The Convergence of Biorthogonal Series for Biharmonic and Stokes Flow Edge Problems. Part I

1977 ◽  
Vol 33 (2) ◽  
pp. 337-347 ◽  
Author(s):  
Daniel D. Joseph
Keyword(s):  
Stokes Flow ◽  
Biorthogonal Series

Stokes Flow in a Driven Sector by Two Different Methods

1980 ◽  
Vol 47 (3) ◽  
pp. 482-484 ◽  
Author(s):  
J. Sanders ◽  
V. O’Brien ◽  
D. D. Joseph
Keyword(s):  
Finite Difference ◽  
Series Expansion ◽  
Stokes Flow ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Mutual Support ◽  
Biorthogonal Series ◽  
Total Angle

A biorthogonal series expansion and a numerical finite-difference approximation are applied to the problem of steady Stokes flow in a driven sector of 10° total angle, providing mutual support of the theoretical techniques. For this problem the method of biorthogonal series is faster, cheaper, and more accurate.

Chaotic Advection by Two-Dimensional Stokes Flow in a Semicircle

2004 ◽  
Vol 31 (4) ◽  
pp. 344-357
Author(s):  
T. A. Dunaeva ◽  
A. A. Gourjii ◽  
V. V. Meleshko
Keyword(s):  
Stokes Flow ◽  
Chaotic Advection ◽  
Two Dimensional

Evolution of unstable system.

2015 ◽  
Vol 9 (3) ◽  
pp. 2487-2502 ◽  
Author(s):  
Igor V. Lebed
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Stokes Flow ◽  
Stable Solution ◽  
The State ◽  
Unstable System ◽  
Unstable Flow ◽  
Unstable Solutions ◽  
Vortex Shedding Modes ◽  
Hydrodynamics Equations

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

Interactions Between Aggregated Particles in Stokes Flow

2008 ◽  
Author(s):  
J. Anushi Weliwita ◽  
Helen J. Wilson ◽  
Robert H. Davis ◽  
Albert Co ◽  
Gary L. Leal ◽  
...  
Keyword(s):  
Stokes Flow

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

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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