Flow Of Viscoplastic Materials Research Articles

Lattice Boltzmann simulations of unsteady Bingham fluid flows

Transient flows of viscoplastic fluids have very peculiar characteristics. The startup and cessation flows of viscoplastic materials have been subject to many theoretical and numerical investigations. The most challenging aspect of numerical solutions of viscoplastic fluids is the viscosity singularity during the transition from yielded to unyielded material. Hence, the proper representation of yield surfaces is the most critical aspect of numerical methods in viscoplastic fluid flow. In the present work, we use a lattice Boltzmann scheme to solve an ideal Bingham fluid’s startup and cessation flows. This numerical scheme advantage is that can represent infinite viscosity without noticeable numerical instabilities, producing yield surfaces with more accuracy and quality. Theoretical solutions for the startup flow are available in the literature. However, it is unclear which is more accurate and what their validity ranges are. Nonetheless, these solutions served as a reference for the present simulations. The overall aspect of the numerical solutions agreed with the theoretical models. The cessation flow of the Bingham fluid was also simulated. Unlike a Newtonian fluid, this type of flow is known to have a finite period until cessation. The simulations correctly reproduced this behavior. The transient yield surfaces matched very well with augmented Lagrangian solutions.

Thermo-mechanical process variables driven microstructure evolution during additive friction stir deposition of IN625

Additive friction stir deposition is an innovative technique for solid-state additive manufacturing involving complex thermo-mechanical processes such as frictional heating, plastic deformation, and viscoplastic material flow, which repeats layer by layer during material deposition. The present study is an attempt to understand the relationship between the complex thermo-mechanical process attributes and the resultant microstructure in additive friction stir deposition of IN625. The estimation of thermo-mechanical process attributes, primarily temperature and strain rate during multi-layer deposition was based on the already established thermo-pseudo-mechanical description of friction stir based processes. The complex thermo-mechanical interaction associated with multi-layer material deformation, deposition, and flash formation can be attributed to variations in the average deposition temperature and the strain rate. Microstructural examination of the additive friction stir deposited sample was performed using electron backscatter diffraction. As a result of the additive friction stir deposition associated thermo-mechanical conditions, the microstructure exhibited fine equiaxed grains in the plane along the build direction along with bands of very fine grains within the interface regions between deposited layers. The observation of fine equiaxed grains and a lower degree of in-grain misorientation in the additively fabricated sample pointed to dynamic recrystallization as the governing restoration mechanism during the deposition process. The grain size refinement during additive friction stir deposition of IN625 resulted in substantial augmentation in the yield strength compared to IN625 feed material and as-cast IN625.

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

PurposeAccording to the research, viscoplastic fluids are sensitive to slipping. The purpose of this study is to determine whether slip affects the Rayleigh–Bénard convection of viscoplastic fluids in cavities and, if so, under what conditions.Design/methodology/approachThe wall slip was evaluated using a model created for viscoplastic (Bingham) fluids. The coupled conservation equations were solved numerically using the finite element method. Simulations were performed for various parameters: the Rayleigh number, yield number, slip yield number and friction number.FindingsWall slip determines two essential yield stresses: a specific yield stress value beyond which wall slippage is impossible (S_Yc); and a maximum yield stress beyond which convective flow is impossible (Y_c). At low Rayleigh numbers, Y_c is smaller than S_Yc. Hence, the flow attained a stable (conduction) condition before achieving the no-slip condition. However, for more significant Rayleigh numbers Y_c exceeded S_Yc. Thus, the flow will slip at low yield numbers while remaining no-slip at high yield numbers. The possibility of slipping on the wall increases the buoyancy force, facilitating the onset of Rayleigh–Bénard convection.Originality/valueAn essential aspect of this study lies in its comprehensive examination of the effect of slippage on the natural convection flow of viscoplastic materials within a cavity, which has not been previously investigated. This research contributes to a new understanding of the viscoplastic fluid behavior resulting from slipping.

