Dukler

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 ... 

FIG. 6-28 Flow patterns in cociirrent upward vertical gas/liqiiid flow. (Ftvm Taitel, Barnea, and Dukler, AIChE J., 26, 345-354 [1.9S0], Beproduced hy permission of the American Institute of Chemical Engineers 1980 AIChE. All tights teseroed.)... 

Figure 1-15. Pictorial plot plan layout. Courtesy of Prengle, Dukler and Crump, Houston, Texas.

The author has compared this method with Dukler [29] and others and reports good agreement for reason-ably good cross section of flow regimes. 

Dukler, A. E., Gas-Liquid Flow in Pipelines, Am. Petrol. Inst. Proc., Sept. 1967. 

Dukler, A. E. and Taitel, Y, Flow Patterns in Horizontal and Near Florizontal Pipes, Design Manual FM-3, DIMP/AIChE, New York, 1982 also see Design Manual WFP/AlChE, same reference. 

Dukler, A. E. et al., Frictional Pressure Drop in Two-Phase Flow1 B—An Approach Through Similarity Analysis, A.I.Ch.E.J. 10,... 

CHENOWETH and Martin 20,21 1 have presented an alternative method for calculating the drop in pressure, which is empirical and based on experiments with pipes of 75 mm and pressures up to 0.7 MN/m2. They have plotted the volume fraction of the inlet stream that is liquid as abscissa against the ratio of the two-phase pressure drop to that for liquid flowing at the same volumetric rate as the mixture. An alternative technique has been described by Baroczy 22). If heat transfer gives rise to evaporation then reference should be made to work by Dukler et al 23). 

Dukler, A. E. Moye Wicks III, and Cleveland, R. G. <4. I. Ch. E. Jl. 10 (1964) 38. Frictional pressure drop in two-phase flow. A comparison of existing correlations for pressure loss and holdup. 

The criterion of Barnea et al. (1983) predicts well flow patterns of air and water in channels several millimeters in diameter. For smaller channels, however, the criteria of Taitel and Dukler (1976) and Barnea et al. (1983) are not suitable. 

The two-phase pressure drop was measured by Kawahara et al. (2002) in a circular tube of d = too pm. In Fig. 5.30, the data are compared with the homogeneous flow model predictions using the different viscosity models. It is clear that the agreement between the experimental data and homogeneous flow model is generally poor, with reasonably good predictions (within 20%) obtained only with the model from Dukler et al. (1964) for the mixture viscosity. 

The purpose of these experiments was to characterize different flow details under conditions when the superficial gas velocity is constant and the superficial liquid velocity increases. The upward flow regimes are presented in Fig. 5.33. Figure 5.33a shows the stratified flow pattern at [/gs = 20 m/s and J/ls = 0.005 m/s. In the region of pure stratified flow the liquid layer is drawn upward by the gas via the interfacial shear stress. No droplets could be observed at the interface. Such a regime was also observed by Taitel and Dukler (1976), and Spedding et al. (1998). 

In Fig. 5.39a-d the local heat transfer coefficients derived in the horizontal tube are compared to those obtained in the 8° upward inclined pipe and presented by Hetsroni et al. (2006). The results show a clear improvement of the heat transfer coefficient with the pipe inclination. Taitel and Dukler (1976) showed that the flow regimes are very sensitive to the pipe inclination angle. In the flow regime maps presented in their work, the transition from stratified to annular flow in the inclined tube occurs for a smaller air superficial velocity than for the case of the horizontal tube. 

Taitel Y, Bamea D, Dukler AE (1980) Modeling flow pattern transitions for steady upward gas-liquid flow in vertical tubes. AlChE J 26 345-354 Triplett KA, Ghiaasiaan SM, Adbel-Khalik SI, Sadowski DL (1999a) Gas-liquid two-phase flow in microchannels. Part 1 two-phase flow patterns. Int J Multiphase Flow 25 377-394 Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, LeMouel A, McCord BN (1999b) Gas-liquid two-phase flow in microchannels. Part 11 void fraction and pressure drop. Int J Multiphase Flow 25 395 10... 

Figure 3.3 Horizontal flow regime map curves A, B, (Fr) versus Xn curve C, K versus Y curve D, T versus X . (AD, annular dispersed DB, dispersed bubble SW, stratified wavy I, intermittent SS, stratified smooth.) (From Taitel and Dukler, 1976b. Copyright 1976 by American Institution of Chemical Engineers, New York. Reprinted with permission.)...

A variety of mechanisms have since been suggested to explain the physical basis for the observed transition between flow patterns (Ishii, 1975 Taitel and Dukler, 1976b Taitel et al., 1980 Barnea, 1987 Taitel and Barnea, 1990). Dukler and Taitel (1991b) summarized the various mechanisms to explain such flow pattern transitions (Table 3.1), where the letters in Table 3.1 identify the theoretical curves shown in the accompanied graphs (Fig. 3.7) for different flow directions. A word of caution was given in the reference ... 

Source Dukler and Taitel (1991b). Copyright 1991 by University of Houston, Houston, TX. Reprinted with permission. 

Pattern transition in horizontal adiabatic flow. An accurate analysis of pattern transitions on the basis of prevailing force(s) with flows in horizontal channels was performed and reported by Taitel and Dukler (1976b). In addition to the Froude and Weber numbers, other dimensionless groups used are... 

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