Session EE: Free-Surface Flows: Computational Studies

Precursors to Droplet Splashing on a Solid Surface

We consider a liquid droplet moving towards a solid surface with sufficiently high velocity. We demonstrate that in the absence of intermolecular attraction between the liquid and the solid, the liquid does not contact the solid, and instead spreads on a very thin air film. The junction between the air film and the spherical droplet develops a high curvature and emits capillary waves. We hypothesize that the amplification of these capillary waves is the primary cause of splashing.   

Numerical simulation of a liquid-metal circular hydraulic jump using a level-set method

New reactor concepts (e.g., Accelerator-Driven Systems) that utilize the impact of a high-energy particle beam onto a liquid-metal surface have driven the need for improved predictive techniques for high-speed flows of high-surface-tension liquid metals. We study here the flow in a liquid-metal circular hydraulic jump (CHJ), to compare the predicted results with those from a companion experimental investigation. The flow differs from the traditional CHJ in that outflow over the weir is confined to a few discrete locations in the experimental protocol. The level-set method was employed for numerical simulations. Theoretically, the height of the CHJ and a height correction at the weir were obtained through balancing surface-tension and gravitational forces using the Young-Laplace equation for a static situation. Results are in good agreement with experiment, including the numerical prediction of ``fingering'' in the flow upstream of the jump under certain wettability and flow conditions.   

Shapes of Floating Liquid Sheets Spreading Against an Imposed Bath Flow

We have investigated the spreading from a central static source of a viscous floating liquid sheet, above a more heavy bath, the bath itself drifting at a constant imposed velocity. This kind of situation is of great interest for environment problems and for industrial processes. The sheet exhibits surprising change of shape depending on its own flow rate and on the velocity of the bath. Circular for a static bath, it becomes oval at low velocity and exhibits a ribbon like shape at high velocity. In this high velocity limit, the sheet shape is initially oval and exhibits a transition to the ``ribbon'' shape, across a transient pear like shape. At low flow rate and high velocity, the ribbon becomes unstable and pinch off occurs. We have also investigated theoretically the evolution of the thickness distribution of the sheet. Because of complicated competitions between the sheet and bath viscosities, surprising behaviors can take place. For instance, in the case of a static bath and depending on the sheet flow rate, the final thickness can be larger than the static equilibrium height predicted by Langmuir.   

Computation of Viscous Free-Surface Hydrodynamics for Ships during Free-Roll, Wave-Excited Roll and Prescribed Motions

Prediction of ship motions in waves and the role of viscous effects remains an important problem in naval hydrodynamics. A computational fluid dynamics (CFD) solver has been developed which can simulate the unsteady turbulent boundary layer, wave field, and 6DOF dynamics of a floating body in waves. The solver is based upon the Reynolds-averaged Navier-Stokes equations, and volume-of-fluid (VOF) and dynamic-meshing algorithms. It is used to study free-roll, wave-excited roll, and forced heave and sway motions. Solution validation is achieved by comparing roll-amplitude decay, natural frequency, and response amplitude operator (RAO) for a 2D box barge in regular waves to experimental data. As a practical example, a ship hullform, with and without bilge keels, is studied when undergoing prescribed roll, sway, and heave motions. Details of the fluid dynamics and forces and moments will be correlated to motion amplitudes and frequencies.   

Swirling flow in presence of a moving free surface

The incompressible swirling flow of a viscous fluid enclosed in a cylindrical container with a freely-moving top surface and driven by the steady rotation of the bottom wall is studied both experimentally and numerically. This work is aimed at increasing our understanding of the influence of the presence of a moving free surface on this swirling flow dynamics. New flow states corresponding to a Reynolds number of $6'000$ are investigated based on the fully three-dimensional solution of the Navier--Stokes equations for this free-surface cylindrical swirling flow, without resorting to any symmetry properties unlike all other results available in the literature. The numerical results are thoroughly compared to PIV measurements for the exact same configuration. To our knowledge, this study delivers the most general available results for this moving free-surface problem due to its original treatment.   

A Numerical Study of Interfacial Turbulent Transport of Passive Scalars

We perform direct numerical simulation (DNS) to study interfacial transport of passive scalars in free-surface turbulence. Based on DNS data, we obtain correlation between surface flux and surface age, which is defined based on the intervals of replacements of fluid elements close to the surface with fluid elements from the bulk of the flow. Contribution of different turbulence structures to interfacial transport has been quantified. It is found that surface age distribution can be used to quantify interfacial scalar transport accurately. The random surface renewal theory of Danckwerts (1951) has been modified to obtain an appropriate distribution of surface age. This modified distribution agrees well with the numerical result obtained with a highly accurate Lagrangian-Eulerian method that we develop for surface element residence time quantification. The new distribution with its clear physical explanation can be used to model interfacial transport of passive scalars including gas and heat.   

The unsteady dynamics of the interface separating two fluids under the influence of electric fields

Direct Numerical Simulations (DNS) are carried out to study the dynamics of a horizontal interface separating two fluids, having different electrical properties, under the influence of AC and uniform DC electric fields. A front tracking/finite difference scheme is used, in conjunction with Taylor's leaky dielectric model, to solve the governing electrohydrodynamics equations in both fluids at finite Reynolds numbers. The methodology and the code are validated by comparing the results with those of the analytical studies developed at the linear stability limit and it is shown that a very good agreement exists between the two. The results of this study show interesting interface behavior depending on the parameters of the problem. In all the cases considered, the interface becomes unstable beyond a critical voltage and starts to oscillate as it moves toward its (quasi) steady-state shape which is a vertical column pointing from the liquid of higher electric conductivity to the one with a lower conductivity. The shape of the column, however, will vary depending on the individual governing parameters.   

Flow Visualization and Pattern Formation in Vertically Falling Liquid Films

Analytical results of a low-dimensional two equation h-q model and results of a direct numerical simulation of the transient two-dimensional Navier Stokes equations are presented for vertically falling liquid films along a solid wall. The numerical study aims at the elucidation of the hydrodynamics of the falling film. The analytical study aims at the calculation of the parameter space where pattern formation occurs for this flow. It has been found that when the wave amplitude exceeds a certain magnitude, flow reversal occurs in the film underneath the minimum of the waves [1]. The instantaneous vortical structures possess two hyperbolic points on the vertical wall and an elliptic point in the film. As the wave amplitude increases further, the elliptic point reaches the free surface of the film and two more hyperbolic points are formed in the free surface that replace the elliptic point. Between the two hyperbolic points on the free surface, the streamwise component of velocity is negative and the film is divided into asymmetric patterns of up and down flows. Depending on the value of the Kapitza number, these patterns are either stationary or oscillatory. Physical reasons for the influence of the Kapitza number on pattern formation are given. Movies are shown where the pattern formation is demonstrated. [1] N.A.Malamataris and V.Balakotaiah (2008), AIChE J., 54(7), p. 1725-1740