A modified lattice boltzmann method for herschel-bulkley fluids

Wu, Weiyang; Huang, Xiaodiao; Yuan, Hong; Xu, Fei; Ma, Jingtao

doi:10.1007/s00397-017-1000-9

Cited by 19 publications

(10 citation statements)

References 34 publications

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“…In particular, some theoretical analysis at the continuum level -i.e. on spatial scales much larger than the colloidal particle size -have been made using generalized Newtonian power-law models, Carreau Yasuda models or quadratic models with selective choice of the power exponents 26,[28][29][30][31][32][33] . It should be pointed out, however, that in all these studies the flow of a mild "continuous" shear thickening fluid has been considered.…”

Section: Introductionmentioning

confidence: 99%

Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation

2017

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Section: Introductionmentioning

confidence: 99%

Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation

2017

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“…where σ 0 is the yield stress, k is the flow consistency, n is the flow index,γ is the local shear-rate magnitude, expressed as [22,31,32,33,34]…”

Section: Non-newtonian Herschel-bulkley Modelmentioning

confidence: 99%

Lattice-Boltzmann simulation of creeping generalized Newtonian flows: Theory and guidelines

Gsell

d'Ortona

Favier

2021

Journal of Computational Physics

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The accuracy of the lattice-Boltzmann (LB) method is related to the relaxation time controlling the flow viscosity. In particular, it is often recommended to avoid large fluid viscosities in order to satisfy the low-Knudsen-number assumption that is essential to recover hydrodynamic behavior at the macroscopic scale, which may in principle limit the possibility of simulating creeping flows and non-Newtonian flows involving important viscosity variations. Here it is shown, based on the continuous Boltzmann equations, that a two-relaxation-time (TRT) model can however recover the steady Navier-Stokes equations without any restriction on the fluid viscosity, provided that the Knudsen number is redefined as a function of both relaxation times. This effective Knudsen number is closely related to the previously-described parameter controlling numerical errors of the TRT model, providing a consistent theory at both the discrete and continuous levels. To simulate incompressible flows, the viscous incompressibility condition M a 2 /Re 1 also needs to be satisfied, where M a and Re are the Mach and Reynolds numbers. This concept is extended by defining a local incompressibility factor, allowing one to locally control the accuracy of the simulation for flows involving varying viscosities. These theoretical arguments are illustrated based on numerical simulations of the two-dimensional flow past a square cylinder. In the case of a Newtonian flow, the viscosity independence is confirmed for relaxation times up to 10 4 , and the ratio M a 2 /Re = 0.1 is small enough to ensure reliable incompressible simulations. The Herschel-Bulkley model is employed to introduce shear-dependent viscosities in the flow. The proposed numerical strategy allows to achieve major viscosity variations, avoiding the implementation of artificial viscosity cut-off in high-viscosity regions. Highly non-linear flows are simulated over ranges of the Bingham number Bn ∈ [1, 1000] and flow index n ∈ [0.2, 1.8], and successfully compared to prior numerical works based on Navier-Stokes solvers. This work provides a general framework to simulate complex creeping flows, as encountered in many biological and industrial systems, using the lattice-Boltzmann method.

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“…In the previous research, a truncated model has been proposed and studied. In the certain ranges, Herschel–Bulkley fluid can be regard as Bingham fluid to avoid the poor stability caused by the varying relaxation time (Wu et al , 2017). The truncated model will be taken here to make a comparison with the proposed model.…”

Section: The Herschel–bulkley Flow In Cement-three-dimensional Printing Extrudermentioning

confidence: 99%

“…Gabbanelli proposed a truncated LBM for power-law fluids and verified its validity by Poiseuille flow (Gabbanelli et al , 2005). Then, Wu et al (2017) proposed a truncated model for Herschel–Bulkley fluid. The difference of the two methods mentioned above is the characteristic of the fluid.…”

Section: Introductionmentioning

confidence: 99%

A modified LBM for non-Newtonian effect of cement paste flow in 3D printing

Huang

et al. 2019

RPJ

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Purpose The screw extruder is applied in cement-three-dimensional (3D) printing. The cement paste flow in 3D printing is the typical Herschel–Bulkley fluid. To understand the flow in the channel, the improved lattice Boltzmann method (LBM) is proposed. Design/methodology/approach For Herschel–Bulkley flow, an improved LBM is presented to avoid the poor stability and accuracy. The non-Newtonian effect is regard as a special forcing term. The Poiseuille flow is taken to discuss the detailed process of the method. With the method, the analytical solution and numerical solution are obtained and compared. Then, the effect of the initial yield stress on the numerical solution is both explored by the shear-thickening fluid and the shear-thinning fluid. Moreover, the variations of the relative errors under different lattice nodes and different power-law indexes are analyzed. Finally, the method is applied into the simulation of the flow in the extruder of cement-3D printing. Findings The results show that the improved method is effective for Herschel–Bulkley fluids, which can simulate the flow in the extruder stably and accurately. Practical implications The simulation can contribute to understand the cement paste flow in the screw extruder, which helps to optimize the structure of the extruder in the following periods. Originality/value The improve method provide a new way to analyze the flow in the extruder of cement-3D printing. Also, in the past research, LBM for Herschel–Bulkley fluid is ignored, whereas the study can provide the reference for the numerical simulation.

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A modified lattice boltzmann method for herschel-bulkley fluids

Cited by 19 publications

References 34 publications

Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation

Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation

Lattice-Boltzmann simulation of creeping generalized Newtonian flows: Theory and guidelines

A modified LBM for non-Newtonian effect of cement paste flow in 3D printing

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