with experiments and direct numerical simulations reported in the literature. The study of the flow in a rotating square duct revealed the influence of the Coriolis force on the spatial distribution of the average velocity fields and Reynolds stresses. At low rotation rates, turbulence-driven secondary flows developed near the corners convect the rotation-generated cross-stream currents. At moderate and high rotation rates, the mean secondary flow structure consists essentially of two large counter-rotating cells convecting low/high momentum fluid from the stable/unstable side to the unstable/stable side. Inspection of the terms of the transport equations of the average axial velocity and vorticity components shows the mechanisms responsible for the changes in the average flow structure. Spatial distributions of the Reynolds stresses are mainly influenced by the changes that rotation induces in the main strain rates. It has been found that, globally, at the low Reynolds number studied, rotation tends to significantly reduce the overall turbulence level of the flow.

The flow induced by a rotationally oscillating and translating circular cylinder

Abstract: The temporal development of two-dimensional viscous incompressible flow induced by an impulsively started circular cylinder which performs time-dependent rotational oscillations about its axis and translates at right angles to this axis is investigated. The investigation is based on the solutions of the unsteady Navier-Stokes equations. A series expansion for small times is developed. The Navier-Stokes equations are also integrated by a spectral-finite difference method for moderate values of time for both moderate and high Reynolds numbers. The numerical method is checked with the results of the analytical solution. The effects of the Reynolds number and of the forcing Strouhal number S on the laminar asymmetric flow structure in the near-wake region are studied. The lift and drag coefficients are also extracted from numerical results. An interesting phenomenon has been observed both in the flow patterns and in the behaviour of drag coefficients for S = π/2 at Reynolds number R = 500 and is discussed. For comparison purposes the start-up flow is determined numerically at a low Reynolds number and is found to be in good agreement with previous experimental predictions.

Slow viscous flows in micropolar fluids

Abstract: A systematic calculation of micropolar fluid flows around a sphere and a cylinder is presented. The explicit velocity fields and the drag forces exerted by the fluid flow in both two and three dimensions are obtained. The solution of a steady micropolar fluid flow inside the cylinder is also obtained and is identical to the form observed in an experiment on granular vibrating beds.

Dynamics of Active Separation Control at High Reynolds Numbers

Abstract: A series of active flow control experiments were recently conducted at high Reynolds numbers on a generic separated configuration. The model simulates the upper surface of a 20 percent thick Glauert-Goldschmied type airfoil at zero angle of attack. The flow is fully turbulent since the tunnel sidewall boundary layer flows over the model. The main motivation for the experiments is to generate a comprehensive data base for validation of unsteady numerical simulation as a first step in the development of a CFD design tool, without which it would not be possible to effectively utilize the great potential of unsteady flow control. This paper focuses on the dynamics of several key features of the baseline as well as the controlled flow. It was found that the thickness of the upstream boundary layer has a negligible effect on the flow dynamics. It is speculated that separation is caused mainly by the highly convex surface while viscous effects are less important. The two-dimensional separated flow contains unsteady waves centered on a reduced frequency of 0.8, while in the three dimensional separated flow, frequencies around a reduced frequency of 0.3 and 1 are active. Several scenarios of resonant wave interaction take place at the separated shear-layer and in the pressure recovery region. The unstable reduced frequency bands for periodic excitation are centered on 1.5 and 5, but these reduced frequencies are based on the length of the baseline bubble that shortens due to the excitation. The conventional swept wing-scaling works well for the coherent wave features. Reproduction of these dynamic effects by a numerical simulation would provide benchmark validation.

LESFOIL: A European Project on Large Eddy Simulations Around a High-lift Airfoil at High Reynolds Number

Abstract: This paper presents work carried out in the LESFOIL project, which studies Large Eddy Simulations (LES) of the flow around high-lift airfoils, during its first 24 months The Reynolds number for the selected Aerospatiale A-airfoil is high (Re =2 1·10 6 based on the freestream velocity and the chord length) If some kind of near-wall treatment could be used, the near-wall streaks would not be resolved and a much coarser grid could be used in the streamwise and spanwise directions Two different near-wall treatment methodologies are used in the LESFOIL project, either hybrid LES-RANS (or DES) or wall functions The angle of incidence is α =1 33 o , and a small separation bubble is, according to experiments, present on the suction side in the trailing edge region Thus the method for treating the near-wall wall region must be able to handle both attached boundary layer flow, including streamwise pressure gradients, and separated flow Subgrid-scale (SGS) models and parallelized numerical methods are two other subjects covered in the LESFOIL project SGS models are developed and evaluated in simple flows such as channel flow The hill flow (Reynolds number 10, 000 based on the hill height) is also used as a test case in which the performance of the wall treatment and SGS models can be evaluated in recirculating flow The first part of the paper presents LES of channel flow The second part presents hill flow computations In the following section, LES around the A-airfoil is shown and conclusion are drawn in the final section

