Falling films turbulent flow

By substituting the well-known Blasius relation for the friction factor, Eq. (45) in Table VII results. Van Shaw et al. (V2) tested this relation by limiting-current measurements on short pipe sections, and found that the Re and (L/d) dependences were in accord with theory. The mass-transfer rates obtained averaged 7% lower than predicted, but in a later publication this was traced to incorrect flow rate calibration. Iribame et al. (110) showed that the Leveque relation is also valid for turbulent mass transfer in falling films, as long as the developing mass-transfer condition is fulfilled (generally expressed as L+ < 103) while Re > 103. The fundamental importance of the Leveque equation for the interpretation of microelectrode measurements is discussed at an earlier point. 

Particles are transported by turbulent diffusion from the core region to the surface of the falling film, where they are trapped and are carried downward. The implication of this assumption is that the net upward particle flow will decrease along the riser height in the core. 

The heat transfer in the lower part of the sphere is highly nonlinear, and no correlation was reported for this region. Karapantsios and Karabelas [184] experimentally examined the influence of flow intermittency on direct contact condensation of a quasistagnant vapor-gas mixture on falling liquid waves. Flow intermittency was found to increase the heat transfer rate by as much as an order of magnitude. Mikielewicz et al. [218] recently included turbulent diffusion effects in studying direct-contact condensation of steam on a horizontal water film. 

The modification of hydrodynamic aspects is exploited in the falling-film cell [12], where the electrolyte flows as a thin fllm in the channel between an inclined plane plate and a sheet of expanded metal which work as electrodes. Other proposal is to include turbulence promoters in the interelectrode gap in conventional parallel plate electrochemical reactors [13-16], or the use of expanded metal electrodes immersed in a fluidized bed of small glass beads, called Qiemelec cell [17]. Likewise, the Metelec cell [18] incorporates a cylindrical foil cathode concentric arranged around an inner anode, with a helical turbulent electrolyte flow between the electrodes. The electrochemical hydrocyclone cell [19] makes use of the good mass-transfer conditions due to the helical downward accelerated flow in a modified conventional hydrocyclone. 

Armbruster and Mitrovic [62] observed that liquid falls from tube to tube in three patterns discrete droplets, jets or columns, and sheets, depending on the flow rate (i.e., film Reynolds number) and fluid properties. In addition, depending on the tube arrangement and spacing, the condensate may cause ripples, waves, and turbulence to occur in the film splashing may occur, as well as nonuniform rivulet runoff of condensate because of tube inclination or local vapor velocity effects. As a result, it is impossible to arrive at an analytical expression to describe these complex bundle phenomena. In general, the effect of inundation may be accounted for using... 

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