Session L30: Flow Instability: Falling Liquid Film

Breakup of rivulet falling over an inclined plate.

The multiscale modeling of solvent absorption in a structured packing is a complex problem. The local hydrodynamics in the packing, specifically existing flow regimes, is a key factor for overall efficiency. A single packing unit is made of corrugated sheets arranged perpendicularly to each other. In this effort, breakup of rivulet over an inclined plate is examined, which might be helpful to explain some fundamental aspects of this system. Rivulet breakup is a complex phenomenon dictated by many factors such as solvent physical properties, contact angle ($\gamma )$, inertia, plate inclination angle ($\theta )$, etc. The multiphase flow simulations using the volume of fluid method were conducted considering these factors. Decreasing solvent flow rate results in the transition of flow regimes from a film to a rivulet and then to a droplet. Demarcation between a stable and an unstable flow regime that leads to breakup is presented in terms of the critical Weber number (We$_{\mathrm{cr}})$. Values of Weber number below We$_{\mathrm{cr}}$ correspond to breakup behavior and above to a stable rivulet. The impact of solvent properties is presented by the Kapitza number (Ka), which only depends on fluid properties. Variation of We$_{\mathrm{cr}}$ with Ka shows two trends depending on the Ka value of the solvent. Solvents with low Ka show a linear variation of We$_{\mathrm{cr}}$ with Ka whereas those with high Ka show a quadratic variation. The effect of plate inclination on the rivulet breakup reveals that We$_{\mathrm{cr}}$ decreases with increased $\theta $ value. In addition, higher values of $\gamma $ promote breakup.   

Flow regimes and traveling waves for a model of gravity-driven film flows in cylindrical domains.

Families of traveling wave solutions will be presented for a model of a falling viscous film on the interior of a vertical rigid tube. Each family contains a single solution at a `turnaround point' with larger film thickness than all others in the family. It was previously conjectured that this turnaround point may represent a critical thickness separating two distinct flow regimes observed in physical experiments as well as two distinct types of behavior in transient solutions to the model. We will verify these hypotheses over a range of parameter values using a combination of numerical and analytical techniques. The linear stability of these solutions will also be discussed; both large- and small-amplitude solutions will be shown to be unstable, though the instability mechanisms are different for each wave type. Specifically, for small-amplitude waves, the region of relatively flat film away from the localized wave crest is subject to the same instability that makes the trivial flat-film solution unstable; for large-amplitude waves, this mechanism is present but dwarfed by a much stronger tendency to relax to a regime close to that followed by small-amplitude waves.   

Hydrodynamic Characterization of Harmonically Excited Falling-Films: A Detailed Experimental and Computational Study

We investigate the hydrodynamic characteristics of harmonically excited liquid-films flowing down a $20~\degree$ incline by simultaneous application of Particle Tracking Velocimetry and Planar Laser-Induced Fluorescence (PLIF) imaging, complemented by Direct Numerical Simulations. By simultaneously implementing the above two optical techniques, instantaneous and highly localised flow-rate data were also retrieved, based on which the effect of local film topology on the flow-field underneath the wavy interface is studied in detail. Our main result is that the instantaneous flow rate varies linearly with the instantaneous film-height, as confirmed by both experiments and simulations. Furthermore, both experimental and numerical flow-rate data are closely approximated by a simple analytical relationship, which is reported here for the first time, with only minor deviations. This relationship includes the wave speed $c$ and mean flow-rate $\overline Q$, both of which can be obtained by simple and inexpensive measurement techniques, thus allowing for spatiotemporally resolved flow-rate predictions to be made without requiring any knowledge of the full flow-field from below the wavy interface.   

Three-dimensional numerical simulations of falling liquid films

Falling liquid films down an inclined or vertical surface have rich wave dynamics, often occurring in many industrial applications, such as condensers, evaporators and chemical reactors. There are some numerical studies for falling liquid films, however most of them have focused on two-dimensional falling films or three-dimensional falling films in a periodic domain. The objective of this study is to investigate flow dynamics of fully developed three-dimensional falling films using the Navier-Stokes equations coupled with interface capturing approach. An adaptive unstructured mesh modelling framework is employed here to study this problem, which can modify and adapt unstructured meshes to better represent the underlying physics of multiphase problems and reduce computational effort without sacrificing accuracy. Numerical examples of two-dimensional and three-dimensional falling films in a long domain with different flow conditions are presented and discussed.   

