Showing papers on "Herschel–Bulkley fluid published in 2019"

Interfacial instability in pressure-driven core-annular pipe flow of a Newtonian and a Herschel–Bulkley fluid

Abstract: The linear stability characteristics of pressure-driven core-annular flow of a Newtonian core fluid and a Herschel–Bulkley annular fluid is investigated. The fluids are assumed to have the same density and separated by a sharp interface. The modified Orr–Sommerfeld equations for each layer are derived and solved using an efficient spectral collocation method considering a configuration without any unyielded region. The effect of various dimensionless parameters, such as the Bingham number (Bn), the flow index (n), the interface radius (R0) and the inverse capillary number (Γ) on the instability characteristics of the flow is investigated, and an energy budget analysis is conducted to explain the physical mechanism of the instability observed. We found that axisymmetric mode is the most dominant unstable mode for the interfacial flow configuration considered in the present work, which is in contrast to miscible core-annular flows. It is observed that increasing Bn has a non-monotonic effect on the growth rate of the axisymmetric mode, and two dominant modes appear at high Bn. We found that increasing the thickness of the core fluid increases the bandwidth of the unstable wavenumbers and destabilises the short waves; however, displays a non-monotonic trend in the growth rate curves. The instability behaviour observed for different sets of parameters are investigated by conducting an energy budget analysis and analysing the disturbance eigenfunctions and the basic velocity profiles.

Effect of Varying Viscosity on Two-Fluid Model of Blood Flow through Constricted Blood Vessels: A Comparative Study

Abstract: Most of the previously studied non-Newtonian blood flow models considered blood viscosity to be constant but for correct measurement of flow rate and flow resistance, the hematocrit dependent viscosity will be better as various literature suggested the variable nature of blood viscosity. Present work concerns the steady and pulsatile nature of blood flow through constricted blood vessels. Two-fluid model for blood is considered with the suspension of all the RBCs (erythrocytes) in the core region as a non-Newtonian (Herschel–Bulkley) fluid and the plasma in the cell free region near wall as a Newtonian fluid. No slip condition on the wall and radially varying viscosity has been taken. For steady flow the analytical approach has been taken to obtain the exact solution. Regular perturbation expansion method has been used to solve the governing equations for pulsatile flow up to first order of approximation by assuming the pulsatile Reynolds number to be very small (much less than unity). Flow rate, wall shear stress and velocity profile have been graphically analyzed and compared with constant viscosity model. A noteworthy observation of the present study is that rise in viscosity index leads to decay in velocity, velocity of plug flow region, flow rate while flow resistance increases with rising viscosity index (m). The results for Power-law fluid (PL), Bingham-plastic fluid (BP), Newtonian fluid (NF) are found as special cases from this model. Like the constant viscosity model, it has been also observed that the velocity, flow rate and plug core velocity of two-fluid model are higher than the single-fluid model for variable viscosity. The two-phase fluid model is more significant than the single-fluid model. Effect of viscosity parameter on various hemodynamical quantities has been obtained. It is also concluded that a rising viscosity parameter (varying nature of viscosity) significantly distinguishes the single and two-fluid models in terms of changes in blood flow resistance. The outcome of present study may leave a significant impact on analyzing blood flow through small blood vessels with constriction, where correct measurement of flow rate and flow resistance for medical treatment is very important.

Enhanced electroosmotic flow of Herschel-Bulkley fluid in a channel patterned with periodically arranged slipping surfaces

Abstract: In this paper, we consider the electroosmotic flow (EOF) of a viscoplastic fluid within a slit nanochannel modulated by periodically arranged uncharged slipping surfaces and no-slip charged surfaces embedded on the channel walls. The objective of the present study is to achieve an enhanced EOF of a non-Newtonian yield stress fluid. The Herschel-Bulkley model is adopted to describe the transport of the non-Newtonian electrolyte, which is coupled with the ion transport equations governed by the Nernst-Planck equations and the Poisson equation for electric field. A pressure-correction-based control volume approach is adopted for the numerical computation of the governing nonlinear equations. We have derived an analytic solution for the power-law fluid when the periodic length is much higher than channel height with uncharged free-slip patches. An agreement of our numerical results under limiting conditions with this analytic model is encouraging. A significant EOF enhancement and current density in this modulated channel are achieved when the Debye length is in the order of the nanochannel height. Flow enhancement in the modulated channel is higher for the yield stress fluid compared with the power-law fluid. Unyielded region develops adjacent to the uncharged slipping patches, and this region expands as slip length is increased. The impact of the boundary slip is significant for the shear thinning fluid. The results indicate that the channel can be cation selective and nonselective based on the Debye layer thickness, flow behavior index, yield stress, and planform length of the slip stripes.

