Showing papers on "Herschel–Bulkley fluid published in 2014"

Analytical solutions of couple stress fluid flows with slip boundary conditions

Abstract: In the present article, the exact solutions for fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible couple stress fluid between parallel plates are obtained using slip boundary conditions. The effect of various parameters on velocity for each problem is discussed. It is found that, for each of the problems, the solution in the limiting case as couple stresses approaches to zero is similar to that of classical viscous Newtonian fluid. The results indicate that, the presence of couple stresses decreases the velocity of the fluid.

Cessation of viscoplastic Poiseuille flow with wall slip

Abstract: We solve numerically the cessation of axisymmetric Poiseuille flow of a Herschel–Bulkley fluid under the assumption that slip occurs along the wall. The Papanastasiou regularization of the constitutive equation is employed. As for the slip equation, a power-law expression is used to relate the wall shear stress to the slip velocity, assuming that slip occurs only above a critical wall shear stress, known as the slip yield stress. It is shown that, when the latter is zero, the fluid slips at all times, the velocity becomes and remains uniform before complete cessation, and the stopping time is finite only when the slip exponent s 1, the decay is much slower. Analytical expressions of the decay of the flat velocity for any value of s and of the stopping time for s < 1 are also derived. Using a discontinuous slip equation with slip yield stress poses numerical difficulties even in one dimensional time-dependent flows, since the transition times from slip to no-slip and vice versa are not known a priori. This difficulty is overcome by regularizing the slip equation. The numerical results showed that when the slip yield stress is non-zero, slip ceases at a finite critical time, the velocity becomes flat only in complete cessation, and the stopping times are finite, in agreement with theoretical estimates.

Influence of surface properties on the flow of a yield stress fluid around spheres

Abstract: This experimental analysis addresses the non-inertial flow of a yield stress fluid around spheres. The analysis was conducted for two spheres with different surface conditions. Friction laws at their interface have been determined. For the bulk behaviour of the fluid, elastoviscoplasticity and viscoelasticity have also been characterised. The resulting parameters have been used to analyse the experimental results. The drag coefficient was determined with respect to hydrophobic properties and surface roughness. From this determination, a criterion enabling the prediction of a sphere’s stability in a yield stress fluid as a function of the fluid/sphere interfacial properties has been proposed. The kinematic fields have also been measured by PIV. These fields enable the quantification of the velocity fields around the spheres according to the adherence conditions of the fluid. This quantification has enabled the characterisation of the extent and the shape of sheared and static rigid zones. Moreover, the calculations of the drag force due to the shear stresses and the drag force due to the normal stresses have revealed the preponderance of the latter in the total drag force.

Peristaltic flow of couple stress fluid through uniform porous medium

Abstract: Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical analysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping.

Viscoplastic Poiseuille flow in a rectangular duct with wall slip

Abstract: We solve numerically the Poiseuille flow of a Herschel–Bulkley fluid in a duct of rectangular cross section under the assumption that slip occurs along the wall following a slip law involving a non-zero slip yield stress. The constitutive equation is regularized as proposed by Papanastasiou. In addition, we propose a new regularized slip equation which is valid uniformly at any wall shear stress level by means of another regularization parameter. Four different flow regimes are observed defined by three critical values of the pressure gradient. Initially no slip occurs, in the second regime slip occurs only in the middle of the wider wall, in the third regime slip occurs partially at both walls, and eventually variable slip occurs everywhere. The performance of the regularized slip equation in the two intermediate regimes in which wall slip is partial has been tested for both Newtonian and Bingham flows. The convergence of the results with the Papanastasiou regularization parameter has been also studied. The combined effects of viscoplasticity and slip are then investigated. Results are presented for wide ranges of the Bingham and slip numbers and for various values of the power-law exponent and the duct aspect ratio. These compare favorably with available theoretical results and with numerical results in the literature obtained with both regularization and augmented Lagrangian methods.

Effects of wall shear stress on unsteady MHD conjugate flow in a porous medium with ramped wall temperature.

