Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

Ohta, Mitsuhiro; Nakamura, Tatsuya; Yoshida, Yutaka; Matsukuma, Yosuke

doi:10.1016/j.jnnfm.2011.01.011

Cited by 32 publications

(17 citation statements)

References 41 publications

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“…[16]. In [28], Papanastasiou proposed the following model as a smoothed version of the Bingham model:…”

Section: A Construction Criterionmentioning

confidence: 99%

“…Moreover, the potential of the LBM in simulating flows of generalized Newtonian fluids, for which the dynamic shear viscosity depends on the shear rate [4], was shown by Aharonov and Rothman [5] as early as 1993. In recent years, this potential has attracted much attention [6,7,8,9,10,11,12,13,14,15,16].There are at least two kinds of LB-BGK models for generalized Newtonian fluids. In the first model, the relaxation time is not a constant anymore but depends on the shear rate.…”

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confidence: 99%

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Asymptotic Analysis of the Lattice Boltzmann Method for Generalized Newtonian Fluid Flows

Yang

Yong

2014

Multiscale Model. Simul.

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In this paper, we present a detailed asymptotic analysis of the lattice Boltzmann method with two different collision mechanisms of BGK-type on the D2Q9-lattice for generalized Newtonian fluids. Unlike that based on the Chapman-Enskog expansion leading to the compressible Navier-Stokes equations, our analysis gives the incompressible ones directly and exposes certain important features of the lattice Boltzmann solutions. Moreover, our analysis provides a theoretical basis for using the iteration to compute the rate-of-strain tensor, which makes sense especially for generalized Newtonian fluids. As a by-product, a seemingly new structural condition on the generalized Newtonian fluids is singled out. This condition reads as "the magnitude of the stress tensor increases with increasing the shear rate." We verify this condition for all the existing constitutive relations which are known to us. In addition, it is straightforward to extend our analysis to multiple-relaxation-time models or to three-dimensional lattices. Introduction.During the last two decades, the lattice Boltzmann method (LBM) has been developed into an effective and viable tool for simulating various fluid flow problems. It has been proved to be quite successful in simulating complex Newtonian fluid flows such as turbulent flows, microflows, multiphase and multicomponent flows, particulate suspensions, and interfacial dynamics. We refer the reader to [1, 2, 3] for a comprehensive account of the method and its applications. Moreover, the potential of the LBM in simulating flows of generalized Newtonian fluids, for which the dynamic shear viscosity depends on the shear rate [4], was shown by Aharonov and Rothman [5] as early as 1993. In recent years, this potential has attracted much attention [6,7,8,9,10,11,12,13,14,15,16].There are at least two kinds of LB-BGK models for generalized Newtonian fluids. In the first model, the relaxation time is not a constant anymore but depends on the shear rate. The non-Newtonian effects are embedded in the LBM through a dynamic change of the relaxation time. The second model has a constant relaxation time, but its equilibrium distribution contains the shear rate.The original goal of this paper is to extend the asymptotic analysis of LBM [17, 18] for classical Newtonian fluids to generalized ones. The analysis is based on the diffusive, instead of convective, scaling developed in [19] for the Boltzmann equation and in [17] for LB equations. It turns out that the diffusive scaling is the most natural choice if the LBE is viewed as a numerical solver of the incompressible Navier-Stokes

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“…[16]. In [28], Papanastasiou proposed the following model as a smoothed version of the Bingham model:…”

Section: A Construction Criterionmentioning

confidence: 99%

mentioning

confidence: 99%

Asymptotic Analysis of the Lattice Boltzmann Method for Generalized Newtonian Fluid Flows

Yang

Yong

2014

Multiscale Model. Simul.

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“…Recently, a lot of effort has been given into investigations of modelling of Bingham plastic rheology by the LBM, see e.g. [24][25][26][27], resulting in an iterative solution [24] of the problem or resulting in various regularization and stabilization techniques in the remaining works. We decided, however, to use the most straightforward and ''naive'' implementation of the Bingham plastic.…”

Section: Implementation Of the Non-newtonian Behaviour -Bingham Plasticmentioning

confidence: 99%

Free surface flow of a suspension of rigid particles in a non-Newtonian fluid: A lattice Boltzmann approach

Svec¹,

Skoček²,

Stang³

et al. 2012

Journal of Non-Newtonian Fluid Mechanics

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“…Our computations were performed via the same strategy utilized in our previous study. 16 In this study, the Carreau model was introduced into our computational code instead of the previous viscoplastic-fluid models. Here, we describe our computational method briefly.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of Carreau‐model fluid flows past a circular cylinder

Ohta

Toyooka

Matsukuma

2020

Asia-Pacific J Chem Eng

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Numerical simulations of shear-thinning and shear-thickening fluid flows past a circular cylinder are performed using a lattice Boltzmann method. In this study, the property of shear-thinning and shear-thickening fluids is expressed by the Carreau model. We focus on the definition of an effective (representative) Reynolds number for describing the flow of shear-thinning and shearthickening fluids past a circular cylinder. The fluid flows and viscosity profiles are clearly shown for fluids flowing across a circular cylinder depending on the Reynolds and Carreau numbers and the power index. A large value of Carreau number lead to the formation of low-viscosity regions for shear-thinning and high-viscosity regions for shear-thickening around a circular cylinder. Meanwhile, the change in the viscosity around the cylinder is not remarkable for a small Carreau number. The formulation of the effective Reynolds number defined using effective shear rate and viscosity is proposed in order to organize and understand the flow of Carreau-model fluids across a circular cylinder. The effective Reynolds number counseled in this study allows one to completely describe the flow state of Carreau-model fluids past a circular cylinder on an equal footing with Newtonian fluid flows. The usefulness of the effective Reynolds numbers is discussed, and the feature of Carreau-model fluid flows past a circular cylinder is considered in terms of the effective Reynolds number.

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Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

Cited by 32 publications

References 41 publications

Asymptotic Analysis of the Lattice Boltzmann Method for Generalized Newtonian Fluid Flows

Asymptotic Analysis of the Lattice Boltzmann Method for Generalized Newtonian Fluid Flows

Free surface flow of a suspension of rigid particles in a non-Newtonian fluid: A lattice Boltzmann approach

Numerical simulations of Carreau‐model fluid flows past a circular cylinder

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