Dukler theory

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 ... 

Neither of the treatments above covers the case of countercurrent gas/film flow, but the behavior of a downward film flow in the absence of a gas stream can be obtained from the original Dukler analysis. It is found that in the laminar zone the film thicknesses predicted by the Dukler theory are in agreement with (19). A comparison of the theory with experimental results will be carried out in Section IV, A. 

In spite of these apparently seriously restricting assumptions, Dukler (D15) has shown that his theory for downward cocurrent flow is in agreement with experimental gas/film thickness data reported by Charvonia (C4) and McManus (M3). Hewitt et al. (H10) and Collier and Hewitt (C13) have carried out analyses of numerous experimental data on the thicknesses of liquid films in upward cocurrent flow in terms of the Dukler theory and other simpler theories such as those due to Anderson and Mantzouranis (A5) and Calvert and Williams (C2) (Section III, F, 4). The experimental and calculated values are in moderate agreement in the case of the Dukler and the Anderson and Mantzouranis treatments. The discrepancies are probably due to the simplifying assumptions made in the theoretical treatments. 

The Dukler theory is applicable for condensate films on horizontal tubes and also for falling films, in general, i.e., those not associated with condensation or vaporization processes. 

The Dukler theory assumes that three fixed factors must be known to establish the value of the average heat transfer coefficient for condensing for vertical tubes. These are the terminal Reynolds number (4r/p ), the Prandtl number (c p /k ) of the condensed phase, and a dimensionless group designated by Aj and defined as follows ... 

Select the calculation method to be used. Use the Dukler theory [18], which assumes that... 

Figure 3.8 Comparison of theory and experiments (water-air horizontal flow at 25°C and 1 atm pressure with diameter of 2.5 cm). Solid lines theory. (From Dukler, 1978. Copyright 1978 by National Council of Canada. Reprinted with permission.) Fuzzy lines experimental data. (From Mand-hane et al., 1974. Copyright 1974 by Elsevier Science Ltd., Kidlington, UK. Reprinted with permission.)...

More recently Hewitt (H5) has adapted a downward-film-flow analysis by Dukler (D4) based upon the Deissler velocity profile, to upward film flow this approach, also requiring numerical solution, is claimed to give better correlation of film thickness with theory, over wider ranges than previous data, and for different types of liquid injections. The Deissler velocity profile was developed specifically to describe the velocity variation in the zone close to a solid wall, and, might be expected to give the best description of film flow. However, when gross wave motion or significant entrainment occurs, this correlation also shows deviations from experiment. 

Attempts have been made to compare the experimentally measured pressure drops with various of the theories discussed in Section III, F and with the more generalized empirical two-phase friction-factor correlations of the type discussed by Dukler and Wicks (D17). Hewitt et al. (H10) have compared their experimental data for upward cocurrent flow with one such empirical correlation and with the theories of Anderson and Mantzouranis (A5) and of Dukler (D12) and Hewitt (H7). In most cases there was good qualitative agreement only. 

Portalski (P4), 1963 Theories of film flow and methods of measuring film thickness are reviewed. Film thicknesses on vertical plate (zero gas flow) reported for glycerol solutions, methanol, isopropanol, water, and aqueous solutions of surfactants. Results compared with values calculated by Nusselt, Kapitsa, and corrected Dukler and Bergelin treatments. 

FIG. 5-8 Dukler plot showing average condensing-film coefficient as a function of physical properties of the condensate film and the terminal Reynolds number. (Dotted line indicates Nusselt theory for Reynolds number < 2100.) [Reproduced hy permission from Chem. Eng. Prog., 55, 64 (1959).]... 

---