Showing papers on "Herschel–Bulkley fluid published in 2003"

Viscoplastic flow around a cylinder in an infinite medium

Abstract: The purpose of the numerical simulations carried out in this study is to determine the flow characteristics of a Herschel–Bulkley viscoplastic fluid around a cylinder in an infinite medium. Inertia is assumed to be negligible. Two types of boundary conditions are considered: the fluid adheres or slips (zero tangential stress) on the cylinder wall. Finite-element modelling involves regularising the Herschel–Bulkley model, as proposed by Papanastasiou [J. Rheol. 31 (1987) 385]. The effect of the yield stress value and shear-thinning index on the kinematic field and drag exerted on the cylinder were explored systematically. The location, dimension and kinematics of the rigid zones were determined. The results are compared with available theoretical data.

Deformation of a Newtonian drop in a viscoelastic matrix under steady shear flow: Experimental validation of slow flow theory

Abstract: The small deformation of a single drop in a Boger fluid under steady-state slow shear flow is here investigated by video-enhanced microscopy and image analysis. Data are compared to predictions of a recent perturbation analysis, dealing with the drop-in-a-flow-field problem for viscoelastic fluid components [J. Non-Newt. Fluid Mech. 107 (2002) 111]. The main experimental result, in agreement with theory, is that drop orientation towards the flow direction is significantly enhanced as compared to the Newtonian case. In fact, based on this result, an optical determination of the first normal stress difference of the matrix fluid can be obtained. Furthermore, it is shown here that the interfacial tension of the fluid pair can be readily obtained by comparison between the theoretical predictions and the optical data taken in both the “side” and “top” views (i.e. along the vorticity and velocity gradient direction, respectively) of the deformed drop.

On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance

Abstract: We consider a compressible viscous fluid effected by general form external force in R3. In part 1, an analysis of the linearized problem based on the weighted- L2 method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if H3-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

Flow instabilities of Herschel–Bulkley fluids

Abstract: We investigate numerically the interactions of two-dimensional jets of Bingham plastic and Herschel–Bulkley fluids with a vertical surface at a distance from the die exit. This problem simulates the early stages of filling of a planar cavity. Our main objective is to explain the flow instabilities observed during the processing of semisolid materials. The effects of the Reynolds and Bingham numbers and of the inlet boundary conditions on both the filling and the stability of the jet are established by means of numerical time-dependent calculations.

Experimental observation of dramatic differences in the dynamic response of Newtonian and Maxwellian fluids

Abstract: An experimental study of the dynamic response of a Newtonian fluid and a Maxwellian fluid under an oscillating pressure gradient is presented. Laser Doppler anemometry is used in order to determine the velocity of the fluid inside a cylindrical tube. In the case of the Newtonian fluid, the dissipative nature is observed. In the dynamic response of the Maxwellian fluid an enhancement at the frequencies predicted by theory is observed.

Incompressible Cake Filtration of a Yield Stress Fluid

Abstract: Filtration of Non-Newtonian fluid occurs frequently in industry. A correlation is developed by introducing the Yield Stress model in place of the Newtonian model used in the Ergun equation. The resulting model has three parameters that are functions of the geometry and roughness of the particle surfaces. Two of the parameters can be deduced in the limit as the yield stress becomes negligible and the model reduces to the Ergun equation for Newtonian fluids. The third model parameter is determined from experimental data. The correlation relates a defined friction factor to the dimensionless Reynolds and Hedstrom numbers that can be used to predict pressure drop for flow of a yield stress fluid through a packed bed of spherical particles. This model is applied to predict incompressible cake filtration performance of a yield stress fluid. Modeling results show that for a constant pressure filtration the cake growth rate and filtrate flow rate for the incompressible filter cake are similar to that for a Newton...

Method for determining rheological parameters of a fluid

Abstract: The inventive method uses the ultrasound Doppler method (UVP) in order to determine a local velocity profile perpendicular to a line for a fluid which flows through said line, carrying suspended or emulsified particles. The wall shear stress of said fluid is measured locally within the range of said local velocity profile. Specific rheological parameters of the flowing fluid thus examined, e.g. viscosity function (shear viscosity), flow limit etc., can be determined from the local velocity profile and the local wall shear stress associated therewith. A suitable model is adapted by iteratively adapting a model-based theoretic velocity profile to a measured velocity profile.