A Semi-Infinite Hydraulic Fracture Driven by a Herschel–Bulkley Fluid

Abstract: Hydraulic fracturing is an industrial process often applied to enhance oil and gas recovery. Under this process, fractures are generated by the injection of highly pressurized fluids, which often exhibit shear-thinning rheology and yield stress. The global fracture propagation is influenced by various processes occurring near the fracture tip. To gain an insight into fracture propagation, the problem of a semi-infinite hydraulic fracture propagating in a permeable linear elastic rock is solved. To investigate the effect of fluid yield stress, we focus on a fracture driven by Herschel–Bulkley fluid. The mathematical model consists of the elasticity equation, the lubrication equation, and the propagation criterion for the semi-infinite plane strain fracture to obtain the fracture opening. The non-linear system of governing equations is represented in the non-singular form and solved numerically using Newton’s method. The solution is influenced by the competing processes related to rock toughness, fluid properties, and leak-off. The effects of these phenomena prevail at different length scales, and the corresponding limits can be described via analytical solutions. For a Herschel-Bulkley fluid, an additional limiting solution related to the fluid yield stress is obtained, and the regions of the dominance of limiting solutions affected by the yield stress are investigated. Finally, a faster approximate solution for the problem is proposed and its accuracy against a numerical solution is evaluated. The obtained result can be applied in hydraulic fracturing simulators to account for the effect of Herschel–Bulkley fluid rheology on the near-tip region.

Performance evaluation of a magnetorheological fluid damper using numerical and theoretical methods with experimental validation

Abstract: Magnetorheological (MR) fluids which can exhibit substantial reversible rheological changes under the excitation of external magnetic fields, have enabled the construction of many novel and robust electromechanical devices in recent years. Generally, Bingham plastic model is utilised for the estimation of the characteristics of MR fluids. However, when the geometry and design of the MR device as well as the rheological conditions of the fluid itself become complicated due to the engineering application requirements, the accuracy of Bingham plastic model, which simplifies the relation between the fluid shear stress and shear rate into a linear function, is degraded. In this paper, a multi-degree-of-freedom (MDOF) magnetorheological fluid damper with a novel ball-and-socket structure was developed, which was aimed to enhance the human shoulder rehabilitation treatment. The performance of the proposed smart device with its complex design was estimated numerically using a finite element method (FEM) with a Herschel-Bulkley model and theoretically with a model that is based on a Bingham plastic fluid characteristics. The performance of the developed damper was validated experimentally using a dedicated testing facility for various input conditions. It was found that the FEM simulations with the Herschel-Bulkley model showed a better agreement with the experimental results in comparison with the theoretical predictions which were somewhat degraded with the employed Bingham plastic model.

Effect of Solid Particle Concentration on Drilling Fluid Rheological Behavior and its Impact on Pressure Losses

Abstract: Solid particles in suspension in a fluid, like barite, lost circulation material (LCM), cuttings or cavings, influence the pressure losses that are experienced when pumping or moving a drill-string in a borehole. As the volume fractions of those different solid particles varies along the hydraulic circuit, it is desirable to estimate the impact of local solid concentrations on pressure drops. The influence of solid particles on the rheological behavior of fluid has mostly been studied for Newtonian fluids, but very little experimental work has been published for non-Newtonian fluids like drilling muds. For that reason, a series of measurements, made with a scientific rheometer has been conducted on a typical KCl/Polymer water-based mud. The experimental investigation covers the effect of particle concentration on the rheological behavior of the mix, in conjunction with the particle size. The change of rheological behavior is slow at low solid concentrations but increases exponentially with larger proportions of solid in suspension. Furthermore, the increase of effective viscosity is larger with fine particles than with coarser ones. Empirical formulas are proposed to describe how the original Herschel-Bulkley rheological behavior of a base fluid can be modified to incorporate the effects of the variation of solid concentrations in the fluid mix. All these results are based on measurements made with a scientific rheometer. As computerized and high precision rheometers are usually not available at the rig site, we describe a methodology to utilize standard model 35 rheometer measurements to estimate the pressure loss gradient as a function of the volumetric solid content.

