Overall Hydrodynamics—Regions

While local hydrodynamics of particle-fluid two-phase flow—phases, regimes and patterns—is concerned with its intrinsic stability, of direct engineering significance is its overall hydrodynamics, which deals with its space-dependent characteristics subject to the boundary conditions set by the retaining vessel. For the axisymmetric equipment generally employed in engineering, overall hydrodynamics is resolved into the axial and the radial 

Therefore, to realize any desired mode of operation, it is necessary to control both the local and the overall conditions. 

The three modes of operation discussed in Section V.A are identified as 

To calculate the two-regioned axial parameter profile in Mode PFC/FD, ea and e are determined as follows. 

For the one-dimensional profile now under consideration, the hydrodynamics of the top dilute region can be described by 

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Then, overall hydrodynamics of fast fluidization—region—will be discussed by extending the EMMS model to both axial and radial directions. Other two aspects of local hydrodynamics—regime and pattern—will not be involved as this book is limited to the fast fluidization regime. 

The results from the SEC investigation combined with MALLS and UV analyses clearly indicate the formation of a supramolecular complex between the laccase, the linear-dendritic copolymer and the mediator. The similarity in the elution profiles of the resolved enzyme and its complex is explained by selective flat-form sorption of [G-2]-PEG5k-[G-2] only to the carbohydrate regions surrounding the three main protein domains (/d) in the laccase macromolecule. Thus the overall hydrodynamic volume of the complex will be minimally affected and the elution volumes of the supermolecule and the individual enzyme will be rather similar, Figure 6. 

A number of points have become apparent as a result of our efforts to simulate the fluidized-bed reactor-preheater system studied by Kizer. Two of the most important are it is imperative to have good kinetic data for the reaction(s) that occur. It has been demonstrated that the interpretation of the results is profoundly affected by relatively small changes in the kinetics. The second important point is the recognition that there are regions of operation where both the reaction kinetics and the bed hydrodynamics influence the overall performance of the reactor. 

Scale-up at constant Reynolds number (proportional to ND ) has often been used in an attempt to obtain hydrodynamic similarity. However, the total power consumption in the turbulent region is proportional to N D. Therefore, if the Reynolds number is kept constant but the physiceLL dimensions of the vessel doubled, the total power input will be halved. This gives the same overall flow pattern but not equality of instcintaneous velocities and seems of improbable validity. Scale-up using constant impeller tip speed (= irDN) ensures that the velocities leaving the impellers are the same in each case and has found fairly wide acceptcince. Consteint tip speed means that power input per unit volune ( N D ) falls cis scale is increased but the total power input increases, which is more recisonable. 

In the low shear rate region, the first normal stress difference increases with the fiber content, which may be due to the hydrodynamic effect associated with fiber orientation in the flow direction. The effect of surface treatment was identical to that in the high shear rate region. The shear viscosity and the first normal stress difference as a function of shear rate for maleic anhydride modified PP (5wt.%) added composites (GF/mPP/PP compositese) are plotted in Fig. 2. Although the overall level of the both functions rj and Nj was higher than that in GF/PP composites (Fig. 1), the effect of surface treatment by lwt.% ASC on rj and NiofGF/PP composites is similar to that of GF/mPP / PP. 

The internals of the bubble column reactor may have a dramatic impact on the flow patterns of the bubbles and the liquid. Companies have not divulged details about the internals to date. Some details of the US DOE pilot plant (22.5 inch 0.57 m diameter) have been published [ 106]. In this report the dimensions of the cooling tubes, their location, and their number are provided. These cooling coils occupied about 10% of the total volume of their commercial reactors slurry volume. The gas holdup and bubble characteristics as well as their radial profiles were determined in a column that was about the size of the US DOE reactor [107-109]. Dense internals were found to increase the overall gas holdup and to alter the radial gas profile at various superficial gas velocities. The tube bundle in the column increased the liquid recirculation and eliminated the rise of bubbles in the wall region of the column. These results indicate that further studies of bubble column hydrodynamics are directed toward larger scale units equipped with heat exchange tubes. 

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