Numerical Methods for Viscoelastic Fluid Flows

Alves, M.A.; Oliveira, Paulo J.; Pinho, F.T.

doi:10.1146/annurev-fluid-010719-060107

Cited by 166 publications

(104 citation statements)

References 164 publications

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“…The hyperbolic nature of polymer conformation tensor evolution equation requires special consideration to ensure numerical convergence especially at high Wi (Alves, Oliveira & Pinho 2021). Adding a global AD term κ∇ 2 C to this equation is a common and successful practice for attaining numerical stability in inertially dominated turbulent flows (Sureshkumar, Beris & Avgousti 1995;Sureshkumar et al 1997;Li et al 2006).…”

Section: Methodsmentioning

confidence: 99%

“…The use of local or global AD in viscoelastic flow simulation has been a subject of debate for decades (Talwar, Ganpule & Khomami 1994;Alves et al 2021). Specifically, it has been shown that convergent and accurate solutions can be obtained when the convective term in the conformation tensor evolution equation is discretized using techniques appropriate for hyperbolic equations (Vaithianathan et al 2006).…”

Section: Methodsmentioning

confidence: 99%

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Direct numerical simulation of inertio-elastic turbulent Taylor–Couette flow

et al. 2021

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The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ( $Re$ ) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Direct numerical simulation of inertio-elastic turbulent Taylor–Couette flow

et al. 2021

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“…A special feature of viscoelastic flows in channels with abrupt contraction is a recirculation zone, the size of which depends on the Weissenberg/Deborah number [ 11 ] and on extensional-flow properties [ 12 ]. The comprehensive review presented in [ 13 ] summarizes key factors influencing secondary entry flows for polymer melts, while outstanding issues in numerical methods and novel and challenging applications of viscoelastic fluids are discussed in [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

The Viscoelastic Swirled Flow in the Confusor

et al. 2021

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A two-dimensional mathematical model for a steady viscoelastic laminar flow in a confusor was developed under the condition of swirled flow imposed at the inlet. Low density polyethylene was considered as a working fluid. Its behavior was described by a two-mode Giesekus model. The proposed mathematical model was tested by comparing it with some special cases presented in the literature. Additionally, we propose a system of equations to find the nonlinear parameters of the multimode Giesekus model (mobility factor) based on experimental measurement. The obtained numerical results showed that in a confusor with the contraction rate of 4:1, an increase in the swirl intensity at Wi < 5.1 affects only the circumferential velocity, while the axial and radial velocities remain constant. The distribution pattern of the first normal stress difference in the confusor is qualitatively similar to the one in a channel with abrupt contraction, i.e., as the viscoelastic fluid flows in the confusor, the value of N1 increases and reaches a maximum at the end of the confusor. Dimensionless damping coefficients of swirl are used to estimate the swirl intensity. The results show that the swirl intensity decreases exponentially.

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“…developing computational models capable of studying highly elastic flows (Afonso et al 2011;Pimenta & Alves 2017;Alves, Oliveira & Pinho 2021). Under negligible inertia (i.e.…”

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confidence: 99%

“…Both studies saw similar flow inversion behaviour as Alves et al (2008), inverting at Wi = 2 for β = 4. Alves et al (2008) and Sousa et al (2011) compared experiments against various numerical approaches, but restricted their studies to steady-state solutions at high Wi due to the numerical burden of solving 3-D transient viscoelastic flows (see the review article of Alves et al (2021)). Afonso et al (2011) were able to solve a β = 4 contraction flow in transience up to Wi = 100 in two dimensions, and in steady state up to Wi = 5000 in three dimensions, via the log conformation approach (Fattal & Kupferman 2005) using the Oldroyd-B (Oldroyd 1950) and Phan-Thien-Tanner (PTT; Thien & Tanner 1977) constitutive models.…”

mentioning

confidence: 99%