Exact and approximate analytical solutions for unsteady fully developed turbulent flow in porous media and fractures for time dependent boundary conditions

The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier–-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.

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Solidification With a Throughflow in a Porous Medium

Journal of Heat Transfer ◽

10.1115/1.2911333 ◽

1992 ◽

Vol 114 (3) ◽

pp. 675-680

Author(s):

T. Banerjee ◽

C. Chang ◽

W. Wu ◽

U. Narusawa

Keyword(s):

Porous Medium ◽

Porous Media ◽

Analytical Solutions ◽

Peclet Number ◽

Flow In Porous Media ◽

Circular Pipe ◽

Parallel Plates ◽

Péclet Number ◽

Solid Interface

A steady throughflow in a porous medium is studied in the presence of a solidified layer due to cooling of the walls. Under the assumption of a moderately sloped melt-solid interface, analytical solutions are obtained for both a flow between parallel plates and a circular pipe. Differences and similarities are examined between the Darcian and the Brinkman porous media, as well as the effects of various parameters, such as the Peclet number, the ratio of diffusivities in the longitudinal and the lateral directions, and a parameter indicating the degree of wall cooling and flow heating, on thermofluid structure of a flow in porous media accompanied by solidification.

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Visualization of the Transition To Turbulent Flow In Porous Media

Journal of Canadian Petroleum Technology ◽

10.2118/76-02-10 ◽

1976 ◽

Vol 15 (02) ◽

Cited By ~ 3

Author(s):

J.D. McFarland ◽

P.M. Dranchuk

Keyword(s):

Porous Media ◽

Turbulent Flow ◽

Flow In Porous Media

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HYSTERESIS AND VORTICES DYNAMICS IN A TURBULENT FLOW

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409024414 ◽

2009 ◽

Vol 19 (08) ◽

pp. 2695-2703 ◽

Cited By ~ 8

Author(s):

JAVIER BURGUETE ◽

ALBERTO DE LA TORRE

Keyword(s):

Turbulent Flow ◽

Additive Noise ◽

Potential Model ◽

Time Dependent ◽

Small Range ◽

Mean Velocity ◽

Fully Developed Turbulent Flow ◽

Bistable Regime ◽

The Mean

Recent results about the slow dynamics present in a fully developed turbulent flow are reported. In a previous paper [de la Torre & Burguete, 2007] we showed that the mean velocity field in a turbulent flow bifurcates subcritically breaking some symmetries of the problem and becomes time-dependent because of equatorial vortices moving with a precession movement. This subcriticality produces a bistable regime, whose main characteristics were successfully reproduced using a three-well potential model with additive noise. In this paper we present the characterization of the hysteresis region, not previously observed, in this bifurcation. This hysteresis appears only for an extremely small range of parameters.

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