Viscoelastic flow in a two-dimensional collapsible channel

Chakraborty, Debadi; Bajaj, Mohit; Yeo, Leslie; Friend, James; Pasquali, Matteo; Prakash, J. Ravi

doi:10.1016/j.jnnfm.2010.06.005

Cited by 15 publications

(20 citation statements)

References 35 publications

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“…where, a 1 , a 2 , a 3 , and a 4 are scalar functions of the invariants of D and T, and [22] have shown numerically that this is true even in the case of flow past a deformable zero-thickness membrane, for all the three viscoelastic fluids considered here. In the present instance as well, we find that the normal component of stress on the elastic wall is solely due to pressure.…”

Section: Pressure and Stressesmentioning

confidence: 65%

“…It is appropriate to note here that in our earlier investigation of viscoelastic flow in a 2D channel with a zero-thickness membrane [22], the fluid-solid interface was always observed to be concave downwards for all the viscoelastic fluids, at all values of membrane tension. Indeed, in contrast to the situation for a finite thickness solid, with decreasing tension, the zero-thickness membrane moves further into the channel, with a concomitant decrease in the narrowest channel gap.…”

Section: Interface Shape and Velocity Contoursmentioning

confidence: 76%

“…It has been well established that the breakdown of viscoelastic computations is typically due to the smallest eigenvalue becoming negative in some regions of the flow domain [22,34,38,47,48]. Figure 4 shows the maximum eigenvalue m 3 In their earlier study with a zero-thickness membrane, Chakraborty et al [22] have shown that the extent of collapse of the membrane also has a significant effect on the limiting Weissenberg number. As the gap in the channel becomes narrower with decreasing tension in the membrane, the fluid is 'squeezed' leading to a greater deformation of the molecules, with a concomitant numerical breakdown at smaller values of Wi.…”

Section: Mesh Convergence and The High Weissenberg Number Problemmentioning

confidence: 95%

“…Chakraborty et al [22] have established that the flow in a collapsible channel with a zero-thickness membrane suffers from the high Weissenberg number problem and have shown that there is a limiting Weissenberg number for each of the fluid models beyond which computations fail. Furthermore, this limiting Wi value M1 400 1705 10972 M2 900 3757 24072 M3 1600 6609 42252 has been shown to increase with mesh refinement.…”

Section: Mesh Convergence and The High Weissenberg Number Problemmentioning

confidence: 99%

“…In viscoelastic flow, mesh convergence is generally studied by examining the values of the invariants of the conformation dyadic, M. The eigenvalues m i of the conformation dyadic represent the square stretch ratios along the principal directions of stretching m i for an ensemble of molecules [27,34]. It has been well established that the breakdown of viscoelastic computations is typically due to the smallest eigenvalue becoming negative in some regions of the flow domain [22,34,38,47,48]. Figure 4 shows the maximum eigenvalue m 3 In their earlier study with a zero-thickness membrane, Chakraborty et al [22] have shown that the extent of collapse of the membrane also has a significant effect on the limiting Weissenberg number.…”

Section: Mesh Convergence and The High Weissenberg Number Problemmentioning

confidence: 99%

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Viscoelastic fluid flow in a 2D channel bounded above by a deformable finite-thickness elastic wall

Chakraborty

Prakash

2015

Journal of Non-Newtonian Fluid Mechanics

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The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond which computations fail to converge is found to increase with increasing dimensionless solid elasticity parameter Γ, following the trend Owens > FENE-P > Oldroyd-B. The highly shear thinning nature of Owens model leads to the elastic solid always collapsing into the channel, for the wide range of values of Γ considered here. In the case of the FENE-P and Oldroyd-B models, however, the fluid-solid interface can be either within the channel, or bulge outwards, depending on the value of Γ. This behaviour differs considerably from predictions of earlier models that treat the deformable solid as a zero-thickness membrane, in which case the membrane always lies within the channel. The capacity of the solid wall to support both pressure and shear stress, in contrast to the zero-thickness membrane that only responds to pressure, is responsible for the observed difference. Comparison of the stress and velocity fields in the channel for the three viscoelastic fluids, with the predictions for a Newtonian fluid, reveals that shear thinning rather than elasticity is the key source of the observed differences in behaviour.

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Section: Pressure and Stressesmentioning

confidence: 65%

Section: Interface Shape and Velocity Contoursmentioning

confidence: 76%

Section: Mesh Convergence and The High Weissenberg Number Problemmentioning

confidence: 95%

Section: Mesh Convergence and The High Weissenberg Number Problemmentioning

confidence: 99%

Section: Mesh Convergence and The High Weissenberg Number Problemmentioning

confidence: 99%

See 3 more Smart Citations

Viscoelastic fluid flow in a 2D channel bounded above by a deformable finite-thickness elastic wall

Chakraborty

Prakash

2015

Journal of Non-Newtonian Fluid Mechanics

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A stabilized cell‐based smoothed finite element method against severe mesh distortion in non‐Newtonian fluid–structure interaction

2022

Numerical Meth Engineering

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Failure is an inevitability for the finite element method (FEM) to be performed on seriously degenerated four-node quadrilateral (Q4) elements whose Jacobians become negative. This article proposes a stabilized selective integration formulation of the cell-based smoothed FEM (CSFEM) for modeling non-Newtonian fluid-structure interaction (NNFSI) where that acute mesh distortion arises. The Carreau-Yasuda and Oldroyd-B fluids, respectively, interact with a geometrically nonlinear solid in NNFSI. The CSFEM is applied to discretize both the fluid and solid media in space. As the fluid mesh accounts for a substantial part of the discretized NNFSI system, seriously distorted Q4 elements are specified exclusively for the fluid field. In this case, each convex Q4 element is subdivided into four smoothing cells (SCs) whereas its concave counterpart is regarded as one single SC. In the meantime, the solid elements are treated as usual. To stabilize the one-SC integral in smoothed Galerkin weak form, an hourglass control is subsequently introduced into the fluid momentum equations as well as the viscoelastic constitutive equation. The transient non-Newtonian fluid equations are advanced with dual time steps of the characteristic-based split scheme in time to further enhance the numerical stability and accuracy. After discussing other aspects of computational NNFSI, two benchmark problems are presented to demonstrate the effectiveness and performance of the developed methodology under the harsh environment.

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Creeping flow of Herschel-Bulkley fluids in collapsible channels: A numerical study

Amini

Eghtesad

Sadeghy

2016

Korea-Aust. Rheol. J.

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Viscoelastic flow in a two-dimensional collapsible channel

Cited by 15 publications

References 35 publications

Viscoelastic fluid flow in a 2D channel bounded above by a deformable finite-thickness elastic wall

Viscoelastic fluid flow in a 2D channel bounded above by a deformable finite-thickness elastic wall

A stabilized cell‐based smoothed finite element method against severe mesh distortion in non‐Newtonian fluid–structure interaction

Creeping flow of Herschel-Bulkley fluids in collapsible channels: A numerical study

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