Constitutive models of electrorheological and magnetorheological fluids using viscometers

Abstract: A key aspect of application of electrorheological (ER) and magnetorheological (MR) fluids is the characterization of rheological properties. For this purpose, two rotational viscometers are theoretically analyzed. One is a rotational coaxial cylinder viscometer, and the second is a rotational parallel disk viscometer. A key goal is to determine the shear stress and shear rate of ER/MR fluids for both viscometers from the torque and angular velocity data. To do this, the equations between shear stress and torque as well as shear rate and angular velocity are derived on the basis of the Bingham-plastic, biviscous, and Herschel-Bulkley constitutive models. For simplicity in mathematical form, the Bingham-plastic model is used to describe the flow behavior of ER/MR fluids. The biviscous model characterized by static and dynamic yield stresses is used to capture the preyield behavior. The preyield region where the local shear stress is smaller than the static yield stress has much larger viscosity than the postyield region. In order to account for the shear thinning or thickening in postyield region, the Herschel-Bulkley constitutive model is used in this study. The shear stress for a rotational coaxial cylinder viscometer can be calculated directly from measured torque. However, three approximation methods are applied to determine the shear rate. For rotational parallel disk viscometers, the shear rate and shear stress can be obtained directly from the torque and angular velocity data. In order to comprehensively understand the flow behavior of ER/MR fluids with respect to the constitutive models, the nondimensional analyses are undertaken in this study.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Electrorheological and Magnetorheological Duct Flow in Shear-Flow Mode using Herschel-Bulkley Constitutive Model

Abstract: A quasi-steady duct flow through a parallel plate model for electrorheological (ER) and magnetorheological (MR) fluids under shear-flow mode is investigated mathematically. To do so Herschel-Bulkley power law constitutive model for ER and MR fluid is adopted to account for postyield shear thinning or shear thickening conditions as indicated in recent research. This approach is selected in order to obtain a more flexible representation of ER or MR postyield behavior rather than using the mostly adopted Bingham plastic model. This will lead to developing a theoretical method for prediction of ER or MR force characteristics.

Estimation of average shear rate in stirred vessels for pipelining shear simulation

Abstract: The existing Metzner_Otto equation for stirring shear rate estimation is only suitable for calculating the average shear rate around the impeller in the laminar flow of some impeller_vessel systems and cannot meet the requirement of shear simulation for the process of oil pipeliningOn the basis of the relationship between the energy dissipation rate in the fluid flow and the shear rate,an approach is presented to estimate the whole_vessel average shear rate in a stirred vessel by using the shaft power of the stirrer Some equations of shear rate estimation for Newtonian fluid and the power law fluid were derivedTaking a small stirring system used for laboratory test as an example, an empirical model to correlate the whole_vessel average shear rate and the stirring speed,fluid volume in the vessel, consistency coefficient and flow behavior index of the power law fluid was developed by using the present approachThe shear rates estimated by the empirical model are in good agreement with those calculated according to the measured torque of the shaftThis approach is available for different types of impeller and flow regime,and can also be applied to the non_Newtonian fluids favorable to other rheological models

Unsteady flow of a dusty conducting non-Newtonian fluid through a pipe

Abstract: In this paper, the unsteady flow of a dusty viscous incompressible electrically conducting non-Newtonian power-law fluid through a circular pipe is investigated A constant pressure gradient in the axial direction and a uniform magnetic field directed perpendicular to the flow direction are applied The particle phase is assumed to behave as a viscous fluid A numerical solution is obtained for the governing nonlinear momentum equations using finite differences The effects of the magnetic-field parameter Ha, the non-Newtonian fluid characteristics (the flow index n), and the particle-phase viscosity β on the transient behavior of the velocity, volumetric flow rates, and skin friction coefficients of both fluid and particle phases are studied It is found that all the flow parameters for both phases decrease as the magnetic field increases or the flow index decreases On the other hand, increasing the particle-phase viscosity increases the skin friction of the particle phase, but decreases the other flow

