Direct numerical simulation of the drag force in bubble swarms

This paper studies the swarm effect on the drag force in bubbly flows. From literature it is well-known that for relatively small bubbles, the drag force increases with the bubble hold-up due to additional hindrance experienced by the bubbles caused by the modified flow field. Very large (spherical cap) bubbles on the other hand may rise cooperatively. The unique capabilities of a 3D Front Tracking model were used to investigate the influence of important parameters like the gas fraction, Reynolds number and the bubble size independently. It was found that the relative drag force increases for bubbles in the range of 2 to 5 mm when the gas fraction is increased up to 13%, while the bubbles become more spherical. Also the influence of the Reynolds number and the bubble aspect ratio on the increased drag force has been determined. It can be concluded that there is only a very weak effect over several decades of the Reynolds number, while there is a strong effect of the bubble aspect ratio.\ud This also helps explaining why the increase in drag is smaller for larger bubbles: when the gas fraction is increased deformable bubbles become more spherical, thus reducing the drag force

Regulation of Autotrophic and Heterotrophic Metabolism in Pseudomonas oxalaticus OX1:Growth on Mixtures of Acetate and Formate in Continuous Culture

Growth of Pseudomonas oxalaticus in carbon- and energy-limited continuous cultures with mixtures of acetate and formate resulted in the simultaneous utilization of both substrates at all dilution rates tested. During growth on these mixtures, acetate repressed the synthesis of ribulosebisphosphate carboxylase. The degree of this repression was dependent on the dilution rate and on the ratio of acetate and formate in the medium reservoir. At fixed acetate and formate concentrations in the infiowing medium of 30 and 100 mM, respectively, and dilution rates above 0.10 h-1, the severe repression of autotrophic enzymes resulted in a marked increase in bacterial dry weight compared to the growth yield of the organisms on the two substrates separately. Also, at these dilution rates a significant increase in isocitrate lyase activity was observed in the cells as compared to growth on acetate alone. This indicated that under these conditions more acetate was assimilated and less dissimilated since acetate was partly replaced by formate as the energy source. When formate was added to the reservoir of an acetate-limited culture (SR = 30 mM), derepression of RuBPCase synthesis was observed at formate concentrations of 50 mM and above. Below this concentration formate only served as an energy source for acetate assimilation; when its concentration was increased above 50 mM a progressively increasing contribution of carbon dioxide fixation to the total carbon assimilation was observed as the activity of RuBPCase in the cells increased. It is concluded that in Pseudomonas oxalaticus the synthesis of enzymes involved in autotrophic carbon dioxide fixation via the Calvin cycle is regulated by a repression/derepression mechanism

Validation of the granular temperature prediction of the kinetic theory of granular flow by particle image velocimetry and discrete particle model

In order to give a detailed description of the hydrodynamics in large industrial scale fluidized beds, continuum models are required. Continuum models often use the kinetic theory of granular flow (KTGF) to provide closure equations for the internal momentum transport in the particulate phase. In this work the outcome of the continuum model is compared with both an experimental technique and detailed simulations, i.e. particle image velocimetry (PIV) and the discrete particle model (DPM).\ud PIV is used for the measurement of an instantaneous velocity field of the flow in the front plane of a fluid bed. The classical PIV analysis is extended to enable the measurement of the local velocity fluctuations in the interrogation area, i.e. the granular temperature. In the DPM, each particle is tracked individually. In this model detailed collision models can be incorporated, rendering the DPM a valuable research tool to validate the underlying assumptions in the KTGF concerning the particle-particle interactions and the particle velocity distribution functions.\ud The aforementioned experimental and numerical techniques are used to measure the granular temperature distribution around a single bubble rising in a gas-fluidized bed. It was found that the results of PIV and the DPM are very similar. Although the initial bubble shape and size are well predicted by the continuum model, it fails once the bubble has detached from the bottom plate. Further research in the area of KTGF closures is needed to improve the predictions of the TFM

Numerical investigation of the lift force acting on single air bubbles in liquids with different viscosities using a 3D Front Tracking method

No abstract

DNS of gas bubbles behaviour using an improved 3D front tracking model—Model development

In recent years CFD has proven to be a valuable and powerful tool to advance our understanding of complex multiphase flow systems arising in industrial applications. However, the predictive capabilities of this tool are determined by many factors of physical and numerical origin but in particular by the quality of the closures adopted for the description of the interface forces. The objective of this study is to improve the front tracking method in order to compute such forces with sufficient accuracy. This paper describes the further development of a 3D front tracking model to achieve improved volume conservation and circumvent problems related to the representation of surface tension. First, we have included a method to handle the pressure jump at the interface. This causes the spurious currents, observed in conventional front tracking, to decrease with two orders of magnitude. Also the advection scheme has been adapted, using higher order velocity interpolation (using cubic splines), and Runge–Kutta time-stepping, in order to prevent considerable volume changes of the dispersed phase. Test simulations involving a stationary bubble, a standard advection test and an oscillating droplet, demonstrate the effect of these improvements. The implementation of these procedures enlarged the computational window and in particular enabled the simulation of very small bubbles, where large surface forces dominate, without any significant spurious currents or volume loss

Front tracking simulations on liquid-liquid systems; an investigation of the drag force on droplets

No abstract