Two-fluid Taylor-Couette flow with countercurrent axial flow: Linear theory for immiscible liquids between corotating cylinders

Abstract: We computationally investigate the stability of a pair of radially stratified immiscible liquids undergoing countercurrent axial flow in the annular gap between rapidly corotating coaxial cylinders: two-fluid Taylor-Couette flow with counterflow. A simple analysis determines conditions under which a nearly cylindrical interface is maintained in the presence of counterflow (i.e., axial pressure gradients). Stability analysis reveals that for small axial Reynolds numbers, the flow is slightly stabilized against Taylor-Couette instability, consistent with results for a single phase. At axial Reynolds numbers greater than about ten, however, the flow is susceptible to a (generally nonaxisymmetric) Kelvin-Helmholtz instability, which precedes the Taylor-Couette mode. Furthermore, new results are presented for the case without axial flow. A bifurcation to vortices that corotate with their counterparts in the other phase is found. Finally, limitations of the generalized Rayleigh criterion developed in our earlie...

Plane Stokes flows with time-dependent free boundaries in which the fluid occupies a doubly-connected region

Abstract: Consider the two-dimensional quasi-steady Stokes flow of an incompressible Newtonian fluid occupying a time-dependent region bounded by free surfaces, the motion being driven solely by a constant surface tension acting at the free boundaries. When the fluid region is simply-connected, it is known that this Stokes flow problem is closely related to a Hele-Shaw free boundary problem when the zero-surface-tension model is employed. Specifically, if the initial configuration for the Stokes flow problem can be produced by injection at N points into an empty Hele-Shaw cell, then so can all later configurations. Moreover, there are N invariants; while the N points at which injection must take place move, the amount to be injected at each of these points remains the same. In this paper, we consider the situation when the fluid region is doubly-connected and show that, provided the geometry has an appropriate rotational symmetry, the same results continue to hold and can be exploited to determine the solution of the Stokes flow problem.

Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow

Abstract: A comprehensive assessment is made of transient and asymptotic two-dimensional perturbation growth in compressible shear flow using unbounded constant shear and the Couette problem as examples. The unbounded shear flow example captures the essential dynamics of the rapid transient growth processes at high Mach numbers, while excitation by nonmodal mechanisms of nearly neutral modes supported by boundaries in the Couette problem is found to be important in sustaining high perturbation amplitude at long times. The optimal growth of two-dimensional perturbations in viscous high Mach number flows in both unbounded shear flow and the Couette problem is shown to greatly exceed the optimal growth obtained in incompressible flows at the same Reynolds number.

Instabilities in viscoelastic flow past a square cavity

Abstract: Elastic flow transitions in viscoelastic flow past a square cavity adjacent to a channel are reported. The critical conditions for the onset of flow transitions and the qualitative and quantitative characterization of the secondary flows generated by the instability have been examined using streakline photography and instantaneous pressure measurements. Cellular type of instabilities inside the cavity is observed for flow rates beyond a critical value. Small and large scale eddies are observed at high flow rates. The flow inside the cavity and in the channel upstream and downstream of the cavity becomes weakly time-dependent for high flow rates.

Isothermal spherical Couette flow

Abstract: We summarise different types of instabilities and flow patterns in isothermal spherical Couette flows as a function of the aspect ratio. The flow of a viscous incompressible fluid in the gap between two concentric spheres was investigated for the case, that only the inner sphere rotates and the outer one is stationary. Flow visualisation studies were carried out for a wide range of Reynolds numbers and aspect ratios to determine the instabilities during the laminar-turbulent transition and the corresponding critical Reynolds numbers as a function of the aspect ratio. It was found, that the laminar basic flow loses its stability at the stability threshold in different ways. The instabilities occurring depend strongly on the aspect ratio and the initial conditions. For small and medium aspect ratios (β ≤ 0.25), experiments were carried out as a function of Reynolds number to determine the regions of existence for basic flow, Taylor vortex flow, supercritical basic flow. For wide gaps, however, Taylor vortices could not be detected by quasistationary increase of the Reynolds number. The first instability manifests itself as a break of the spatial symmetry and non-axisymmetric secondary waves with spiral arms appear depending on the Reynolds number. For β = 0.33, spiral waves with an azimuthal wave number m = 6, 5and 4 were found, while in the gap with an aspect ratio of β = 0.5spiral waves with m = 5, 4 and 3 spiral arms exist. For β = 1.0, we could detect spiral waves with m = 4, 3 and 2 arms. We compare the experimental results for the critical Reynolds numbers and wave numbers with those obtained by numerical calculations. The flow modes occurring at the poles look very similar to those found in the flow between two rotating disks. Effects of non-uniqueness and hysteresis are observed in this regime.

