Search

We study the flow of a thixotropic fluid around a cylinder. The rheology of the fluid is described by means of a structural viscoplastic model based on the Bingham constitutive equation, regularised using the Papanastasiou regularisation. The yield stress is assumed to vary linearly with the structural parameter, which varies from zero (completely broken structure) to one (fully developed skeleton structure), following a first-order rate equation which accounts for material structure break-down and build-up. The results were obtained numerically using the Finite Element Method. Simulations were performed for a moderate Reynolds number of 45, so that flow recirculation is observed behind the cylinder, but vortex shedding does not occur. The effects of the Bingham number and of the thixotropy parameters are studied. The results show that the viscous character of the flow can be controlled within certain limits through these parameters, despite the fact that the Reynolds number is fixed. © 2014 Elsevier B.V. 220 44 56 Cited By :2

30 3

A standard method used to determine material properties of semi-solid slurries is the squeeze flow experiment a fixed amount of material is squeezed under constant force or velocity and the relation between the force and the displacement of the sample provides information about the rheology of the slurry. The objective of this work is to contribute to the further development of the squeeze flow methodology in order to accurately determine material properties. This is achieved by a model that accounts for the finite yield stress and the thixotropy of the slurry. More specifically a structural viscoplastic model based on the Bingham plastic constitutive equation is proposed. The yield stress is assumed to vary linearly with the structural parameter which follows a first-order rate equation accounting for the material structure break-down and build-up. Numerical experiments of squeeze flow under either constant load or constant velocity are presented and discussed. Comparisons with their non-thixotropic counterparts are made in the case of compression under constant load. The development of the yielded/unyielded regions in relation to material structural changes is analyzed. The numerical results show that initially thixotropy does not affect the flow. However, once the structure is destroyed, the unyielded regions grow slower than the non-thixotropic case allowing for longer compression of the sample. Under constant force the structure may be destroyed at the early stages of the compression but at a later time it re-builds steadily till the cessation of the flow experiment. Under constant velocity, however, the structure is destroyed steadily. Depending then on the case, the final internal structure of the squeezed material can vary significantly. This is an important issue that needs to be taken into consideration in the evaluation of the material parameters. © 2012 Elsevier B.V. 193 103 115 Cited By :13

In this work we revisit the issue of obtaining true material constants for semisolid slurries. Therefore, we consider the circular Couette flow of Herschel-Bulkley fluids. We first show how true constants can be obtained using an iterative procedure from experimental data to theory and vice versa. The validity of the assumption that the rate-of-strain distributions across the gap share a common point is also investigated. It is demonstrated that this is true only for fully-yielded Bingham plastics. In other cases, e.g., for partially-yielded Bingham plastics or fully-yielded Herschel-Bulkley materials, the common point for the fully-yielded Bingham case provides a good approximation for determining the material constants only if the gap is sufficiently small. It can thus be used to simplify the iterative procedure in determining the material constants. © 2016 Trans Tech Publications, Switzerland. 256 153 172 Sponsors: Conference code: 184809

The flow and shape evolution during the compression of a finite amount of a Bingham plastic is investigated by means of numerical simulations. The problem relates to the popular compression test used for the rheological characterization of non-Newtonian fluids. The flow is modelled in Lagrangian coordinates using the Papanastasiou regularization for the Bingham plastic and a mixed-Galerkin finite element method. Simulations have been performed for compression under both constant load and constant velocity. Results for various Reynolds and Bingham numbers are presented and discussed. © 2007 Elsevier B.V. All rights reserved. 143 1 38 47 Cited By :15

The singular function boundary integral method (SFBIM) is applied for the numerical solution of a 2-D Laplace model problem of a perfectly elastic wedge beam under plane stress conditions. The beam has a point boundary singularity, it includes a curved boundary part and is subjected to non-trivial distributed external loading. The implemented solution method converges for this special model problem extremely fast. The numerical estimates attained for the leading singular coefficients of the local asymptotic expansion and the stress and strain fields are highly accurate, as verified by comparison with the available analytical solution. © 2014 Elsevier Inc. 248 93 100

