Elastic instability in crossflow of polymer solutions through periodic arrays of cylinders

Chmielewski, C.; Jayaraman, K.

doi:10.1016/0377-0257(93)87025-k

Cited by 44 publications

(24 citation statements)

References 18 publications

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“…Liu [21] found a transition from a two-dimensional flow to a three-dimensional, time-dependent asymmetric flow for closely spaced periodic array of cylinders in a channel at a critical Weissenberg number. Chmielewski and Jayaraman [12] and Khomami and Moreno [19] also observed similar instabilities for square arrays of circular cylinders by using flow visualization.…”

Section: Introductionmentioning

confidence: 72%

“…Viscoelastic flow past a periodic array of cylinders has received considerable attention and has been studied by many researchers [5,12,[16][17][18][19]21,22,[35][36][37]. For this flow we consider a circular cylinder of radius R positioned symmetrically between two parallel plates separated by a distance 2H.…”

Section: Periodic Linear Array Of Confined Circular Cylindersmentioning

confidence: 99%

“…Georgiou et al [16] used both numerical and experimental simulations to study Newtonian and non-Newtonian flow obstructed by the antisymmetric positioning of an array of equally spaced cylinders in a channel. Chmielewski and Jayaraman [12] experimentally studied the kinematics of viscous and viscoelastic fluid flows through square and hexagonal arrays of circular cylinders with a porosity of 70%. Khomami and Moreno [19] studied low Reynolds number flow of Newtonian and viscoelastic Boger fluids past a periodic square array of cylinders with a porosity of 0.45 and 0.86.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 72%

Section: Periodic Linear Array Of Confined Circular Cylindersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Although this method managed to provide accurate results without increasing the computational domain [8,20,42], it experiences some diculties in handling ow with recirculation, especially when inertia is present. Recirculation regions were predicted only for large amplitude modulation and creeping ow [3].…”

Section: Introductionmentioning

confidence: 95%

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

Abu-Ramadan

Khayat

2005

Numerical Methods in Fluids

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SUMMARYThe ow inside a spatially modulated channel is examined for viscoelastic uids of the Oldroyd-B type. The lower wall is at and the upper wall is sinusoidally modulated. The modulation amplitude is assumed to be small. Thus, a regular perturbation expansion of the ow ÿeld coupled to a variable-step ÿnite-di erence scheme is used to solve the problem. Convergence and accuracy assessment against earlier experimental results indicate that there is a signiÿcant range of validity of the perturbation approach. The in uences of wall geometry, inertia and viscoelasticity on the ow kinematics and stresses are investigated systematically. In particular, the interplay between the ow and uid parameters e ects on the conditions for the onset of back ow, number of vortices, their size and location is revealed. The distance between the ow separation and reattachment locations identiÿes the vortex size. Nonmonotonic dependence of the vortex size on elasticity is reported. The critical conditions for the onset of negative elasticity e ects on vortex size are identiÿed. The critical Reynolds number for the onset of back ow initially decreases then levels o or even increases as elasticity increases. For highly elastic uid and large enough Reynolds number, more than one vortex appear near the lower wall.

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“…Usually packed beds and rock cores are used as a tool to study the pressure drop and flow characteristics of viscoelastic fluids [2][3][4]. Undulating channels, channels with obstacles, and microfluidic devices have been used to study the flow of polymeric fluid in a controlled and simplified manner [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic flow simulations in model porous media

Kuipers

Peters

et al. 2017

Phys. Rev. Fluids

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We investigate the flow of unsteadfy three-dimensional viscoelastic fluid through an array of symmetric and asymmetric sets of cylinders constituting a model porous medium. The simulations are performed using a finite-volume methodology with a staggered grid. The solid-fluid interfaces of the porous structure are modeled using a second-order immersed boundary method [S. De et al., J. Non-Newtonian Fluid Mech. 232, 67 (2016)]. A finitely extensible nonlinear elastic constitutive model with Peterlin closure is used to model the viscoelastic part. By means of periodic boundary conditions, we model the flow behavior for a Newtonian as well as a viscoelastic fluid through successive contractions and expansions. We observe the presence of counterrotating vortices in the dead ends of our geometry. The simulations provide detailed insight into how flow structure, viscoelastic stresses, and viscoelastic work change with increasing Deborah number De. We observe completely different flow structures and different distributions of the viscoelastic work at high De in the symmetric and asymmetric configurations, even though they have the exact same porosity. Moreover, we find that even for the symmetric contraction-expansion flow, most energy dissipation is occurring in shear-dominated regions of the flow domain, not in extensional-flow-dominated regions.

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Elastic instability in crossflow of polymer solutions through periodic arrays of cylinders

Cited by 44 publications

References 18 publications

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

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

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

Viscoelastic flow simulations in model porous media

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