Flow behavior of LDPE and its blends with LLDPE I and II: A comparative study

Studies on melt rheological properties of blends of low density polyethylene (LDPE) with selected grades of linear low density polyethylene (LLDPE), which differ widely in their melt flow indices, are reported, The data obtained in a capillary rheometer are presented to describe the effects of blend composition and shear rate on flow behavior index, melt viscosity, and melt elasticity. In general, blending of LLDPE I that has a low melt flow index (2 g/10 min) with LDPE results in a decrease of its melt viscosity, processing temperature, and the tendency of extrudate distortion, depending on blending ratio. A blending ratio around 20-30% LLDPE I seems optimum from the point of view of desirable improvement in processability behavior. On the other hand, blending of LLDPE II that has a high melt flow index (10 g/10 min) with LDPE offers a distinct advantage in increasing the pseudoplasticity of LDPE/LLDPE II blends.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter = 9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 10(8). Under these conditions the convection is turbulent, and the time-averaged velocity at any point is `zero'. The Reynolds number based on the Taylor microscale, Re-lambda, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6-7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as (RaSc1/2)-Sc-1/2, and the Reynolds number would scale as (RaSc-1/2)-Sc-1/2. The velocity and the flux measurements appear to be consistent with the Ra-1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are Much higher compared to what would be obtained in Rayleigh-Benard (R-B) convection for similar density differences.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Flow of metal into the flash gap in the last stages of a plane-strain closed-die forging operation

In closed-die forging the flash geometry should be such as to ensure that the cavity is completely filled just as the two dies come into contact at the parting plane. If metal is caused to extrude through the flash gap as the dies approach the point of contact — a practice generally resorted to as a means of ensuring complete filling — dies are unnecessarily stressed in a high-stress regime (as the flash is quite thin and possibly cooled by then), which reduces the die life and unnecessarily increases the energy requirement of the operation. It is therefore necessary to carefully determine the dimensions of the flash land and flash thickness — the two parameters, apart from friction at the land, which control the lateral flow. The dimensions should be such that the flow into the longitudinal cavity is controlled throughout the operation, ensuring complete filling just as the dies touch at the parting plane. The design of the flash must be related to the shape and size of the forging cavity as the control of flow has to be exercised throughout the operation: it is possible to do this if the mechanics of how the lateral extrusion into the flash takes place is understood for specific cavity shapes and sizes. The work reported here is part of an ongoing programme investigating flow in closed-die forging. A simple closed shape (no longitudinal flow) which may correspond to the last stages of a real forging operation is analysed using the stress equilibrium approach. Metal from the cavity (flange) flows into the flash by shearing in the cavity in one of the three modes considered here: for a given cavity the mode with the least energy requirement is assumed to be the most realistic. On this basis a map has been developed which, given the depth and width of the cavity as well as the flash thickness, will tell the designer of the most likely mode (of the three modes considered) in which metal in the cavity will shear and then flow into the flash gap. The results of limited set of experiments, reported herein, validate this method of selecting the optimum model of flow into the flash gap.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.

Classical and Cosserat plasticity and viscoplasticity models for slow granular flow

We consider models for the rheology of dense, slowly deforming granular materials based of classical and Cosserat plasticity, and their viscoplastic extensions that account for small but finite particle inertia. We determine the scale for the viscosity by expanding the stress in a dimensionless parameter that is a measure of the particle inertia. We write the constitutive relations for classical and Cosserat plasticity in stress-explicit form. The viscoplastic extensions are made by adding a rate-dependent viscous stress to the plasticity stress. We apply the models to plane Couette flow, and show that the classical plasticity and viscoplasticity models have features that depart from experimental observations; the prediction of the Cosserat viscoplasticity model is qualitatively similar to that of Cosserat plasticity, but the viscosities modulate the thickness of the shear layer.

Laminar flow of a suspension in a curved pipe with varying curvature

The laminar flow of a fairly concentrated suspension (in which the volume fraction Z of the solid particles < 0.4) in a spatially varying periodically curved pipe has been examined numerically. Unlike the case of interacting suspension flows, the particles are found to flow in a well-mixed fashion, altering both the axial and circumferential velocities and consequently the fluid flux in the tube, depending on their diffusivity and inertia. The magnitude of shear stress at the wall is enhanced, suggesting that, if applied to vascular system, the vascular wall could be prone to ulceration during pathological situations like polycythemia. The delay in adaptation of the deviation in Poiseuille flow velocity to the curvature changes is also discussed in detail.

