A new model describing the dynamics of large-amplitude waves on laminar falling wavy films at high Reynolds numbers (Re≳300) is presented. The model is based on second-order boundary layer theory and includes the pressure variation across the film as well as higher-order viscous terms. The consistency and accuracy of the model is verified by comparing the linear stability results with Kapitza’s classical boundary layer model and Orr–Sommerfeld studies of the two-dimensional Navier–Stokes equations. Numerical integration of a traveling wave simplification of the model predicts the existence of chaotic large-amplitude, nonperiodic waves, as observed in the experiments. The computed wave statistics such as wave celerities, root-mean-square (RMS) values of film thickness, probability density function (PDF), and film thickness power spectrum using the present model are in reasonable agreement with those measured on naturally excited fully developed flows at Re≳300. The present model also overcomes the main deficiency of the classical boundary layer model (namely, negative wall shear stress) predicts large-amplitude waves (with peak to substrate ratios of 3 to 4) and gives better agreement with data.

An experimental study of the liquid entry region during flooding is reported for a 50.8 mm i.d. vertical tube. The liquid entry device was a porous plastic tube into which film thickness measurement probes were mounted. Simultaneous measurements of the time-varying film thickness were made at locations below, inside and above the porous inlet. The weight of the evidence from cross-covariance analysis of these data does not appear to support models which assume upward propagation of waves above the feed point as the mechanism by which steady-state flooding takes place. Neither was there evidence that waves grow large enough to bridge the tube. Instead, the liquid film appears to undergo a transition from countercurrent to cocurrent flow inside the liquid feed. The pressure drop across the length of the porous tube was also measured and found to be significantly higher than that previously reported at locations above the liquid inlet. In part II [Int. J. Multiphase Flow20, 235–247 (1994)] a film model based on these data is explored.

A new flooding mechanism is explored for porous tube feed systems based on the concept that flow reversal takes place inside the liquid film at the feed location. The model is developed, assuming that the flow field in the liquid film at any axial position can be represented by the time-average film thickness existing there. Thus, it makes the radical assumption that the interfacial waves exert their influence only by modifying the shear stress in the gas flowing over the film. A 2-D numerical simulation was constructed which solved for both the flow field inside the film and the shape of the free interface. The numerical results show that this film mechanism is a viable approach for modeling flooding, as reasonable values of the interfacial shear stress from the upward gas flow can reproduce the experimentally measured film thickness. This work also suggests that the pressure gradient developed inside the entry is only partially due to interfacial shear. Gas-phase accelerations, due to the wave motion, contribute the remainder of the measured pressure gradient.

Mass transfer from a solid boundary into a thin wavy film was studied for a wide range of laminar flow rates with a novel experimental technique. Speculations that large waves control the transport process through a convection mechanism are validated through an examination of the time variation of the film thickness and solute concentration. Statistical analyses of the data demonstrate that the occurrence of large waves with higher local flow rates coincides with an increased mass transfer both locally and globally. Accordingly, the relative importance of small waves or ripples is shown to decrease rapidly with increasing flow rate.

The structure of thin, wavy falling films was studied to evaluate whether the random-appearing wave structure is a result of deterministic chaos or a purely stochastic process. The time-varying film thickness was obtained at different spatial locations near the point of wave inception for flow rates in the range of Re = 3-10. Under all conditions the wave structure was aperiodic in nature and displayed none of the known transitions to chaos. However, the power spectra followed an exponential decay law at high frequencies that is characteristic of chaotic systems. The estimated attractor dimension, used to characterize the complexity of a chaotic system, was much higher than those of known model chaotic systems. It is demonstrated that these high values could be explained due to small levels of noise present in experimental situations. Since experimental data are seldom noise free, a basic limitation in applying these methods to experimental measurements is demonstrated.

Numerical simulations of mass transfer into falling liquid films, both through the wavy interface and from the wall, have been performed for experimentally measured large waves within which the flow fields have been computed. Experiments have shown that the occurrence of waves on free falling films causes dramatic increases in mass transfer into the film, even under laminar flow conditions. Wave effects have been modeled in several ways, none of which predicts the observed rate of enhancement. The present numerical procedure includes solving the convective-diffusion equation for wavy films by extending a technique developed for hydrodynamic simulation. The presence of waves is shown to cause significant velocities normal to each interface. In conjunction with recirculation within the large waves, these flow patterns produce transfer rates for large waves that are several times larger than predicted for quasiparallel velocity fields. Experimental wave structure data were used to define the dimensions and frequency of an average large wave and surrounding substrate. Computed transfer rates at both the gas-liquid interface and the wall for a film composed of a periodic sequence of average waves agree well with published data. These simulations confirm the inadequacy of parabolic, or Kapitza-type velocity profiles in formulating transport models.

Research on adiabatic gas-liquid flows under reduced gravity condition is presented together with experimental data obtained using a NASA-Lewis RC 100-ft drop tower and in a LeRC Learjet. It is found that flow patterns and characteristics remain unchanged after the first 1.5 s into microgravity conditions and that the calculated time for a continuity wave to traverse the test section is less than 1.2 s. It is also found that the dispersed bubbles move at the same velocity as that of the front of the slug and that the transition between bubbly and slug flow is insensitive to diameter. Both the bubbly and the slug flows are suggested to represent a continuum of the same physical process. The characteristics of annular, slug, and bubbly flows are compared.