We extend our recent work on the creeping flow of a Bingham fluid in a lid-driven cavity, to the study of inertial effects, using a finite volume method and the Papanastasiou regularisation of the Bingham constitutive model (Papanastasiou, 1987) [7]. The finite volume method used belongs to a very popular class of methods for solving Newtonian flow problems, which use the SIMPLE algorithm to solve the discretised set of equations, and have matured over the years. By regularising the Bingham constitutive equation it is easy to extend such a solver to Bingham flows since all that this requires is to modify the viscosity function. This is a tempting approach, since it requires minimum programming effort and makes available all the existing features of the mature finite volume solver. On the other hand, regularisation introduces a parameter which controls the error in addition to the grid spacing, and makes it difficult to locate the yield surfaces. Furthermore, the equations become stiffer and more difficult to solve, while the discontinuity at the yield surfaces causes large truncation errors. The present work attempts to investigate the strengths and weaknesses of such a method by applying it to the lid-driven cavity problem for a range of Bingham and Reynolds numbers (up to 100 and 5000 respectively). By employing techniques such as multigrid, local grid refinement, and an extrapolation procedure to reduce the effect of the regularisation parameter on the calculation of the yield surfaces (Liu et al., 2002) [55], satisfactory results are obtained, although the weaknesses of the method become more noticeable as the Bingham number is increased. © 2014 Elsevier B.V. 208-209 88 107 Cited By :15

We investigate the performance of the finite volume method in solving viscoplastic flows. The square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385- 404]. The numerical results obtained for Bingham numbers up to 10 and Reynolds numbers up to 5000 compare favourably with reported results obtained through other methods. The effects of the Reynolds and Bingham numbers are also investigated. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely deteriorates as the Bingham number increases, with a corresponding increase in the non-linearity of the equations. Using the SIMPLE algorithm in a multigrid context [Syrakos & Goulas, Int. J. Numer. Methods Fluids 52 (2006) 1215-1245] dramatically improves convergence, although the multigrid convergence rates are not as high as those for Newtonian flows. 70 81 Sponsors: Conference code: 104618

We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385-404]. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely deteriorates as the Bingham number increases, with a corresponding increase in the non-linearity of the equations. It is shown that using the SIMPLE algorithm in a multigrid context dramatically improves convergence, although the multigrid convergence rates are much worse than for Newtonian flows. The numerical results obtained for Bingham numbers as high as 1000 compare favourably with reported results of other methods. © 2013 Elsevier B.V.. 195 19 31 Cited By :18

International audience

The time-dependent, compressible extrusion of a Carreau fluid is solved over the reservoir-die-extrudate region using finite elements in space and a fully implicit scheme in time. A nonmonotonic slip law based on experimental data on polyethylene melts is assumed to hold along the die wall and the velocity at the entrance of the reservoir is taken to be fixed and uniform. As in the case of the extrudate-swell flow, the combination of compressibility and nonlinear slip leads to self-sustained oscillations of the pressure drop and of the mass flow rate in the unstable regime. The effects of the reservoir volume, the imposed flow rate, and the capillary length on the amplitude and the frequency of the pressure and free surface oscillations are studied and comparisons are made with experimental observations. © 2006 Elsevier B.V. All rights reserved. 146 1-3 30 44 Cited By :16

An essential element for the integration of the semisolid metal (SSM) process in the production of complex commercial components is the availability of accurate mathematical and computational tools that could describe both the material characteristics and the dynamics of semisolid slurries during die filling. Computational simulation and modeling is also a powerful and an effective tool that can be used to understand complex physical phenomena, such as those observed with semisolid slurries, and to support theoretical models describing them. We show how important physics can be revealed using experiments combined with numerical simulations. More specifically, we investigate the flow details and the shape evolution during the compression of a finite amount of a Herschel-Bulkley fluid, and the flow of such a material in a rotational viscometer. These two flows relate to popular experiments that are commonly used to determine rheological constants of semisolid slurries. The goal is to use mathematical and computational tools to test postulates for physical and theoretical models used to describe semisolid slurry behavior. The ultimate objective of this work is to contribute to the development of a methodology, which relates simulations to actual experimental results in order to determine the material constants of semisolid slurries. 359 361 Sponsors: American Foundry Society (AFS) American Society for Metals International (ASM) The Institute of Materials, Minerals and Mining (IOM3) North American Die Casting Association (NADCA) Conference code: 66060 Cited By :1 Centre Technique des Industries de la Fonderie (CTIF)