Flow Of Viscoplastic Fluid Research Articles

The Structure of a Viscoplastic Fluid Flow during Filling of a Circular Pipe/Plane Channel

The viscoplastic fluid flow initiated in a circular pipe/plane channel during its filling in the gravity field at the flow rate specified at the inlet section is investigated. A mathematical formulation of the problem is stated based on complete equations of motion, the continuity equation, the natural boundary conditions on a free surface, and no-slip boundary condition on the solid wall. The rheological behavior of the medium is described by the Schwedoff–Bingham law, which presupposes the existence of quasi-solid motion zones (unyielded zones) in regions of low strain rates. The numerical solution of the problem is based on the finite-difference approach including the finite volume method and SIMPLE algorithm for calculating velocity and pressure fields at the internal nodes of a staggered grid. The method of invariants is used to satisfy the boundary conditions on the free surface. To provide a through computation of the flow with unyielded regions, regularization of the rheological equation is implemented. The behavior of a free boundary, flow structure, and flow characteristics as a function of the main parameters is investigated. It is found that in the course of time the initially flat free boundary acquires a stationary convex shape, which remains invariant while moving through the pipe/channel at the rate-average velocity. In the flow near and far away from the free boundary, one can distinguish fountain flow zones and one-dimensional flow regions, respectively. The typical flow structures with different numbers and various locations of unyielded regions in the flow are shown. The topograms of the above-mentioned flow structures as functions of the ratio of viscous and gravity forces and plasticity in the fluid flow are plotted. The stable and unstable behavior of the free boundary shape is shown to be related to the values of the constitutive parameters.

Non-Newtonian fluid flow through a sudden pipe contraction under non-isothermal conditions

• Simulation of a non-isothermal viscoplastic fluid flow through a sudden contraction. • Investigation of the flow structure with unyielded regions and rigid static zones. • Extension of two-dimensional flow zones in the contraction plane vicinity. • Effect of the governing parameters on the local resistance coefficient. A steady-state laminar flow of a viscoplastic fluid through an axisymmetric sudden pipe contraction under non-isothermal conditions has been studied numerically. Mathematical formulation of the problem is given using stream function – vorticity – temperature variables. Rheological properties of the fluid are described by the Herschel–Bulkley model, which implies an unyielded region formation in the flow. Viscous dissipation effects and temperature dependence of the viscosity are taken into account when simulating the process. An asymptotic time solution of unsteady flow equations is used to obtain a steady-state solution to the initially formulated problem. The finite-difference method based on the alternative directions scheme is applied to solve the problem numerically. Regularization of the rheological equation is performed to provide a through computation of the flow with unyielded regions. A parametric investigation of the flow structure, which includes dead zones and yielded/unyielded regions, is implemented in order to show the impact of main dimensionless parameters.

A quantitative evaluation of viscosity regularization in predicting transient flows of viscoplastic fluids

We present an assessment of viscosity regularization (VR) in predicting transient flows of viscoplastic fluids (VPF). Although VR has been the most popular approach for computational studies of VPF in the last decade, the understanding of its effects on the predicted flow behaviour has remained largely qualitative. To reveal the effects of VR, we present a systematic quantitative comparison of the solutions of the regularized and exact (i.e. not regularized) problems. We consider free convection of a Bingham fluid in a two-dimensional square cavity with differentially heated sidewalls. We use bi-viscosity as a representative VR model and use augmented Lagrangian (AL) method to solve the exact problem. We show that common methods of assessing the solution error can hugely overestimate the accuracy of the results of VR. In particular, complete loss of accuracy is observed when flow conditions approach the motionless state, rendering the lower computational cost and algorithmic simplicity of VR irrelevant. Furthermore, we quantify the accuracy of bi-viscosity regularization in predicting the unyielded regions. This analysis disproves by counterexample that using yield stress contours produces convergent numerical estimates of the unyielded regions.

Lattice Boltzmann method for viscoplastic fluid flow based on regularization of ghost moments