An unsteady analysis of nonlinear two‐layered 2D model of pulsatile flow through stenosed arteries 1

Abstract: The effects of red cell concentration and peripheral layer viscosity on physiological characteristics of pulsatile flow in presence of mild stenosis are investigated. The flowing blood is represented by a two‐fluid model, consisting of a core region of suspension of all the erythrocytes assumed to be non‐Newtonian (inhomogeneous Newtonian) and a peripheral plasma layer free from cells of any kind as a Newtonian fluid. In the realm of the flow characteristics of blood the viscosity is taken to be a function of hematocrit in a manner that it varies radially only in the central core characterising its non‐Newtonian behaviour while it remains constant in the plasma region. The arterial wall motion and its effect on local fluid mechanics is also incorporated in the present theoretical study. Finite difference scheme has been used to solve the unsteady Navier‐Stokes equations in cylindrical coordinates assuming axial symmetry under laminar conditions, so that the problem effectively becomes two‐dimensi...

A study on viscoelastic fluid flow in a square-section 90-degrees bend

Abstract: It is well known that the drag-reducing effect is obtained in a surfactant solution flow in a straight pipe. We investigate about a viscoelastic fluid flow such as a surfactant solution flow in a square-section 90° bend. In the experimental study, drag-reducing effect and velocity field in a surfactant solution flow are investigated by measurements of wall pressure loss and LDV measurements. For the numerical method, LES with FENE-P model is used in the viscoelastic fluid flow in the bend. The flow characteristics of viscoelastic fluid are discussed compared with that of a Newtonian fluid.

Effect of hydrostatic pressure and temperature on rheological characteristics of alpha-lactalbumin.

Abstract: The flow behavior of pressure and temperature-treated α-lactalbumin dispersions was studied using a controlled rate rheometer. Dispersions 10% (w/w) of α-lactalbumin were subjected to high hydrostatic pressure from 100 MPa to 400 MPa at 20°C for 30 min or thermal treatment from 20°C to 80°C for 15 min at atmospheric pressure, followed by rheological characterisation at shear rates between O/s and 200/s. The shear stress-shear rate data of both pressure and heat-treated α-lactalbumin dispersions were described with the Herschel Bulkley model with yield stress. Dispersions exhibited shear-thinning behavior with flow behavior indices less than unity. Hydrostatic pressure treatment of α-lactalbumin samples did not change the magnitude of rheological parameters (p>0.05) and there was no gel formation. Consistency coefficient and apparent viscosity at 100/s decreased linearly with temperature and followed the Arrhenius relationship. The flow activation energy was found to be 10.18 kJ/mol and 11.57 kJ/mol for consistency index and apparent viscosity, respectively. Lower flow activation energy signified lesser molecular interaction or denaturation of protein molecules during thermal treatment of α-lactalbumin.

Nondimensional Analysis of Electrorheological and Magnetorheological Dampers Using a Herschel-Bulkley Constitutive Model

Abstract: Quasisteady modeling of linear stroke flow mode magnetorheological (MR) and electrorheological (ER) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the yield stress of the fluid, τy , is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a preyield condition where the local shear stress is less than the yield stress, τ τy , so that the material flows with a constant postyield viscosity. The objective of this paper is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits postyield shear thinning or thickening behavior, that is, the postyield viscosity is a function of shear rate. A Herschel-Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results—velocity profile, shear stress profile, and damping coefficient—are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.Copyright © 2003 by ASME

Computed Synovial Fluid Flow in a Simple Knee Joint Model

Abstract: Prediction of shear stress induced by the fluid flow on knee joint cells is the main aim of this study. Oscillatory flow of a Newtonian synovial fluid is examined in two-dimensional joint geometries. The experimental model is a fluid driven shear loader test rig, which features a finite plate oscillating at 1Hz, that is 1mm over a stationary cell culture surface. Oscillating Couette flow in the thin gap is generated by the finite span plate. An incompressible two-dimensional transient and laminar CFD model is developed using the STAR-CD® code. The infinite oscillating plate Couette flow solutions (Stoke’s Second Problem with a finite gap) are reviewed and used in the grid sensitivity and validation tests of the computational finite oscillating plate model. The resulting flow features and vorticity convection are discussed and shear stress induced on the stationary plate due to an oscillating finite plate is compared with its infinite counterpart. As an extension, the effect of articular cartilage curvature is studied in a topologically equivalent model with and without menisci.Copyright © 2003 by ASME

