Film flow model

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). 

Robertson, J.M., (1982), The correlation of boiling coefficients in Plate-Fin Heat Exchanger passages with a film flow model, in 7 Int Heat Transfer Conference Munich, pp341-345. 

Film Flow Modeling for Co-current Vapor Flow with Evaporation 3.1. MODEL DEVELOPMENT... 

Thus it is necessary to find alternative approach to describe the physical mechanism of two-side filling of conical capillaries with hquids. Theoretical model of film flow in conical dead-end capillary is based on the concept of disjoining pressure II in thin liquid film [13]... 

Physical mechanism of two-side filling of dead-end capillaries with liquids, based on liquid film flow along the wall, is proposed for the first time. Theoretical model correlates with experimental data. 

Mitsuya, Y., Modified Reynolds Equation for Ultra-thin Film Gas Lubrication Using 1.5-order Slip-Flow Model and Considering Surface Accommodation Coefficient," ASME J. Tri- [25] fcoZ.,Vol. 115,1993, pp. 289-294. 

As a result of asperity contact, the nominal contact zone is split into a number of discrete areas that can be cataloged either to the lubrication region or asperity contact area (Fig. 2). The mean hydrodynamic pressure in the lubrication regions, pi, can be calculated by the average flow model, while contact pressure is estimated via Eq (7). Consequently, the film thickness is determined through numerical iterations to... 

Patir, N., Effects of Surface Roughness on Partial Film Lubrication Using an Average Flow Model Based on Numerical Simulation. Ph.D. Thesis, Northwestern University, 1978. 

Two flow models are used to estimate the mean condensation coefficient in horizontal tubes stratified flow, Figure 12.45a, and annular flow, Figure 12.45. The stratified flow model represents the limiting condition at low condensate and vapour rates, and the annular model the condition at high vapour and low condensate rates. For the stratified flow model, the condensate film coefficient can be estimated from the Nusselt equation, applying a suitable correction for the reduction in the coefficient caused by... 

Falling film flow. The extent of basic modeling of two-phase annular flow is still very limited, because annular flow is the pattern that is least well understood... 

Levy, Healzer, and Abdollahian (1980) predicted the dryout flux in vertical pipes by a semiempirical adiabatic model (Levy and Healzer, 1980) for liquid film flow and entrainment. It starts with a heat balance along the flow direction and a mass balance perpendicular to the flow direction ... 

The CHF in high-quality annular flow uses a liquid film dryout model, i.e., the concept of liquid film dryout (zero film flow rate) in annular flow. Sugawara (1990) reported an analytical prediction of CHF using FIDAS computer code based on a three-fluid and film dryout model. 

Sudo, Y., T. Usui, and M. Kaminaga, 1991, Experimental Study of Falling Water Limitation under a Counter-current Flow in a Vertical Rectangular Channel, JSMEInt. J. Ser. H 34 169-174. (5) Sugawara, S., 1990, Analytical Prediction of CHF by FIDAS Code Based on Three-Fluid and Film-Dryout Model, J. Nuclear Sci. Technol. 27. 12 29. (5)... 

Cross-file patent searches, 18 243-244 CrossFire Beilstein, 6 19 Cross-flow filtration, 11 383 15 827, 829 in porous pipes, 11 387-388 with rotating elements, 11 383-387 Cross flow model, 21 706 Cross-flow packed scrubber, 26 687-688 Crossflow plates, 6 762-763 Cross-flow screens, 22 282 Cross-flow velocity, 15 725 Crosshead mandrel, in VDC film extrusion, 25 732-733 Cross-lapping, 17 501 Cross-linkable epoxy thermoplastic system (CET), 10 436... 

Two-phase flow model in channels mist flow X mist flow annular film mist flow X X X un- specified... 

The problem of absorption accompanied by a chemical reaction in a liquid film flowing along a vertical wall was often treated by using the framework of the penetration theory [28 - 32]. This theory also constitutes the starting point of the renewal models of turbulence [31,33,34]. 

Ultrahigh-vacuum (UHV) surface spectroscopy has been used with molecular beams of SiH4 and mass spectroscopy to elucidate the Si growth mechanism (67, 143). Joyce et al. (67) found that Si growth is preceded by an induction period when surface oxide was removed as SiO. The subsequent film growth proceeds by growth and coalescence of adjacent nuclei with no apparent formation of defects. Henderson and Helm (144) proposed a step-flow model in which adatoms from SiH4 surface reactions difluse to kink sites. 

For the calculation of the heat transfer coefficient of the external film, some models are also available [2], describing the hydraulics of the flow in the jacket or in the half-welded coils. The results depend strongly on the technical design of the equipment. Thus, the direct experimental determination is mostly preferred. 

The thickness of the liquid film on the rotor packing helps determine mass transfer rates. Film thickness can be shown to be inversely proportional to rotor speed to the 0.8 power (17). Visual measurements using a video camera attached to the rotor show a water film thickness of 20-80 microns on foam metal packing and 10 microns on wire gauze packing (15). Theoretical models estimate similar film thickness values (13,18,19). Film flow is expected to be laminar. In addition to rotor speed, liquid flow rate and fluid properties affect the film thickness (14). 

While the fluid dynamics of the actual film-flow process across the disc is daunt-ingly complex, a very approximate interim how model may be based upon Nusselt s treatment of the how of a condensate him. This assumes that the how is stable (i.e., ripple free), that there is no circumferential slip at the disc/liquid surface, and that there is no shear at the gas/liquid interface. The treatment is based... 

Counter-current gas/vapor-liquid film flows in SP above the load conditions are extremely complicated. For this reason, it appears improbable that the CFD-based virtual experiments replace real experiments entirely in the near future. However, even single-phase CFD simulations can improve predictivity of pressure drop models, since all correlations pressure drop - gas load used in practice contain some dry pressure drop correlation as a basic element. Replacing this correlation by the rigorous CFD analysis helps to avoid heuristic assumptions on possible correlation structure, which are inevitable both in conventional mechanistic models (Rocha et ah, 1993) and in more sophisticated considerations (Olujic, 1997). 

Mersmann s correlation and Madkowlak s correlation. Mersmann (73) postulated that a thin liquid film forms in the flow channel of the packing. The ratio of film thickness to equivalent packing diameter is a function of the liquid load. Mersmann combined this function with a trickle flow model to yield an expression for dry packing pressure drop at flood as a function of liquid rate. Mafikowiak (78a) surveyed sources that followed up and improved on Mersmann s initial model. 

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