Liquid Reynolds number

Reentrainment is generally reduced by lower inlet gas velocities. Calvert (R-12) reviewed the hterature on predicting the onset of entrainment and found that of Chien and Ibele (ASME Pap. 62-WA170) to be the most reliable. Calvert applies their correlation to a liquid Reynolds number on the wall of the cyclone, Nrcl = 4QilhjVi, where is the volumetric liquid flow rate, cmVs hj is the cyclone inlet height, cm and Vi is the Idnematic liquid viscosity, cmVs. He finds that the onset of entrainmeut occurs at a cyclone inlet gas velocity V i, m/s, in accordance with the relationship in = 6.516 — 0.2865 lu A Re,L ... 

Equation 5.2 is found to hold well for non-Newtonian shear-thinning suspensions as well, provided that the liquid flow is turbulent. However, for laminar flow of the liquid, equation 5.2 considerably overpredicts the liquid hold-up e/,. The extent of overprediction increases as the degree of shear-thinning increases and as the liquid Reynolds number becomes progressively less. A modified parameter X has therefore been defined 16 171 for a power-law fluid (Chapter 3) in such a way that it reduces to X both at the superficial velocity uL equal to the transitional velocity (m )f from streamline to turbulent flow and when the liquid exhibits Newtonian properties. The parameter X is defined by the relation... 

Figure 5.47 shows a plot of the ratio of the experimental heat transfer coefficient obtained by Bao et al. (2000) divided by the predicted values of Chen (1966) and Gungor and Winterton (1986) for heat transfer to saturated flow boiling in tubes versus liquid Reynolds number. It can be seen that both methods provide reasonable predictions for Rcls > 500, but that both overpredict the heat transfer coefficient at lower values of Rols- For comparison it was assumed that the boiling term of these correlations is zero. 

The suppression factor fs is obtained from Figure 12.57. It is a function of the liquid Reynolds number ReL and the forced-convection correction factor fc. 

Based on these data, particle-liquid Reynolds numbers were calculated to range from Re = 25 (50 rpm) to Re = 90 (150 rpm) for coarse grade particles with a median diameter of 236 pm. In contrast, Reynolds numbers for a batch of micronized powder of the same chemical entity with a median diameter of 3 pm were calculated to be significantly lower (Re < 1), indicating less sensitivity towards convective hydrodynamics [(10), Chapter 12.3.8]. Based on the aforementioned considerations for spheres, bulk Reynolds numbers of about Re > 50 appear to be sufficient to produce the laminar-turbulent transition around a rough drug particle of coarse grade dimensions. 

The diameter of drug particles and hence the surface specific length L is much smaller than the pipe diameter. For this reason, particle-liquid Reynolds numbers characterizing the flow at the particle surface are considerably lower than the corresponding bulk Reynolds numbers. Particle-liquid Reynolds numbers for particle sizes below 250 pm were calculated to be below Re 1 for flow rates up to 100 mL/min. However, this circumstance does not limit the applicability of the boundary layer concept, since in aqueous hydrodynamic... 

Reynolds numbers calculated for the in vivo hydrodynamics are considerably lower than those of the corresponding in vitro numbers, both for bulk and particle-liquid Reynolds numbers. Remarkably, bulk Reynolds numbers in vivo appear to have about the same magnitude as particle-liquid Reynolds numbers characterizing the flow at the particle surface in vitro using the paddle apparatus. In other words, it appears that hydrodynamics per se play a relatively minor role in vivo compared to the in vitro dissolution. This can be attributed to physiological co-factors that greatly affect the overall dissolution in vivo but are not important in vitro (e.g., absorption and secretion processes, change of MMC phases,... 

Perhaps the simplest classification of flow regimes is on the basis of the superficial Reynolds number of each phase. Such a Reynolds number is expressed on the basis of the tube diameter (or an apparent hydraulic radius for noncircular channels), the gas or liquid superficial mass-velocity, and the gas or liquid viscosity. At least four types of flow are then possible, namely liquid in apparent viscous or turbulent flow combined with gas in apparent viscous or turbulent flow. The critical Reynolds number would seem to be a rather uncertain quantity with this definition. In usage, a value of 2000 has been suggested (L6) and widely adopted for this purpose. Other workers (N4, S5) have found that superficial liquid Reynolds numbers of 8000 are required to give turbulent behavior in horizontal or vertical bubble, plug, slug or froth flow. Therefore, although this classification based on superficial Reynolds number is widely used... 

The corresponding equation for vertical flow, again for liquid Reynolds number above 8000 and for void fractions to 0.80, was given by Nicklin et al. (see Section V, A), and was shown to agree with experiment ... 

For turbulent upward liquid flow, it was found experimentally that the slug velocity is given for superficial liquid Reynolds numbers over 8000 by... 

An expression for fia has to be derived from experimental data, by means of a power-product equation containing the gas density, the interstitial mean gas velocity, and a film-liquid Reynolds number. They found a value of-0.37 for both the exponent of pa and of ug, indicating that fiG depends on a gas-phase Reynolds number. For the exponent of the liquid film Reynolds number the value was about zero. 

Figure 5.2-26. Dynamic liquid hold-up versus liquid Reynolds number at different gas velocities and total pressures for the N2-H2O system (after Wammes [17]).

From an hydrodynamical point of view, koa is related to the liquid motion at the interface hence, results have been correlated using the liquid Reynolds number ReL leading to the following correlation with a mean standard deviation of 30% (figure 8) ... 

The physical absorption technique (manometric method) is suitable to determine the liquid side volumetric mass transfer coefficient as well as the gas-side one. Results show that kLa is independant of pressure and depends mainly on the system s hydrodynamics and secondly, that koa is inversely proportional to the total pressure and can be related to the liquid Reynolds number. 

Figure 6-7 Dynamic liquid holdup as a function of liquid Reynolds number." ...

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