Numbers for condensation

The Reynolds number for condensation on the outer surfaces of vertical tube or plates increases in the flow direction due to the increase of the liquid filn thickness S. The flow of liquid film exhibits different regimes, depending 01 the value of the Reynolds number. It is observed that the outer surface of th liquid film remains smooth and wave-free for about Re < 30, as shown ii Fig. 10 -23, and thus the flow is clearly laminar. Ripples or waves appear 01 the free surface of the condensate flow as the Reynolds number increases, anr the conden.sale flow becomes fully turbulent at about Re 1800. The con densate flow is called wavy-laminar in the range of 450 < Re < 1800 an turbulent for Re > 1800. However, some disagreement exists about the valu of Re at which the flow becomes wavy-laminar or turbulent. 

Table 2. Magic electron numbers for condensed Nb60i2 clusters.

Condensed Empty Clusters 405 ftble 5-5. Optimal electron numbers for condensed Nb60]2 dusters. [16]... 

In the last section we examined some of the categories into which polymers can be classified. Various aspects of molecular structure were used as the basis for classification in that section. Next we shall consider the chemical reactions that produce the molecules as a basis for classification. The objective of this discussion is simply to provide some orientation and to introduce some typical polymers. For this purpose a number of polymers may be classified as either addition or condensation polymers. Each of these classes of polymers are discussed in detail in Part II of this book, specifically Chaps. 5 and 6 for condensation and addition, respectively. Even though these categories are based on the reactions which produce the polymers, it should not be inferred that only two types of polymerization reactions exist. We have to start somewhere, and these two important categories are the usual place to begin. 

The high T] values above conflict with the common behef that distillation is always inherendy inefficient. This behef arises mainly because past distillation practices utilized such high driving forces for pressure drop, tedux ratio, and temperature differentials in teboilets and condensers. A teal example utilizing an ethane—ethylene sphtter follows, in which the relative number for the theoretical work of separation is 1.0, and that for the net work potential used before considering driving forces is 1.4. 

The physical properties of the liquid, rather than those of the vapor, are used For determining the film coefficient for condensation. Nus-selt [2. Ver. Dt.sch. Ing., 60, 541, 569 (1916)] derived theoretical relationships for predicting the film coefficient of heat transfer for condensation of a pure saturated vapor. A number of simplifying assumptions were used in the derivation. 

Vertical Tubes For the following cases Reynolds number < 2100 and is calculated by using F = Wp/ KD. The Nusselt equation for the heat-transfer coefficient for condensate films may be written in the following ways (using liquid physical properties and where L is the cooled lengm and At is — t,) ... 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

For condensing vapor in vertical downflow, in which the hquid flows as a thin annular film, the frictional contribution to the pressure drop may be estimated based on the gas flow alone, using the friction factor plotted in Fig. 6-31, where Re is the Reynolds number for the gas flowing alone (Bergelin, et al., Proc. Heat Transfer Fluid Mech. Inst., ASME, June 22-24, 1949, pp. 19-28). 

To obtain a low flash zone pressure, the number of plates in the upper section of the vacuum pipe still is reduced to the minimum necessary to provide adequate heat transfer for condensing the distillate with the pumparound streams. A section of plates is included just above the flash zone. Here the vapors rising from the flash zone are contacted with reflux from the product drawoff plate. This part of the tower, called the wash section, serves to remove droplets of pitch entrained in the flash zone and also provides a moderate amount of fractionation. The flash zone operates at an absolute pressure of 60-90 mm Hg. 

W = flowrate, Ib/hr, condensate Do = outside diameter of tubes, ft Nj = total number of tubes in bundle used for condensation... 

For horizontal tubes, use Figure 10-68 to determine the equivalent number of condensate streams, n, based on the total number in a circular bundle, Nj. 

N, = number of effective tubes for condensation L = tube length, ft W = condensate flow rate, Ib/hr... 

For a system composed of any number of condensed chemically homogeneous phases and a homogeneous gas phase we have the symbol ... 

If G is the mass rate of flow of condensate, the mass rate of flow per unit area G is G/S and the Reynolds number for the condensate film is then given by ... 

This technique bus been applied by Rhodes and Younger(107) to obtain the values of h0 for condensation of a number of organic vapours, by Pratt(92) to obtain the inside coefficient for coiled tubes, and by Coulson and Mehta(i08) to obtain the coefficient for... 

It is clear from the forgoing discussions that the important material properties of liquid crystals are closely related to the details of the structure and bonding of the individual molecules. However, emphasis in computer simulations has focused on refining and implementing intermolecular interactions for condensed phase simulations. It is clear that further work aimed at better understanding of molecular electronic structure of liquid crystal molecules will be a major step forward in the design and application of new materials. In the following section we outline a number of techniques for predictive calculation of molecular properties. 

Above a Reynolds number of around 2000, the condensate film becomes turbulent. The effect of turbulence in the condensate film was investigated by Colburn (1934) and Colburn s results are generally used for condenser design, Figure 12.43. Equation 12.51 is also shown on Figure 12.43. The Prandtl number for the condensate film is given by ... 

For condensation inside horizontal tubes, the Nusselt Equation can be applied with a correction for the reduction in condensing coefficient caused by the accumulation of condensation. The correction usually applied is 0.8. No correction for the number of tubes is required. Thus, for condensation inside horizontal tubes ... 

---