Rivulet model

Ponchon-Savarit diagram. 26 Ponter underwetting theory, 516, 517 Porter rivulet model. 542 Porter and Jenkins packing HETP, 532-534 regime transition. 332 Poynting factor. 7 Prado and Fair tray efficiancy, 375 PRO/II. 169, 170,180... 

Since liquid does not completely wet the packing and since film thickness varies with radial position, classical film-flow theory does not explain liquid flow behavior, nor does it predict liquid holdup (30). Electrical resistance measurements have been used for liquid holdup, assuming liquid flows as rivulets in the radial direction with little or no axial and transverse movement. These data can then be empirically fit to film-flow, pore-flow, or droplet-flow models (14,19). The real flow behavior is likely a complex combination of these different flow models, that is, a function of the packing used, the operating parameters, and fluid properties. Incorporating calculations for wetted surface area with the film-flow model allows prediction of liquid holdup within 20% of experimental values (18). 

Magnetic resonance imaging permitted direct observation of the liquid hold-up in monolith channels in a noninvasive manner. As shown in Fig. 8.14, the film thickness - and therefore the wetting of the channel wall and the liquid hold-up -increase nonlinearly with the flow rate. This is in agreement with a hydrodynamic model, based on the Navier-Stokes equations for laminar flow and full-slip assumption at the gas-liquid interface. Even at superficial velocities of 4 cm s-1, the liquid occupies not more than 15 % of the free channel cross-sectional area. This relates to about 10 % of the total reactor volume. Van Baten, Ellenberger and Krishna [21] measured the liquid hold-up of katapak-S . Due to the capillary forces, the liquid almost completely fills the volume between the catalyst particles in the tea bags (about 20 % of the total reactor volume) even at liquid flow rates of 0.2 cm s-1 (Fig. 8.15). The formation of films and rivulets in the open channels of the structure cause the further slight increase of the hold-up. 

In this work, microscale evaporation heat transfer and capillary phenomena for ultra thin liquid film area are presented. The interface shapes of curved liquid film in rectangular minichannel and in vicinity of liquid-vapor-solid contact line are determined by a numerical solution of simplified models as derived from Navier-Stokes equations. The local heat transfer is analyzed in term of conduction through liquid layer. The data of numerical calculation of local heat transfer in rectangular channel and for rivulet evaporation are presented. The experimental techniques are described which were used to measure the local heat transfer coefficients in rectangular minichannel and thermal contact angle for rivulet evaporation. A satisfactory agreement between the theory and experiments is obtained. 

Figure 11. Wave patterns on rivulet interface depending on wall superheat, value as for creeping flow model.

Figure 10 presents the interface shape of the rivulet for wall superheat as 0.5 K and Re = 2.5. Here also presented the data on pressure in liquid and heat flux density in rivulet cross-section. The intensive liquid evaporation in near contact line region causes the interface deformation. As a result the transversal pressure gradient creates the capillarity induced liquid cross flow in direction to contact line. Finally the balance of evaporated liquid and been bring by capillarity is established. This balance defines the interface shape and apparent contact angle value.For the inertia flow model, the solution is obtained from a non-stationary system of equations, i.e., it is time-dependable. In this case the disturbances in flow interface can create the wave flow patterns. The solutions of unsteady state liquid spreading on heat transfer surface without and with evaporation are presented on Fig. 11. When the evaporation is not included (for zero wall superheat) the wave pattern appears on the interface. When the evaporation includes, the apparent contact angle increase immediately and deform the interface. It causes the wave suppression due to increasing of the film curvature.

Numerical procedure to calculate the heat transfer during evaporation has heen developed for the rectangular minichannel. Some conductive calculations are shown to compare with the experimental data. They illustrate the non-uniform nature of local heat transfer around the perimeter of the channel. Rivulet and dry spot formation are descrihed. Numerical calculations show the enhancement of the heat transfer at large liquid Reynolds numbers caused at least in part by liquid suction to channel s corner where the area of microscale heat transfer arises. At small liquid Reynolds numbers the heat transfer reduction occurs due to dry spot formation. By comparing the model with the experimental data, it is shown that these conclusions are in consistent with the experimental results. 

Wetting is an important aspect of the SDR. If the disk is not wetted then dry spots are created and rivulets are formed, which significantly reduce the transport rates achieved on the disk. Hartley and Murgatroyd provided a list of theoretical models for calculating the wetting film for liquid flows under gravity. The equations derived for these models were based on physical principles rather than empirical data but have compared favorably with experimental results. Because... 

In the case of trickle flow, it has been shown that under certain conditions the slit-flow approximation yields a very satisfactory set of constitutive equations for the gas-liquid and the liquid-solid drag forces [20, 21]. As a matter of fact, the slit flow becomes well representative of the trickle-flow regime when the liquid texture is contributed by solid-supported liquid Aims and rivulets. This generally occurs at low liquid flow rates that allow the transport of film-like liquids [20]. We will assume, without proof though, that such hypotheses also hold in the case of artificial-gravity operation. The validity of these assumptions and of the several others outlined above will be evaluated later in terms of model versus experiment comparisons. Choosing the drag force closures of the simplified Holub slit model [20], the equations system becomes ... 

The spontaneous emergence of avalanches, droplets and rivulets is very difficult to simulate with classical fluid dynamical models, due to the critical nature (self-organized criticality) and threshold character of these nonlinear phenomena. Therefore, the role of statistical fluctuations in thin-film dynamics cannot be underestimated, especially in the mesoscale. Unlike the classical approaches, we need not introduce any external and artificial perturbations. All phenomena occur spontaneously due to thermal noise inherent in the nonlinearly interacting particle dynamics. 

The modelling of the bed scale hydrodynamic contributions to these processes always requires the introduction of the parameter Ljjj. This term characterizes the interactions between the liquid and the solid. As pointed out above, it represents the local liquid velocity in an isolated rivulet inder its more stable flow configuration. This configuration and consequently may be dependent on the actual operating conditions i.e. the ones prevailing under reactor operation (and not the ones prevailing for isolated rivulets). 

---