Stability for boundary layers formed by salt water flow in a porous medium ( figuren)
Gert-Jan Pieters

Plaats van afstuderen:
TU Delft en CWI

Start van afstuderen: februari 2000 De afstudeeropdracht is in september 2000 afgerond met het schrijven van het afstudeerverslag. Huidige adresgegevens etc. zijn te vinden op onze alumnipagina.

Korte omschrijving van de afstudeeropdracht:
Upflowing salty groundwater, evaporating completely at the ground surface, leads to the buildup of a saline boundary layer, usually with solid salt on the surface. The diffusion layer below the surface, if stable, may grow to a finite thickness at equilibrium between the upflowing salt and downward diffusion. Because of the different densities of the fluids (low fresh water density in the deeper underground and high salt water density at the boundary layer), gravitation plays a crucial role in the process and therefore it cannot be neglected. For the instable case, at a critical Rayleigh number, perturbation of the system results in fresh-salt fingering of the boundary layer. The process described above is mathematically modelled using a scaled, coupled and non-linear set of partial differential equations for the incompressible fluid including a convection-diffusion equation and Darcy's law. In this report we first give an overview of semi-analytical methods to analyse the stability of the boundary layer. Subsequently we focus on Finite Element (FEM) solutions of the governing equations to validate numerically the semi-analytical stability bounds. Furthermore, we analyse stability with respect to several kinds of perturbations.

References
C.J. van Duijn, R.A. Wooding and A. van der Ploeg.
Stability criteria for the boundary layer formed by throughflow at a horizontal surface of a porous medium.> submitted to Water Resources, 1999.

Guus Segal. SEPRAN manuals. Leidschendam, 1984.

Hieronder staan een aantal figuren uit het afstudeerverslag.

Transport of water to the surface, accumulation of salts and evaporation of water at the surface.

Saturation profiles

Unstable situation (Ra = 75). The diffusion layer at the subsurface is perturbed with a small perturbation (5E-4). Now we have a full deformation of the layer and fresh-salt fingering occur.

Unstable situation (Ra = 50). The diffusion layer at the subsurface is perturbed with a sinusoidal perturbation (alpha = 0.5) with small amplitude (5E-4). Again we have a full deformation of the layer and fresh-salt fingering occur.