A numerical model on pulsatile flow of magnetic nanoparticles as drug carrier suspended in Herschel–Bulkley fluid through an arterial stenosis under external magnetic field and body force

Abstract: A theoretical model for blood flow through an artery with stenosis carrying magnetic particles in the presence of magnetic field and periodic body acceleration is analysed. In the present study, bl...

Mathematical Modeling of Swirling Herschel–Bulkley Pseudoplastic Fluid Flow in a Cylindrical Channel

Abstract: Results of investigations into the swirling flow of a pseudoplastic fluid with a Herschel–Bulkley yield stress in a cylindrical channel have been presented. It has been established that a growth in the rates of shear strains in flows with a swirl causes the values of effective viscosity to decrease. It has been shown that at one and the same Rossby number, the recirculation strength is the greater the smaller the values of the limiting shear stress, the consistency, and the nonlinearity index.

A Two-Dimensional Axisymmetric Finite Element Analysis of Coupled Inertial-Viscous-Frictional-Elastic Transients in Magnetorheological Dampers Using the Compressible Herschel-Bulkley Fluid Model

Abstract: It has been challenging to accurately predict the unique characteristics of magnetorheological (MR) dampers, due to their inherent nonlinear nature. Multidimensional flow simulation has received increasing attentions because it serves as a general methodology for modelling arbitrary MR devices. However, the compressibility of MR fluid which greatly affects the hysteretic behavior of an MR damper is neglected in previous multidimensional flow studies. This paper presents a two-dimensional (2D) axisymmetric flow of the compressible Herschel-Bulkley fluid in MR dampers. We simulated the fully coupled inertial-viscous-frictional-elastic transients in MR dampers under low-, medium- and high frequency excitations. An arbitrary Lagrangian-Eulerian kinematical description is adopted, with the piston movements represented by the moving boundaries. The viscoplasticity and compressibility of MR fluid are respectively modeled by the modified Herschel-Bulkley model and the Tait equation. The streamline-upwind Petrov–Galerkin finite element method is used to solve the model equations including the conservation laws and mesh motion equation. We tested the performances of an MR damper under different electric currents and different frequency displacement excitations, and the model predictions agree well with the experimental data. Results showed that the coupled transients of an MR damper are frequency dependent. The weak compressibility of MR fluid, which mainly happens in the chamber rather than in the working gap, is crucial for accurate predictions. A damper’s transition from the pre-yield to the post-yield is essentially a step-response of a second order mass-spring-viscous system, and we give such step-response a detailed explanation in terms of mass flow rate.

Axisymmetric squeeze flow of a Herschel–Bulkley medium

Abstract: We develop an asymptotic solution for the axisymmetric squeeze flow of a viscoplastic Herschel–Bulkley fluid, extending recent solutions for the Bingham and Casson models, obtained by Muravleva [20,26]. We use the asymptotic technique proposed by Balmforth and Craster [36] and Frigaard and Ryan [37]. The no-slip and slip yield boundary conditions at the wall are considered. The combined effects of the power index and the Bingham number are investigated. We confirm numerically obtained solution, using Augmented Lagrangian methods.

Mathematical Simulation of the Swirling Flow of a Dilatant Herschel–Bulkley Fluid in a Cylindrical Channel

Abstract: Results of an investigation of the swirling flow of a dilatant Herschel–Bulkley fluid with a yield point in a cylindrical channel are presented. It was established that the effective viscosity of such a fluid at the input cross section of a cylindrical channel increases with increase in the intensity of its vortex, which can cause plugging of the channel. As the Rossby number of this fluid increases, its effective viscosity in the region of unstable flow at the axis of the channel decreases, and the opposite effect takes place in the near-wall zone of the channel. As the fluid flow stabilizes downstream, the effective viscosity of the fluid in the near-wall region of the channel decreases, and the effective viscosity of the fluid near the channel axis increases, which leads to the formation of a quasi-solid fluid flow.

