Turbulence turbulent

Turbulence. Turbulence is important to achieve efficient mixing of the waste, oxygen, and heat. Effective turbulence is achieved by Hquid atomization (in Hquid injection incinerators), soHds agitation, gas velocity, physical configuration of the reactor interior (baffles, mixing chambers), and cyclonic flow (by design and location of waste and fuel burners). 

In homogeneous turbulence, turbulence properties are independent of spatial position. The kinetic energy of turbulence k is given by... 

Flow in the atmospheric boundary layer is turbulent. Turbulence may be described as a random motion superposed on the mean flow. Many aspects of turbulent dispersion are reasonably well-described by a simple model in which turbulence is viewed as a spectrum of eddies of an extended range of length and time scales (Lumley and Panofsky 1964). 

Figure 10-113. The factor 4> for two-phase turbulent-turbulent flow. Note Reference number on chart is in Fair s article. (Used by permission Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. Gulf Publishing Company. All rights reserved.)...

X(( = Correlation parameter, dimensionless (tt refers to the turbulent-turbulent flow mechanism)... 

X(( = correlation for turbulent-turbulent flow, dimensionless W = mass flow rate, lb/sec... 

X = correlating parameter, dimensionless for turbulent-turbulent flow mechanism, Eigure Rf ... 

When a fluid flowing with a uniform velocity enters a pipe, a boundary layer forms at the walls and gradually thickens with distance from the entry point. Since the fluid in the boundary layer is retarded and the total flow remains constant, the fluid in the central stream is accelerated. At a certain distance from the inlet, the boundary layers, which have formed in contact with the walls, join at the axis of the pipe, and, from that point onwards, occupy the whole cross-section and consequently remain of a constant thickness. Fulty developed flow then exists. If the boundary layers are still streamline when fully developed flow commences, the flow in the pipe remains streamline. On the other hand, if the boundary layers are already turbulent, turbulent flow will persist, as shown in Figure 11.8. 

An iterative procedure to calculate the pressure drop was suggested by Cheremisinoff and Davis (1979) for turbulent/turbulent stratified flow ... 

Cheremisinoff, N. P, and E. J. Davis, 1979, Stratified Turbulent-Turbulent Gas-Liquid Flow, AIChE J. 25 48-56. (3)... 

In general, only turbulent-turbulent flows are of pragmatic interest. The basic Regime I mass balances for the steady state turbulent-turbulent case are... 

Most examples of flow in nature and many in industry are turbulent. Turbulence is an instability phenomenon caused, in most cases, by the shearing of the fluid. Turbulent flow is characterized by rapid, chaotic fluctuations of all properties including the velocity and pressure. This chaotic motion is often described as being made up of eddies but it is important to appreciate that eddies do not have a purely circular motion. 

Lumley, J. L., ed. 1990. Whither turbulence Turbulence at the crossroads. Lecture notes in physics. Vol. 357. New York, NY Springer-Verlag. 

In summary, the calculation of pressure drops by the Lockhart-Marti-nelli method appears to be reasonably useful only for the turbulent-turbulent regions. Although it can be applied to all flow patterns, accuracy of prediction will be poor for other cases. Perhaps it is best considered as a partial correlation which requires modification in individual cases to achieve good accuracy. Certainly there seems to be no clear reason why there should be a simple general relationship between the two-phase frictional pressure-drop and fictitious single-phase drops. As already pointed out, at the same value of X in the same system, it is possible to have two different flow patterns with two-phase pressure-drops which differ by over 100%. The Loekhart-Martinelli correlation is a rather gross smoothing of the actual relationships. 

This correlation (C3) is intended to apply for turbulent-turbulent horizontal flow in pipes, and was developed to give better pressure-drop prediction for higher pressures and larger-diameter pipes. On an entirely empirical basis, the quantity APtp/aPl is given as a function of liquid volume-fraction of the feed, with a quantity >Pq pl/ l po as a parameter. For this correlation aP l is evaluated as the pressure-drop based on the total mass-flow using the liquid-phase properties. The parameter po ph/ Lpo is defined as... 

Davis (Dl) has suggested that the introduction of the Froude number into the Lockhart-Martinelli parameter. A, gives a description of gravitational and inertial forces so that this model can be applied to vertical flow. The revised parameter, X, is defined empirically for turbulent-turbulent flow as,... 

Another modification of the Lockhart-Martinelli approach has been proposed by Chisholm and Laird (C4) to account for the effect of pipe roughness. For the turbulent-turbulent region, it is suggested that the Lockhart-Martinelli correlations, which were presented graphically, can be represented by the equation... 

Currents in rivers and streams are turbulent. Turbulent mixing can be described by the Fickian laws (Eqs.18-6 and 18-14) and by empirical turbulent diffusion coefficients Ea, where a stands for x, y, z (Chapter 22). The main source of turbulence is the friction between the water and the river bed. It can be expected that increasing roughness of the river leads to increasing turbulence, much in the same way as a large roughness causes the mean flow u to become slow (see the effect on Eq. 24-4 if the friction coefficient f increases). In fact, turbulence in rivers can be scaled by the shear velocity, u, defined in Eq. 24-5. 

Practical flotation processes, however, take place under conditions of turbulence. Turbulent flow, as opposed to laminar flow (see Section 6.1), is characterized by rapid, almost random, fluctuations in flow velocity. Turbulence helps keep the solid particles suspended, helps disperse the injected air phase into bubbles, and helps induce particle-bubble collisions and attachments. With regard to the role of turbulence in mineral flotation, a rule of thumb for suspension stability is the one-second criterion which states that the particles in a suspension are sufficiently well dispersed for flotation if individual particles do not remain settled at the bottom of the flotation vessel for longer than one second [53]. 

Diffusion combustion of small samples (<0.2-0.3 m) is mostly laminar, but as the combustion zone and, correspondingly, the flame height, increase the flame may become turbulent. Turbulent convective heat transfer is essential in the case of such flames. And finally, in medium and large-sized samples (>0.2-0.3 m) radiation is the prevailing heat transfer mechanism... 

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