• A viscoplastic fluid flow solver is developed with lattice Boltzmann method (LBM). • “Infinite viscosity” is computed by setting the relaxation frequency to zero. • Regularization of ghost moments keeps the simulations numerically stable. • The numerical scheme is second-order accurate and good yield surfaces are obtained. • With GPU computation typical execution time for 3D simulations is 90 min. In the Lattice Boltzmann Method (LBM) the viscosity is inversely proportional to the relaxation frequency. Hence, it should be possible to represent the singularity of some viscoplastic models by setting the relaxation frequency to zero. In the present paper we take full advantage of the LBM capabilities to propose an efficient and stable numerical scheme for viscoplastic fluid flow simulations invoking the exact Bingham constitutive equation. This scheme is expected to suit the need for more accurate viscoplastic simulations because it does compute the “infinite viscosity”, therefore dismissing the need for any viscosity regularization. Although allowing for a wide range of relaxation frequencies varying in space and time, we demonstrate that the present implementation does not degrade the standard LBM's error order. Numerical stability was promoted by of regularization of ghost moments for the lattice Boltzmann equation with force term. Since the locality of the LBM is preserved, so is the scheme's ability to be highly scalable in large computer clusters. We outline the method and the theory behind it through a detailed Chapman–Enskog expansion. Three laminar test cases are analyzed: parallel channel Poiseuille flow, square duct Poiseuille flow and lid-driven cavity flow. We show conformity with the standard LBM's error order for different wall boundary conditions and yield stress levels. Comparisons are made with other numerical studies employing augmented Lagrangian and viscosity regularization methods.

Effect of viscous dissipation on the flow structure and pressure losses for a viscoplastic fluid flow through a sudden pipe contraction

A viscoplastic fluid flow through an axisymmetric sudden pipe contraction is studied numerically in a laminar regime under non-isothermal conditions. Governing equations are written in terms of stream function – vorticity – temperature variables. A modified Schwedoff -Bingham rheological model is used to describe characteristics of the fluid. The problem is solved by the finite-difference method based on the alternative directions scheme. Simulation of the process involves taking into account viscous dissipation effects and temperature dependence of viscosity. Distributions of flow characteristics and flow structures are shown and compared with those obtained in the case when viscous dissipation is neglected. A local resistance coefficient is calculated and presented as a function of the Brinkman number.

Structure of a viscoplastic fluid flow in a pipe with a given obstruction shape

In this paper, we present a study of the axisymmetric steady-state laminar flow of a viscoplastic fluid in a pipe with variable cross section. Mathematical formulation of the problem is written in terms of stream function and vorticity variables in a cylindrical coordinate system. Rheological behavior of the medium is described by the Shvedov-Bingham model. Coordinate transformation is carried out to implement a numerical algorithm. The problem is solved numerically using the finite-difference method and the false transient method. This paper demonstrates the effect of Reynolds number, Bingham number, and geometric parameters of a flow domain on the flow structure.

Computing the yield limit in three-dimensional flows of a yield stress fluid about a settling particle

Calculating the yield limit Yc (the critical ratio of the yield stress to the driving stress), of a viscoplastic fluid flow is a challenging problem, often needing iteration in the rheological parameters to approach this limit, as well as accurate computations that account properly for the yield stress and potentially adaptive meshing. For particle settling flows, in recent years calculating Yc has been accomplished analytically for many antiplane shear flow configurations and also computationally for many geometries, under either two dimensional (2D) or axisymmetric flow restrictions. Here we approach the problem of 3D particle settling and how to compute the yield limit directly, i.e. without iteratively changing the rheology to approach the yield limit. The presented approach develops tools from optimization theory, taking advantage of the fact that Yc is defined via a minimization problem. We recast this minimization in terms of primal and dual variational problems, develop the necessary theory and finally implement a basic but workable algorithm. We benchmark results against accurate axisymmetric flow computations for cylinders and ellipsoids, computed using adaptive meshing. We also make comparisons of accuracy in calculating Yc on comparable fixed meshes. This demonstrates the feasibility and benefits of directly computing Yc in multiple dimensions. Lastly, we present some sample computations for complex 3D particle shapes.

Simulations for the flow of viscoplastic fluids in a cavity driven by the movement of walls by Lattice Boltzmann Method

The current paper is focused on analyzing the flow of viscoplastic fluid in a cavity that is driven by the two walls. The Lattice Boltzmann method (LBM) is used to solve the discrete Boltzmann equation. To represent the stress-strain rate relationship of viscoplastic fluids, the Bingham Papanastasiou constitutive model is considered. Cavity flow filled with Bingham fluids is considered for validating the present LBM code. After successful validation of the code, the analysis is extended for three dissimilar wall motions-simultaneous and opposed movement of the parallel facing walls, and the simultaneous motion of non-facing walls. The flow dynamics of Bingham fluid is influenced by Reynolds and Bingham numbers which can be studied using velocity and streamline plots. Subsequently, the yielded and un-yielded zones in a cavity have been effectively tracked using the limiting condition of yield stress. Further, the effect of wall motion on the variation of those zones inside a cavity has been studied. Finally, the drag coefficient for considered wall motions is presented.