The influence of mechanical input amplitude on the dynamic response of an electrorheological fluid in squeeze flow

Abstract: An investigation was carried out to determine the effect of mechanical input amplitude on the performance of an electrorheological (ER) fluid in oscillatory squeeze flow. The ER fluid, consisting of a suspension of a semi-conducting compound in a dielectric liquid carrier, was contained in a squeeze cell, which during motion subjects the fluid to both compressive and tensile loading. The ER fluid was excited by a constant DC voltage and its response was assessed for various input mechanical amplitudes. The results were analysed in terms of force-displacement and force-velocity characteristics and showed a great dependence on device inertia, compressibility and on the input displacement provided by the oscillation of the lower electrode. In addition, the performance of the fluid was compared with that predicted by a theoretical model, which assumes a bi-viscous fluid characteristic. This model is optimised when the power-law used to estimate the fluid yield stress is replaced by a quadratic law. Finally, the implications of the results for vibration control, where the ER fluid is employed in an engine mount, are discussed.

Studies on the axisymmetric sphere–sphere interaction problem in Newtonian and non-Newtonian fluids

Abstract: In this research, experimental studies have been performed on the hydrodynamic interaction between two spheres by using particle image velocimetry and measuring the force between the spheres. To approach the system as a resistance problem, a servo-driving system was set-up by assembling a microstepping motor, a ball screw and a linear motion guide for the particle motion. Glycerin and a dilute solution of polyacrylamide in glycerin were used as Newtonian and non-Newtonian fluids, respectively. The polymer solution behaves like a Boger fluid when the concentration is 1000 ppm or less. The experimental results were compared with the asymptotic solution of Stokes equation. The result shows that fluid inertia and unsteadiness play important roles in the particle–particle interaction in the Newtonian fluid. This implies that the motion of two particles in suspension is not reversible even in the Newtonian fluid. In the non-Newtonian fluid, in addition to inertial effect, normal stress differences and viscoelasticity play important roles as expected. In dilute solutions weak shear thinning and the migration of polymer molecules in the inhomogeneous flow field also appear to affect the physics of the problem.

Nondimensional Analysis of Electrorheological and Magnetorheological Dampers Using a Herschel-Bulkley Constitutive Model

Abstract: Quasisteady modeling of linear stroke flow mode magnetorheological (MR) and electrorheological (ER) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the yield stress of the fluid, τy , is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a preyield condition where the local shear stress is less than the yield stress, τ τy , so that the material flows with a constant postyield viscosity. The objective of this paper is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits postyield shear thinning or thickening behavior, that is, the postyield viscosity is a function of shear rate. A Herschel-Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results — velocity profile, shear stress profile, and damping coefficient — are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.Copyright © 2003 by ASME

Indirect on-line determination of Newtonian fluid viscosity based on numerical flow simulations

Abstract: A new indirect method of determining the viscosity of a Newtonian fluid flowing in a tube with a geometrical singularity is proposed. Due to this singularity, the shape of the dimensionless velocity profiles is closely correlated with the Reynolds number of the flow. Newtonian fluid flows were simulated numerically with various Reynolds numbers. Based on the results of these calculations, an abacus was plotted showing the relationship between the dimensionless velocity and the dimensionless viscosity. On the other hand, dimensionless velocities were also obtained by measuring velocity profiles on a hydrodynamic bench with an ultrasonic Doppler velocimeter. These experimental values were plotted on the abacus and the viscosity of the actual fluid was thus determined. Comparisons were made with viscometer measurements in order to assess the accuracy of the method and its range of validity. This method is of great potential interest for application to industrial plans when it is necessary to know the viscosity of a fluid undergoing a transformation without interrupting the process by taking fluid samples.