Hall device-controlled ciliated flow of viscoplastic material due to the non-uniform complex ciliated pump subject to inclined magnetic force

In the last two decades, the applications of peristaltic and ciliated pumps in diverse domains of engineering and medicine are increasing because of their efficiency and easy operation with fewer errors in performing a task than the other biological pumps. The current study describes a mathematical formulation of the ciliated flow of viscoplastic material through an infinite length under the impact of heat transfer. The rheological impact of viscoplastic material is inspected using the robust Casson model. The motion is also controlled by the two external simulated powers: one is an inclined magnetic field and the other is the Hall device. The governing equations are simplified using the two biological approximations: one is the creeping phenomena and the other is the long wavelength. Analytical solutions of the flow equations are obtained by the integration method. The impact of rheological and thermo-physical parameters is physically incorporated. The Cilia-length parameter and the Brinkman number are vibrant in the enhancement of the heat phenomena and the heat transfer rate at the upper wall (HTRUW). Applications of the current formulation include the chemical industry, magnetic material processing, and the medical domain under the creeping phenomenon.

Viscoplastic corner eddies

When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous ‘Moffatt eddies’. In this study we examine corner flows of viscoplastic materials, a class of non-Newtonian fluids which exhibit solid-like behaviour for stresses below a yield stress. Specifically, we consider a Bingham fluid, for which the material is perfectly rigid at stresses below the yield stress. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-Lagrangian method, and analytically, by employing a viscoplastic boundary layer formulation and scaling arguments. We measure the depth of the static plug as a function of the Bingham number (dimensionless yield stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid adjacent to the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.

Течение маслосодержащего материала в канале шнека маслопресса

The paper presents an analysis of the basic operational concepts for the screw channel of the oil press. The channel is chosen by the authors as the object of research. The subject of the study is the the flow velocities distribution for the oil-containing material in the channel of the local auger of the second section of the oil press and the influence of the channel parameters on the performance of the press. The mathematical modeling of the flow of oil-containing material in the channel of the oil press screw is used as a research method. Of the proposed simplifying assumptions for the flow in the auger channel, three assumptions are considered and further developed. The cross section of the channel is assumed to be rectangular. The developed hydrodynamic model, in contrast to previously published works, takes into account the presence of a gap δ between the edge of the screw spiral and the inner surface of the pressing cage, as well as the non-uniformity of the movement velocity for points on the screw. A fundamentally new point in the formulation of the problem is that the velocity is not assumed to be constant on the side walls of the channel. The coordinate dependence of the velocity vz on the rectangular boundaries of the screw is presented. The flow of viscoplastic material is obtained in the form of four components, which are determined by the pressure gradient, the flow of material along the axis of the screw channel, the movement of the side walls of the channel and the viscoplastic material through the gap between the screw spiral and the pressing cage. Simple analytical expressions containing only simple elementary functions are derived for the flow velocity of a viscoplastic material. The found solutions of hydrodynamics use the Newtonian model of fluid flow but can be easily generalized to non-Newtonian Bingham viscoplastic rheology. The results demonstrated can be employed to optimize the parameters of the oil press augers, increase its productivity and oil yield.

Theoretical studies of crimping process of cylindrical blanks in conditions of viscoplastic material flow

The forming process of cylindrical tubular blanks with heating of the wrought material, which is due to its mechanical characteristics is considered. Algorithm for developing of process model, which makes it possible to assess the crimping pressure and the continuity of the material is presented. The dependences of the effect of the main parameters on the crimping pressure and the continuity of the material are plotted. Secondary mathematical models are obtained to assess the pressure of the process under study. The die tooling is designed and recommendations are developed for the implementation of the titanium alloys crimping technology.

