van der J John Schaaf

Non-intrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series

Abstract In this paper we show that spectral analysis of non-intrusive time dependent pressure measurements in bubbling and circulating gas–solid fluidized beds permits to obtain the first estimates of bubble, gas slug, and solids cluster length scales from pressure fluctuation data. These length scales are calculated from the incoherent cross power spectra of pressure signals measured in the bubbling or circulating bed and in the plenum. Remarkable quantitative agreement with bubble diameter data is found, and equally remarkable agreement is obtained with independent estimates of gas slug lengths by others in circulating fluidized beds. These results demonstrate the possibility of greatly expanding the information that can be obtained non-intrusively from gas–solid fluidized beds.

Experimental validation of Lagrangian-Eulerian simulations of fluidized beds

Abstract The present study aims to validate two-dimensional Lagrangian–Eulerian simulations of gas–solid fluidized beds by comparing these with dedicated experimental data obtained with polystyrene Geldart type D particles of 1.545 mm size. Experimental data on pressure, voidage, and bed height fluctuations, and the power spectral density are compared with three different implementations of the Lagrangian–Eulerian model. Though qualitative trends found in the experiment are correctly reproduced by the simulations, it is found that the simulations are particularly sensitive to porosity estimation procedures used in the three different simulation strategies employed. Furthermore, the phenomenon of particle clustering predicted by the model does not conform to experimental observations; this is because the physics of the break-up of clusters is not properly captured in the Lagrangian-Eulerian model.

Boundary layer development in the flow field between a rotating and a stationary disk

This paper discusses the development of boundary layers in the flow of a Newtonian fluid between two parallel, infinite disks. One of the disks is rotating at a constant angular velocity while the other remains stationary. An analytical series approximation and a numerical solution method are used to describe the velocity profiles of the flow. Both methods rely on the commonly used similarity transformation first proposed by Von Karman [T. von Karman, ZAMM 1, 233 (1921)]10.1002/zamm.19210010401. For Reh 300, with two boundary layers near the disks and a non-viscous core in the middle. A remarkable conclusion of the current work is the coincidence of the power series’ radius of convergence, a somewhat abstract mathematical notion, with the physically tangible concept of the boundary layer thickness. The coincidence shows a small deviation of only 2% to 4%.

Influence of particles and electrolyte on gas hold-up and mass transfer in a slurry bubble column

In this paper, the influence of carbon and silica particle slurry concentration up to 20 g/l (4 vol%) on regime transition, gas hold-up, and volumetric mass transfer coefficient is studied in a 2-dimensional slurry bubble column. From high speed video image analysis, the average large bubble diameter, the frequency of occurrence of large bubbles, the gas-liquid interfacial area, and the large bubble hold-up are obtained. The liquid side mass transfer coefficient is calculated from the volumetric mass transfer coefficient and the gas-liquid interfacial area. The lyophilic silica particles are rendered lyophobic by a methylation process to study the influence of particle wettability. The influence of organic electrolyte (sodium gluconate) and the combination of electrolyte and particles is also studied. It is found that lyophilic silica, lyophobic silica, and lyophobic carbon particles at concentrations larger than 2 g/l (0.4 vol%) decrease the gas hold-up and shift the regime transition point (where the first large bubbles appear) to a lower gas velocity. The volumetric mass transfer coefficient increases with gas velocity, increases with electrolyte concentration, decreases with slurry concentration, and is higher for lyophobic particles. The liquid side mass transfer coefficient increases with gas velocity, bubble diameter, and is higher for lyophobic particles. A correlation for the mass transfer coefficient based on dimensionless numbers is proposed for the heterogeneous regime.

Lyapunov-stability of solution branches of rotating disk flow

This paper investigates the stability of solutions to the problem of viscous flow between an infinite rotating disk and an infinite stationary disk. A random perturbation, satisfying the Von Karman similarity transformation, is applied to the steady velocity profiles for four solution branches, after which the disturbance propagation is tracked as a function of time. It was found that three of the four solution branches (including the Batchelor solution) were Lyapunov-stable and the development of the Lyapunov-coefficients as a function of the Reynolds number was determined. Stewartson-type of flow was found to be unstable and developed into a flow field corresponding to the Batchelor-solution. The mechanism with which the non-viscous core in this latter type of flow acquired its angular momentum was identified as being dominated by radial convection towards the axis of rotation.