Coupled Magnetic and CFD Modelling of a Structural Magnetorheological Vibration Absorber with Experimental Validation

Abstract: Magnetorheological fluid is a smart material which can change its viscosity in milliseconds depending on the magnetic field applied. This brings a great advantage to create variable damping ability if it is used in an absorber. The stiffness of the absorber can be manipulated by an external magnetic field which effects the apparent viscosity of the magnetorheological fluid inside the absorber. Various control algorithms can be used to provide an effective absorption for any kind of structural vibration. Because of these features, magnetorheological absorbers have received great attention of researchers in the last decade. In this study, it is aimed to simulate a magnetorheological absorber under a sinusoidal vibration with Computational Fluid Dynamics and Magnetic Field Finite Elements Analysis. The magnetorheological fluid is modelled as a Non-Newtonian fluid and Herschel-Bulkley viscosity model is used to determine the apparent viscosity. Magnetic field is modelled for a constant current which generates different magnetic flux densities inside the absorber body. The Computational Fluid Dynamics and Finite Elements Analysis solutions are coupled in a two-dimensional axisymmetric domain and the results are revealed. The coupled solution of both are realized for the first time in the literature by means of an apparent viscosity approach. The numerical solution is compared with the experiments. A good agreement is observed between both results.

Lubrication solution of the flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters in an asymmetric channel

Abstract: The lubrication flow of a Herschel-Bulkley fluid in a long asymmetric channel, the walls of which are described by two arbitrary functions h1(x) and h2(x) such that h1(x) < h2(x) and h1(x) + h2(x) are linear, is solved extending a recently proposed method, which avoids the lubrication paradox approximating satisfactorily the correct shape of the yield surface at zero order [P. Panaseti et al., “Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters,” Phys. Fluids 30, 030701 (2018)]. Both the consistency index and the yield stress are assumed to be pressure-dependent. Under the lubrication approximation, the pressure at zero order is a function of x only, is decoupled from the velocity components, and obeys a first-order integro-differential equation. An interesting feature of the asymmetric flow is that the unyielded core moves not only in the main flow direction but also in the transverse direction. Explicit expressions for the two yield surfaces defining the asymmetric unyielded core are obtained, and the two velocity components in both the yielded and unyielded regions are calculated by means of closed-form expressions in terms of the calculated pressure and the two yield surfaces. The method is applicable in a range of Bingham numbers where the unyielded core extends from the inlet to the outlet plane of the channel. Semi-analytical solutions are derived in the case of an asymmetric channel with h1 = 0 and linearly varying h2. Representative results demonstrating the effects of the Bingham number and the consistency-index and yield-stress growth numbers are discussed.The lubrication flow of a Herschel-Bulkley fluid in a long asymmetric channel, the walls of which are described by two arbitrary functions h1(x) and h2(x) such that h1(x) < h2(x) and h1(x) + h2(x) are linear, is solved extending a recently proposed method, which avoids the lubrication paradox approximating satisfactorily the correct shape of the yield surface at zero order [P. Panaseti et al., “Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters,” Phys. Fluids 30, 030701 (2018)]. Both the consistency index and the yield stress are assumed to be pressure-dependent. Under the lubrication approximation, the pressure at zero order is a function of x only, is decoupled from the velocity components, and obeys a first-order integro-differential equation. An interesting feature of the asymmetric flow is that the unyielded core moves not only in the main flow direction but also in the transverse direction. Explicit expressions for the two yield surfaces defining the asym...

