Flow phenomena

Some common time constants, relating to particular chemical engineering flow applications, are 

Various empirical equations are available for the circulation time constant, Xcirc in stirred vessels, columns, etc. Usually the value of the time constant, however, will represent a mean value, owing to the stochastic nature of flow. 

Mixing time constants, Tmix are also available based on an empirical correlation and are usually closely related to the value of Xcirc (Joshi et al., 1982). A value of Tmix = 4 Tcirc is often used for stirred vessels and a value of mix = 2 to 4 Tcirc for columns. The exact value strongly depends on the degree of mixing obtained. 

There are three important phenomena seen is polymeric liquids that make them different from simple fluids a non-Newtonian viscosity, normal stresses in shear flow, and elastic effects. All these effect are a result of the complex molecular structure of polymer macromolecules. 

Non-Newtonian Viscosity. A Newtonian fluid is one where the deviatoric stresses that occur during deformation, t, are directly proportional to the rate of deformation tensor, 7, 

To take into consideration these non-Newtonian effects, it is common to use a viscosity which is a function of the strain rate and temperature to calculate the stress tensor in eqn. (2.42) 

The temperature dependence of the polymer s viscosity is normally factored out as 

However, as mentioned in Chapter 1, a variation in temperature corresponds to a shift in the time scale. A shift commonly used for semi-crystalline polymers is the Arrhenius shift, which is written as 

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This article is intended to provide a useful first understanding of flow phenomena and techniques and to provide an entry to more precise and detailed methods where these are required. Although the main concern is the proper design and operation of plant equipment, the importance of preservation of the environment is recognized. Thus data from the fields of meteorology and oceanography are occasionally needed by the technologist (see also Flowl asurel nt Fluidization). 

The starting point for obtaining quantitative descriptions of flow phenomena is Newton s second law, which states that the vector sum of forces acting on a body equals the rate of change of momentum of the body. This force balance can be made in many different ways. It may be appHed over a body of finite size or over each infinitesimal portion of the body. It may be utilized in a coordinate system moving with the body (the so-called Lagrangian viewpoint) or in a fixed coordinate system (the Eulerian viewpoint). Described herein is derivation of the equations of motion from the Eulerian viewpoint using the Cartesian coordinate system. The equations in other coordinate systems are described in standard references (1,2). 

TurbulentPremixedFlames. Combustion processes and flow phenomena are closely coimected and the fluid mechanics of a burning mixture play an important role in forming the stmcture of the flame. Laminar combusting flows can occur only at low Reynolds numbers, defined as... 

That this is not always the case should be expected. In fact, if it was not for heterogeneous localization of some flow phenomena, it would be very diflicult to initiate secondary explosives, or to effect shock-induced chemical reactions in solids. Heterogeneous shear deformation in metals has also been invoked as an explanation for a reduction in shear strength in shock compression as compared to quasi-isentropic loading. We present here a brief discussion of some aspects of heterogeneous deformation in shock-loaded solids. 

Chemical reaction engineering is part of chemical engineering in general. It aims at controlling the chemical conversion on a technical scale and will ultimately lead to appropriate and successful reactor design. An important part is played by various factors, such as flow phenomena, mass and heat transfer, and reaction kinetics. It will be clear that in the first place it is necessary to know these factors separately. 

Boyce. M.P., Fluid Flow Phenomena in Dusty Air, (Thesis), University of Oklahoma Graduate College, 1969, p. 18. 

This example illustrates the simplified approach to film blowing. Unfortunately in practice the situation is more complex in that the film thickness is influenced by draw-down, relaxation of induced stresses/strains and melt flow phenomena such as die swell. In fact the situation is similar to that described for blow moulding (see below) and the type of analysis outlined in that section could be used to allow for the effects of die swell. However, since the most practical problems in film blowing require iterative type solutions involving melt flow characteristics, volume flow rates, swell ratios, etc the study of these is delayed until Chapter 5 where a more rigorous approach to polymer flow has been adopted. 

Flow phenomena can be divided into three main types ... 

The research and technical evaluations have provided industry tvith extremely valuable information and design procedures, including, but not limited to, two-phase flow phenomena and runaway reactions during safety/over-pressure relief. 

Hammitt, F. G., Cavitation and Multiphase Flow Phenomena. McGraw-Hill, New York (1980)... 

E. (2007) Study of scalar macro- and microstmctures in a confined jet. 5th International Symposium on Turbulence and Shear Flow Phenomena,... 

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. 

A micro reactor is a casing for performing reactions that was designed or selected to induce and exploit deliberately micro-flow phenomena, i.e. flow guidance and flow processing with characteristic dimensions much below that of conventional apparatus, typically below the sub-millimeter range. 

In general, a multitude of different phenomena of flow, heat and mass transfer occur during a liquid/liquid or gas/liquid reaction. Rather than discussing all relevant effects, which would be a tremendous task, the focus of this section is solely on flow phenomena in either single-phase aqueous systems or air/water systems. 

The flow phenomena described by the Navier-Stokes equation fall into two classes discriminated by the nature of the compressibility effects to be taken into account. For compressible flow, the Navier-Stokes equation [Eq. (1)] has to be solved in com-... 

Flow phenomena time constant 90 Flow terms... 

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