On the effects of viscoelasticity on two-dimensional vortex dynamics in the cylinder wake

Şahin, Mehmet; Owens, Robert G.

doi:10.1016/j.jnnfm.2004.08.002

Cited by 48 publications

(29 citation statements)

References 54 publications

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“…Hence, essentially the same phenomenon as described above is predicted for L 2 = 100 but being triggered at higher levels of elasticity. Since the simulations of Sahin and Owens [3] at their highest Deborah number, for increasing Reynolds number (see their Fig. 7), were effected at De = 1.2 there is no basic disagreement with the present findings, in which flow separation at the back of the cylinder is predicted to occur only at Deborah numbers above 2.5.…”

Section: Unsteady Flowcontrasting

confidence: 55%

“…Along the previous paragraphs the extensibility parameter of the FENE-CR model was fixed at the base value of L 2 = 144, as suggested by [24] on account of their experimental data, and later used by [3] in their numerical calculations. It is interesting now (following the recommendation of one referee) to assess the effect on the phenomena described above of varying L 2 , especially at that allows some clarification regarding the recently published work of Sahin and Owens [3], who have carried out careful time-dependent simulations on very fine meshes of flow around a cylinder with the same blockage ratio as here. To this purpose, we have considered an additional value of L 2 = 100, often used in connection with viscoelastic simulations with the FENE-CR model (see references in [2]).…”

Section: Unsteady Flowmentioning

confidence: 99%

“…Examples include the pitchfork transition of two-dimensional steady symmetric to two-dimensional steady asymmetric states in flows through expansions (Oliveira [1]) and the decreasing frequency of the unsteady instability of shear layers (vortex shedding, e.g. Oliveira [2], Sahin and Owens [3]). However, for low or negligible inertia, the situation is reversed.…”

Section: Introductionmentioning

confidence: 99%

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A numerical study of steady and unsteady viscoelastic flow past bounded cylinders

Oliveira

Miranda

2005

Journal of Non-Newtonian Fluid Mechanics

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We consider two-dimensional, inertia-free, flow of a constant-viscosity viscoelastic fluid obeying the FENE-CR equation past a cylinder placed symmetrically in a channel, with a blockage ratio of 0.5. Through numerical simulations we show that the flow becomes unsteady when the Deborah number (using the usual definition) is greater than De ≈ 1.3, for an extensibility parameter of the model of L 2 = 144. The transition from steady to unsteady flow is characterised by a small pulsating recirculation zone of size approximately equal to 0.15 cylinder radius attached to the downstream face of the cylinder. There is also a rise in drag coefficient, which shows a sinusoidal variation with time. The results suggest a possible triggering mechanism leading to the steady three-dimensional Gortler-type vortical structures, which have been observed in experiments of the flow of a viscoelastic fluid around cylinders. The results reveal that the reason for failure of the search for steady numerical solutions at relatively high Deborah numbers is that the two-dimensional flow separates and eventually becomes unsteady. For a lower extensibility parameter, L 2 = 100, a similar recirculation is formed given rise to a small standing eddy behind the cylinder which becomes unsteady and pulsates in time for Deborah numbers larger than De ≈ 4.0-4.5.

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Section: Unsteady Flowcontrasting

confidence: 55%

Section: Unsteady Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A numerical study of steady and unsteady viscoelastic flow past bounded cylinders

Oliveira

Miranda

2005

Journal of Non-Newtonian Fluid Mechanics

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“…These values tend to suggest that viscoelasticity plays a minor role. Note however that Sahin et al [25] found a small effect of We to a value below 0.1 for viscoelastic fluids. Fig.…”

Section: Case Of Yield Stress Fluidsmentioning

confidence: 81%

Experimental study of stationary inertial flows of a yield-stress fluid around a cylinder

Mossaz

Jay

Magnin

2012

Journal of Non-Newtonian Fluid Mechanics

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“…However, the experimental results of Liu [21] predicted a critical Weissenberg number of 1.36 with a wavenumber of 4.0 for L = 6.0R; our lower value is due to the extremely large extra stresses in the wake predicted by the Oldroyd-B model. Further numerical work is needed in order to investigate the effect of finite extensibility properties of the viscoelastic fluid to the onset of three-dimensional instabilities, similar to the two-dimensional work of Sahin and Owens [31].…”

Section: Periodic Linear Array Of Confined Circular Cylindersmentioning

confidence: 99%

A parallel adaptive unstructured finite volume method for linear stability (normal mode) analysis of viscoelastic fluid flows

Şahin

Wilson

2008

Journal of Non-Newtonian Fluid Mechanics

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A parallel unstructured finite volume method is presented for analysis of the stability of two-dimensional steady Oldroyd-B fluid flows to small amplitude three-dimensional perturbations. A semi-staggered dilation-free finite volume discretization with Newton's method is used to compute steady base flows. The linear stability problem is treated as a generalized eigenvalue problem (GEVP) in which the rightmost eigenvalue determines the stability of the base flow. The rightmost eigenvalues associated with the most dangerous eigenfunctions are computed through the use of the shift-invert Arnoldi method. To avoid fine meshing in the regions where the flow variables are changing slowly, a local mesh refinement technique is used in order to increase numerical accuracy with a lower computational cost. The CUBIT mesh generation environment has been used to refine the quadrilateral meshes locally. In order to achieve higher performance on parallel machines the algebraic systems of equations resulting from the steady problem and the GEVP have been solved by implementing the MUltifrontal Massively Parallel Solver (MUMPS). The proposed method is applied to the linear stability analysis of the flow of an Oldroyd-B fluid past a linear periodic array of circular cylinders in a channel and a linear array of circular half cylinders placed on channel walls. Two different leading eigenfunctions are identified for close and wide cylinder spacing for the periodic array of cylinders. The numerical results indicate good agreement with the numerical and experimental results available in the literature. Crown

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On the effects of viscoelasticity on two-dimensional vortex dynamics in the cylinder wake

Cited by 48 publications

References 54 publications

A numerical study of steady and unsteady viscoelastic flow past bounded cylinders

A numerical study of steady and unsteady viscoelastic flow past bounded cylinders

Experimental study of stationary inertial flows of a yield-stress fluid around a cylinder

A parallel adaptive unstructured finite volume method for linear stability (normal mode) analysis of viscoelastic fluid flows

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