Abstract: This study investigates the effects of an arbitrary wall shear stress on unsteady magnetohydrodynamic (MHD) flow of a Newtonian fluid with conjugate effects of heat and mass transfer. The fluid is considered in a porous medium over a vertical plate with ramped temperature. The influence of thermal radiation in the energy equations is also considered. The coupled partial differential equations governing the flow are solved by using the Laplace transform technique. Exact solutions for velocity and temperature in case of both ramped and constant wall temperature as well as for concentration are obtained. It is found that velocity solutions are more general and can produce a huge number of exact solutions correlative to various fluid motions. Graphical results are provided for various embedded flow parameters and discussed in details.

Magnetohydrodynamic Natural Convection Flow with Newtonian Heating and Mass Diffusion over an Infinite Plate that Applies Shear Stress to a Viscous Fluid

Abstract: Abstract Unsteady magnetohydrodynamic natural convection flow with Newtonian heating and constant mass diffusion over an infinite vertical plate that applies an arbitrary time-dependent shear stress to a viscous optically thick fluid is studied in the presence of a heat source. Radiative effects are taken into consideration and exact solutions for the dimensionless velocity and temperature are established under Boussinesq approximation. The solutions that have been obtained, uncommon in the literature, satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion problem with technical relevance of this type. For illustration, a special case is considered and the influence of pertinent parameters on the fluid motion is graphically underlined.

Using the Euler–Lagrange variational principle to obtain flow relations for generalized Newtonian fluids

Abstract: The Euler–Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in theflow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models, which include power law, Bingham, Herschel–Bulkley, Carreau, and Cross, are used for demonstration.

Scaling laws for the flow of generalized Newtonian suspensions

Abstract: It has been observed that flow curves (viscosity vs shear rate) of spherical solid inclusions suspended in a generalized Newtonian fluid medium can be rescaled so as to collapse onto the flow curve of the fluid medium. This result is surprising given the range of values and the spatial heterogeneity of local shear rates and viscosity in such systems. We consider such scaling for the cases of shear thinning, Newtonian, and shear-thickening fluid media. Results from experiment and computational modeling are presented that examine the microscopic origins of this scaling behavior. Over a wide range of volume fractions (5–50%), it is shown that the distribution of local shear rates can be collapsed onto a single universal curve. The parameters for rescaling the shear rate distributions can be analytically related to the macroscopic rescaling parameters for the viscosity. As a result of this rescaling capability, one may measure the properties of the fluid medium and predict the macroscopic behavior of the suspension.

Determination of the flow curve of complex fluids using the Rabinowitsch–Mooney equation in sensorless microrheometer

Abstract: In this work, we present a way to make rheological measurements on a microfluidic chip. The originality of our approach relies on the determination of the flow curve of a fluid using the Rabinowitsch–Mooney equation. For this purpose, we use a parallel flow between a reference fluid and a studied fluid to measure the pressure drop inside the channel. Using a Newtonian fluid of known viscosity, knowing the flow rates of the two liquids and measuring the geometrical features of the two-phase flow allows determining the pressure drop in the channel. The Rabinowitsch–Mooney equation is used to calculate the local shear rate and shear stress at the wall for the studied sample. We validate our method for several complex fluids.

Mathematical model and experiment validation of fluid torque by shear stress under influence of fluid temperature in hydro-viscous clutch

Abstract: The current design of hydro-viscous clutch(HVC) in tracked vehicle fan transmission mainly focuses on high-speed and high power. However, the fluid torque under the influence of fluid temperature can not be predicted accurately by conventional mathematical model or experimental research. In order to validate the fluid torque of HVC by taking the viscosity-temperature characteristic of fluid into account, the test rig is designed. The outlet oil temperature is measured and fitted with different rotation speed, oil film thickness, oil flow rate, and inlet oil temperature. Meanwhile, the film torque can be obtained. Based on Navier-Stokes equations and the continuity equation, the mathematical model of fluid torque is proposed in cylindrical coordinate. Iterative method is employed to solve the equations. The radial and tangential speed distribution, radial pressure distribution and theoretical flow rate are determined and analyzed. The models of equivalent radius and fluid torque of friction pairs are introduced. The experimental and theoretical results indicate that tangential speed distribution is mainly determined by the relative rotating speed between the friction plate and the separator disc. However, the radial speed distribution and pressure distribution are dominated by pressure difference at the lower rotating speed. The oil film fills the clearance and the film torque increases with increasing rotating speed. However, when the speed reaches a certain value, the centrifugal force will play an important role on the fluid distribution. The pressure is negative at the outer radius when inlet flow rate is less than theoretical flow, so the film starts to shrink which decreases the film torque sharply. The theoretical fluid torque has good agreement with the experimental data. This research proposes a new fluid torque mathematical model which may predict the film torque under the influence of temperature more accurately.