Finite Element Analysis on Bingham–Papanastasiou Viscoplastic Flow in a Channel with Circular/Square Obstacles: A Comparative Benchmarking

A CFD (computational fluid dynamics) analysis was carried out for the Bingham viscoplastic fluid flow simulations around cylinders of circular and square shapes. The governing equations in space were discretized with the finite element approach via a weak formulation and utilizing Ladyzhenskaya–Babuška–Brezzi-stable pair Q 2 / P 1 disc for approximation of the velocity and pressure profiles. The discrete non-linear system was linearized through Newton’s method, and a direct linear solver was iterated as an inner core solver. The study predicts the functional dependence and impact of Bingham number, B n , on the drag coefficient and lift coefficient. The effect of the shape of an obstacle is also provided by providing comparative data for the hydrodynamic forces with the published results.

Flow Analysis and Approximate Expressions of Factors Related to Frictional Loss for Laminar Flow of Viscoplastic Fluids through a Concentric Annulus

Flow Analysis and Approximate Expressions of Factors Related to Frictional Loss for Laminar Flow of Viscoplastic Fluids through a Concentric Annulus

Flow of viscoplastic fluids containing hybrid nanoparticles: Extended Buongiorno’s model

This paper investigates numerically the flow of a temperature-dependent viscoplastic fluid containing hybrid Ag and MgO nanoparticles through a ventilated heated cavity. A new approach for modeling the hybrid nanoparticle migration is proposed. The proposed model, which is based on Buongiorno’s non-homogeneous model, takes into account the nanoparticles mass flux due to both Brownian and thermophoretic diffusion, for each solid constituent. This is done by adding a mass conservation equation for each nanoparticle type, considering no mass flux at the walls. The results reveal that the nanoparticle distribution is the same for both constituents due to the dominance of inertia and buoyancy forces over slip mechanisms.

Turbulent displacement flow of viscoplastic fluids in eccentric annulus: Experiments

We study displacement flows in strongly eccentric annuli, where the in situ fluid is viscoplastic and the displacing fluid is Newtonian. This mimics the situation found in the cementing of horizontal oil and gas wells. In this configuration, it is common that the yield stress of the displaced fluid prevents displacement from the narrow side of the annulus, where it remains static. We address the question of whether a turbulent flow of the displacing fluid will be effective in removing the static narrow side channel and by what means. The flows proceed with rapid displacement along the wide side of the annulus, leaving behind a gelled channel of fluid on the narrow side. The narrow side is displaced either slowly or not at all. This depends on both the yield stress of the displaced fluid and the turbulence characteristics of the displacing fluid. We influence the latter through the use of drag-reducing polymers. We show that secondary flows in the turbulent displacing fluid are essential to the displacement and also the increased pressure drops in the turbulent flow. We hypothesize that the displacement is enhanced by the transmission of normal stresses into the gelled layer.

Viscoplastic fluid flow modeling with the “solidification” effect in the straight channel of the annular cross section

On the basis of the viscoplastic fluid rheological model, which takes into account the manifestation of the “solidification” effect, a flow has been simulated in the annular cross section channel. It is shown that, depending on the pressure drop level, three different flow patterns are possible. For each pattern, the expressions that determine the fluid velocity distribution in the channel’s cross section have been obtained. It is shown that the dependence of the volume fluid flow rate on the pressure drop is not monotonic. Moreover, the increase in the pressure drop critical level ultimately leads to the flow rate decrease due to the narrowing of the channel’s passage section, which is caused by the formation of the “solidified” liquid layers.

Behavior of viscoplastic rocks near fractures: mathematical modelling

Starting from conservation laws and basic thermodynamic principles, we derive equations for a two-phase granular fluid. The first phase is the granular viscoplastic Bingham fluid and the second phase is the viscous Newtonian fluid. We perform an asymptotic analysis of the equations for the flows in the Hele-Show cell when the channel width is well much below its length. While calculating the fluid fluxes-pressure gradient relationship, we derive laws of flow of the two-phase granular viscoplastic fluid through porous media. A criterium is formulated for the start up of the granular phase flow through a porous medium. Given a yield stress, we prove that such a phase does not flow if either or both pressure gradient and channel width are small. We calculated phase flows varying phase viscosities, phase resistivities and yield stress. We reveal reasons which slow down particle intrusion into a porous medium.

