Projects / Programmes
Development of the boundary-domain integral method for the investigation of transport phenomena in porous media
| Code |
Science |
Field |
Subfield |
| 2.05.05 |
Engineering sciences and technologies |
Mechanics |
Fluid mechanics |
| Code |
Science |
Field |
| P240 |
Natural sciences and mathematics |
Gases, fluid dynamics, plasmas |
boundary-domain integral method, porous media, natural convection, Newtonian and non-Newtonian fluids, turbulence
Researchers (1)
| no. |
Code |
Name and surname |
Research area |
Role |
Period |
No. of publicationsNo. of publications |
| 1. |
11343 |
PhD Renata Jecl |
Hydrology |
Head |
2002 - 2004 |
219 |
Organisations (1)
Abstract
Boundary-domain integral method (BDIM) represent a further extension of the cxlassical Boundary element method and is efficiently used for solving complicated diffusion-convective problems. Fluid transport phenomena in porous media refer to the processes related to and accompanied with the transport of fluid linear momentum, its mass and heath, through the material consisting of a solid and fluid phase. Governing equations describing these phenomena are modified Navier-Stokes equations for porous media representing the basic conservation laws of mass, momentum and energy. Momentum equation used in above mentioned system could be classical Darcy law or some of its further extension including inertia, viscous shear stress, time dependent and turbulent terms. In the earlier studies, the classical Darcy law is usualy used but the experimental results have never agreed with the theoretical predictions derived from it. For this reason it was necessary to include into the system of modified Navier-Stokes equations the extended momentum equations, among which the Brinkman equation is often used. Such a system of equations is being solved by using one of various approximate numerical methods awailable which are the well-knowm finite element, finite diference and finite volume method.
The aim of the proposed research programme is in the investigation of the possible improvement in engineering solutions over those as obtained by the above mentioned classical, methods. This is expected to be accomplished by the inclusion of the extended Brinkman equation in the system of governing equations and to solve the obtained coupled system by the boundary-domain integral method. It is expected that it will be possible to prove that the Brinkman equation, satisfying the non-slip boundary conditions on solid walls that bounds the porous media, yields physically more realistic results than those obtained when only the classical Darcy law is taken into account. Also the suitability of the BDIM representing efficient alternative to various other approksimative numerical methods will be exhibited. When dealing with BDIM using the velocity-vorticity formulation, the highly non-linear set of PDE is partitioned into its kinematic (velocity) and kinetic (vorticity and temperature) computational part, then using the suitable Green functions transformed into the equivalent integral equations. The derived analytical equations will be, after being suitably discretized and written in a matrix form solved using an upgraded, originally for solutions of classical fluid dynamic problems developed, computer package BEEAS, Boundary Element Engineering Analysing System, as developed in the Laboratory for transport phenomena in solids and fluids, Faculty of mechanical Engineering, University of Maribor. By the addition of an appropriate numeric algorithm, this package will be further specifically developed, encompassing all the necessary input data, allowing the problems of fluid transport phenomena in porous media to be stated and appropriately solved.
Likewise, the aim of the proposed research is to widen the above described method to the investigations of porous media saturated with non-Newtonian fluids. In addition it is expected, that towards the final stages of the proposed research some at least specific turbulent transport phenomena in porous media will be possible to investigate in a quantitative and also qualitative details.The proposed research programme will result in a novel, an improved computational scheme to be utilized in the evolved field of modelling the transport phenomena in porous media as a special branch of the general area of engineering fluid mechanics.
