On a Powder Consolidation Problem
The problem of the consolidation of an aerated fine powder under gravity is considered. The industrial relevance of the problem is discussed and a mathematical model is introduced. The mathematical structure is that of a coupled system for three unknowns, pressure, stress, and height of the powder in the (axisymmetric) bunker containing it. The system itself consists of a parabolic PDE, an ODE, and an integral equation determining a free boundary corresponding to the height of the powder. Existence and uniqueness of a solution is established. A numerical method based on a formulation of the semidiscretized problem as an index 1 DAE is proposed and implemented. The feasibility of the approach is illustrated by computational results.
Riser hydrodynamics: Simulation using kinetic theory
Computational fluid dynamics (CFD) for fluidization is reaching maturity (Roco, 1998). It has become common practice to compare time-averaged solid velocities and concentrations to measurements of fluxes and densities. The dynamic behavior of the riser, however, has not been previously compared to experiments. This article shows that the dynamics of solids flow in the riser is in the form of clusters, but the time-averaged particle concentrations and fluxes give us the core-annular flow regime in agreement with measurements. The computed clusters, which are essentially compressible gravity waves, produce major frequencies of density oscillations in agreement with measurements. The model and the CFD code compute granular temperature distributions, agreeing qualitatively with data. For volume fraction around 3–4%, which is the average particle concentration in the riser, the computed viscosity agrees with our experimental measurements.
Nietzsche's Moral Philosophy
Expounds and criticizes the moral consequences of Nietzsche's basic concept of the will to power. This study argues that Nietzsche's doctrines on moral subjects reveal a man profoundly torn between different and conflicting impulses.