Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks

Scenario of appearance and development of instability in problem of a flow around a solidÂ sphere at rest is discussed. The scenario was created by solutions to the multimomentÂ hydrodynamics equations, which were applied to investigate the unstable phenomena. TheseÂ solutions allow interpreting Stokes flow, periodic pulsations of the recirculating zone in the wakeÂ behind the sphere, the phenomenon of vortex shedding observed experimentally. In accordanceÂ with the scenario, system loses its stability when entropy outflow through surface confining theÂ system cannot be compensated by entropy produced within the system. The system does not findÂ a new stable position after losing its stability, that is, the system remains further unstable. AsÂ Reynolds number grows, one unstable flow regime is replaced by another. The replacement isÂ governed tendency of the system to discover fastest path to depart from the state of statisticalÂ equilibrium. This striving, however, does not lead the system to disintegration. Periodically,Â reverse solutions to the multimoment hydrodynamics equations change the nature of evolutionÂ and guide the unstable system in a highly unlikely direction. In case of unstable system, unlikelyÂ path meets the direction of approaching the state of statistical equilibrium. Such behavior of theÂ system contradicts the scenario created by solutions to the classic hydrodynamics equations.Â Unstable solutions to the classic hydrodynamics equations are not fairly prolonged along time toÂ interpret experiment. Stable solutions satisfactorily reproduce all observed stable medium states.Â As Reynolds number grows one stable solution is replaced by another. They are, however,Â incapable of reproducing any of unstable regimes recorded experimentally. In particular, stableÂ solutions to the classic hydrodynamics equations cannot put anything in correspondence to anyÂ of observed vortex shedding modes. In accordance with our interpretation, the reason for this isthe classic hydrodynamics equations themselves.

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Adaptive Navier Stokes Flow Solver for Aerospace Structures

10.21236/ada424479 ◽

2004 ◽

Author(s):

R. P. Selvam ◽

Zu-Qing Qu

Keyword(s):

Stokes Flow ◽

Navier Stokes ◽

Aerospace Structures ◽

Flow Solver

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Interactions Between Aggregated Particles in Stokes Flow

10.1063/1.2964847 ◽

2008 ◽

Author(s):

J. Anushi Weliwita ◽

Helen J. Wilson ◽

Robert H. Davis ◽

Albert Co ◽

Gary L. Leal ◽

...

Keyword(s):

Stokes Flow

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Melt Modification and Microstructure Homogeneity of Solidified TiC-TiB2 Composites Prepared by Combustion Synthesis in Ultrahigh Gravity Field

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.833.125 ◽

2013 ◽

Vol 833 ◽

pp. 125-129

Author(s):

Hao Zhang ◽

Zhong Min Zhao ◽

Long Zhang ◽

Shuan Jie Wang

Keyword(s):

Gravity Field ◽

Combustion Synthesis ◽

Stokes Flow ◽

High Energy ◽

Adiabatic Temperature ◽

Full Density ◽

Reactive System ◽

Refined Microstructure ◽

Ultrafine Grained ◽

Ultrafine Grained Microstructure

By introducing (CrO3+Al) high-energy thermit into (Ti+B4C) system and designing adiabatic temperature of reactive system as 3000°C,3200°C, 3400°C, 3600°C and 3800°C respectively, a series of solidified TiC-TiB2were prepared by combustion synthesis in ultrahigh gravity field with the acceleration 2000 g. XRD, FESEM and EDS results showed that the solidified TiCTiB2were composed of a number of TiB2primary platelets, irregular TiC secondary grains, and a few of isolated Al2O3inclusions and Cr-based alloy. Because of the enhanced Stokes flow in mixed melt with the increased adiabatic temperature, Al2O3droplets were promoted to float up and separate from TiC-TiB2-Me liquid while constitutional distribution became more and more uniform in TiC-TiB2-Me liquid, resulting in not only the sharply-reduced Al2O3inclusions in the solidified ceramic but also the refined microstructure and the improved homogeneity in the ceramic, and ultrafine-grained microstructure with a average thickness of TiB2platelets smaller than 1μm began to appear in near-full-density ceramic as the adiabatic temperature exceeded 3600°C, so the densification, fracture toughness and flexural strength of the ceramic were enhanced with the increased adiabatic temperature of the reactive system.

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Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

Journal of Fluid Mechanics ◽

10.1017/s0022112075000614 ◽

1975 ◽

Vol 67 (4) ◽

pp. 787-815 ◽

Cited By ~ 300

Author(s):

Allen T. Chwang ◽

T. Yao-Tsu Wu

Keyword(s):

Exact Solutions ◽

Stokes Flow ◽

Fundamental Solutions ◽

The Body ◽

Circular Cylinders ◽

Geometrical Parameters ◽

Flow Problems ◽

Singularity Method ◽

Wide Range ◽

Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

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