Off-centered stagnation point flow of a couple stress fluid towards a rotating disk.

Abstract: An investigation has been made to study the off-centered stagnation flow of a couple stress fluid over a rotating disk. The model developed for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most promising analytical approach, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The effects of couple stress and nondimensional parameters have been observed on the flows of couple stress fluid. Also comparison has been made with the Newtonian fluid as the special case of considered problem.

Radial Flow of Non-Newtonian Power-Law Fluid in a Rough-Walled Fracture: Effect of Fluid Rheology

Abstract: Fluid flow in a single rough-walled rock fracture has been extensively studied over the last three decades. All but few of these studies, however, have been done with Newtonian fluids and unidirectional flow in rectangular fractures. Notwithstanding the importance of such setups for theoretical understanding of fundamental issues in fracture flow, practical applications in drilling and petroleum engineering often involve radial flow of a non-Newtonian fluid. An example is a borehole intersecting a natural fracture during drilling in a fractured rock. In this study, steady-state incompressible radial flow from a circular well into a self-affine rough-walled fracture was simulated numerically using the lubrication theory approximation. The fluid rheology was power law. The flow behavior index was equal to 0.6, 0.8, 1.0 (Newtonian), 1.2, or 1.4. Asperities diverted the flow from an axisymmetric radial pattern that would be observed in a smooth-walled fracture. The extent of the deviation from radial flow was found to increase as the fluid became more shear-thickening. To reveal finer details of the flow, a tracer was introduced at the borehole wall and was transported by the flow. The front of the tracer propagating into the fracture was found to become slightly smoother with a more shear-thickening fluid. In the vicinity of contacts between fracture faces a more shear-thickening fluid could deliver the tracer closer to the contact spots.

Numerical simulation of the settling behaviour of particles in thixotropic fluids

Abstract: A numerical study on the settling behaviour of particles in shear‑thinning thixotropic fluids has been conducted. The numerical scheme was based on the volume of fluid model, with the solid particle being likened to a fluid with very high viscosity. The validity of this model was confirmed through comparisons of the flow field surrounding a sphere settling in a Newtonian fluid with the analytical results of Stokes. The rheology model for the fluid was time‑dependent, utilising a scalar parameter that represents the integrity of a “structural network,” which determines its shear thinning and thixotropic characteristics. The results of this study show that the flow field surrounding the settling sphere is highly localised, with distinct regions of disturbed/undisturbed fluids. The extension of these regions depends on the relaxation time of the fluid, as well as its shear thinning characteristics, and reflects the drag force experienced by the sphere. As the sphere settles, a region of sheared fluid that has significantly lower values of viscosity is formed above the sphere. This region slowly recovers in structure in time. As a result, a sphere that falls in a partially recovered domain (e.g., due to the shearing motion of an earlier sphere) tends to attain a greater velocity than the terminal velocity value. This was found to be true even in cases where the “resting time” of the fluid was nearly twice the relaxation time of the fluid. The results of this study could provide a framework for future analysis on the time‑dependent settling behaviour of particles in thixotropic shear‑thinning fluids.

The shear-driven Rayleigh problem for generalised Newtonian fluids

Abstract: We consider a variant of the classical ‘Rayleigh problem’ (‘Stokes’s first problem’) in which a semi-infinite region of initially quiescent fluid is mobilised by a shear stress applied suddenly to its boundary. We show that self-similar solutions for the fluid velocity are available for any generalised Newtonian fluid, regardless of its constitutive law. We demonstrate how these solutions may be used to provide insight into some generic questions about the behaviour of unsteady, non-Newtonian boundary layers, and in particular the effect of shear thinning or thickening on the thickness of a boundary layer.

