Georg F. Dietze

Investigation of the backflow phenomenon in falling liquid films

The phenomenon of backflow in the capillary wave region of laminar falling liquid films is studied in detail. For the first time, the mechanism leading to the origination of the phenomenon is identified and explained. It is shown that backflow forms as the result of a separation eddy developing at the bounding wall similar to the case of classical flow separation. Results show that the adverse pressure distribution causing the separation of the flow in the capillary wave region is induced by the strong third-order deformation (i.e. change in curvature) of the liquid–gas free surface there. This deformation acts on the interfacial pressure jump, and thereby the wall pressure distribution, as a result of surface tension forces. It is shown that only the capillary waves, owing to their short wavelength and large curvature, impose a pressure distribution satisfying the conditions for flow separation. The effect of this capillary separation eddy on momentum and heat transfer is investigated from the perspective of modelling approaches for falling liquid films. The study is centred on a single case of inclined liquid film flow in the visco-capillary regime with surface waves externally excited at a single forcing frequency. Investigations are based on temporally and spatially highly resolved numerical data obtained by solving the Navier–Stokes equations for both phases. Computation of phase distribution is performed with the volume of fluid method and the effect of surface tension is modelled using the continuum surface force approach. Numerical data are compared with experimental data measured in the developed region of the flow. Laser-Doppler velocimetry is used to measure the temporal distribution of the local streamwise velocity component, and confocal chromatic imaging is employed to measure the temporal distribution of film thickness. Excellent agreement is obtained with respect to film thickness and reasonable agreement with respect to velocity.

Experimental study of flow separation in laminar falling liquid films

In a previous publication, Dietze, Leefken & Kneer ( J. Fluid Mech. , vol. 595, 2008, p. 435) showed that flow separation takes place in the capillary wave region of falling liquid films. That investigation focused on the mechanistic explanation of the phenomenon mainly on the basis of numerical data. The present publication for the first time provides clear experimental evidence of the phenomenon obtained by way of highly resolving velocity measurements in a specifically designed optical test set-up. Characteristically, the refractive index of the working fluid was matched to that of the glass test section to provide optimal access to the cross-section of the film for the employed optical velocimetry techniques, namely, laser doppler velocimetry (LDV) and particle image velocimetry (PIV). Using LDV, time traces of the streamwise velocity component were recorded in high spatial (0.025 mm) and temporal resolutions (0.4 ms) showing negative velocity values in the capillary wave region. In addition, simultaneous film thickness measurements were performed using a Confocal Chromatic Imaging (CCI) technique enabling the correlation of velocity data and wave dynamics. Further, using PIV the spatio-temporal evolution of the velocity field in the cross-section of the film was measured with high spatial (0.02 mm) and temporal (0.5 ms) resolutions yielding insight into the topology of the flow. Most importantly these results clearly show the existence of a separation eddy in the capillary wave region. Due to the high temporal resolution of the PIV measurements, enabled by the use of a high-speed camera with a repetition rate of up to 4500 Hz, the effect of wave dynamics on the velocity field in all regions of the wavy film was elucidated. All experiments were performed using a dimethylsulfoxide (DMSO)–water solution and focused on laminar vertically falling liquid films with externally excited monochromatic surface waves. Systematic variations of both the Reynolds number ( Re = 8.6–15.0) and the excitation frequency ( f = 16–24 Hz) were performed. Results show that an increase in the wavelength of large wave humps, produced either by an increase in the Reynolds number or a decrease in the excitation frequency, leads to an increase in the size of the capillary separation eddy (CSE). Thereby, the CSE is shown to grow larger than the local film thickness, assuming an open shape with streamlines ending at the free surface.

Investigation of the thermal entry length in laminar wavy falling films

The use of liquid films flow offers solutions for the problems associated with the microgravity applications. The thermal entry length of laminar wavy falling films was experimentally determined under full gravity conditions by means of infrared thermography. A dependence of the entry length on the Reynolds, Prandtl, and Kapitza number as well as the ratio Pr0/PrW between the Prandtl numbers at inflow and wall temperatures was found.

Capillary Flow Separation in 2- and 3-Dimensional Laminar Falling Liquid Films

Due to the selective use of liquid films in specialized technical equipment (e.g. new generation nuclear reactors), a fundamental understanding of underlying momentum and heat transport processes inside these thin liquid layers (with a thickness of approximately 0.5 mm) is required. In particular, the influence of surface waves (which develop due to the film’s natural instability) on these transport processes is of interest. For a number of years, experimental and numerical observations in wavy falling liquid films have suggested that momentum and heat transfer in the capillary wave region, preceding large wave humps, undergo drastic modulations. Indeed, some results have indicated that upward flow, i.e. counter to the gravitational acceleration, takes place in this region. Further, evidence of a substantial increase in wall-side and interfacial transfer coefficients has also been noted. Recently, Dietze et al. [1,2] have established that flow separation takes place in the capillary wave region of 2-dimensional laminar falling liquid films, partially explaining the above mentioned observations. Thereby, it was shown that the strong third order deformation (i.e. change in curvature) of the liquid-gas interface in the capillary wave region causes an adverse pressure gradient sufficiently large to induce flow detachment from the wall. In the present paper, a detailed experimental and numerical account of the capillary flow separation’s kinematics and governing dynamics as well as its effect on heat transfer for two different 2-dimensional flow conditions is presented. Experimentally, velocity measurements (using Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV)) and film thickness measurements (using a Confocal Chromatic Imaging technique) were performed in a specifically designed optical test setup. On the numerical side, simulations of the full Navier-Stokes equations as well as the energy equation using the Volume of Fluid (VOF) method were performed. In addition to the 2-dimensional investigations, the characteristics of capillary flow separation under 3-dimensional wave dynamics were studied based on the 3-dimensional numerical simulation of a water film, which was previously investigated experimentally by Park and Nosoko [3]. Results show that flow separation persists over a wide area of the 3-dimensional capillary wave region, with multiple capillary separation eddies occurring in the shape of vortex tubes. In addition, strong spanwise flow induced by the same governing mechanism is shown to occur in this region, which could explain the drastic intensification of transfer to 3-dimensional liquid films.Copyright

A New Empirical Model for Bubble Growth: Boiling in an Infinite Medium and on a Wall at High Superheat

At high superheat bubble growth is rapid and the heat transfer is dominated by radial convection. This has been found, in the case of a droplet boiling within another liquid and in the case of a bubble growing on a heated wall, leading to similar bubble growth curves. Based on experiments conducted for the first case, an empirical model is developed for the prediction of bubble growth within the radial convection dominated regime (the RCD model), occurring only at high superheat (0.26<Ste<0.41). This model shows a dependence of R∼t1/3 equivalent to Nusselt number decreasing over time (Nu∼t1/3 ) as opposed to R∼t1/2 appearing in most other models, leading to a highly unlikely constant Nusselt number. The new model is shown to give accurate predictions for the first case and for the second case at medium-high superheat (0.19<Ste<0.30, experimental data taken from literature). A comparison of the RCD model to other models, shows a more consistent and accurate prediction. However, in the second case (nucleate boiling) the RCD model requires the foreknowledge of the departure diameter, for which a reliable model still is lacking.Copyright