Complex flow

Improvements ia membrane technology, vahdation of membrane iategrity, and methods to extend filter usage should further improve the performance of membrane filters ia removal of viral particles. Methods to improve or extead filter life and iacrease flow rates by creating more complex flow patterns could possibly be the focus of the next generation of membrane filters designed to remove viral particles. 

Characterization and influence of electrohydro dynamic secondary flows on convective flows of polar gases is lacking for most simple as well as complex flow geometries. Such investigations should lead to an understanding of flow control, manipulation of separating, and accurate computation of local heat-transfer coefficients in confined, complex geometries. The typical Reynolds number of the bulk flow does not exceed 5000. 

This equation is based on the approximation that the penetration is 800 at the softening point, but the approximation fails appreciably when a complex flow is present (80,81). However, the penetration index has been, and continues to be, used for the general characteristics of asphalt for example asphalts with a P/less than —2 are considered to be the pitch type, from —2 to +2, the sol type, and above +2, the gel or blown type (2). Other empirical relations that have been used to express the rheological-temperature relation are fluidity factor a Furol viscosity P, at 135°C and penetration P, at 25°C, relation of (H—P)P/100 and penetration viscosity number PVN again relating the penetration at 25°C and kinematic viscosity at 135 °C (82,83). 

Complex Flow Sheets Operating plants do not consist of single flashes, neat exchangers, distilfation towers, or reac tors. As the number of pieces of eqmpment increases within the unit under study, the reconciliation becomes more difficult. For example. Fig. 30-21 presents a more comphcated, three-module unit. 

Boyce, M.P., A Practical Three-Dimensional Flow Visualization Approach to the Complex Flow Characteristics in a Centrifugal Impeller, ASME Paper No. 66-GT-83, June 1983. 

The dispersed plug flow model has been successfully applied to describe the flow characteristics in the Kenics mixer. The complex flow behavior in the mixer is characterized by the one-parameter. The Peclet number, Np, is defined by ... 

The Schlichting finite-boundaries profile is another one that is ftequently used.- Utilization of this profile is specifically fruitful fot describing velocity distribution in complex flows, e.g., a jet in a cross-flow " and jet interaction under the right angle.In such cases, distance from the jet axis, r to the point with an air velocity V, is replaced by the parameter r, = where S, is... 

Often the inlet device (air supply) in a ventilated room is geometrically complicated. To resolve the flow around such a device would require a very fine grid. Instead of trying to resolve the complex flow near the inlet device, one can choose to use the box method or the prescribed velocity method.Both methods are based on the observation that downstream of the inlet, the flow behaves like a wall jet. Thus it is important that the bound-... 

Chen, H. C, Patel, V. C. Near-wall turbulence models for complex flows including separation, AIAA J., vol. 26, pp. 641-648, 1988. 

As discussed in Section 9.4.4, the complex flow pattern on the shell-side and the great number of variables involved make the prediction of coefficients and pressure drop very difficult, especially if leakage and bypass streams are taken into account. Until about 1960. empirical methods were used to account for the difference in the performance... 

The models of Chapter 9 contain at least one empirical parameter. This parameter is used to account for complex flow fields that are not deterministic, time-invariant, and calculable. We are specifically concerned with packed-bed reactors, turbulent-flow reactors, and static mixers (also known as motionless mixers). We begin with packed-bed reactors because they are ubiquitous within the petrochemical industry and because their mathematical treatment closely parallels that of the laminar flow reactors in Chapter 8. 

In all of the above equations, is assumed to be constant and uniform throughout the flow field. In most items of bioprocess equipment, however, there is a spatial distribution of energy dissipation. The definition of an average or a maximum energy dissipation rate is notoriously difficult in the case of bioprocess equipment such as high pressure homogenisers, centrifuges, pumps and microfiltration units which all have complex flow fields. 

Another important challenge is to enhance the reliability of the design and scale up of multi-phase reactors, such as fluidized bed reactors and bubble-colunms. The design uncertainty caused by the complex flow in these reactors has often led to the choice of a reactor configuration that is more reliable but less efficient. An example is Mobil use a packed-bed reactor for the methanol to gasoline process in New Zealand, even though a... 

Many industrial processes which employ bubble column reactors (BCRs) operate on a continuous liquid flow basis. As a result these BCR s are a substantially more complicated than stationary flow systems. The design and operation of these systems is largely proprietary and there is, indeed a strong reliance upon scale up strategies [1]. With the implementation of Computational Fluid Dynamics (CFD), the associated complex flow phenomena may be anal)rzed to obtain a more comprehensive basis for reactor analysis and optimization. This study has examined the hydrodynamic characteristics of an annular 2-phase (liquid-gas) bubble column reactor operating co-and coimter-current (with respect to the gas flow) continuous modes. 

The hypothesis that the transition to complex flow is buoyancy driven is supported by a scaling analysis to estimate the bulk density difference A q required to reverse a viscous flow. For the viscous and gravitational contributions to the flow to be comparable, one needs,... 

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