Numerical and Experimental Analysis of the Fluid-Structure Interaction in Presence of a Hyperelastic Body

Abstract: In this study, a numerical algorithm is developed for simulating the interaction between a fluid and a 2D/axisymmetric hyperelastic body based on a full Eulerian fluid-structure interaction (FSI) method. In this method, the solid volume fraction is used for describing the multicomponent material and the deformation tensor for describing the deformation of the hyperelastic body. The core elements of the simulation method are the constitutive law in the Cauchy stress form and an equation for the transport of the deformation tensor field. A semi-implicit formulation is used for the elastic stress to avoid instability especially for solid with high stiffness. The strain rate has a discontinuity across the fluid/ solid interface. For improving the accuracy in capturing the interface, solid is treated as a highly viscous fluid. The viscosity term has the effect of smoothing the velocity and keeping the simulation stable. An experimental setup is used to validate the numerical results. The movement of a sphere made of silicone in air and its impact on a rigid substrate are investigated. The images are captured using a high speed CCD camera and the image processing technique is employed to obtain the required data from the images. For all cases considered, the results are in good agreement with those of the experiment performed in this study and other numerical results reported in the literature. [DOI: 10.1115/1.4027893]

Non-modal stability in Hagen-Poiseuille flow of a Bingham fluid

Abstract: Linear stability in Hagen-Poiseuille flow of a Bingham fluid is considered. Bingham fluid exhibits a yield stress in addition to a plastic viscosity. A Bingham number B, which describes the ratio of yield and viscous stresses, is used to characterize the behavior of Bingham-Hagen-Poiseuille flow. The effects of B on the stability are investigated using the energy method and the non-modal stability theory. The energy analysis shows that the non-axisymmetric disturbance has the lowest critical energy Reynolds number for all B. The global critical energy Reynolds number Re-g increases with B. At sufficient large B, Re-g has the order of B-1/2. For the non-modal stability, we focus on response to external excitations and initial conditions. The former is studied by examining the epsilon-pseudospectrum, and the latter is by examining the energy growth function G(t). For the problem of response to external excitations, the maximum response is achieved by non-axisymmetric and streamwise uniform disturbances at the frequency of omega = 0, with a possible choice of the azimuthal wavenumbers of n = 1, 2, or 3. For the problem of response to initial conditions, it is found that there can be a rather large transient growth even though the linear operator of the Bingham-Hagen-Poiseuille flow has no unstable eigenvalue. For small B, the optimal disturbance is in the form of streamwise uniform vortices and streaks. For large B, the optimal disturbance is in the form of oblique waves. The optimal energy growth decreases and the optimal azimuthal wavenumber increases with the increase of B. (C) 2014 AIP Publishing LLC.

General Aspects of Yield Stress Fluids - Terminology and Definition of Viscosity

Abstract: This work contributes to general theoretical aspects of yield stress fluids with significance for practical phenomenological material modeling. It introduces a terminology so that the material class ‘yield stress fluid’ is defined and can be distinguished from the terms ‘solid’ and ‘liquid’. This new material classification is based on two criteria, the equilibrium relation and the flow function. In line with this terminology, an experimental procedure for classifying the material behavior is presented. The second key aspect of this paper is a discussion on the proper definition of the term ‘viscosity’. The benefit of the differential viscosity over the dynamic viscosity in case of non-Newtonian fluids in general is worked out. This is shown by the most elementary yield stress fluid, the friction element, because it is the basis of the yield stress concept. Its constitutive equations are given for positive as well as negative strain rates and are also able to represent the preyield behavior. The theory presented in this article is also applied to the Maxwell, Kelvin-Voigt, and Bingham element to demonstrate the working principle.

Influence of the Rheological Model Used in Pipe-Flow Prediction Techniques for Homogeneous Non-Newtonian Fluids

Abstract: Pressure gradients were measured for shear-thinning (5% CMC), Bingham plastic (7% bentonite), and viscoplastic (6% kaolin) fluids in pipe diameters of O40 to O200 mm, in laminar and turbulent flow. The fluids were characterized as power law, Bingham plastic, and Herschel-Bulkley fluids respectively, and additionally as Casson fluids. The study considered the effect of the rheological model in reproducing experimental laminar flow, and on transitional velocity and turbulent flow predictions. For the fluids tested, the model was found to have little effect on laminar flow calculations. Transitional velocities were predicted using three well-known techniques and found to depend on the model, although no preferences were apparent. Errors in transitional velocity predictions varied from 2.5 to 31%. Turbulent predictions too were made using three common and widely published methods, and varied significantly with rheology. All the methods, however, predicted turbulent flow similarly when using the Casson...

