An asymptotically self-similar solution of the problem of three-dimensional gas flow through a porous medium

1988 ◽  
Vol 23 (5) ◽  
pp. 792-794
Author(s):  
G. M. Chernomashentsev
Keyword(s):  
Porous Medium ◽  
Gas Flow ◽  
Three Dimensional ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Flow Through ◽  
Self Similar

scholarly journals Formation of corner waves in the wake of a partially submerged bluff body

2015 ◽  
Vol 771 ◽  
pp. 547-563 ◽  
Author(s):  
P. Martínez-Legazpi ◽  
J. Rodríguez-Rodríguez ◽  
A. Korobkin ◽  
J. C. Lasheras
Keyword(s):  
Bluff Body ◽  
Physical Mechanism ◽  
Essential Feature ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Point Of View ◽  
Similar Solution ◽  
Physical Point ◽  
Self Similar Solution ◽  
Self Similar

We study theoretically and numerically the downstream flow near the corner of a bluff body partially submerged at a deadrise depth ${\rm\Delta}h$ into a uniform stream of velocity $U$, in the presence of gravity, $g$. When the Froude number, $\mathit{Fr}=U/\sqrt{g{\rm\Delta}h}$, is large, a three-dimensional steady plunging wave, which is referred to as a corner wave, forms near the corner, developing downstream in a similar way to a two-dimensional plunging wave evolving in time. We have performed an asymptotic analysis of the flow near this corner to describe the wave’s initial evolution and to clarify the physical mechanism that leads to its formation. Using the two-dimensions-plus-time approximation, the problem reduces to one similar to dam-break flow with a wet bed in front of the dam. The analysis shows that, at leading order, the problem admits a self-similar formulation when the size of the wave is small compared with the height difference ${\rm\Delta}h$. The essential feature of the self-similar solution is the formation of a mushroom-shaped jet from which two smaller lateral jets stem. However, numerical simulations show that this self-similar solution is questionable from the physical point of view, as the two lateral jets plunge onto the free surface, leading to a self-intersecting flow. The physical mechanism leading to the formation of the mushroom-shaped structure is discussed.

scholarly journals Far Field of a Three-Dimensional Laminar Wall Jet

2021 ◽  
Vol 56 (6) ◽  
pp. 812-823
Author(s):  
I. I. But ◽  
A. M. Gailfullin ◽  
V. V. Zhvick
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Plane Surface ◽  
Three Dimensional ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar

Abstract We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

Self-similarity in coupled Brinkman/Navier–Stokes flows

2012 ◽  
Vol 699 ◽  
pp. 94-114 ◽  
Author(s):  
Ilenia Battiato
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Flexural Rigidity ◽  
Similar Solution ◽  
Navier Stokes ◽  
Self Similar Solution ◽  
Hydrodynamic Shear ◽  
Self Similar ◽  
Definition Of ◽  
Similar Solutions

AbstractIn this paper we derive self-similar solutions of flows through both a porous medium and a pure fluid. Self-similar filtration velocity and hydrodynamic shear profiles are obtained by means of asymptotic analysis in the limit of infinitely small permeability, and for both laminar and turbulent regimes over the porous medium. We show that a spatial length scale, related to the porous layer thickness, naturally emerges from the limiting process and suggests a more formal definition of thick and thin porous media. We finally specialize the analysis to porous media constituted of patterned cylindrical obstacles, which can freely deflect under the aerodynamic shear exerted by the fluid flowing through and over the forest. A self-similar solution for the bending profile of the elastic cylindrical obstacles is obtained as intermediate asymptotics, and applied to carbon nanotube (CNT) forests’ response to aerodynamic stresses. This self-similar solution is successfully used to estimate flexural rigidity of CNTs by linear fit of appropriately rescaled maximum deflection and average velocity measurements.

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