Polyelectrolyte layer grafting effect on the rotational electroosmotic flow of viscoplastic material

Due to growing importance of study of bio-fluids in rotational microfluidic platforms, discussion of flow of viscoplastic materials in such situations becomes very important. Bio-fluids also generally flow in soft channel microfluidic environment and therefore studying the effect of softness of channels on flow of such viscoplastic bio-fluids becomes critical. We, in the present study, investigate the effect of the rotation of the channel and yield stress of the fluid on the flow of viscoplastic material in a soft microchannel for three constitutive models viz. Bingham, Casson and Herschel–Bulkley models. It is found that the soft grafted layer, the channel rotation and the fluid yield stress play vital roles in determining the flow behaviour. We find that that larger rotational speeds tend to destabilize the flow. We also find the critical rotational speed for which secondary flow magnitude is maximum. We also find that this non-linear interaction between rotation of channel and fluid yield stress leads to the generation of multiple yield planes within the flow domain. Our study will help in obtaining good designs of rotational microfluidic platforms for studying bio-fluids with yield stress.

NUMERICAL SIMULATION OF A ELASTO-VISCOPLASTIC FLUID FLOW INSIDE A CAVITY

This article addresses finite element approximations for elasto-viscoplastic flows. Numerical simulations aiming at investigating the role of elasticity for inertialess flows of viscoplastic materials within lid-driven cavity.The mechanical model is made up of the usual governing equations for incompressible fluids coupled with a Oldroyd-B type equation (de Souza Mendes, 2011) modified to incorporate the dependency both of relaxation and retardation time as the viscoplastic viscosity on the strain rate. These parameters depend on the material microstructure, which level is described by an structure parameter . This model is approximated by a multi-field Galerkin least-squares formulation (Behr et al., 1993) in terms of extra-stress tensor, the pressure field and the velocity vector. Results, focused on the determination of yield surface topology, investigate the influence of elastic and viscous governing parameters on the flow pattern.

Flow of non-Newtonian fluids in open channels

This report details progress made in a Maths in Industry Study Group Project. The key conclusions of the study group were that correctly choosing an appropriate rheological model, and using appropriate data to compute the parameters of that model, is vital in recovering the correct fluid behaviour; and that exact mathematical solutions that exist for simplistic channel shapes can be used to approximate the flow in more complicated geometries. The problems of accurate numerical computation for highly non-Newtonian channel flow, as well as the complications that arise from turbulence, were identified as important areas of further research. References N. J. Alderman and R. Haldenwang, ``A review of Newtonian and non-Newtonian flow in rectangular open channels.'' Hydrotransport 17: The 17th International Conference on the Hydraulic Transport of Solids , The Southern African Institute of Mining and Metallurgy and the BHR Group, 2007. http://hdl.handle.net/11189/5192 J. Burger, R. Haldenwang and N. Alderman, ``Experimental database for non-Newtonian flow in four channel shapes.'' Journal of Hydraulic Research , 48 (2010): 363–370. doi:10.1080/00221686.2010.481849 P. Coussot, ``Steady, laminar, flow of concentrated mud suspensions in open channel.'' Journal of Hydraulic Research , 32 (1994): 535–559. doi:10.1080/00221686.1994.9728354 D. A. Rojas and R. H. A. Janssen, ``Design of open channels for non-Newtonian fluids'', in Proceedings of the 16th International Seminar on Paste and Thickened Tailings , Eds R. J. Jewell, A. B. Fourie, J. Caldwell and J. Pimenta, Australian Centre for Geomechanics, 2013. S. W. McCue, J. R. King and D. S. Riley, ``Extinction behaviour for two-dimensional inward-solidification problems.'' Proceedings of the Royal Society of London A , 459 (2003): 977–999. doi:10.1098/rspa.2002.1059 C. C. Mei and M. Yuhi, ``Slow flow of a Bingham fluid in a shallow channel of finite width.'' Journal of Fluid Mechanics , 431 (2001): 135–159. doi:10.1017/S0022112000003013 H. Schlichting and K. Gersten, Boundary-Layer Theory . Springer-Verlag, Berlin Heidelberg, 2000. doi:10.1007/978-3-662-52919-5 K. X. Whipple, ``Open-channel flow of Bingham fluids: applications in debris-flow research.'' The Journal of Geology , 105 (1997): 243–262. doi:10.1086/515916 R. Chhabra and J. F. Richardson, Non-Newtonian Flow: Fundamentals and Engineering Applications , Butterworth-Heinemann, 1999. P. Coussot, Mudflow rheology and dynamics , Balkema, 1997. F. Holland and R. Bragg, Fluid Flow for Chemical and Process Engineers , Butterworth-Heinemann, 1995. E. Mitsoulis, Flows of viscoplastic materials: models and computations, Rheology reviews , 2007 (2007), pp. 135–178. http://www.bsr.org.uk/rheology-reviews/RheologyReviews/viscoplastic-materials-Mitsoulis.pdf D. Pritchard, B. R. Duffy, and S. K. Wilson, Shallow flows of generalised Newtonian fluids on an inclined plane, Journal of Engineering Mathematics , 94 (2015), pp. 115–133. doi:10.1007/s10665-014-9725-2 J. N. Reddy and D. K. Gartling, The finite element method in heat transfer and fluid dynamics , CRC press, 2010.

