DNS and LST stability analysis of Oldroyd-B fluid in a flow between two parallel plates

Brandi, Analice Costacurta; Mendonça, Márcio; Souza, Leandro Franco de

doi:10.1016/j.jnnfm.2019.03.003

Cited by 18 publications

(15 citation statements)

References 21 publications

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“…A similar non-monotonic behaviour of with has been obtained for elasto-inertial wall mode instabilities in plane Poiseuille flow of Oldroyd-B (Sadanandan & Sureshkumar 2002; Brandi et al. 2019) and FENE-P (Zhang et al. 2013) fluids.…”

Section: Neutral Stability Curvessupporting

confidence: 69%

“…(2013) using the FENE-P model which, like the FENE-CR model, accounts for the finite extensibility of polymer chains. The recent effort of Brandi, Mendonça & Souza (2019) also explored the role of elasticity on the TS (wall) mode using the Oldroyd-B model, focusing on smaller range of (). Both linear stability analysis (using a shooting procedure) and direct numerical simulations (DNS) were used to analyse the unstable flow structures corresponding to the wall mode, and good agreement was found between the two.…”

Section: Introductionmentioning

confidence: 99%

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The centre-mode instability of viscoelastic plane Poiseuille flow

et al. 2021

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Section: Neutral Stability Curvessupporting

confidence: 69%

Section: Introductionmentioning

confidence: 99%

The centre-mode instability of viscoelastic plane Poiseuille flow

et al. 2021

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“…A fim de simplificar o problema e eliminar o tratamento da pressão na equação do momento, utiliza-se a formulação vorticidade-velocidade [2]. A vorticidade ω z , em coordenadas bidimensionais, é matematicamente definida como…”

Section: Formulação Raiz Quadrada-conformaçãounclassified

“…Este trabalho, em particular, dedica-se à investigação da estabilidade hidrodinâmica do escoamento [2], com o objetivo de prever mudanças que ocorram no regime de escoamento laminar de um fluido levando-o potencialmente ao regime turbulento. Este processo é conhecido como transição laminar-turbulenta, e ainda não é completamente estabelecido, principalmente para escoamentos não-Newtonianos.…”

Section: Introductionunclassified

Aplicação da transformação raiz quadrada-conformação na análise de estabilidade de escoamentos viscoelásticos

Carreira¹,

Brandi²,

Furlan³

et al. 2021

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Uma das dificuldades encontradas no tratamento de escoamentos viscoelásticos é o Problema do Alto Número de Weissenberg. Essa limitação consiste no surgimento de instabilidades ou na não-convergência da solução decorrentes de um colapso dos esquemas numéricos. Neste sentido, o objetivo deste trabalho é aplicar a transformação raiz quadrada como técnica estabilizadora do Problema do Alto Número de Weissenberg, a partir da decomposição do tensor conformação na simulação de um escoamento de Poiseuille para um fluido viscoelástico do tipo Giesekus. A Simulação Numérica Direta foi utilizada para investigar a estabilidade hidrodinâmica desse escoamento na transição laminar-turbulenta e comparando com escoamentos Newtonianos.

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“…This rich phenomenology can also be interpreted as an explanation of the well-known shear-thinning effect through the following sequence of comprehensive arguments. (1) The strain rate of the flow stretches the polymers in the axial direction, a phenomenon also known from earlier literature; (2) Such an extension causes contraction in the radial direction, due to the resistance to elongation exerted by restoring force between the ends of the polymer molecules; (3) This triggers a nonzero negative correlation between the x−component and r−component of the end-to-end polymer vector, resulting in an elastic shear stress (τ 12 ) to develop; (4) Since there is no strain rate at the pipe center, this correlation is zero due to the liberty of the ends of the polymers to be at random motion; (5) Due the increase of the elastic modulus with respect to r, a feature of the FENE-P model, the stretching rate with respect to r slows down, giving rise to convexity of C 11 (i.e., C 11rr < 0), which in turn causes concavity in τ 12 ; (6) The points in (3), (4) and (5) imply that the divergence of elastic shearstress, i.e, the resistive force contribution to the flow by the polymers decreases with r; (7) The driving force, i.e., the pressure gradient, which is balanced completely by the Newtonian viscous force and elastic force, is a constant; (8) Since the elastic force decrease radially, the Newtonian viscous force should increase with r; (9) Finally, this is achieved by enhancing strain rate owing to the fact that the dynamic viscosity of the solvent is a constant, thus increasing the flow rate. The last point in this sequence could be perceived as shear-thinning by introducing a variable viscosity as a factoring function together with ∇ 2 U , which balances the total dissipation.…”

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confidence: 99%

Viscoelastic laminar drag bounds in pipe flow

2020

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The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the solution. The lower friction factor for the flow of the solution when compared to the latter is tracked to an increased strain rate needed to enhance viscous dissipation. Lastly, we show analytically that the effective viscosity varies similarly to the radial diagonal component of the conformation tensor as observed numerically in turbulent flows, and give a lucid interpretation of shear-thinning through a sequence of underlying constitutive physical phenomena.Elasticity effects have long been known to affect transition to turbulence and drag in fluid flows, whether these effects are induced by fluid-structure interaction 1-3 , or by viscoelastic rheological aspects associated with non-Newtonian fluids 4-8 . For instance, the addition of low concentrations of long-chain polymers generates an astounding 80% drag reduction (DR) in turbulent regimes 9,10 , which has significant implications for practical applications. At relatively low Reynolds numbers, elasto-inertial effects sets in 11,12 , which are also observed in the instabilities of flow bounded by compliant walls 1-3 .When considering turbulent dilute polymeric solutions, the exhibited DR has been attributed to the interplay between flow turbulence and elasticity of the polymers in the near-wall region 9,10,13,14 . DR is most prominent when the time scale of the polymer elastic dynamicsknown to be dependent on the number and length of monomers making the polymer-is of the same order or higher than that of the turbulent fluid flow 15 . In addition, such fluids exhibit a maximum drag asymptote with respect to the polymer concentration 15-20 , which is suggested to be associated with elasto-inertial instability 11,12 . A phenomenon of reverse transition has even been uncovered in such flow recently 21,22 . The energy cascade is also different from that of the Newtonian counterpart 23 since some energy is rerouted to the polymer stretching dynamics, thereby reducing the formation of the smallest eddies and the associated viscous energy dissipation.However, this DR phenomenology is absent in steady laminar flows with polymers 9,16 due to absence of small time scale in the flow dynamics. Here, we show analytically that the laminar drag of a FENE-P fluid (the solution) in a cylindrical pipe exhibits a set of lower and upper bounds. Specifically, the laminar drag is lower than that of a Newtonian fluid with a viscosity matching that of the total viscosity of the solution, while being higher than that of the pure solvent. This previously una) This letter accepted by Physics of Fluids could be found after publication at https://aip.scitation.org/journal/phf reported phenomenon is due to the effective viscosity of the solution being bounded by the limits of that of two Newtonian flows: (i) the flow of pure solvent and (ii) that of a ...

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DNS and LST stability analysis of Oldroyd-B fluid in a flow between two parallel plates

Cited by 18 publications

References 21 publications

The centre-mode instability of viscoelastic plane Poiseuille flow

The centre-mode instability of viscoelastic plane Poiseuille flow

Aplicação da transformação raiz quadrada-conformação na análise de estabilidade de escoamentos viscoelásticos

Viscoelastic laminar drag bounds in pipe flow

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