Turbulence flow Subject

Damage will be confined to the bubble-collapse region, usually immediately downstream of the low-pressure zone. Components exposed to high velocity or turbulent flow, such as pump impellers and valves, are subject. The suction side of pumps (Case History 12.3) and the discharge side of regulating valves (Fig. 12.6 and Case History 12.4) are frequently affected. Tube ends, tube sheets, and shell outlets in heat exchanger equipment have been affected, as have cylinder liners in diesel engines (Case History 12.1). 

Static mixers are typically less effective in turbulent flow than an open tube when the comparison is made on the basis of constant pressure drop or capital cost. Whether laminar or turbulent, design correlations are generally lacking or else are vendor-proprietary and are rarely been subject to peer review. 

In view of secondary nucleation in crystallizers, Ten Cate et al. (2004) were interested in finding out locally about the frequencies of particle collisions in a suspension under the action of the turbulence of the liquid. To this end, they performed a DNS of a particle suspension in a periodic box subject to forced turbulent-flow conditions. In their DNS, the flow field around and between the interacting and colliding particles is fully resolved, while the particles are allowed to rotate in response to the surrounding turbulent-flow field. 

In order to compare various reacting-flow models, it is necessary to present them all in the same conceptual framework. In this book, a statistical approach based on the one-point, one-time joint probability density function (PDF) has been chosen as the common theoretical framework. A similar approach can be taken to describe turbulent flows (Pope 2000). This choice was made due to the fact that nearly all CFD models currently in use for turbulent reacting flows can be expressed in terms of quantities derived from a joint PDF (e.g., low-order moments, conditional moments, conditional PDF, etc.). Ample introductory material on PDF methods is provided for readers unfamiliar with the subject area. Additional discussion on the application of PDF methods in turbulence can be found in Pope (2000). Some previous exposure to engineering statistics or elementary probability theory should suffice for understanding most of the material presented in this book. 

In order to be sure of good quality analytical data, the analyst is recommended to construct a Levich plot such as that shown in Figure 7.5 before starting a series of analyses analysts will avoid those rotation speeds represented on the graph as turbulent flow. In the jargon of the subject, the analyst may say that a laminar regime is maintained. 

Authors efforts in this part of the work have been concentrated on developing turbulence closures for the statistical description of two-phase turbulent flows. The primary emphasis is on development of models which are more rigorous, but can be more easily employed. The main subjects of the modeling are the Reynolds stresses (in both phases), the cross-correlation between the velocities of the two phases, and the turbulent fluxes of the void fraction. Transport of an incompressible fluid (the carrier gas) laden with monosize particles (the dispersed phase) is considered. The Stokes drag relation is used for phase interactions and there is no mass transfer between the two phases. The particle-particle interactions are neglected the dispersed phase viscosity and pressure do not appear in the particle momentum equation. 

In turbulent flow the eddies, which are superimposed on the over-all flow pattern, have dimensions large compared with a mean free path. Hence turbulent motion is macroscopic rather than molecular and the equations of change do apply to turbulent flow. This subject is discussed further in Sec. II,D,2. 

It is now required to obtain the spatial distribution of the concentration of the tracer for two cases—center injection and wall ring injection. In general, it is difficult to theoretically obtain the spatial distribution of the concentration of tracer, and the number of experimental results with regard to this subject is insufficient because a very long pipe is required for performing experiments. However, it is possible to estimate the distribution of the tracer concentration based on the mean velocity profile, the intensity of velocity fluctuations, and so on, during the turbulent flow in a circular pipe. 

It turns out that Eq. (5-56) can also be applied to turbulent flow over a flat plate and in a modified way to turbulent flow in a tube. It does not apply to laminar tube flow. In general, a more rigorous treatment of the governing equations is necessary when embarking on new applications of the heat-trans-fer-fluid-friction analogy, and the results do not always take the simple form of Eq. (5-56). The interested reader may consult the references at the end of the chapter for more information on this important subject. At this point, the simple analogy developed above has served to amplify ouf understanding of the physical processes in convection and to reinforce the notion that heat-transfer and viscous-transport processes are related at both the microscopic and macroscopic levels. 

For situations where the droplets are subjected for a very short time to the disruptive stress (e.g., in turbulent flow), the viscosity of the internal phase will cause the droplet to react slowly to the external stress, and the definition into has to be extended ... 

