The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t = 0) steady and then at t > 0 it becomes unsteady. The semi-similar solution of the unsteady Navier-Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier-Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier-Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time. (C) 1999 Elsevier Science Ltd. All rights reserved.

Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field

The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant velocity which is in the same or opposite direction to that of free stream velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free stream velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.

Experimental study and optimization of Plasma Actuators for Flow control in subsonic regime

Experimental study and optimization of Plasma Ac- tuators for Flow control in subsonic regime PRADEEP MOISE, JOSEPH MATHEW, KARTIK VENKATRAMAN, JOY THOMAS, Indian Institute of Science, FLOW CONTROL TEAM | The induced jet produced by a dielectric barrier discharge (DBD) setup is capable of preventing °ow separation on airfoils at high angles of attack. The ef-fect of various parameters on the velocity of this induced jet was studied experimentally. The glow discharge was created at atmospheric con-ditions by using a high voltage RF power supply. Flow visualization,photographic studies of the plasma, and hot-wire measurements on the induced jet were performed. The parametric investigation of the charac- teristics of the plasma show that the width of the plasma in the uniform glow discharge regime was an indication of the velocity induced. It was observed that the spanwise and streamwise overlap of the two electrodes,dielectric thickness, voltage and frequency of the applied voltage are the major parameters that govern the velocity and the extent of plasma.e®ect of the optimized con¯guration on the performance characteristics of an airfoil was studied experimentally.

Continuous distribution kinetics for the thermal degradation of LDPE in solution

Polymer degradation in solution has several advantages over melt pyrolysis, The degradation of low-density polyethylene (LDPE) occurs at much lower temperatures in solution (280-360degreesC) than in conventional melt pyrolysis (400-450degreesC). The thermal degradation kinetics of LDPE in solution was investigated in this work. LDPE was dissolved in liquid paraffin and degraded for 3 h at various temperatures (280-360degreesC). Samples were taken at specific times and analyzed with high-pressure liquid chromatography/gel permeation chromatography for the molecular weight distribution (MWD), The time evolution of the MWD was modeled with continuous distribution kinetics. Data indicated that LDPE followed random-chain-scission degradation. The rapid initial drop in molecular weight, observed up to 45 min, was attributed to the presence of weak links in the polymer. The rate coefficients for the breakage of weak and strong links were determined, and the corresponding average activation energies were calculated to be 88 and 24 kJ/mol, respectively. (C) 2002 John Wiley Sons, Inc.

Oscillatory flow and temperature fields in an open tube with temperature difference across the ends

The oscillating flow and temperature field in an open tube subjected to cryogenic temperature at the cold end and ambient temperature at the hot end is studied numerically. The flow is driven by a time-wise sinusoidally varying pressure at the cold end. The conjugate problem takes into account the interaction of oscillatory flow with the heat conduction in the tube wall. The full set of compressible flow equations with axisymmetry assumption are solved with a pressure correction algorithm. Parametric studies are conducted with frequencies of 5-15 Hz, with one end maintained at 100 K and other end at 300 K. The flow and temperature distributions and the cooldown characteristics are obtained. The frequency and pressure amplitude have negligible effect on the time averaged Nusselt number. Pressure amplitude is an important factor determining the enthalpy flow through the solid wall. The frequency of operation has considerable effect on penetration of temperature into the tube. The density variation has strong influence on property profiles during cooldown. The present study is expected to be of interest in applications such as pulse tube refrigerators and other cryocoolers, where oscillatory flows occur in open tubes. (C) 2011 Elsevier Ltd. All rights reserved.

High-pressure kinetics of oxidative copolymerization of styrene with alpha-methyl styrene

This is the first report on the study carried out on high-pressure free-radical initiated oxidated copolymerization of styrene (STY) with alpha-methylstyrene (AMS) at various temperatures (45-65degreesC) at constant pressure (100 psi) and then at various pressures (50-300 psi) keeping the temperature (50degreesC) constant. The compositions of the copolyperoxides obtained from the H-1 NMT spectra were utilized to determine the reactivity ratios of the monomers. The reactivity ratios indicate that STY forms an ideal copolyperoxide with AMS and the copolyperoxide is richer in AMS. The effect of temperature and oxygen pressure in the reactivity ratios of the monomers was studied. The rates of copolymerization (R-p) were used to determine the overall activation energies (E-a) and activation volume (DeltaV(#)) of copolymerization. The unusually higher values of the DeltaV(#) may be due to the pressurizing fluid oxygen which itself is a reactant in the copolymerization, the side reactions, and the chain-transfer reactions occuring during copolymerizations.

Kinetics of hydrogen evolution on submicron size Co, Ni, Pd and CoNi alloy powder electrodes by d.c. polarization and a.c. impedance studies

Submicron size Co, Ni and Co-Ni alloy powders have been synthesized by the polyol method using the corresponding metal malonates and Pd powder by reduction of PdOx in methanol. The kinetics of the hydrogen evolution reaction ( HER) in 6 M KOH electrolyte have been studied on electrodes made from the pressed powders. The d.c. polarization measurements have resulted in a value close to 120 mV decade(-1) for the Tafel slope, suggesting that the HER follows the Volmer-Heyrovsky mechanism. The values of exchange current density (i(o)) are in the range 1-10 mA cm(-2) for electrodes fabricated in the study. The a.c. impedance spectra measured at several potentials in the HER region showed a single semicircle in the Nyquist plots. Exchange current density (i(o)) and energy transfer coefficient (alpha) have been calculated by employing a nonlinear least square-fitting program.