Bed Shear from Velocity Profiles: A New Approach

A new binary law of velocity distribution has been developed to describe the velocity profile for the entire flow region. The law is a combination of logarithmic law, valid in the wall (inner) region, and parabolic law, valid in the core (outer) region of the flow. The validity of the law has been established based on earlier data on flat plates, rough and smooth pipes and experimental data obtained from rigid-walled open channels with plane sand beds. A procedure of estimating bed shear stress from the proposed law of velocity distribution using the measured velocity profile has been evolved. Bed shear estimates made according to this procedure are in agreement with the values obtained from uniform flow analysis in the case of open channel flow over a sediment bed. The proposed method of estimating the bed shear stress from the observed velocity profiles is found to be particularly useful in cases where it is difficult to determine precisely the true bed level, such as in the case of flow over sediment beds.

A simulation study of the mixing, atomic flow and velocity profiles of crystalline materials during sliding

Self-contained Non-Equilibrium Molecular Dynamics (NEMD) simulations using Lennard-Jones potentials were performed to identify the origin and mechanisms of atomic scale interfacial behavior between sliding metals. The mixing sequence and velocity profiles were compared via MD simulations for three cases, viz.: sell-mated, similar and hard-softvcrystal pairs. The results showed shear instability, atomic scale mixing, and generation of eddies at the sliding interface. Vorticity at the interface suggests that atomic flow during sliding is similar to fluid flow under Kelvin-Helmholtz instability and this is supported by velocity profiles from the simulations. The initial step-function velocity profile spreads during sliding. However the velocity profile does not change much at later stages of the simulation and it eventually stops spreading. The steady state friction coefficient during simulation was monitored as a function of sliding velocity. Frictional behavior can be explained on the basis of plastic deformation and adiabatic effects. The mixing layer growth kinetics was also investigated.

Comprehensive Path-sensitive Data-flow Analysis

Data-flow analysis is an integral part of any aggressive optimizing compiler. We propose a framework for improving the precision of data-flow analysis in the presence of complex control-flow. W initially perform data-flow analysis to determine those control-flow merges which cause the loss in data-flow analysis precision. The control-flow graph of the program is then restructured such that performing data-flow analysis on the resulting restructured graph gives more precise results. The proposed framework is both simple, involving the familiar notion of product automata, and also general, since it is applicable to any forward data-flow analysis. Apart from proving that our restructuring process is correct, we also show that restructuring is effective in that it necessarily leads to more optimization opportunities. Furthermore, the framework handles the trade-off between the increase in data-flow precision and the code size increase inherent in the restructuring. We show that determining an optimal restructuring is NP-hard, and propose and evaluate a greedy strategy. The framework has been implemented in the Scale research compiler, and instantiated for the specific problem of Constant Propagation. On the SPECINT 2000 benchmark suite we observe an average speedup of 4% in the running times over Wegman-Zadeck conditional constant propagation algorithm and 2% over a purely path profile guided approach.

Magnetohydrodynamic unsteady flow in a tube of variable cross section in an axial magnetic field

Oscillatory flow in a tube of slowly varying cross section is investigated in the presence of a uniform magnetic field in the axial direction. A perturbation solution including steady streaming is presented. The pressure and shear stress on the wall for various parameters governing the flow are discussed. Physics of Fluids is copyrighted by The American Institute of Physics.

A hydrodynamical study of the flow in renal tubules

The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q 0 can be expressed as a Fourier integral (whereQ 0 is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.

Wall Shear Fluctuations in a Turbulent Boundary Layer

IN the last two decades, the instantaneous structure of a turbulent boundary layer has been examined by many in an effort to understand the dynamics of the flow. Distinct and well-defined flow patterns that seem to have great relevance to the turbulence production mechanism have been observed in the wall region.1'2 The flow near the wall is intermittent with periodic eruptions of the fluid, a phenomenon generally termed "bursting process." Earlier investigations in this field were limited to liquid flows at low speeds and the entire flowpattern was observed using flow visualization techniques.Study was later extended to boundary-layer flows in windtunnels at higher speeds and Reynolds numbers using hot-wiresignals for the analysis of the bursting phenomenon.

Pulsatile flow in tubes of varying cross-sections

The pulsatile flow of an incompressible viscous fluid in a cylindrical tube of varying cross section is investigated for small Reynolds numbers. The solutions consist of a stedy and an oscillatory part. The shear stress distribution on the wall is evaluated and discussed in detail for special geometries like tapered tubes, locally constricted tubes and peristaltic tubes. The existence of separation in the flow field is noticed.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.