Modeling fluid displacement in a well system environment

Abstract: In some aspects, a one-dimensional flow model is generated. The one-dimensional flow model can represent flow of a first fluid and a second fluid in a flow path in a well system environment. The one-dimensional flow model comprises an effective diffusion coefficient model for a composite fluid volume comprising the first and second fluids. The effective diffusion coefficient model calculates an effective diffusion coefficient for the composite fluid volume based on a difference between the respective densities and viscosities of the first fluid and the second fluid.

A new utility calculation model for axial flow of non-Newtonian fluid in concentric annuli

Abstract: A new utility approach that is independent of the rheological model is presented for the flow of non-Newtonian fluids in concentric annulus. The novel model was developed without assuming that the generalised flow index remains constant over all shear rate ranges. Based on the slot model, the flow rate expressions for all common rheological models flowing in annuli were obtained, such as the Herschel–Bulkley model, the Robertson–Stiff model, and the Four-parameter model, and they all can be solved numerically to obtain accurate wall shear rate and shear stress. Following Metzner and Reed's study, we defined a generalised flow index for non-Newtonian fluid flow in annuli. Through a theoretical analysis, we also defined a new effective diameter for non-Newtonian fluid flow in annuli, which accounts for the effects both of annulus geometry and fluid rheology but which is different from that was proposed by Reed and Pilehvari. Through the generalised effective diameter we linked non-Newtonian annular flow with Newtonian pipe flow. A general annular Reynolds number expression was derived from this method for conditions under which the generalised flow index is variable. A theoretical calculation method for the generalised flow index and a uniform pressure loss calculation model for non-Newtonian flow in concentric annuli were developed, which are applicable to all time-independent non-Newtonian fluid. The predictions of this model have been compared with an extensive set of data from the literature. The comparisons of different fluids in different size annuli show very good agreement over the entire range of flow types.

Fluid viscosity under confined conditions

Abstract: Closed equations of fluid transfer in confined conditions are constructed in this study using ab initio methods of nonequilibrium statistical mechanics. It is shown that the fluid viscosity is not determined by the fluid properties alone, but becomes a property of the “fluid-nanochannel walls” system as a whole. Relations for the tensor of stresses and the interphase force, which specifies the exchange by momentum of fluid molecules with the channel-wall molecules, are derived. It is shown that the coefficient of viscosity is now determined by the sum of three contributions. The first contribution coincides with the expression for the coefficient of the viscosity of fluid in the bulk being specified by the interaction of fluid molecules with each other. The second contribution has the same structure as the first one but is determined by the interaction of fluid molecules with the channel-wall molecules. Finally, the third contribution has no analog in the usual statistical mechanics of transport processes of a simple fluid. It is associated with the correlation of intermolecular forces of the fluid and the channel walls. Thus, it is established that the coefficient of viscosity of fluid in sufficiently small channels will substantially differ from its bulk value.

Experimental Study and Numerical Modeling of Rheological and Flow Behavior of Xanthan Gum Solutions Using Artificial Neural Network

Abstract: This study investigated effect of temperature, concentration, and shear rate on rheological properties of xanthan gum aqueous solutions using a Couette viscometer at temperatures between 25°C and 55°C and concentrations of 0.25 wt% to 1.0 wt%. The Herschel–Bulkley model described very well the non-Newtonian behavior of xanthan gum solutions. Shear rate, temperature, and concentration affected apparent viscosity and an equation was proposed for the temperature and concentration effect valid for each shear rate. This article also presents an artificial neural network (ANN) model to predict apparent viscosity. Based on statistical analysis, the ANN method estimated viscosity with high accuracy and low error.

Melting Heat Transfer in Boundary Layer Stagnation Point Flow of MHD Micro - polar Fluid towards a Stretching / Shrinking Surface

Abstract: The present study investigates the fluid flow and heat transfer characteristics occurring during the melting process due to a stretching / shrinking surface in micropolar fluid. A uniform magnetic field is applied normally to the surface. The governing equations representing fluid flow were transformed into nonlinear ordinary differential equations using similarity transformation. The equations thus obtained were solved numerically using the Runge–Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of the magnetic parameter on the fluid flow, couple stress coefficient and heat transfer characteristics, are illustrated graphically and discussed in detail. Significant changes were observed in the fluid flow, couple stress coefficient and heat transfer with respect to magnetic parameter.