Free-surface laminar flow of a Herschel–Bulkley fluid over an inclined porous bed

Abstract: The current work presents a mathematical solution for the flow of a Herschel--Bulkley fluid over a porous bed. To obtain the velocity profile, a dimensional analysis is firstly conducted for the Darcian-like flow, showing that the ratio between pore and flow scales impose the domain of validity for the Beaver-like kinematic boundary condition. A friction velocity dependent only on fluid and porous medium properties was found to identify the scale of the Darcian velocity. After applying a modified kinematic boundary condition between free flow and Darcian-like flow, free-surface flow velocity profile was obtained, which can effectively predicts non-porous solutions for less rheological complex fluids. Dimensional analysis was then performed for the velocity profile solution, which allowed to identify the effect of the porous bed on flow properties. Experimental results from the literature were employed to identify the necessary conditions for yield stress fluids to have Darcian-like flow in natural open-channel flows. Sensitivity analysis pointed out that the porous medium permeability and non-Newtonian fluid parameters have greater influence on the velocity profile for pseudoplastic fluids than for dilatant ones.

A Numerical Study on Unsteady Flow of Herschel–Bulkley Nanofluid Through an Inclined Artery with Body Acceleration and Magnetic Field

Abstract: The present paper deals with the mathematical model for pulsatile flow of Herschel–Bulkley fluid through an inclined artery with stenosis and tapering. The governing equations of Herschel–Bulkley nanofluid are highly non-linear which are simplified in the case of artery having mild stenosis and slightly tapering. The effects of heat and mass transfer have been considered in the model. The solutions for velocity profile, wall shear stress distribution, flow impedance, temperature and concentration profiles are evaluated numerically using finite difference schemes for different values of the parameters associated with the model. The obtained results are represented graphically and the influences of involved parameters on the flow of nanofluid are discussed in detail. It is observed from the computed numerical results that the velocity profile enhances with increase in Grashof numbers. The magnitude of shear stress at the arterial wall increases with increase in stenotic height and Hartmann number and decreases with increase in Grashof numbers. The value of flow resistance enhances with increase in stenotic height, Hartmann number, time and thermophoresis parameter and decreases with increase in inclination parameters, Grashof numbers, Brownian motion parameter and Prandtl number. The combined effects of rheology of blood and parameters associated with heat and mass transfer on flow resistance have been analysed from which the significance of rheology of blood can be understood.

Investigation of numerical simulation of non-Newtonian flows dam break and dam breach in open channels using modified VOF method

Abstract: This paper concerns modelling dam break flows of non-Newtonian Herschel-Bulkley (HB) fluid by using the volume of fluid (VOF) method and high resolution advection schemes. The VOF method is based on the fact that two or more fluids (or phases) are not interpenetrating. In the present study, a modified approach is used to overcome this problem. The OpenFoam software is employed and inter-Foam solver is used in two and three-dimensional model with non-Newtonian fluid. The numerical results of the present study are compared with analytical, numerical and experimental results found in literature. The numerical code which is used showed better agreement with the experimental data than those using shallow water equations and PLIC method.

Influence of Velocity and Thermal Slip on the PeristalticTransport of a Herschel-Bulkley Fluid Through anInclined Porous Tube

Abstract: The present paper investigates the impact of velocity slip and thermal slip on the peristaltic transport of a Herschel-Bulkley fluid, flowing through a uniform twodimensional porous tube under the assumptions of long wavelength and low Reynolds number. The mathematical representations of temperature and velocity fields, pressure gradient, and stream function have been found through the closed-form solutions of the energy and momentum equations. Numerical integration has been employed to compute the frictional force and pressure rise. The influence of relevant parameters in the problem have been discussed and presented graphically. The results reveal the increasing effects of thermal and velocity slip on pressure rise and temperature. Also, trapping phenomena of the Herschel-Bulkley fluid is discussed. The volume of the bolus is observed to increase along with the velocity slip parameter

Verification of the Herschel-Bulkley Model by a Visualization Experiment of a Elastoviscoplastic Yield-Stress Fluid Flow in Straight and Bended Tubes

Abstract: The elastoviscoplastic yield-stress fluid flows in a horizontal straight tube and a bended tube have been investigated using hydrogen bubble visualization method. The experimental results are used to verify the empirical Herschel-Bulkley model. Both experimental and theoretical investigations well predict the yield-stress fluid flow behaviors. It is found that the significant factors influencing on the predictions of the Herschel-Bulkley model are the yield stress, viscosity and viscoelasticity. For the yield-stress flows in the bended tube, a more delicate constitutive model with consideration of the viscoelastic effects is expected for accurately predicting the flow behaviors.