Simulation of strain rate, material flow, and nugget shape during dissimilar friction stir welding of AA6061 aluminum alloy and Al-Mg2Si composite

A three-dimensional model was developed based on computational fluid dynamics (CFD) to study the visco-plastic material flow during friction stir welding of AA6061 aluminum alloy and Al-Mg2Si composite dissimilar joint. To model the dissimilar joint, the volume of fluid (VOF) method was used. The volumetric equation was defined for the heat which generated through the viscous dissipation. The model was investigated for three rotational speeds of 720, 920 and 1120 rpm. The nugget shape was in good agreement with the corresponding experimental results. The results showed that maximum velocity and strain rate occurred at the top surface of the workpiece and outer edge of the shoulder. Also, peak temperature was obtained at the advancing side. The strain rate at the advancing side and the retreating side was about 975s−1 and 926s−1, respectively. In a region of the stir zone where material mixing is dominant, the volume fraction of the AA6061 aluminum alloy is 0.4–0.8.

Confined viscoplastic flows with heterogeneous wall slip

The steady, pressure-driven flow of a Herschel-Bulkley fluid in a microchannel is considered, assuming that different power-law slip equations apply at the two walls due to slip heterogeneities, allowing the velocity profile to be asymmetric. Three different flow regimes are observed as the pressure gradient is increased. Below a first critical pressure gradient G 1, the fluid moves unyielded with a uniform velocity, and thus, the two slip velocities are equal. In an intermediate regime between G 1 and a second critical pressure gradient G 2, the fluid yields in a zone near the weak-slip wall and flows with uniform velocity near the stronger-slip wall. Beyond this regime, the fluid yields near both walls and the velocity are uniform only in the central unyielded core. It is demonstrated that the central unyielded region tends towards the midplane only if the power-law exponent is less than unity; otherwise, this region rends towards the weak-slip wall and asymmetry is enhanced. The extension of the different flow regimes depends on the channel gap; in particular, the intermediate asymmetric flow regime dominates when the gap becomes smaller than a characteristic length which incorporates the wall slip coefficients and the fluid properties. The theoretical results compare well with available experimental data on soft glassy suspensions. These results open new routes in manipulating the flow of viscoplastic materials in applications where the flow behavior depends not only on the bulk rheology of the material but also on the wall properties.

Numerical simulations of complex yield-stress fluid flows

Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito.

