Distributed Level Hydrodynamics

The development of an hydrodynamic model involves the prediction of pressure drop, hold-up, contact areas between phases, phases ratios and residence time distributions for a given column internal. Although various predictive models are available in the open domain (see e.g. Kooijman and Taylor (2000)), the model developed by The University of Texas Separations Research Program (SRP model) (Rocha et al., 2004, 1996 Fair et al., 2000) enjoys a widespread preference within packed columns internals. Lately, the Delft model has been introduced (Fair et al, 2000) and vahdated for the case of zig-zag triangular flow channels. Note that the following descriptions are referred to a VL system. 

Holdup models are extensively reported in the open literature and validated for specific types of packing and under specific operating conditions. Generally, a holdup expression is a function of the internals geometry, flow regime and physical properties of the involved phases. 

A reliable pressure drop model should contain all the hydrodynamic interactions that occur between the liquid-gas-internal (Fair et al, 2000). Thus, the corresponding generic expression is given by, 

The interfacial area is directly related to the liquid holdup in the internal (Rocha et al, 2004). Thus, the generic correlation for the contact area between phases is. 

For a three-phase system special attention should be paid to the areas between aU phases i.e. apv, aps and ays) in particular when incomplete wetting occurs. 

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As we consider simultaneous fluid flow and heat transfer in porous media, the role of the macroscopic (Darcean) and microscopic (pore-level) velocity fields on the temperature field needs to be examined. Experiments have shown that the mere inclusion of u0 V(T) in the energy equation does not accurately account for all the hydrodynamic effects. The pore-level hydrodynamics also influence the temperature field. Inclusion of the effect of the pore-level velocity nonuniformity on the temperature distribution (called the dispersion effect and generally included as a diffusion transport) is the main focus in this section. 

DIVER METHOD- This is a modification of the hydrometer method. Variation in effective density i and hence concn, is measured by totally immersed divers. These are small glass vessels of approximately streamline shape, ballasted to be in stable equilibrium, with the axis vertical, and to have a known density slightly greater than that of the sedimentation liq. As the particles settle, the diver moves downwards in hydrodynamic equilibrium at the appropriate density level. The diver indicates the position of a weight concn equal to the density difference between the diver and the sedimentation liq. Several divers of various densities are required, since each gives only one point on the size distribution curve... 

Micromixing Models. Hydrodynamic models have intrinsic levels of micromixing. Examples include laminar flow with or without diffusion and the axial dispersion model. Predictions from such models are used directly without explicit concern for micromixing. The residence time distribution corresponding to the models could be associated with a range of micromixing, but this would be inconsistent with the physical model. 

Fitzgerald et al. (1984) measured pressure fluctuations in an atmospheric fluidized bed combustor and a quarter-scale cold model. The full set of scaling parameters was matched between the beds. The autocorrelation function of the pressure fluctuations was similar for the two beds but not within the 95% confidence levels they had anticipated. The amplitude of the autocorrelation function for the hot combustor was significantly lower than that for the cold model. Also, the experimentally determined time-scaling factor differed from the theoretical value by 24%. They suggested that the differences could be due to electrostatic effects. Particle sphericity and size distribution were not discussed failure to match these could also have influenced the hydrodynamic similarity of the two beds. Bed pressure fluctuations were measured using a single pressure point which, as discussed previously, may not accurately represent the local hydrodynamics within the bed. Similar results were... 

Remark. Instability and bistability are defined as properties of the macroscopic equation. The effect of the fluctuations is merely to make the system decide to go to one or the other macroscopically stable point. Similarly the Taylor instability and the Benard cells are consequences of the macroscopic hydrodynamic equations. ) Fluctuations merely make the choice between different, equally possible macrostates, and, in these examples, determine the location of the vortices or of the cells in space. (In practice they are often overruled by extraneous influences, such as the presence of a boundary.) Statements that fluctuations shift or destroy the bistability are obscure, because on the mesoscopic level there is no sharp separation between stable and unstable systems. Some authors call a mesostate (i.e., a probability distribution P) bistable when P has two maxima, however flat. This does not correspond to any observable fact, however, unless the maxima are well-separated peaks, which can each be related to separate macrostates, as in (1.1). 

Phytoplankton is at one of the initial levels of the trophic hierarchy of the ocean system. As field observations have shown, the World Ocean has a patchy structure formed by a combination of non-uniform spatial distributions of insolation, temperature, salinity, concentration of nutrient elements, hydrodynamic characteristics, etc. The vertical structure of phytoplankton distribution is less diverse and possesses rather universal properties. These properties are manifested by the existence of one to four vertical maxima of phytoplankton biomass. 

Subsequent work by Kruglikov and coworkers [217, 316] explored the action of levelers under well defined hydrodynamic conditions. The analogy between the diffusive flux distribution and the primary current distribution (i.e. Laplace equation) was used for calculating the leveling power. The expression for the attenuation of the amplitude of a sinusoidal profile was shown to be ... 

In practice, this local scale is considered to correspond to the size of the characterization techniques of local soil properties, let s say a small laboratory column. As such the microscopic pore scale variability is no longer explicitly modelled but encoded through effective flow and transport properties at the macroscopic level. The effective macroscopic properties contain of course the signature of the lower level microscopic variability. As such macroscopic effective moisture retention function, hydraulic conductivity or hydrodynamic dispersivity is determined by microscropic pore size distribution, connectivity and tortuosity within the macroscopic sample. 

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