Integral Approach of Asymptotic Expansions for Low Reynolds Number Flow Past an Arbitrary Cylinder

Kida, Takuro; Take, Takanori

doi:10.1299/jsmeb1988.35.2_138

Cited by 4 publications

(2 citation statements)

References 5 publications

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“…Note that there is the possibility of the existence of other local regions arising from the nonlinear term F. For steady flow at low Reynolds number, this possibility is zero (Kida & Take 1992a), so it also may be zero for the present problem. Further, we have to note that the above discussion shows the possibility of existence of five local regions in the asymptotic analysis.…”

Section: Asymptotic Analysismentioning

confidence: 83%

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Asymptotic solutions for two-dimensional low Reynolds number flow around an impulsively started circular cylinder

1997

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The unsteady flow field of an incompressible viscous fluid around an impulsively started cylinder with slow motion is studied in detail. Integral expressions are derived from the nonlinear vorticity equation, and are solved by the method of matched asymptotic expansions. To complete the matching process five regions are necessary and their regions are essentially governed by the following relations: (i) the initial flow is unsteady Stokes flow (I), (ii) the early transient flow near the cylinder is steady Stokes flow (II), but the far-field flow is unsteady Stokes flow (III), so that Stokes&–Oseen-like matching is necessary, and (iii) as time increases the inertia terms become significant far downstream; thus the far flow is unsteady Oseen flow (IV), but the flow near the cylinder is steady Stokes flow (V), so that the matching of the Stokes–Oseen equations is necessary. The asymptotic analytical solutions are given for five flow fields around a circular cylinder. Also presented are the drag coefficient, the vorticity, and the streamline. The drag coefficient is verified quantitatively by comparing with earlier theories of the initial flow and the steady flow. The streamline patterns calculated show the generation of a circulating zone close to the circular cylinder just as for the transient flow around a sphere, and the difference between two-dimensional and three-dimensional flows is discussed.

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Section: Asymptotic Analysismentioning

confidence: 83%

“…where σ 0 =ζ, and µ 0 = ∂ζ/∂n on S. We note that the second term in square brackets in the right hand side of (76) is derived from the matching procedure between the solutions in regions (IV) and (V) (see Kida & Take 1992a). For the circular cylinder, the solutions in region (V) are given from (75) and (76) byζ…”

Section: Regions (Ii) and (Iii)mentioning

confidence: 99%

Asymptotic solutions for two-dimensional low Reynolds number flow around an impulsively started circular cylinder

1997

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Götz

2002

Journal of Engineering Mathematics

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Kinematics of a symmetrically confined cylindrical particle in a “Stokes-type” regime

Champmartin

Ambari

2007

Physics of Fluids

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To contribute to the study of the influence of the hydrodynamic interactions governing the dynamics of solid particles such as fibers in nondilute regimes, we consider in this work a cylindrical particle confined between two parallel walls at low Reynolds numbers. The particle moves with its axis always parallel to both walls. Our numerical results, derived with a projection method and a finite-volume approach, turn out to be very accurate and enable us to solve different problems using the matrix resistance technique. The first problem considers the consequences of these interactions on the settling velocity of a particle. In such confined situations, the hydrodynamic interactions are expressed by a backflow leading to a decrease of the settling velocity when the confinement increases with an asymptotical behavior varying like ε5∕2, where ε stands for the gap between the plane walls and the cylinder. The second problem consists in the accurate determination of the actual velocity of a neutrally buoyant particle transported in a Poiseuille flow, with its axis perpendicular to the mean flow. The hydrodynamic interactions lead to the existence of a relative velocity between the free particle and the flow unperturbed by the particle. This result reconsiders the assumption commonly used in some studies (same velocity for the particle and the unperturbed fluid) to analyze the transportation of fibers in the processing of composite materials (extrusion, injection molding) for concentrated regimes. In the third problem describing the transportation of a non-neutrally buoyant particle in a vertical Poiseuille flow, as in a fluidized bed, for instance, we obtain two regimes depending on the relative magnitude of the sedimentation velocity to the mean Poiseuille flow, and this suggests a potential method to separate the particles according to their density or size. On this occasion, we give the various flow patterns arising with each problem.

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Integral Approach of Asymptotic Expansions for Low Reynolds Number Flow Past an Arbitrary Cylinder

Cited by 4 publications

References 5 publications

Asymptotic solutions for two-dimensional low Reynolds number flow around an impulsively started circular cylinder

Asymptotic solutions for two-dimensional low Reynolds number flow around an impulsively started circular cylinder

Untitled

Kinematics of a symmetrically confined cylindrical particle in a “Stokes-type” regime

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