Weber-Reynolds number

The Weber-Reynolds number (Re/We) is defined as the ratio of surf ace tension of a bubble to viscous shear on the bubble surface due to bubble motion ... 

Based on such analyses, the Reynolds and Weber numbers are considered the most important dimensionless groups describing the spray characteristics. The Reynolds number. Re, represents the ratio of inertial forces to viscous drag forces. 

Equations (6-236) to (6-239) are based on experiments on cube-oc tahedrons, octahedrons, cubes, and tetrahedrons for which the sphericity f ranges from 0.906 to 0.670, respectively. See also Chft, Grace, and Weber. A graph of drag coefficient vs. Reynolds number with y as a parameter may be found in Brown, et al. (Unit Operations, Whey, New York, 1950) and in Govier and Aziz. 

The first dimensionless group on the right is the Reynolds number, the second represents the ratio of the gas velocity to the impeller tip speed, the third is the Weber number, and the fourth is the Froude number. 

This is, of course, the Reynolds number, which determines the nature of the flow, as shown in Chapter 3. In similar fashion, the constancy of the ratios between other forces results in Froude and Weber numbers as follows ... 

Weber number based on superficial liquid velocity Weber number based on superficial gas velocity Reynolds number based on superficial liquids velocity Reynolds number based on superficial gas velocity... 

The effect of various parameters on the difference between vapor and liquid pressure is illustrated in Figs. 8.3 and 8.4. The effect of the Fuler and Weber numbers as well as the thermal parameter is highly noticeable. An increase in Fu, We and d- leads to a decrease in AP, whereas the difference of both phase pressures is practically independent of Reynolds number. An increase in the Froude number is accompanied by an increase in AP for a small Fr. At Fr > 10 the effect of Fr on AP is negligible. 

Fig. 14 shows the comparison of the photographs from Chandra and Avedisian (1991) with simulated images of this study for a subcooled 1.5 mm n-heptane droplet impact onto a stainless-steel surface of 200 °C. The impact velocity is 93 cm/s, which gives a Weber number of 43 and a Reynolds number of 2300. The initial temperature of the droplet is room temperature (20 °C). In Fig. 14, it can be seen that the evolution of droplet shapes are well simulated by the computation. In the first 2.5 ms of the impact (frames 1-2), the droplet spreads out right after the impact, and a disk-like shape liquid film is formed on the surface. After the droplet reaches the maximum diameter at about 2.1ms, the liquid film starts to retreat back to its center (frame 2 and 3) due to the surface-tension force induced from the periphery of the droplet. Beyond 6.0 ms, the droplet continues to recoil and forms an upward flow in the center of the... 

For scale-up from system 1 to system 2 for the same liquid properties and system geometry, equation 5.14 which defines the Reynolds number for mixing ReM, equation 5.15 which defines the Froude number for mixing FrM, and equation 5.16 which defines the Weber number for mixing WeM, can be written respectively in the following forms ... 

Some other correlations that have been specifically developed for liquid metals include those proposed by Nichiporenko)488 Schmitt)489 Thompson)491 and Date et al)494] Nichiporenkol488 correlated the diameter of particles (powder) of predominant fraction, D h with the arithmetic mean particle diameter (linear average diameter), Z)10, and the Reynolds number as well as the Weber... 

Out of these, six, viz. Weber number, Reynolds number, volume fraction X, viscosity ratios, density ratios, and length ratios were finally used for correlation. The other four were used but found not to improve the correlation. 

NFr Froude number Npr Substitution given in the text NFr Modified Froude group NRe Reynolds number Nrc Substitution given in the text Nr, Modified Reynolds number NwlCr Critical Weber number of maximum bubble size capable of survival... 

Sy et al (S8, S9) and Morrison and Stewart (M12) analyzed the initial motion of fluid spheres with creeping flow in both phases. For bubbles (y = 0, k = 0), the condition that internal and external Reynolds numbers remain small is sufficient to ensure a spherical shape. However, for other k and y, the Weber number must also be small to prevent significant distortion (S9). For k = 0, the equation governing the particle velocity may be transformed to an ordinary differential equation (Kl), to give a result corresponding to Eq. (11-16), i.e.,... 

The letters R, F, and W stand for so-called Reynolds, Froude, and Weber numbers, respectively these are dimensionless numbers, as indicated. For example, if we make the Reynolds number the same in model and prototype, using the same fluid, the dimension of length is smaller in the model and hence the velocity v will have to be greater. In other words, the water would have to flow faster in the model. If we now consider the Froude number as the same in model and prototype, and that the same fluid is used in both, we see that the velocity would have to be less in the model than in the prototype. This may be regarded as two contradictory demands on the model. Theoretically, by using a different fluid in the model (thus changing p0 and p), it is possible to eliminate the difficulty. The root of the difficulty is the fact that the numbers are derived for two entirely different kinds of flow. In a fluid system without a free surface, dynamic similarity requires only that the Reynolds number be the same in model and prototype the Froude number does not enter into the problem. If we consider the flow in an open channel, then the Froude number must be the same in model and prototype. 

Splashing can be seen to begin in droplets with Weber (We) numbers of 100-1000, and fingers have been observed in droplets that have a Reynolds (Re) number of 15000 and a We of 1000. (Re = p.u.d)/iJL and We = p.u. d)fa, where p,u,d,pt and a are the liquid density, droplet impact velocity, droplet diameter, liquid viscosity, and hquid surface tension respectively.) As the drops used in inkjet printing typically have diameters below 100 microns, values of Re = 2.5—2000, and We = 2.7-1000 can be expected. 

Although they used droplets with diameters of 2 mm and more, the work of Park et alP is interesting on account of the fact that they used four different substrates and four different hquids. They observed the impact of droplets of distilled water, n-Octane, n-Tetradecane or n-Hexadecane onto glass slides, sihcon wafers, HMDS (Hexamethyl dishazane) coated sihcon wafers or Teflon, for Reynolds numbers from 180 to 5513 and Weber numbers from 0.2 to 176. A model was constructed to predict the maximum spreading ratio, which is the ratio of the maximum spreading diameter to the initial droplet s diameter, for low impact velocities. 

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