Numerical study of driven flows of shear thinning viscoelastic fluids in rectangular cavities

Dalal, Swapnil; Tomar, Gaurav; Dutta, Pradip

doi:10.1016/j.jnnfm.2016.01.009

Cited by 17 publications

(12 citation statements)

References 65 publications

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“…One can see that the general trend from Refs. [82][83][84][85] is recovered semiquantitatively, with the exception of the nonlinear deviation of the x-component of the vortex center. Results vary significantly between these references, so that a quantitative comparison is not drawn.…”

Section: Lid-driven Cavitymentioning

confidence: 99%

“…5, which also illustrates the shape of the resulting flow: a primary vortex develops near the top center of the flow cell and secondary vortices arise in the lower corners. The exact position of the center of the primary vortex, as well as the position y of the minimum of u x ((L/2, y) , ∞) and the positions x of the minimum and maximum of u y ((x, L/2) , ∞), varies with the flow parameters and has been extensively studied in literature [81][82][83][84][85], making them well-suited for comparison in the following. We choose width and height L = 194 for the flow cell, Newtonian viscosity η n = ρΔx 2 /Δt − η p , applied velocity u 0 = 10 −4 Δx/Δt, polymer viscosity ratio β = 0.5, and polymer relaxation times λ p such that Weissenberg numbers Wi ∈ [0, 1] are obtained.…”

Section: Lid-driven Cavitymentioning

confidence: 99%

“…The same regularization is employed by Refs. [82][83][84][85] and shall be used in the comparison below. Figure 6 shows the positions of the primary vortex and the flow velocity extrema in our simulations.…”

Section: Lid-driven Cavitymentioning

confidence: 99%

“…Values differ between Refs. [82][83][84][85] by factors of up to 2, so we only plot the comparison to Ref. [85].…”

Section: Lid-driven Cavitymentioning

confidence: 99%

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An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

et al. 2021

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Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids. Graphic abstract

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Section: Lid-driven Cavitymentioning

confidence: 99%

Section: Lid-driven Cavitymentioning

confidence: 99%

Section: Lid-driven Cavitymentioning

confidence: 99%

“…Values differ between Refs. [82][83][84][85] by factors of up to 2, so we only plot the comparison to Ref. [85].…”

Section: Lid-driven Cavitymentioning

confidence: 99%

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An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

et al. 2021

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“…In the same spirit [20] proposed using the square root of the conformation tensor to preserve the positive definiteness. Although less extended than the log conformation kernel, the square root conformation kernel has been used recently to analyze the lid cavity problem [21,10]. Although other conformation kernels are possible [22,9], these seem to be the most accurate.The FV is, at present, the method of reference in CFD (included commercial codes).…”

mentioning

confidence: 99%

An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of weakly viscoelastic droplets

López-Herrera

Popinet

Castrejón‐Pita

2019

Journal of Non-Newtonian Fluid Mechanics

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We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal & Kupferman [1,2] combined with the time-split scheme proposed by Hao & Pan [3]. The use of this time-split scheme has been proven to increase the stability of the numerical computation of two-phase flows. We show that the adaptive computational technique can be used to simulate viscoelastic flows efficiently. The solver is coded using the opensource libraries provided by the Basilisk [4] platform. In particular, the method is implemented for Oldroyd-B type viscoelastic fluids and related models (FENE-P and FENE-CR). The numerical scheme is then used to study the splashing of weakly viscoelastic drops. The solvers and tests of this work are freely available on the Basilisk [4] web site [5]. arXiv:1807.00103v1 [physics.flu-dyn] 30 Jun 2018as the Smoothed-Particle-Hydrodynamics (SPH) method, can also be found in the literature on computational rheology [11,12].The Finite-Element method applied to viscoelastic flows goes back to the pioneering work of [13,14,15]. Successful implementations of viscoelastic fluids using FE have recently been conducted [16,17] and is the basis of commercial codes as Polyflow R . The FE implementation of the log conformation schemes done by Hulsen et al. [18] follows right after the original scheme is published. the FE implementation of the log conform performed by Hao & Pan [3] is particularly relevant for the present work since we use the time-split scheme proposed in that work.Most of the numerical simulations loose convergence and destabilize when the relaxation parameter, or its dimensionless counterpart, the Weissenberg number, is increased above a threshold value. This behaviour, known as the High-Weissenberg number problem (HWNP), has been a severe hindrance for computational rheology. Fortunately, a major relief of the HWNP problem has been provided by Fattal & Kupferman [1,2]. These authors proposed formulating the equations in terms of the logarithm of the conformation tensor. Interestingly, this log-conformation (kernel) formulation guarantees the positive definiteness of the conformation tensor during the entire simulation. The success of this kernel method has been immediate, and is substituting, in practice, the classic approach in computational rheology. The log conformation kernel has been implemented within the FD method [1,2], the FE method [18,3] and the FV method [19]. In the same spirit [20] proposed using the square root of the conformation tensor to preserve the positive definiteness. Although less extended than the log conformation kernel, the square root conformation kernel has been used recently to analyze the lid cavity problem [21,10]. Although other conformation kernels are possible [22,9], these seem to be the most accurate.The FV is, at present, the method of reference in CFD (included commercial codes). Several reasons support its popularity. Remarkably, the metho...

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Analytical and numerical solutions of the unsteady 2D flow of MHD fractional Maxwell fluid induced by variable pressure gradient

Zhang

Zhao

Liu

et al. 2018

Computers & Mathematics with Applications

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Numerical study of driven flows of shear thinning viscoelastic fluids in rectangular cavities

Cited by 17 publications

References 65 publications

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of weakly viscoelastic droplets

Analytical and numerical solutions of the unsteady 2D flow of MHD fractional Maxwell fluid induced by variable pressure gradient

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