Taylor bubbles rising through liquids in vertical circular tubes and between parallel planes are axisymmetric and nearly spherical at the top. In a vertical annulus, however, the bubbles are radially asymmetric and never occupy the whole cross-sectional area. Analysis indicates that axisymmetric bubbles rise in an annulus at lower rates than those observed experimentally and hence are never observed in practice. In contrast, the asymmetric bubbles take an elliptic shape which results in higher rise velocities. A theoretical model for the rise velocity of an elliptic bubble has been developed and the comparison with experiment is satisfactory.

Flow patterns were investigated in vertical upward gas-liquid flow in a concentric and an eccentric annulus (eccentricity 50%). A new method for flow pattern identification is proposed based on probability density function analysis of conductance probe signals. Flow pattern maps have been constructed and mathematical models are proposed which predict the flow pattern transitions.

Three isolated waves of differing amplitude and shape were selected from experimental measurements of a falling liquid film at Re = 880 for study using an algorithm developed for solution of the Navier-Stokes equations. The method computes the velocity and pressure fields as well as the velocity of the wave. The results show that large streamwise accelerations exist along with regions of recirculating flow in a moving coordinate system. These features can explain the enhanced rates of heat and mass transfer observed in wavy film flow. Computed wave velocities and wall shear stress were in reasonably good agreement with measurements. Wave velocity is shown to be sensitive to small variations in the wave shape and explains the apparent random variation of wave velocity with amplitude that has been observed experimentally. This numerical experiment points to the shortcomings of the many methods used to model large waves on falling films that have been based on parabolic velocity profiles.

From experimental measurements of a free falling liquid film at Re880, four representative large, evolving or interacting waves were selected for computational domains in which the Navier-Stokes equations were numerically solved. The algorithm computed velocity and pressure fields within each wave, as well as the shape necessary to match experimental wall shear stress data. Results show interaction effects significantly modify flow fields, compared to large solitary waves. Waves having two peaks had two closed recirculation regions, with a mixing layer separating them. The size of the recirculation regions was dependent on the extent of separation of the wave peaks. As with solitary waves, strong streamwise accelerations exist, with both location and magnitude varying with shape and evolutionary character of the wave. Heat and mass transfer rates must be enhanced by these flow properties, which are shown to have a complicated dependence on wave structure. Examination of the flow fields suggests parabolic streamwise velocity profiles are generally deficient, explaining shortcomings experienced by hydrodynamic models based on such simple velocity profiles.

A long-wave equation for film thickness as a function of position is derived for a general case incorporating viscous, surface tension, and interfacial shear effects. The derivation considers both the parabolic and the power-law velocity profiles. The analysis is aimed at revealing the wave velocity that induces infinitely long (homoclinic) periods as well as substrate thickness and wave peak amplitude. Phase plane analysis shows that at Re ≫ 1, due to time-scale separation, the homoclinic velocity is near that at the Hopf bifurcation. That enables analytical derivation of the wave characteristics. Comparison with experimental results in the range of Re -310–3, 100 with countercurrent gas flow, shows encouraging agreement. At very high Re the wave velocity suggests the onset of turbulence, in agreement with theory. Phase plane analysis predicts also that the wave shape consists of a simple peak with a steep front, with short waves riding on the main wave at low Re .

It has been established through the identification and evaluation of characteristic forces dominant in two-phase gas–liquid flow field that Suratman number is the key dimensionless group in slug–annular flow pattern transition under microgravity. Furthermore, the intrinsic physical mechanism underlying the transition has been explored with the aid of experimental results. It is revealed that slug–annular flow pattern transition depends on Suratman number and the ratio of superficial gas to liquid Reynolds numbers. This result provides a physical basis to the existing empirical transition equation which is based on the same two dimensionless groups.

The structure of the wavy interface on a falling liquid film is studied for conditions of countercurrent gas flow in order to investigate mechanisms for flooding. Measurements taken just below the liquid feed and at 1.7 m down the tube show that under all conditions, including flooding, the waves propagate only downward and are never of such amplitude as to bridge the tube. These observations are in contrast to speculations in the literature that upward flow of waves or bridging of liquid due to waves cause flooding. In the mechanism suggested, flooding is due to flow reversal in the film just at the liquid entry.

The prediction of flow patterns during gas-liquid flow in conduits is central to the modern approach for modelling two-phase flow and heat transfer. The mechanisms of transition are reasonably well understood for flow pipes on earth where it has been shown that body forces largely control the behavior observed. This work explores the patterns which exist under conditions of microgravity when these body forces are suppressed. Data are presented which were obtained for air-water flow in tubes during drop tower experiments and Learjet trajectories. Preliminary models to explain the observed flow pattern map are evolved.

AIChE JournalVolume 33, Issue 8 p. 1405-1406 Book Review Encylcopedia of fluid mechanics volume III: Gas-liquidflows, 1,535 pp A. E. Dukler, A. E. Dukler Dept. of Chemical Engineering, University of Houston, Houston, TX 77004Search for more papers by this author A. E. Dukler, A. E. Dukler Dept. of Chemical Engineering, University of Houston, Houston, TX 77004Search for more papers by this author First published: August 1987 https://doi.org/10.1002/aic.690330822AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume33, Issue8August 1987Pages 1405-1406 RelatedInformation

A partir d'information sur la vitesse de l'onde, on peut evaluer les caracteristiques de l'onde et la dimension du substrat qui sont en bon accord avec les valeurs moyennes mesurees

This paper analyzes the hydrodynamics near the discharge of a pipe carrying gas and liquid in horizontal stratified flow. It is shown that for high-viscosity liquids, pipe length may have a considerable effect on the transition from the stratified to nonstratified (annular or intermittent) flow pattern. This leads to a flow-pattern map which contains the pipe length as a parameter for this transition boundary.