WITHDRAWN: Mixed convection flow of viscoplastic Casson fluid over an impermeable slender sheet with Cattaneo–Christov heat flux

WITHDRAWN: Mixed convection flow of viscoplastic Casson fluid over an impermeable slender sheet with Cattaneo–Christov heat flux

An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modeled by generalized Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelizable computations on block-structured grids. In this context, geometric features are handled by the embedded boundary approach, which requires specialized treatment only in cells intersecting or adjacent to the boundary. This constitutes the first published implementation of an embedded boundary algorithm for simulating flow of viscoplastic fluids on structured grids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretization, in which viscous terms are treated semi-implicitly and projection methods are utilized to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since the viscosity depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After performing convergence analysis and validating the code against standard test cases, we present the first ever fully three-dimensional simulations of creeping flow of Bingham plastics around translating objects. Our results shed new light on the flow fields around these objects.

Mixed convective heat transfer analysis for the peristaltic transport of viscoplastic fluid: Perturbation and numerical study

Mixed convective peristaltic flow of incompressible viscoplastic fluid is investigated in a two-dimensional symmetric channel. The rheology of viscoplastic material is characterized by the constitutive equation for Bingham plastic model. The coupling between momentum and energy equations is achieved through Boussinesq approximation. The coupled nonlinear partial differential equations are transformed in wave frame using Galilean transformation and then simplified under realistic assumptions of long wavelength and low Reynolds number. Approximate solution is obtained using regular perturbation method which is restricted to the smaller values of Grashof and Bingham numbers. The validity of approximate solution is established by comparing it with the numerical solution obtained via Matlab built-in routine bvp4c. Based on the numerical solution an extensive analysis is performed in order to analyze the effects of various parameters of interest on flow characteristics, pumping and trapping phenomena. It is found that velocity decreases at the center by increasing Bingham number showing a boundary layer character for large values. However, it increases by increasing Brinkman and Grashof numbers. Moreover, pressure rise per wavelength increases with Bingham number, Brinkman number and Grashof number, in the pumping region. The result further indicate that larger values of Bingham number circumvent bolus growth.

An adaptive finite element method for elastoviscoplastic fluid flows

Elastoviscoplastic fluids are a class of yield-stress fluids that behave like neoHookean (or viscoelastic) solids when the imposed stress is less than the yield stress whereas after yielding, their behaviour is described by a viscoplastic fluid with an additional elastic history. This exceptional behaviour has been recently observed by many yield-stress fluids in rheometric tests such as waxy crude oil, Carbopol gel, etc. Moreover, interesting phenomena have been evidenced experimentally such as the presence of a negative wake and a loss of fore-aft symmetry about a settling particle which are predominantly related to the elastic behaviour of yield-stress fluids (i.e., coupling of elasticity and plasticity). Here, we present a numerical scheme based on the so-called augmented Lagrangian method for numerical simulation of elastoviscoplastic fluid flows. The method is benchmarked by two rheometric flows: Poiseuille and circular Couette flows for which analytical solutions are derived. Moreover, anisotropic adaptive mesh procedure (which was previously introduced for viscoplastic fluid flows by Saramito and Roquet, Comput. Meth. Appl. Mech. Eng., vol. 190, 2001, pp. 5391–5412) is coupled to obtain a fine resolution of the yield surfaces. Finally, the presented method is applied to study more complex flows: elastoviscoplastic fluid flow in a wavy channel.

NUMERICAL STUDY OF VISCOPLASTIC FLOW IN A T-BIFURCATION: IDENTIFICATION OF STAGNANT REGIONS

Abstract Identification of stagnant regions of viscoplastic fluid flows in production lines and equipment is of paramount importance owing to potential material degradation and process contamination. The present work introduces an assessment strategy to identify, classify and quantify unyielded regions with the objective of optimizing the flow conditions with the purpose of minimizing stagnant regions. Flow of Carbopol® 980 in a T-bifurcation channel is adopted to illustrate the procedure. The rheological behavior of Carbopol® 980 was simulated using the Herschel-Bulkley viscoplastic model regularized by Papanastasiou’s exponential approach. The analysis shows that three distinct types of stagnant unyielded regions take place in the bifurcation channel depending upon the Reynolds condition. Furthermore, the rheological characteristics of the fluid indicate the existence of an ideal Reynolds condition which allows the smallest flow stagnant area at the bifurcation zone.

Homogenization of Bingham flow in thin porous media

By using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham fluid on the small parameters describing the geometry of the thin porous medium under consideration. Three different problems are obtained in the limit when the small parameter \begin{document}$ \varepsilon $\end{document} tends to zero, following the ratio between the height \begin{document}$ \varepsilon $\end{document} of the porous medium and the relative dimension \begin{document}$ a_\varepsilon $\end{document} of its periodically distributed pores. We conclude with the interpretation of these limit problems, which all preserve the nonlinear character of the flow.