Rotating electroosmotic flow of viscoplastic material between two parallel plates

This study aims to investigate electroosmotic flow of a viscoplastic material, modeled as either Bingham plastic or Casson fluid, through a parallel-plate channel that rotates about an axis perpendicular to the plates. A relatively small yield stress, comparable to that of human blood, is considered in order to confine to the condition there is only one yield surface in the flow. An iterative finite-difference numerical scheme is developed to solve the Cauchy momentum equations and nonlinear constitutive equations. The location of the yield surface, and velocity and stress components in both the sheared and unsheared regions are found as functions of the yield stress, rotation speed and Debye parameter. Numerical results are presented to reveal that the system rotation and yield stress may counteract each other in controlling the resultant flow rate and flow direction. The effect of yield stress may even be reversed for a sufficiently large rotation speed.

Viscoplastic dimensionless numbers

In the present paper we analyze the dimensionless numbers that concern the flow of viscoplastic materials. The Bingham material is used to conduct the main discussion but the ideas are generalized to more complex viscoplastic models at the end of the article. Although one can explore the space of solutions with a set of dimensionless numbers where only one of them takes into account the yield stress, like the Bingham number for example, we recommend that the characteristic stress should be defined as the extra-stress intensity evaluated at a characteristic (maximum) deformation rate. Such a definition includes the yield stress in every dimensionless number that is related to viscous effects like the Reynolds number, the viscosity ratio, and the Rayleigh number. This procedure was shown to be more effective on collapsing data into master curves and to provide a fairer comparison with the Newtonian case. This happens because a more representative viscous effect is taken into account, concentrating the plastic effects into a single parameter. The plastic number, the ratio of the yield stress to the maximum stress of the domain, is shown to better capture plastic effects than the usual Bingham number. The analysis of problems where a characteristic stress, but not a characteristic velocity, is provided, indicates that a more representative characteristic velocity should be defined with respect to the driving potential for the motion, i.e., the difference between the characteristic and yield stresses. This method is in contrast to the majority of the literature, where for Bingham materials, the dimensionless numbers are maintained in the same form as the original Newtonian ones, replacing the Newtonian viscosity by the viscous parameter of the Bingham model.

Heat transfer to Herschel–Bulkley materials flowing in the entrance of tubes with an imposed wall temperature profile

Heat transfer to the flow of viscoplastic materials in tubes is quite common and its analysis is fundamental to achieve a good performance in many industrial processes. This kind of phenomenon has been successfully studied over the years, but the main results are focused on the two well-known thermal boundary conditions: an imposed constant wall temperature and an imposed constant heat flux. In this work we conduct a numerical study by means of the Galerkin finite element method. The goal here is to investigate the effect of the Reynolds and Peclet numbers together with the rheological properties on the Nusselt coefficient along the tube length when a wall temperature profile is prescribed. This kind of thermal boundary condition is more reliable to characterize the process of pumping oil through risers into the sea. It is worth noting that Nu assumes infinite value at a critical point which is related to changes in the heat direction. As expected, Nu increases as the rheological fluid behavior departs from the Newtonian.

Determining the viscosity and yield surface of marine sediments using modified Bingham models

The rheology of marine sediment-laden flows in a submarine environment is examined. The viscosity and yield stress of marine sediments are key parameters controlling landslide mobility: the former is related to the peak velocity and the latter is related to the final deposition of debris flow. One of the simplest rheological models is the ideal plastic Bingham model, which is often applied to diverse materials. For marine sediments, the flow behavior can be approximated by modified Bingham models, such as the bi-viscosity and Papanastasiou models. The flow of viscoplastic materials can then be described by unyielded (local shear stress τ is lower than a yield stress τ y ), yield surface (τ = τ y ), and post-yield (τ > τ y ) characteristics. It is concluded that modified Bingham models with a proper choice of flow parameters can be used to predict the unyielded, yielding and yielded zones for marine sediments. It is also demonstrated that in some cases the yield surface can be effectively obtained using the relationship between viscosity and shear rate.

