Selective withdrawal of a three-layer viscous fluid

Two dimensional, selective withdrawal of a three-layer fluid in a rectangular tank is considered. Each fluid is viscous, weakly compressible and miscible. The lowermost, heaviest fluid flows with constant speed out through line sinks located on the base and lower side walls of the tank. The uppermos...

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Vydáno v:Journal of engineering mathematics Ročník 133; číslo 1
Hlavní autoři: West, Lachlan, Cosgrove, Jason M., Bassom, Andrew P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.04.2022
Springer Nature B.V
Témata:
Applications of Mathematics
Compressibility
Computational Mathematics and Numerical Analysis
Fluid dynamics
Fluid flow
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Theoretical and Applied Mechanics
Transition layers
Viscous fluids
Vorticity
Walls
76D50
Nonlinear
76T30
Three-layered fluids
Selective withdrawal
Viscous fluids
Spectral methods
76M22
ISSN:0022-0833, 1573-2703
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Popis
Shrnutí:Two dimensional, selective withdrawal of a three-layer fluid in a rectangular tank is considered. Each fluid is viscous, weakly compressible and miscible. The lowermost, heaviest fluid flows with constant speed out through line sinks located on the base and lower side walls of the tank. The uppermost and lightest fluid recharges the tank via line sources located along the top and on the upper side walls at a rate that matches the outward flux. If the line sinks are turned on suddenly, the interfaces between the fluids are drawn downward at different rates; this disparity arises due to the fact that the wave configurations that propagate along the two interfaces are not the same. Density and vorticity contours are presented and used to determine the time at which the middle transition layer of fluid begins to be withdrawn from the tank; at this point the rate of extraction of the most dense fluid is its greatest. Inviscid linearised interfaces are calculated which serve as checks on the early stage evolution of the full nonlinear model.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-022-10209-8