Kinetics of thermal degradation of vinyl polyperoxides in solution

The thermal degradation of vinyl polyperoxides, poly(styrene peroxide, (PSP), poly(alpha-methylstyrene peroxide) (PAMSP) and poly(alpha-phenylstyrene pet-oxide) (PAPSP), was carried out at different temperatures in toluene. The time evolution of molecular weight distributions (MWDs) was determined by gel permeation chromatography (GPC). A continuous distribution model was used to evaluate the random chain degradation rate coefficients. The activation energies, determined from the temperature dependence of the rate coefficients, suggest that thermal degradation of polyperoxides is controlled by the dissociation of the O-O bonds in the backbone of the polymer chain. Among the three polyperoxides investigated, the thermal stability is the highest for PAPSP and the lowest for PAMSP. (C) 2002 Elsevier Science Ltd. All rights reserved.

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation. (C) 2002 Published by Elsevier Science Ltd.

Stability of fluid flow past a membrane

The stability of fluid flow past a membrane of infinitesimal thickness is analysed in the limit of zero Reynolds number using linear and weakly nonlinear analyses. The system consists of two Newtonian fluids of thickness R* and H R*, separated by an infinitesimally thick membrane, which is flat in the unperturbed state. The dynamics of the membrane is described by its normal displacement from the flat state, as well as a surface displacement field which provides the displacement of material points from their steady-state positions due to the tangential stress exerted by the fluid flow. The surface stress in the membrane (force per unit length) contains an elastic component proportional to the strain along the surface of the membrane, and a viscous component proportional to the strain rate. The linear analysis reveals that the fluctuations become unstable in the long-wave (alpha --> 0) limit when the non-dimensional strain rate in the fluid exceeds a critical value Lambda(t), and this critical value increases proportional to alpha(2) in this limit. Here, alpha is the dimensionless wavenumber of the perturbations scaled by the inverse of the fluid thickness R*(-1), and the dimensionless strain rate is given by Lambda(t) = ((gamma) over dot* R*eta*/Gamma*), where eta* is the fluid viscosity, Gamma* is the tension of the membrane and (gamma) over dot* is the strain rate in the fluid. The weakly nonlinear stability analysis shows that perturbations are supercritically stable in the alpha --> 0 limit.

Studies on the effects of test gas on the flow field around large angle blunt cone flying at hypersonic Mach number

The effect of the test gas on the flow field around a 120degrees apex angle blunt cone has been investigated in a shock tunnel at a nominal Mach number of 5.75. The shock standoff distance around the blunt cone was measured by an electrical discharge technique using both carbon dioxide and air as test gases. The forebody laminar convective heat transfer to the blunt cone was measured with platinum thin-film sensors in both air and carbon dioxide environments. An increase of 10 to 15% in the measured heat transfer values was observed with carbon dioxide as the test gas in comparison to air. The measured thickness of the shock layer along the stagnation streamline was 3.57 +/- 0.17 mm in air and 3.29 +/- 0.26 mm in carbon dioxide. The computed thickness of the shock layer for air and carbon dioxide were 3.98 mm and 3.02 mm, respectively. The observed increase in the measured heat transfer rates in carbon dioxide compared to air was due to the higher density ratio across the bow shock wave and the reduced shock layer thickness.

Continuous distribution kinetics for ultrasonic degradation of poly(methyl methacrylate)

Ultrasonic degradation of poly(methyl methacrylate) (PMMA) was carried out in several solvents and some mixtures of solvents. The time evolution of molecular weight distribution (MWD), determined by gel permeation chromatography, is analysed by continuous distribution kinetics. The rate coefficients for polymer degradation are determined for each solvent. The variation of rate coefficients is correlated with the vapour pressure of the solvent, kinematic viscosity of the solution and solvent-polymer interaction parameters. The vapour pressure and the kinematic viscosity of the solution are found to be more critical than other parameters (such as the Huggins and Flory-Huggins constants) in determining the degradation rates. (C) 2001 Society of Chemical Industry.

Influence of temperature and strain rate on the flow stress of an FeAl alloy

The deformation behavior of an FeAl alloy processed by hot extrusion of water atomized powder has been investigated. Compression tests are performed in the temperature range 1073–1423 K and in the strain rate range 0.001–100 s−1 up to a true plastic strain of 0.5. The flow stress has been found to be strongly dependent on temperature as well as strain rate. The stress exponent in the power law rate equation is estimated to be in the range 7.0–4.0, decreasing with temperature. The activation energy for plastic flow in the range 1073–1373 K varies from 430 kJ mol−1 at low stresses to 340 kJ mol−1 at high stresses. However, it is fairly independent of strain rate and strain. The activation area has similarly shown a stress dependence and lies in the range 160–45b2. At 1423 K and at strain rates lower than 0.1 s−1 a strain rate sensitivity of 0.3 is observed with an associated activation energy of 375 kJ mol−1. The plastic flow in the entire range of temperature and strain rate investigated appears to be controlled by a diffusion mechanism. The results have revealed that it is possible to process the alloy by superplastic forming in the range 1373–1423 K at strain rates lower than 0.1 s−1.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier-Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier-Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.