Disturbance wave

Fig. 5.35a-h Flow regimes in the pipe of 25 mm at f/os = 36 m/s (a) Uis = 0.016 m/s, disturbance waves with motionless droplets (b) Uis = 0.027 m/s, disturbance waves with moving droplets (c) U s = 0.045 m/s, disturbance waves and liquid film on the upper tube part (d) Uis = 0.17 m/s, disturbance air-water waves and liquid film on the upper tube part (e) Uis = 0.016 m/s, small air-water clusters (f) Ui = 0.027 m/s, air water clusters fe) Uis = 0.045 m/s, huge air-water clusters (h) Uis = 0.17 m/s, huge air-water clusters that block the tube cross-section. Reprinted from Hetsroni et al. (2003b) with permission... 

Recoverable work disturbances and heating disturbances waves... 

Nonequilibrium state instability is similar to flow-regime transition instability. Nonequilibrium state instability is caused by transformation wave propagation along the system. This is characterized by recoverable work disturbances and heating disturbances waves. 

Taylod205 also conducted mathematical analysis of the generation of ripples by wind blowing over a viscous fluid. Using a relationship between the growth of the amplitude of disturbance waves and the surface stress, Taylor derived a criterion for the instability of waves. In Taylor s instability theory, the disintegration of a liquid sheet/film is visualized as a process in which droplets are detached from the liquid surface with a wave of optimum amplitude. The diameter of the most frequent droplets is then formulated as a function of air velocity over the liquid surface, liquid density, surface tension and viscosity, as well as air density. 

Taylor et al. (T6, T7) have reported on wave velocities in upward cocurrent gas/film flow. It was found that the wave velocity increased rapidly with increasing gas flow rate but varied little with liquid flow rate. It was found, furthermore, that the individual wave velocities were not uniformly distributed around the mean value under given flow conditions, but that certain preferred velocities appeared to exist. The reasons for such behavior are not clear at present. More recently, Nedderman and Shearer (Nla) have carried out similar studies over a wider range of gas and liquid flow rates. Although the results were similar in many respects, it seems that the wave frequencies, of the large disturbance waves in particular, are dependent on the geometry of the apparatus. These results showed that, at constant water flow rate, the wave velocity for upward cocurrent flow varied with the square root of the air velocity relative to the waves. 

Considers the motion and frequency of large disturbance waves in upward cocurrent flow of air and water films. 

Taylor et al. (T7), 1963 cocurrent gas/film flow,- and comparison with various theories. Study of large disturbance waves in upward cocurrent flow of air and water film in vertical tubes. A preferred wave velocity is reported. 

T6. Taylor, N. H., and Hewitt, G. F., The motion and frequency of large disturbance waves in annular two-phase flow of air-water systems. At. Energy Res. Estab. (Gt. Brit.) Harwell AERE-R 3952 (1962). 

Figure 2.3 Contour plots of disturbance wave number in Reynolds number- circular frequency plane...

FIGURE 15.107 TUrbulent viscosity distribution in a disturbance wave (from Jayanti and Hewitt [277], with permission from Elsevier Science). (Horizontal scale foreshortened.)... 

If we insert some absorbing and scattering object at this point, the expression above will still represent the wave provided the outgoing part (proportional to e ) is changed. Introducing the complex amplitude rji for the Z-th partial wave, the disturbed wave is now represented by ... 

An infinitely long cylindrical Newtonian liquid jet, is disturbed with a spatially harmonic surface displacement of a cosine shape R = a — Cocoskz, where k = Ina/X, and a is determined such that the volume of the jet is kept constant when the initial amplitude is changed. Therefore, a = (1 — Co/2) - The dynamics of this jet due to capillary forces was investigated for various values of initial disturbance wave number k, and initial amplitude i o> and of the jet Ohnesorge number, Oh. 

For a viscous liquid sheet, assuming to have the same pressure distribution as the inviscid liquid, the liquid velocity components can be described as u = ui + uy and vi = Vi + vy. The potential and stream functions that satisfy the continuity equations may have the following forms (p = (p y) exp ikx + (ot), =Oi(y) xp ikx + cot), and i/r = (y) exp ikx + cot). Similar analysis is completed on the gas phase. After substitution, a relation between the complex growth rate and the disturbance wave number k is obtained. Senecal et al. [20] provided the following relation for the growth rate for the sinuous mode ... 

The instability theories for the breakup of a liquid sheet are discussed in Chap. 3. In those models, the growth rate of the fastest growing disturbance wave is used to... 

The interface of PP/HDPE system can become unstable in both converging and diverging channels when the layer/ depth ratio and disturbance wave number lie in a certain region Khomami and Wilson 1995... 

When a water surface is disturbed, waves are created that radiate outward from the site. 

Now we can reproduce numerically points which have been observed for artificially disturbed waves. Let us assume that liquid properties and flow rates are known. Based on this data the similarity parameter 8 could be calculated. Then from the list of the dominating waves for this b value we pick up the diniensionaJ parameters of waves in acceptable physical plane. Thus numerical calculations could be exploited to obtain base points on the i)roperties of regular waves instead of physical experiments. 

The interfacial shear stress is influenced by both the interface velocity and the mixture side velocity. Moreover, the entrainment from a liquid film is associated with the onset of disturbance waves at the interface and, in general, depends on both the vapor and the liquid flow rates. In fully turbulent flow, above a film Reynolds number of 3000 the condition for the onset of entrainment depend mainly upon the vapor velocity [5]. For this reason, the fothers in Equation (2) is correlated as. 

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