Low Reynolds number flow inside straight micro channels with irregular cross sections

Abstract: This paper presents an analysis of the compound effect of finite temperature differences and fluid friction on the existence of an optimum laminar flow regime in singly connected micro channels with complex free flow area cross sections. A widespread conviction has been established that the two competing irreversibility sources in a channel flow with heat transfer lead to the existence of an optimum flow regime. The results presented in this paper clearly shows the opposite. When an objective function is represented by the entropy generation rate per unit heat capacity rate of the fluid stream, the thermodynamic optimum flow regime represents a rather rare occurrence in the laminar region of irregularly shaped ducts. The presence of an extremum is more probable for very small diameters, the ones of an order of magnitude of O(≤10−3 m). The analysis is performed for selected ranges of relevant geometric, flow, and thermal parameters of a set of straight micro channels with irregular free flow area cross-sections. The following geometries of the free flow area cross section were investigated: (i) sine duct, (ii) circular duct, (iii) elliptical duct, (iv) moon-shaped ducts, and (v) four-cuspped duct. The range of Reynolds numbers has been established between O(102) and O(104). The existence of the objective function minimum is confirmed for ducts with an irregular cross section only for very small hydraulic diameters. These minima are relatively weak, and as a general rule, the sets of optimum parameters are close to the onset of turbulence or possibly even in the transitional or turbulent regions.

A low-dimensional approach to nonlinear plane-Poiseuille flow of viscoelastic fluids

Abstract: The nonlinear stability of the one-dimensional plane Couette flow is examined for a Johnson–Segalman fluid. The velocity and stress are represented by symmetric and antisymmetric Chandrasekhar functions in space. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. For given Reynolds number and viscosity ratio, two critical Weissenberg numbers are found at which an exchange of stability occurs between the Couette and other steady flows. The critical points coincide with the two extrema of the stress/rate-of-strain curve. At low (high) Reynolds number, the flow decays monotonically (oscillatorily) toward the steady-state solution. The number and stability of the nontrivial branches around the critical points are examined using the method of multiple scales. Comparison between the approximate and the numerical branches leads to excellent agreement in the vicinity of the critical points. The influence of the higher-order modes is assessed, showing low-order convergence and good accuracy when the flow profiles are compared against existing finite-element results.

Testing for Erosion-Corrosion Under Disturbed Flow Conditions Using a Rotating Cylinder with a Stepped Surface

Abstract: Erosion-corrosion is most severe in the vicinity of flow disturbances. In the past, erosion-corrosion under disturbed flow conditions has been studied experimentally in flow loops and numerically by performing flow simulations. In this study, a new, compact experimental setup was tested, intended for the study of erosion-corrosion under disturbed flow conditions, involving a rotating cylinder geometry with a sudden step. A thorough characterization of this new setup was initiated, involving wall mass-transfer measurements complemented with direct numerical simulation of the turbulent flow around it. A large variation of the wall mass-transfer rates behind the step was measured, similar in character to the one obtained in flow through a sudden pipe expansion. Flow simulations have confirmed that this flow geometry will create a qualitatively similar mean flow pattern as observed in a sudden pipe expansion flow involving flow separation and reattachment. Simulations also have shown that there is a ...

Local and overall flow in composites predicted by micromechanics

Abstract: Rate-dependent inelastic flow in metal matrix composites subjected to multiaxial stress states is quantified by flow surfaces, which are geometrically analogous to yield surfaces. The definition of flow is important because the most meaningful definition from a theoretical viewpoint, dissipation, is not measurable in the laboratory. Inelastic power is measurable, but differs from the dissipation due to residual stresses and evolution of the material state. Since experiments are necessary for development and validation of models, both definitions are important and considered here. The relationship between local flow in the matrix and overall flow of the composite is explored using finite element and generalized method of cells micromechanical analyses. The loci of flow surfaces in the axial–transverse and transverse–transverse stress planes are plotted. At the threshold, the overall flow surface is the intersection of all the local flow surfaces. Beyond the threshold, the intersection of all the local flow surfaces is smaller than the overall flow surface and differences between the dissipation and inelastic power are notable. Most importantly, the directions of the overall inelastic strain rate vectors are generally not normal to the overall surface of constant dissipation after the material state has begun to evolve. Thus, an associative macroscale continuum model will be, at best, approximate. Interestingly, local flow surfaces beyond the threshold are not necessarily convex when plotted in the overall stress plane. This is due to the existence of residual stresses. In addition, the generalized method of cells was found to accurately estimate the inner and outer envelopes of the local flow surface cluster with a surprisingly small number of subcells.