Interfacial shear in downward two-phase annular co-current flow

Abstract

Pressure drop has been determined experimentally for downward co-current annular two-phase flow, with water and air flow Reynolds numbers in the ranges 5100–27 200 and 3400–21 600, respectively. In order to investigate the effect of tube diameter, four tubes, of I.D.'s ranging from 1.56–4.12 cm, were tested. Special care was taken to eliminate effects of surfactants. The resulting skin friction coefficients were only in qualitative agreement with most previously reported data. At a fixed gas Reynolds number, a large increase in friction accompanied a decrease in tube diameter. Existing correlations were found to be unsuccessful for the present data.

Introduction

There have been many studies of vertical two-phase annular flow, with upward flow of gas, and either an upward or downward flow of the liquid film on the tube wall. In contrast, there have been relatively few studies of the combination of downward flows of gas and liquid. The former combinations are encountered more often in engineering equipment, and also are characterized by critical flooding phenomena. However, the latter combination is also encountered in equipment, for example, in co-current gas scrubbers. In such equipment, pressure drop is often an important consideration, and thus the designer requires data for the friction factor (or, equivalently, the skin friction coefficient). In planning an experiment the gas and liquid flow rates are obvious parameters to be varied. In an early study, Bergelin et al. (1949) noted that waves on the liquid film act much like surface roughness in single-phase flow, causing increased friction due to form drag. Then, the ratio of a characteristic wave height to tube diameter should be an important dimensionless parameter affecting friction, indicating that diameter should be varied as an independent parameter. Chu and Dukler (1975) found that small capillary waves, rather than large amplitude gravity waves, were the major cause of increased form drag; thus, surface tension should also affect friction (as should the presence of surfactants).

In the few experimental studies of downward flow, attention has been focused on rather small areas of the parameter space, and a comprehensive and consistent data base is lacking. The present study was motivated by the need to design equipment for which (i) a clean water–air system is an appropriate model, (ii) liquid flow rates are relatively high (film Reynolds numbers in the range 5000–25 000), (iii) gas flow rates are relatively low (superficial gas flow Reynolds numbers in the range 5000–25 000), (iv) there is negligible liquid entrainment, and (v) tube diameter is an important design parameter. The specific objective was to obtain friction data for this area of the general parameter space.

Relevant experimental measurements of pressure drop in downward co-current flow are as follows. Bergelin et al. (1949) measured pressure drop in a 2.54 cm diameter, 3.3 m long tube, for superficial water and air Reynolds numbers of 0–10 000 and 3100–65 000, respectively. Their results were presented graphically and showed some friction coefficients lower than values expected for smooth wall, single-phase flow. Chien and Ibele (1964) measured pressure drop and mean film thickness in a 5.08 cm diameter, 3.2 m long tube for both the annular and annular-mist flow regimes, and water and air Reynolds number ranges of 1250–22 000 and 28 000–350 000, respectively. For the annular flow regime, the skin friction coefficient was correlated as

$$\text{f=0.92×10}{}^{\mathrm{-7}}\text{Re}{}_{\mathrm{<mtext>G</mtext>}}{}^{0.582}\text{Re}{}_{\mathrm{<mtext>L</mtext>}}{}^{0.705}\text{,}$$

where f=τ_i/0.5ρ_GU_G², Re_G=U_GD/ν_G, Re_L=U_LD/ν_L; τ_i is the interfacial shear stress, and the velocities are superficial values, determined as if the fluid in question flows alone in the test section. The superficial bulk gas velocity is thus U_G=Q_G/(πD²/4), where Q_G is the volume flow rate of gas and D is the tube diameter. Note that also, Re_L=4Γ/μ_L, is the usual film Reynolds number defined for falling films, where Γ is the mass flow rate per unit width of perimeter. Ueda and Tanaka (1974) measured pressure drop and film thickness in a 2.88 cm diameter, 1.825 m long tube for water and air Reynolds numbers of 185–13 500 and 6000–100 000, respectively. Their results are presented as plots of friction factor versus gas Reynolds number based on air velocity relative to the water surface velocity (taken to be 50% greater than the bulk value). Tishkoff et al. (1979) used a tube of 2.86 cm diameter, 1.83 m long, and presented plots of friction coefficient and mean film thickness versus air Reynolds number for $\text{15}\text{800<Re}{}_{\mathrm{<mtext>G</mtext>}}\text{<86}\text{400}$ and $\text{4040<Re}{}_{\mathrm{<mtext>L</mtext>}}\text{<18}\text{690}$. Effects of swirl generation of air and water on film thickness were also investigated. Chung and Mills (1974) studied gas absorption into falling films with co-current gas flow in a 2.03 cm diameter, 1.56 m long glass tube. Their results include plots of f versus Re_G for 0<Re_L<8030 and $\text{8000<Re}{}_{\mathrm{<mtext>G</mtext>}}\text{<30}\text{000}$. Fedotkin et al. (1979) measured pressure drop and film thickness in a 3 cm diameter, 2.38 m long tube for annular flow without liquid droplet entrainment, and the following correlation was suggested for $\text{2000<Re}{}_{\mathrm{<mtext>L</mtext>}}\text{<20}\text{000}$ and $\text{6000<Re}{}_{\mathrm{<mtext>G</mtext>}}\text{<30}\text{000}$.

