On the validity of the perturbation approach for the flow inside weakly modulated channels

Zhou, Heng; Khayat, Roger E.; Martinuzzi, Robert J.; Straatman, Anthony G.

doi:10.1002/fld.355

Cited by 21 publications

(27 citation statements)

References 18 publications

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“…If the amplitudes are large, then the same governing equations hold, but the boundary conditions are difficult to handle analytically. In that case, numerical finite differences (e.g., Zhou et al 2002) or boundary integrals (e.g., Pozrikidis 1987) may be used.…”

Section: Discussionmentioning

confidence: 99%

Darcy–Brinkman Flow Through a Corrugated Channel

Wang

2010

Transp Porous Med

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A perturbation analysis is carried out to the second order to give effective equations for Darcy-Brinkman flow through a porous channel with slightly corrugated walls. The flow is either parallel or normal to the corrugations, and the corrugations of the two walls are either in phase or half-period out of phase. The present study is based on the assumptions that the corrugations are periodic sinusoidal waves of small amplitude, and the channel is filled with a sparse porous medium so that the flow can be described by the Darcy-Brinkman model, which approaches the Darcian or Stokes flow limits for small or large permeability of the medium. The Reynolds number is also assumed to be so low that the nonlinear inertia can be ignored. The effects of the corrugations on the flow are examined, quantitatively and qualitatively, as functions of the flow direction, the phase difference, and the wavelength of the corrugations, as well as the permeability of the channel. It is found that the corrugations will have greater effects when it is nearer the Stokes' flow limit than the Darcian flow limit, and when the wavelength is shorter. For the same wavelength and phase difference, cross flow is more affected than longitudinal flow by the corrugations. Opposite effects can result from 180 • out-of-phase corrugations, depending on the flow direction, the wavelength, as well as the permeability.

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Section: Discussionmentioning

confidence: 99%

Darcy–Brinkman Flow Through a Corrugated Channel

Wang

2010

Transp Porous Med

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“…For Newtonian uid ow inside modulated channels, Zhou et al [13,14] compared the ÿrst-order perturbation results to simulations obtained using ÿnite volume approach [44]. The validity of the ÿnite-volume code itself was established by comparison with the experimental results of Nishamura et al [33,34].…”

Section: Introductionmentioning

confidence: 99%

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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“…Overall, the results from the wavywalled channel are seen to be extremely well predicted using the periodic boundary condition. A full, parametric study of wavy-walled channels conducted using a perturbation method and the boundary condition developed herein is given in Zhou et al [8].…”

Section: Validationmentioning

confidence: 99%

The prediction of spatially periodic flows using a finite‐volume model

Soukkary

Straatman

2002

Numerical Methods in Fluids

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SUMMARYA periodic boundary condition has been developed that can be used in conjunction with a speciÿed ow rate to produce accurate results in spatially periodic geometries. This condition is useful in situations where the ow rate is known, or more importantly, in cases where the pressure gradient is not known a priori, such as in countercurrent ows. Using the present condition, the ow rate is imposed at the inlet in terms of a bulk velocity, but the velocity ÿeld evolves as part of the solution. The condition is formulated to be suitable for both ÿxed and moving periodic domains. For the case of a moving domain, a correction is introduced to account for changes in the instantaneous velocity through the periodic edges. Under periodic conditions, these corrections integrate to zero over a complete (temporal) period. The new periodic condition is shown to produce accurate results for at and wavy-walled channels under both induced ow and countercurrent conditions.

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On the validity of the perturbation approach for the flow inside weakly modulated channels

Cited by 21 publications

References 18 publications

Darcy–Brinkman Flow Through a Corrugated Channel

Darcy–Brinkman Flow Through a Corrugated Channel

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

The prediction of spatially periodic flows using a finite‐volume model

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