Laminar flames in turbulent flows are subjected to strain and develop curvature as consequences of the velocity fluctuations. These influences modify the internal structure of the flame and thereby affect its response to the turbulence. The resulting changes are expected to be of negligible consequence at sufficiently large values of Jb in Figure 10.5, but as turbulence scales approach laminar-flame thicknesses, they become important. Therefore, at least in part of the reaction-sheet regime, consideration of these effects is warranted. The effects of curvature were discussed in Section 9.5.2.3. Here we shall focus our attention mainly on influences of strain. 

The objective of this survey is to provide a brief but reasonably complete account of the state of the art of turbulent-flow computations, and to reflect the excitement of current debate on equation models in this field. The review has been written for readers with a basic background in turbulent transport, such as is given in a contemporary graduate course on this subject. 

An additional complication that occurs with oscillating flow is the existence of several regimes of laminar and turbulent flow that are functions of frequency as well as Reynolds number, as shown in Figure 3 for the case of smooth circular tubes [2]. These flow regimes are the subject of much research [3]. They are shown as a function of the peak Reynolds number Nr,peak and the ratio of channel radius R to the viscous penetration depth Sv This ratio is sometimes referred to as the dynamic Reynolds number and is similar to the Womersley number Wo = D 28y). In the weakly turbulent regime... 

During food engineering operations, many fluids deviate from laminar flow when subjected to high shear rates. The resulting turbulent flow gives rise to an apparent increase in viscosity as the shear rate increases in laminar flow, i.e., shear stress = viscosity x shear rate. In turbulent flow, it would appear that total shear stress = (laminar stress + turbulent stress) x shear rate. The most important part of turbulent stress is related to the eddies diffusivity of momentum. This can be recognized as the atomic-scale mechanism of energy conversion and its redistribution to the dynamics of mass transport processes, responsible for the spatial and temporal evolution of the food system. 

Because of the interaction of the two complicated and not well-understood fields, turbulent flow and non-Newtonian fluids, understanding of DR mechanism(s) is still quite limited. Cates and coworkers (for example, Refs. " ) and a number of other investigators have done theoretical studies of the dynamics of self-assemblies of worm-like micelles. Because these so-called living polymers are subject to reversible scission and recombination, their relaxation behavior differs from reptating polymer chains. An additional form of stress relaxation is provided by continuous breaking and repair of the micellar chains. Thus, stress relaxation in micellar networks occurs through a combination of reptation and breaking. For rapid scission kinetics, linear viscoelastic (Maxwell) behavior is predicted and is observed for some surfactant systems at low frequencies. In many cationic surfactant systems, however, the observed behavior in Cole-Cole plots does not fit the Maxwell model. 

The minimum circulation velocity Wcirc min for the two limiting cases of flow (turbulent, laminar) can be calculated from this balance, if it is assumed that the power number Ne is not changed by the presence of the particles and iVjs is not subject to turbulence effects. In the case of turbulent flow Cf = const, for laminar flow Cf = const/Pe, where Re = WcuqD/vsusp-... 

Willetts and Murray [171] studied the lift on spheres fixed in turbulent flows. The spheres were located both near and far from a boundary. They found that particles near a wall experienced lift away from the wall, while a sphere in a shear flow away from a wall experienced a lift towards the wall. The forces were found to be of the same magnitude as the forces in laminar flow, and they were consistent with the laminar results of Segre and Silberberg [131, 132]. Spheres that were not close to a boundary, and not subjected to a velocity gradient, experienced randomly fluctuating instantaneous lift which was strongly associated with the wake deflection. They suggested that the lift... 

The other two methods are subject to both these errors, since both the form ofi the RTD and the extent of micromixing are assumed. Their advantage is that they permit analytical solution for the conversion. In the axial-dispersion model the reactor is represented by allowing for axial diffusion in an otherwise ideal tubular-flow reactor. In this case the RTD for the actual reactor is used to calculate the best axial dififusivity for the model (Sec. 6-5), and this diffusivity is then employed to predict the conversion (Sec. 6-9). This is a good approximation for most tubular reactors with turbulent flow, since the deviations from plug-flow performance are small. In the third model the reactor is represented by a series of ideal stirred tanks of equal volume. Response data from the actual reactor are used to determine the number of tanks in series (Sec. 6-6). Then the conversion can be evaluated by the method for multiple stirred tanks in series (Sec. 6-10). 

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