Visco-potential free-surface flows and long wave modelling

In a recent study [DutykhDias2007] we presented a novel visco-potential free surface flows formulation. The governing equations contain local and nonlocal dissipative terms. From physical point of view, local dissipation terms come from molecular viscosity but in practical computations, rather eddy viscosity should be used. On the other hand, nonlocal dissipative term represents a correction due to the presence of a bottom boundary layer. Using the standard procedure of Boussinesq equations derivation, we come to nonlocal long wave equations. In this article we analyse dispersion relation properties of proposed models. The effect of nonlocal term on solitary and linear progressive waves attenuation is investigated. Finally, we present some computations with viscous Boussinesq equations solved by a Fourier type spectral method.Comment: 29 pages, 13 figures. Some figures were updated. Revised version for European Journal of Mechanics B/Fluids. Other author's papers can be downloaded from http://www.lama.univ-savoie.fr/~dutyk

Modeling of Free Surface Flows with Elastic Bodies Interactions

In this paper, a series of new fluid and structure interactions test cases with strong free surface effects are presented and computations of such flows with the Particle Finite Element Method (PFEM) (Idelsohn, Oiiate, Del Pin and Calvo, 2006) are documented. The structures object of study are elastic cantilever bars clamped inside sloshing tanks subjected ro roll motion. The possibilities of PFEM for the coupled simulation of moderately violent free surface flows interacting with elastic bodies are investigated. The problem can be described as the coupling of a sloshing flow with an easily deformable elastic body. A series of experiments designed and executed specifically for these tests are also described. The experiments comprise cases with different liquid height and liquids of different viscosity. The aim is to identify canonical benchmark problems in FSI (Fluid and Structure Interactions), including free surfaces, for future comparisons between different numerical approaches

Instabilities in free-surface electroosmotic flows

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.With the recent development of novel microfluidic devices electroosmotic flows with fluid/fluid interfaces have emerged as very important subjects of investigation. Two immiscible fluids may need to be transported in a microchannel, or one side of a channel may be open to air for various purposes, including adsorption of airborne molecules to liquid for high-sensitivity substance detection. The liquid/liquid or liquid/gas interface in these cases can deform, resulting in significant corrugations followed sometimes by incipient rupture of liquid layers. For electroosmotic flow the rupture, leading to shortcircuit, can cause overall failure of the device. It is thus imperative to know the conditions for the rupture as well as the initial interfacial instability. Studies based on the Debye-Huckle approximation reveal that all free-surface electroosmotic flows of thickness larger than the Debye screening length are unstable and selectively lead to rupture. Layers of the order of Debye screening length, however, are not properly described by the Debye-Huckle approximation. Even for micro-scale layers, the rupture phenomenon can make local layer thickness to be nanoscale. A fully coupled system of hydrodynamics, electric field, and ionic distribution need to be analyzed. In this paper linear instability and subsequent nonlinear developments of a nanoscale free-surface electroosmotic flow are reported.This study is sponsored by the Ministry of Education, Science and Technology of Korea through the World Class University Grant

Efficient computation of two-dimensional steady free-surface flows

We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable techniques, these problems are formulated in terms of a coupled system of Bernoulli's equation and an integral equation. When applying a numerical collocation scheme, the Jacobian for the system is dense, as the integral equation forces each of the algebraic equations to depend on each of the unknowns. We present here a strategy for overcoming this challenge, which leads to a numerical scheme that is much more efficient than what is normally employed for these types of problems, allowing for many more grid points over the free surface. In particular, we provide a simple recipe for constructing a sparse approximation to the Jacobian that is used as a preconditioner in a Jacobian-free Newton-Krylov method for solving the nonlinear system. We use this approach to compute numerical results for a variety of prototype problems including flows past pressure distributions, a surface-piercing object and bottom topographies.Comment: 20 pages, 13 figures, under revie

Surface tension driven convection

In a normal gravitational environment, the free surface of a liquid in a container plays a passive role in the transport processes. However, at microgravity, the free surface can become the dominant factor. A simple but meaningful spaceflight experiment is proposed to investigate the nature and extent of flows induced by surface-tension gradients along the free surface. The influences of container geometry, wetability, contamination, and imposed heating modes will be investigated

Computing stationary free-surface shapes in microfluidics

A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven pressure and flow fields compete with the surface tension for the shape of a stationary free surface. The free surface shape is represented by the boundaries of finite elements that move according to the stress applied by the adjacent fluid. Additionally, the surface tends to minimize its free energy and by that adapts its curvature to balance the normal stress at the surface. The numerical approach consists of the iteration of two alternating steps: The solution of a fluidic problem in a prescribed domain with slip boundary conditions at the free surface and a consecutive update of the domain driven by the previously determined pressure and velocity fields. ...Comment: Revised versio

Unsteady, Free Surface Flows; Solutions Employing the Lagrangian Description of the Motion

Numerical techniques for the solution of unsteady free surface flows are briefly reviewed and consideration is given to the feasibility of methods involving parametric planes where the position and shape of the free surface are known in advance. A method for inviscid flows which uses the Lagrangian description of the motion is developed. This exploits the flexibility in the choice of Lagrangian reference coordinates and is readily adapted to include terms due to inhomogeneity of the fluid. Numerical results are compared in two cases of irrotational flow of a homogeneous fluid for which Lagrangian linearized solutions can be constructed. Some examples of wave run-up on a beach and a shelf are then computed