$$\text{τ}{}_{\mathrm{<mtext>i</mtext>}}\text{/(μ}{}_{\mathrm{<mtext>L</mtext>}}{}^2\text{ρ}{}_{\mathrm{<mtext>L</mtext>}}\text{g}{}^2\text{)}{}^{\mathrm{1/3}}\text{=1.35×10}{}^{\mathrm{-9}}\text{Re}{}_{\mathrm{<mtext>L</mtext>}}{}^{0.75}\text{Re}{}_{\mathrm{<mtext>G</mtext>}}{}^{1.75}\text{,}$$

where g is acceleration due to gravity. With property values evaluated at 295 K, Eq. (2) becomes

$$\text{f=3.943×10}{}^{\mathrm{-3}}\text{Re}{}_{\mathrm{<mtext>L</mtext>}}{}^{0.75}\text{Re}{}_{\mathrm{<mtext>G</mtext>}}{}^{\mathrm{-0.25}}\text{.}$$

The results of these studies are summarized in Fig. 1. Ignoring the results of Fedotkin et al. (1979) for the present, we can say that the qualitative effects of liquid and gas flow rates are in general agreement. For a given tube diameter, f always increases with liquid flow rate. There is characteristic S-shaped variation of f with gas flow rate. For low liquid and gas flow rates f decreases with Re_G and approximates smooth wall single-phase behavior. At higher flow rates, f increases rapidly with Re_G, primarily due to wave induced form drag. At higher values of Re_G a maximum can be reached with a subsequent gradual decrease. The maximum is attributed to the onset of liquid entrainment by Chien and Ibele (1964), but Tishkoff et al. (1979) observed entrainment before the maximum in f was reached. In none of these prior studies was diameter varied as an experimental parameter, though the values used varied from 2.05 to 5.08 cm. Unfortunately, poor quantitative agreement between the results and insufficient overlap of parameter values precludes a satisfactory evaluation of the effect of diameter. Nevertheless, there is a general indication of a marked increase in f with decreasing tube diameter. The results of Fedotkin et al. (1979) are clearly inconsistent with the other studies. These workers state that their data are in qualitative agreement with those of Chien and Ibele (1964), but this contradicts the effect of diameter noted above. It was necessary to rely on a correlation given by Fedotkin et al. (1979) since the original data were not given in accessible form. Thus, it will not be profitable to give this study any further attention.

Since all the studies involved the water–air system, nothing can be deduced about the effect of fluid properties, in particular, surface tension. Different results can be expected for Freon refrigerants that have much lower surface tensions than does water. Furthermore, little attention has been paid to the possible effect of surfactants on the capillary waves, and hence on friction. The effect of surfactants on the behavior of water–air interfaces has been studied for many years. Surfactants are known to change surface properties, and to have a pronounced effect on the general characteristics of the interfacial wave structure. In studies of gas absorption into turbulent falling films, Chung and Mills (1974), Won and Mills (1982) and others have found that trace amounts of surfactants can appreciably affect gas absorption rates, a result that is attributed to the effect of the surfactants on capillary waves. In industrial equipment, surfactant introduced in the manufacturing and assembly stages is usually flushed out the system after days or weeks of operation. However, in laboratory experiments, tests have a relatively short duration and surfactant concentrations remain close to initial values. The ring test introduced by Crits (1961) is a simple and reliable test for determining if trace amounts of organic contaminants are present in water. This test proved indispensable in the gas absorption studies mentioned above, but has not seen much use in two-phase flow studies. It is possible that some of the inconsistency seen in Fig. 1 is due to different levels of surfactants, and in further experimental work it is essential to ensure that surfactants do not play a role.