The effect of hydrodynamic dispersion on reactive flows in porous media

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.

The Optimal Design for an Internal Stiffener Plate in a Penstock Bifurcation

This paper presents the optimum design of an internal stiffener plate in a penstock bifurcation. It is assumed that the monetary cost of the structure is dependent on the amount of material used. Hence, the weight (volume) of the plate is minimized subject to an allowable stress constraint. This is accomplished by determining the shape of the moving, free boundary of the plate, while the loaded boundary remains fixed. The mathematics of the problem is based on the variational principles of elasticity, the material derivative concept of continuum mechanics, and a gradient projection method of analysis. A sensitivity analysis is performed to examine the influence of the moving boundary of the plate on the stress constraint. At the optimum design the moving boundary reaches the predefined allowable stress. The finite element analysis package ANSYS is used for the stress calculations.