| dc.contributor.author | Han, Sangyoon. | en_US |
| dc.date.accessioned | 2014-10-21T12:35:52Z | |
| dc.date.available | 2007 | |
| dc.date.issued | 2007 | en_US |
| dc.identifier.other | AAINR35794 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/54983 | |
| dc.description | Mathematical and numerical studies on the dynamics of highly unsteady non-Darcy flow through porous media were performed under the constraints implied by a relatively simple hypothetical experiment, i.e. the sudden introduction of a fixed head at the upstream end of a conduit filled with a saturated porous medium. A wide range of possible equilibrium pore Reynolds numbers was considered admissible. Theoretical developments then proceeded on the basis of the momentum and continuity equations. It was found that the functional dependence of the dimensional parameter was not unique, and dimensional analysis was used to reduce the complexity of the problem. Dimensionless forms of the momentum and continuity equations were obtained and seven dimensionless groups resulted. These groups gave direct indication of the relative significance or contribution of each effect, whether viscosity, inertia, local acceleration, convective acceleration or elevation. | en_US |
| dc.description | The behaviour of the momentum-continuity model, and of sub-models having different degrees of sophistication was then compared, under different applied hydraulic gradients. The Darcy model, the Ergun-type model, the local-acceleration-included model, and the complete model showed only small differences in dimensionless head patterns for flow regimes from laminar to completely turbulent. However, the differences in dimensionless velocity for these models were not always small. The solutions obtained using various numerical methods, including the method of characteristics and certain finite-difference schemes, were also compared. | en_US |
| dc.description | Comparison of the solutions arising from the various models did not give information about the individual effects of various terms in, or components of, the momentum and continuity equations, i.e. viscosity, inertia, local acceleration, convective acceleration, and elevation. Even though the magnitudes of most1 of these components were found to be small, it was considered to be of interest to discover their relative magnitudes, whether some could be safely neglected, and any curious aspects of their behaviour across the time-space continuum implied by the physical problem. The regular perturbation method was used to answer these questions. The effects of each term were expressed in terms of head or velocity, depending on the choice of the dependent variable. | en_US |
| dc.description | Even though some of the terms in the governing partial differential equations (PDE's) were multiplied by parameter-groups that were found to have very small magnitudes, application of this perturbation method revealed that these terms could not simply be neglected, because the problem was found to depend on these small parameters in a "singular" way. Matched asymptotic expansions were then used to solve these singular problems near the upstream boundary at very small times. The resulting inner and outer expansions were developed for the laminar, partially-developed turbulent (PDT), and fully-developed turbulent (FDT) flow regimes. It was found that an inner zone existed in which highly unsteady flow induced behaviours fundamentally different from those predicted by widely-accepted PDE's. The inner expansion of the complete momentum and continuity equations gave rise to an evolving-wave equation which cannot be obtained when Darcy's Law or an Ergun-like equation replace the momentum equation. It was also found that the local acceleration component, negligibly small in the outer zone, played an important role in the inner zone, near the valve face. The extent of the inner zone in time-space varied was found to strongly depend on the applied hydraulic gradient. | en_US |
| dc.description | 1depending on the applied hydraulic gradient. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 2007. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Engineering, Civil. | en_US |
| dc.title | Dynamics of highly unsteady non-Darcy flow through confined porous media. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