Hydrodynamic balance of solitary waves on falling liquid films

Falling liquid films at sufficiently high Reynolds numbers are unstable to long-wave perturbations which at low frequencies evolve into fast moving solitary waves. These solitary waves are strongly nonlinear structures characterised by a dominant elevation with a long tail and steep front, typically with capillary ripples preceding the main wave hump. The objective of our work is to identify the key physical mechanisms governing these solitary waves through direct numerical simulations and experiments. Our results demonstrate that the height and shape of solitary waves is governed by a subtle balance between inertia and surface tension [Denner et al., Phys. Rev. E 93 (2016), 033121]. This leads, for instance, to a stabilisation of the wave height after the onset of flow recirculation in the solitary waves in the moving frame of reference, since the flow rate and, consequently, the effective inertia acting on the waves, are reduced as a result of the recirculation. In addition, the capillary ripples in front of the main solitary humps are strongly contributing to the hydrodynamic balance of solitary waves and we establish a connection between the creation of capillary ripples and the height, stability and speed of the solitary wave.   

Thermocapillary control of falling liquid films by substrate heating

We analyse the problem of controlling a falling liquid film by selective heating of the substrate supporting the flow. Such heating affects the film dynamics through Marangoni stresses, and will be chosen in response to real-time observations of the film height profile. We begin by developing a new low-dimensional (LD) model for the dynamics of a thin film subject to heating which varies in space and time. The model includes the effects of convection and diffusion, so that local heating applied briefly at the substrate can have a long-lasting and wide-ranging effect on the surface temperature. We demonstrate that our LD model is in good agreement with full Navier-Stokes (NS) equations and we use it to develop heating strategies which drive the film towards either a uniform state or into a desired non-uniform profile. We further develop a hierarchy of control strategies subject to realistic limitations, such as having influence over only a few localised heating strips, the ability to sense the height profile at a few fixed locations, and dealing with time delays and uncertainty in observation or application of heating. We test the robustness of our control strategies in closed- and open-domain simulations of the LD model and also in fully coupled NS calculations.   

Three-dimensional direct numerical simulations of co/counter-current vertical gas-Liquid annular flows

We carry out three-dimensional numerical simulations of co/counter current Gas-Liquid annular flows using the parallel code, BLUE, based on a projection method for the resolution of the Navier-Stokes equations and a hybrid Front-Tracking/Level-Set method for the interface advection. Gas-Liquid annular flows and falling films in a pipe are present in a broad range of industrial processes. This configuration consists of an important multiphase flow regime where the liquid occupies the area adjacent to the internal circumference of the pipe and the gas flows in the pipe core. Experimentally, four distinctive flow regimes were identified (‘dual-wave’, ‘thick ripple’, ‘disturbance wave’ and ‘regular wave’ regimes), that we attempt to simulate. In order to visualize these different regimes, various liquid (water) and gas (air) flow-rates are investigated.   

Interfacial turbulence and regularization in electrified falling films

Consider a liquid film flowing down an inclined wall and subjected to a normal electric field. Previous studies on the problem [1] invoked the long-wave approximation. Here, for the first time, we analyze the Stokes-flow regime using both a non-local long-wave model and the full system of governing equations. For an obtuse inclination angle and strong surface tension, the evolution of the interface is chaotic in space and time. However, a sufficiently strong electric field has a regularizing effect, and the time-dependent solution evolves into an array of continuously interacting pulses, each of which resembles a single-hump solitary pulse. This is the so-called interfacial turbulence regime. For an acute inclination angle and a sufficiently small supercritical value of the electric field, solitary-pulse solutions do not exist, and the time-dependent solution is instead a modulated array of short-wavelength waves. When the electric field is increased, the evolution of the interface first becomes chaotic, but then is regularized so that an array of pulses is generated. A coherent-structure theory for such pulses is developed and corroborated by numerical simulations.\\ [1][1] T.S. Lin, M. Pradas, S. Kalliadasis, D.T. Papageorgiou, D. Tseluiko, SIAM J Appl Math 75, 538-563 (2015)   

Attracting wave regimes for two layer falling films.

We analyze flows of two-layer falling films by using approximate long-wave model. There is a non-uniqueness of steady-traveling wave regimes as solutions of the problem which is utilised in mass transfer technologies. To select the wave regimes developing in two-layer films, systematic transient computations have been carried out to create a map of the attracting wave regimes, so-called dominating waves, which can be used to model real-life processes.   

Three-dimensional direct numerical simulation of falling liquid films

The dynamics of a thin film falling down an inclined solid surface have attracted the attention of many researchers because of the richness and variety of waves which develop on its liquid-air interface. Besides experimental work, the problem has been widely studied in the literature but direct numerical simulations have been limited to two-dimensions or low-dimensional modeling for three-dimensional problems. We present a computational study of falling liquid films in a three-dimensional inclined rectangular domain (45$^\circ$) using the massively parallel code BLUE for Lagrangian tracking of arbitrarily deformable phase interfaces. Calculations are carried out on O($10^3$) cores in a large domain (24cm $\times$ 12cm $\times$ 1.5 cm) for Reynolds and Kapitza numbers of 100 and 10, respectively, in order to obtain several three-dimensional wave patterns and solitary waves.