Analysis of non-newtonian flows through contractions and expansions

Abstract: Flow of non-Newtonian fluids through contractions and expansions are found in several industrial processes. In this work, a numerical simulation of non-Newtonian fluid flows through an axysimetric expansion followed by a con- traction is performed. The numerical solution of conservation equations of mass and momentum is obtained via finite volume method. In order to model the non-Newtonian behavior of the fluid, it is used the Generalized Newtonian Fluid constitutive equation, with the Carreau viscosity function. The results obtained show the influence of rheological para- meters on flow patterns.

Nondimensional quasi-steady analysis of magnetorheological dampers utilizing a Herschel-Bulkley model with preyield viscosity

Abstract: Dampers based on electrorheological (ER) and magnetorheolgical (MR) fluids can be analyzed under assumptions of quasi-steady, fully developed flow behavior. Models that have been used to characterize ER and MR dampers include the Bingham-plastic, the Herschel-Bulkley and biviscous models. In the Bingham-plastic and the Herschel-Bulkley models, the fluid exhibits rigid behavior in the preyield flow region. The difference between these two models lie in the modeling of the postyield behavior. In the case of the Bingham-plastic model, the postyield behavior is such that the shear stress is proportional to the shear rate. In contrast, the Herschel-Bulkley model assumes that the shear stress is proportional to a power law of the shearrate. In the biciscous model, the relationship between the shear stres and shear rate is linear in both the preyield and postyield regions with constant values of viscosities for the two regions. However, the preyield flow behavior exhibits a much high viscosity than that in the postyield. In the propose model, the assumption of preyield rigid behavior within the Herschel-Bulkley model has been relaxed while the postyield relationship based on the power law has been retained. Here the fluid undergoes Newtonian preyield viscous flow and has a non-Newtonian postyield behavior. Based on this model, we have analyzed the performance of a rectangular duct ER or MR valve. Typical results include shear stress and velocity profiles across the valve gap, equivalent damping and damping coefficients.

Stability of rheometric viscoelastic fluid flow with respect to shear perturbations

Abstract: Flow between two plates is considered for a fluid obeying the DeWitt rheological equation of state with the Jaumann derivative. It is found analytically that the steady-state Couette flow is stable or unstable with respect to plane shear perturbations when the Weissenberg numbers are less or greater than unity, respectively. The flow acceleration stage is studied analytically and numerically, a comparison with the case of an Oldroyd fluid is carried out, and the neutral stability curves are constructed. The fundamental role of perturbations of the type considered among the set of instability types which can act on the fluid in such a flow is noted.

Effects of viscosity variations in steady and oscillatory Couette flow

Abstract: A Newtonian fluid with small variations in the viscosity in the primary flow direction of steady and oscillatory Couette flow is studied. These variations in viscosity create a coupling of the components of the momentum equations between the flow-direction component and the gradient-direction component. The coupling leads to secondary flows even in planar Couette flow where a rectilinear flow may be expected for a purely viscous fluid under creeping flow conditions. A perturbation solution has been applied for small-amplitude oscillations in the viscosity in both steady and oscillatory Couette flow. Because many rheological measurements are made assuming rectilinear flow, these results may have important consequences and may allow error caused by heterogeneity to be estimated. Finally, the relation between the momentum and the assumption of a symmetric stress tensor is discussed by introducing an alternative constitutive equation that is linear in the velocity gradient tensor and objective, but gives an a...

On the dispersion of a solute in Poiseuille flow of a third-grade fluid in a channel

Abstract: Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls are extended to the flow of non-Newtonian viscoelastic fluid (known as third-grade fluid) using a generalized dispersion model which is valid for all times after the solute injection. The exact expression is obtained for longitudinal convective coefficient K 1 ( Γ ), which shows the effect of the added viscosity coefficient Γ on the convective coefficient. It is seen that the value of the K 1 ( Γ ) for Γ ≠0 is always smaller than the corresponding value for a Newtonian fluid. Also, the effect of the added viscosity coefficient on the K 2 ( t , Γ ) (which is a measure of the longitudinal dispersion coefficient of the solute) is explored numerically. Finally, the axial distribution of the average concentration C m of the solute over the channel cross-section is determined at a fixed instant after the solute injection for several values of the added viscosity coefficient.