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Heat transfer between parallel continuous streams
DOI 10.1615/hedhme.a.000213
2.10.2 Heat Transfer between Parallel Continuous Streams
H. R. Jacobs
A. Falling films
In cooling towers, wetted wall towers, packed beds, etc., so-called falling films play an important role. Thus, they constitute one of the most commonly found forms of direct contact heat transfer. The initial work on falling films can be traced to the work of Nusselt (1916) in 1916. Since that time, large numbers of studies have been performed. Hassan (1967) investigated a vertically falling film neglecting surface tension, interfacial shear and pressure gradients. He obtained a universal non-dimensional curve for the developing film thickness. Murty and Sastri (1974) studied the problem of a film exiting a slot flowing down an inclined plane of defined height. The surrounding gas was assumed to be quiescent, and pressure variation and surface tension effects were assumed negligible. Assuming a smooth interface and continuity of velocity and shear at the interface, they determined the film thickness as a function of length along the plate. Murty and Sarma (1976) presented an expression for film thickness for either laminar or turbulent film flow down an inclined wall with a co-current gas stream and incorporated interfacial shear and gravity effects in the non-dimensional film thickness. Experimental non-dimensional velocity profiles were used to present a universal, non-dimensional film thickness. Tekic, et al. Tekic et al. (1984) repeated the model of Murty and Sastri (1974), but incorporated normal and tangential stresses on the film interface and neglected the interfacial shear of the still air. Their results presented a family of curves for liquids with different physical properties, but underpredicted the film entrance length.
While the above studies are interesting, co-current flows result in minimum heat transfer, whilst countercurrent flows maximize heat transfer. Countercurrent flows, however, can lead at high velocities, to stripping of a falling film from the supporting substructure. This is a common problem in cooling towers and can lead to the requirement for excessive make-up water and a highly visible plume. Usually, the falling film develops a rough wavy interface, followed by the formation of larger waves on its surface prior to entrainment of liquid in the gas stream. The waves can be a result of either Tollmein-Schlichting or Kelvin-Helmholtz instabilities. Ostrach and Koestel (1965) discussed these and other instabilities associated with two-phase flows. The Tollmein-Schlichting waves are associated with transition from laminar to turbulent flows and do not apply for the situation of laminar gas and liquid flows. The Kelvin-Helmholtz instabilities are interfacial phenomena resulting from the shear at the interface due to relative velocity differences between the two flows.
Ishii and Grolmes (1975) discussed entrainment of liquid into the gas stream. For the case of vertical falling films in countercurrent flow, shearing droplets from the top of roll waves and the formation of large amplitude bulges in the liquid near the flooding point are possible mechanisms for entrainment. With an increase in velocity, partial or total fluid reversal can occur.
The problem of flooding in annular countercurrent devices (wetted-wall towers) was reviewed by Bharathan et al. (1978). Tien and Liu (1979) outlined an overview of theory and experiment. More recently Bankoff and Lee (1986) and McQuillan et al. (1985) reviewed this problem and established a data bank of experimental flooding points. Stephan and Mayinger (1990) studied such systems at high gas pressure.
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