On the interplay between inertial and viscoelastic effects for the flow in weakly modulated channels

Abu-Ramadan, Ehab; Khayat, Roger E.

doi:10.1002/fld.1092

Cited by 3 publications

(2 citation statements)

References 48 publications

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“…The separation vortex has been observed in numerical simulations and experiments of both Newtonian and non-Newtonian fluid flows in wavy-walled channels [20,41]. The results we have obtained are consistent with those of the earlier studies in the point that both the convective and elastic terms influence on the flow pattern formation [47].…”

Section: Discussion and Concluding Remarkssupporting

confidence: 90%

Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows

Yatou

2010

Phys. Rev. E

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We numerically find three types of steady solutions of viscoelastic flows and flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Weissenberg (Wi) and Reynolds (Re) numbers using a spectral element method. The solutions are called "convective," "transition," and "elastic" in ascending order of Wi. In the convective region in the Wi-Re parameter space, convective effect and pressure gradient balance on average. As Wi increases, elastic effect becomes comparable, and the first transition sets in. Through the transition, a separation vortex disappears, and a jet flow induced close to the wall by the viscoelasticity moves into the bulk; the viscous drag significantly drops, and the elastic wall friction rises sharply. This transition is caused by an elastic force in the streamwise direction due to the competition of the convective and elastic effects. In the transition region, the convective and elastic effects balance. When the elastic effect becomes greater than the convective effect, the second transition occurs but it is relatively moderate. The second transition seems to be governed by the so-called Weissenberg effect. These transitions are not sensitive to driving forces. By a scaling analysis, it is shown that the stress component is proportional to the Reynolds number on the boundary of the first transition in the Wi-Re space. This scaling coincides well with the numerical result.

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Section: Discussion and Concluding Remarkssupporting

confidence: 90%

Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows

Yatou

2010

Phys. Rev. E

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“…It is observed that an increase in the wall amplitude leads to a larger vortex size and a smaller critical Reynolds number for the onset of back flow at either wall. In addition, it has been shown that the flow configuration in the converging-diverging nature of the periodically modulated channels provides an ideal setting for evaluating constitutive equations [38,40,41,[45][46][47] and for developing and testing the accuracy and efficiency of numerical methods in viscoelastic flow calculations [47][48][49]. Finite difference numerical solutions have been presented by Chiba et al [50] for the flow of dilute suspensions of rigid, high aspect-ratio fibres in Newtonian fluids flowing in an axisymmetric circular 4 to 1 contraction.…”

Section: Introductionmentioning

confidence: 97%

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

Mukhopadhyay

Usha

Tulapurkara

2008

Numerical Methods in Fluids

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SUMMARYThe particle migration effects and fluid-particle interactions occurring in the flow of highly concentrated fluid-particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse-flux model. Semi-implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration.

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Stability of vortex flow in a modulated channel

Abu-Ramadan

Khayat²

2007

Phys. Rev. E

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Linear stability analysis of a fully developed two-dimensional periodic steady flow in a spatially modulated symmetric channel is investigated numerically. Both walls are sinusoidally modulated. The modulation amplitude is assumed to be small. The base steady flow is calculated using a regular perturbation expansion of the flow field coupled to a variable-step finite-difference scheme. The disturbance flow equations are derived within the framework of Floquet theory and solved using a two-point boundary value method. The implemented procedure is simple, direct, and very efficient. The accuracy of this method is established. The influence of geometric parameters on the threshold for the onset of instability is systematically investigated. It is established that the critical Reynolds number for the onset of hydrodynamic instability decreases as the wall modulation amplitude or wave number increases. Modulated channel flow is characterized by the formation of a recirculation region or vortices beneath the modulation crest as the Reynolds number exceeds a certain critical threshold. The relation between the thresholds for the onset of instability and vortex flow is examined over a wide range of geometric parameters. Vortex flow effects on the conditions for the onset of instability are systematically investigated. The parameter regime of stable vortex flow is established. It is found that the parameter regime of stable vortex flow increases significantly with the wall modulation wave number for small wave numbers. This increase become less pronounced as the wave number is further increased.

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On the interplay between inertial and viscoelastic effects for the flow in weakly modulated channels

Cited by 3 publications

References 48 publications

Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows

Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

Stability of vortex flow in a modulated channel

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