Turbulent phenomena

Fluid flow usually affects many phenomena that occur in chemical equipment. Keeping in mind that almost all the operations in chemical equipment are performed in a turbulent flow field and few operations are performed in a laminar flow field, knowledge on the structure of a turbulent flow field is very important for a discussion regarding the phenomena in the chemical equipment. 

Turbulent fluid motion is defined as follows An irregular flow condition in which various quantities such as velocity and temperature show a random variation with space and time coordinates, and a statistically distinct value is discerned. Experiments have yielded most of the knowledge on turbulent flows. 

Turbulence is classified into two groups based on the cause of occurrence  

Additionally, the ideal turbulence for investigation is classified into three groups  

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J. T. Davies, Turbulence Phenomena, Academic Press, New York, 1972. 

In laminar flow,/is independent of /D. In turbulent flow, the friction factor for rough pipe follows the smooth tube curve for a range of Reynolds numbers (hydrauhcaUy smooth flow). For greater Reynolds numbers,/deviates from the smooth pipe cui ve, eventually becoming independent of Re. This region, often called complete turbulence, is frequently encountered in commercial pipe flows. The Reynolds number above which / becomes essentially independent of Re is (Davies, Turbulence Phenomena, Academic, New York, 1972, p. 37) 20[3.2-2.46ln( /D) ... 

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

A turbulent free jet is normally considered to consist of four flow regions (Tuve, Heat. Piping Air Cond., 25(1), 181-191 [1953] Davies, Turbulence Phenomena, Academic, New York, 1972) as shown in Fig. 6-17 ... 

Davies (Turbulence Phenomena, Academic, New York, 1972) presents a good discussion of the spectrum of eddy lengths for well-developed isotropic turbulence. The smallest eddies, usually called Kolmogorov eddies (Kolmogorov, Compt. Rend. Acad. Sci. URSS, 30, 301 32, 16 [1941]), have a characteristic velocity fluctuation given by... 

Nevertheless, despite all these remarkable achievements, some open questions still remain. Among them is the influence of the molecular transport properties, in particular Lewis number effects, on the structure of turbulent premixed flames. Additional work is also needed to quantify the flame-generated turbulence phenomena and its relationship with the Darrieus-Landau instability. Another question is what are exactly the conditions for turbulent scalar transport to occur in a coimter-gradient mode Finally, is it realistic to expect that a turbulent premixed flame reaches an asymptotic steady-state of propagation, and if so, is it possible, in the future, to devise an experiment demonstrating it ... 

Bird RB, Stewart WE, Lightfoot EN (1960) Transport Phenomena, WUey Davies JT (1972) Turbulence Phenomena, Academic Press, New York, international edition, John WUey and Sons, Singapore... 

Even though the Reynolds number gives some measure of turbulent phenomena, flow quantities characteristic of turbulence itself are of more direct relevance to modeling turbulent reacting systems. The turbulent kinetic energy q may be assigned a representative value <7o at a suitable reference point. The relative intensity of the turbulence is then characterized by either q()KH2 U2) or (77(7, where (/ = (2q0)m is a representative root-mean-square velocity fluctuation. Weak turbulence corresponds to U /U < 1 and intense turbulence has (77(7 of the order unity. 

What is turbulent flow We will use the simple illustration of a free-surface flow given in Figure 5.1 to describe the essential points of the turbulence phenomena. Turbulent open-channel flow can be described with a temporal mean velocity profile that reaches a steady value with turbulent eddies superimposed on it. These turbulent eddies are continually moving about in three dimensions, restricted only by the boundaries of the flow, such that they are eliminated from the temporal mean velocity profile, u in Figure 5.1. It is this temporal mean velocity profile that is normally sketched in turbulent flows. 

When the expression of E k) in an equipment is the same as that in another equipment, it can be said that the structure of the turbulent flow fields in both equipment is identical. Anyway, turbulent phenomena can be expressed as probability terms. In other words, a discussion of the structure of turbulence in a chemical equipment is possible by making use of information entropy. 

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