High shear helical flow of a Sisko fluid

The Sisko fluid model was proposed in response to observed failure of the well-known Bingham model to represent the flows of viscoplastic materials in high shear regimes, such failure increasing with shear rate. We consider the flow of a Sisko fluid between infinitely long coaxial cylinders, when the inner cylinder rotates with constant angular speed and a constant axial fluid flow is maintained. High shear rates are ensured by assuming an inter-cylindrical gap small in relation to the overall geometry. Such a helical flow and geometry is of relevance to a number of applications, including rheometry. We assume a laminar flow and apply a perturbation procedure based on a scaled form of the inter-cylindrical gap dimension as a perturbation parameter to obtain simple explicit approximations for the fluid velocity field as well as the fluid viscosity variation in this gap. We also derive an approximate form of the Reiner--Riwlin equation, linking the defining fluid parameters to measurable quantities in the flow. References R. B. Bird, R. C. Armstrong and D. Hassager, Dynamics of Polymetric liquids, Vol. 1, John Wiley and Sons, 1987. C. Chiera, Perturbation Analysis of the Helical Flow of Generalized Newtonian Fluids, Ph.D. Thesis, RMIT, 2004 C. Chiera, H. J. Connell and J. J. Shepherd, Perturbation analysis of the helical flow of non-Newtonian fluids with application to a recirculating coaxial cylinder rheometer, Mathematical and Computer Modelling, 18, No 10: 131--140, 1993. doi:10.1016/0895-7177(93)90222-K C. Chiera, H. J. Connell and J. J. Shepherd, On the helical flow of a Sisko model fluid, Proc. 2nd Pacific Rim Conf. Rheology (PRCR2), Melbourne, Australia, 33--34, July 1997 B. D. Coleman and W. Noll, Helical flow of General Fluids, J. App. Phys., 10: 1508--1512, 1959. doi:10.1063/1.1734990 M. T. Farrugia, J. J. Shepherd and A. J. Stacey, A perturbation analysis of the flow of a Powell--Eyring fluid between coaxial cylinders, ANZIAM J., 52 257--270, 2011. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/3748 W. E. Langlois, Slow Viscous Flow, Macmillan, New York, 1964 A. W. Sisko, The flow of lubricating greases, Ind. and Eng. Chem., 50 (12), 1789--1792, 1958 http://pubs.acs.org/doi/abs/10.1021/ie50588a042

Load bearing capacity of tool pin during friction stir welding

Although friction stir welding (FSW) is now widely used for the welding of aluminum and other soft alloys, premature tool failure limits its application to hard alloys such as steels and titanium alloys. The tool pin, the weakest component of the tool, experiences severe stresses at high temperatures due to both bending moment and torsion. It is shown that the optimum tool pin geometry can be determined from its load bearing capacity for a given set of welding variables and tool and work-piece materials. The traverse force and torque during friction stir welding are computed using a three-dimensional heat transfer and viscoplastic material flow model considering temperature and strain rate-dependent flow stress of the work-piece material. These computed values are used to determine the maximum shear stress experienced by the tool pin due to bending moment and torsion for various welding variables and tool pin dimensions. It is shown that a tool pin with smaller length and larger diameter will be able to sustain more stress than a longer pin with smaller diameter. The proposed methodology is used to explain the failure and deformation of the tool pin in independent experiments for the welding of both L80 steel and AA7075 alloy. The results demonstrate that the short tool life in a typical FSW of steels is contributed by low values of factor of safety in an environment of high temperature and severe stress.

Optimization of mixed variational inequalities arising in flow of viscoplastic materials

Optimal control problems of mixed variational inequalities of the second kind arising in flow of Bingham viscoplastic materials are considered. Two type of active-inactive set regularizing functions for the control problems are proposed and approximation properties and optimality conditions are investigated. A detailed first order optimality system for the control problem is obtained as limit of the regularized optimality conditions. For the solution of each regularized system a globalized semismooth Newton algorithm is constructed and its computational performance is investigated.