Flow of Bingham plastics in a lid-driven square cavity

Mitsoulis, Evan; Zisis, Th.

doi:10.1016/s0377-0257(01)00147-1

Cited by 128 publications

(134 citation statements)

References 9 publications

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“…The present code has been subject to two validation tests: The mixed convection in two-sided lid driven differentially heated square cavity [6], and Flow of Bingham fluid in a lid-driven square cavity [8]. The streamline and isotherm plots for the case two, velocity profiles and pressure distribution presented in Fig.2, Fig.3, Fig.4 respectively present good agreement comparing with the previous results.…”

Section: Code Validationsupporting

confidence: 69%

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Mixed Convection Heat Transfer for Bingham Fluid in Square Cavity With Partitions

Benmalek¹,

Souidi²,

Yssaad³

2017

Topical Problems of Fluid Mechanics 2017

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Two-dimensional steady mixed convection flow in an enclosure with partitions filled with a Bingham fluid is considered. The vertical walls are maintained at different constant temperatures and they are moving in opposite direction. The upper and the bottom walls are fixed and thermally insulated. The governing equations are normalized and solved numerically by the finite volume control. A parametric investigation is performed and a set of isotherms and streamlines are presented. The results shown that the decrease of Richardson number increase the fluid flow and enhanced the heat transfer. The effect of the yield-stress in the presence of the partition is to drop the fluid motion and to augment heat transfer where the conduction mode is dominant.

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Section: Code Validationsupporting

confidence: 69%

“…The effects of aspect ratio, Reynolds number and imposed temperature gradients are analyzed. E. Mitsoulis and Th.Zisis [8] conducted a study on the purely dynamic flow of a plastic Bingham fluid in lid driven cavity.…”

Section: Introductionmentioning

confidence: 99%

Mixed Convection Heat Transfer for Bingham Fluid in Square Cavity With Partitions

Benmalek¹,

Souidi²,

Yssaad³

2017

Topical Problems of Fluid Mechanics 2017

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“…Figure 6.7 presents the equally distributed velocity streamlines and the isoline of (2µ + τ s |Du| −1 ε )|Du| = τ s , the latter may be interpreted as a reasonable approximation of the yield surfaces [35]. Comparing these statistics to those found in [29,30] we assure that sufficiently accurate solutions are computed. A 2D computation on non-rectangular domains.…”

Section: Newton Methods With Continuation Triangular Elementsmentioning

confidence: 80%

A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution

Aposporidis

Haber

Olshanskii

et al. 2011

Computer Methods in Applied Mechanics and Engineering

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In this paper we introduce a mixed formulation of the Bingham fluid flow problem. We consider both the original and a regularized version of the problem, where a parameter ε is introduced, forcing the entire domain to be formally a fluid region. In general, common solvers for the regularized problem experience performance degradation when the parameter ε gets smaller. The method studied here introduces an auxiliary tensor variable and shows enhanced numerical properties for small values of ε. Good performance is also observed for the non-regularized case. The well posedness for the regularized problem and the equivalence -at the continuous level -between the original (primitive variables) and the mixed formulation are demonstrated. We analyze properties of linearized problems that are relevant for the convergence of numerical solvers. A finite element method for the mixed formulation is discussed. Numerical results confirm the predicted better performances of the mixed formulation comparing to the primitive variables formulation. A comparison to a non regularized solver based on the augmented Duvaut-Lions-Glowinski formulation of the problem is carried out as well.

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“…The latter condition, however, does not hold exactly for the numerical solution, especially if a regularized model is used. For the driven cavity problem, some numerical results, including the prediction of the rigid zones, can be found in [10,11,22,26,38]. In [22,11], a regularized model was used, while [10,26,38] Tables 5.3 and 5.4 show that for small ε the number of outer nonlinear iterations increases.…”

Section: Analytical Testmentioning

confidence: 99%

An Iterative Method for the Stokes-Type Problem with Variable Viscosity

Grinevich¹,

Olshanskii²

2009

SIAM J. Sci. Comput.

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Abstract. This paper concerns an iterative technique for solving discretized Stokes-type equations with varying viscosity coefficient. We build a special block preconditioner for the discrete system of equations and perform an analysis revealing its properties; the theoretical analysis is based on the weighted Nečas inequality. The subject of this paper is motivated by numerical solution of incompressible non-Newtonian fluid equations. In particular, the general analysis is applied to the linearized equations of the regularized Bingham model of viscoplastic fluid. Numerical experiments show that the suggested preconditioner leads to an iterative method insensitive to the variation of mesh size and the regularization parameter of the fluid model.

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Flow of Bingham plastics in a lid-driven square cavity

Cited by 128 publications

References 9 publications

Mixed Convection Heat Transfer for Bingham Fluid in Square Cavity With Partitions

Mixed Convection Heat Transfer for Bingham Fluid in Square Cavity With Partitions

A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution

An Iterative Method for the Stokes-Type Problem with Variable Viscosity

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