DISSOCIATED GAS FLOW IN THE BOUNDARY LAYER IN THE CASE OF A POROUS CONTOUR OF THE BODY WITHIN FLUID UDC 533.6; 536.7 (original) (raw)

Dissociated gas flow in the boundary layer in the case of a porous contour of the body within fluid

Facta universitatis-series: Mechanics, …, 2003

This paper studies the ideally dissociated gas flow in the boundary layer when the contour of the body within fluid is porous. Firstly, the momentum equation has been obtained from the corresponding starting boundary layer equations and the necessary set of porosity parameters has been introduced. Then, the boundary layer equations of the considered problem have been brought to a generalized form by means of transformations. The obtained equations have been numerically solved in a threeparametric approximation. A necessary program has been written to solve them. Based on the obtained solutions, conclusions concerning behaviour of certain boundary layer characteristics have been drawn.

Boundary layer of the dissociated gas flow over a porous wall under the conditions of equilibrium dissociation

Theoretical and Applied …, 2005

This paper studies the ideally dissociated air flow in the boundary layer when the contour of the body within the fluid is porous. By means of adequate transformations, the governing boundary layer equations of the problem are brought to a general form. The obtained equations are numerically solved in a three-parametric localized approximation. Based on the obtained solutions, very important conclusions about behaviour of certain boundary layer physical values and characteristics have been drawn.

Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development

International Journal of Heat and Mass Transfer, 1995

The momentum transfer condition that applies at the boundary between a porous medium and a homogeneous fluid is developed as a jump condition based on the non-local form of the volume averaged momentum equation, Outside the boundary region this non-local form reduces to the classic transport equations, i,e, Darcy's law and Stokes' equations, The structure of the theory is comparable to that used to develop jump conditions at phase interfaces, thus experimental measurements are required to determine the coefficient that appears in the jump condition, The development presented in this work differs from previous studies in that the jump condition is constructed to join Darcy's law with the Brinkman correction to Stokes' equations, This approach produces a jump in the stress but not in the velocity, and this has important consequences for heat transfer processes since it allows the convective transport to be continuous at the boundary between a porous medium and a homogeneous fluid,

A Homogenized Flux-Body Force Approach for Modeling Porous Wall Boundary Conditions in Compressible Viscous Flows

arXiv: Fluid Dynamics, 2019

A homogenized flux and body force approach for modeling compressible viscous flows through porous wall is described. The homogeneous model computes the flux through the porous wall as a weighted average of the flux on the wall and the flux through the pore, and takes into account the friction loss on the pore boundary as a body force term. The approach avoids the pore-level resolution mesh, therefore, allows for incorporating porosity for practical use in complex problems, like space landing parachute simulations. Moreover, the proposed model takes account of the compressibility of the flow and does not require the prescribed mass flow rate or discharge coefficient, which marks key differences from other homogenized porous models. To test the homogenized model, a series of pore-level resolved direct numerical simulations with different simple pore geometries and inflow Mach numbers are conducted. The comparisons with these simulations show that the proposed model provides accurate p...

A New Exact Solution for the Flow of a Fluid through Porous Media for a Variety of Boundary Conditions

Fluids

The viscous fluid flow past a semi-infinite porous solid, which is proportionally sheared at one boundary with the possibility of the fluid slipping according to Navier’s slip or second order slip, is considered here. Such an assumption takes into consideration several of the boundary conditions used in the literature, and is a generalization of them. Upon introducing a similarity transformation, the governing equations for the problem under consideration reduces to a system of nonlinear partial differential equations. Interestingly, we were able to obtain an exact analytical solution for the velocity, though the equation is nonlinear. The flow through the porous solid is assumed to obey the Brinkman equation, and is considered relevant to several applications.

Fluid mechanics of the interface region between two porous layers

Applied Mathematics and Computation, 2002

Flow through and over a fluid-saturated porous layer is investigated. The flow through a porous channel (which is assumed to be governed by Forchheimer equation) is terminated by a porous layer possessing a different structure (the flow through which is governed by the Brinkman equation). At the interface between the physical regions, matching conditions on the velocity and shear stress are imposed. The flow through this configuration admits solutions which are linear combinations of polynomial and exponential functions. The effect of the Reynolds number and the Darcy numbers on the interface velocity is presented in this work. Ó

On a boundary layer problem related to the gas flow in shales

Journal of Engineering Mathematics, 2013

The development of gas deposits in shales has become a significant energy resource. Despite the already active exploitation of such deposits, a mathematical model for gas flow in shales does not exist. Such a model is crucial for optimizing the technology of gas recovery. In the present article, a boundary layer problem is formulated and investigated with respect to gas recovery from porous low-permeability inclusions in shales, which are the basic source of gas. Milton Van Dyke was a great master in the field of boundary layer problems. Dedicating this work to his memory, we want to express our belief that Van Dyke's profound ideas and fundamental book Perturbation Methods in Fluid Mechanics (Parabolic Press, 1975) will live on-also in fields very far from the subjects for which they were originally invented.

On the effect of boundaries in two-phase porous flow

Nonlinearity, 2015

In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.