Modulation Equations for Roll Waves of a liquid film Down an Inclined Plane as a Power-Law Fluid

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.Roll waves of finite amplitude on a thin layer of non-Newtonian fluid modeled as a power-law fluid are considered. In the long wave approximation, the flow is governed by a non-homogeneous hyperbolic system of equations. As the linearized instability analysis of a uniform flow delivers only a diagnosis of instability, the nonlinear stability is investigated and the criterion for roll waves based on the hyperbolicity of the modulation equation is suggested. The main problem in defining the roll wave stability region on a roll wave diagram is due to the singularities of functions for the mean values and their derivatives near the boundaries of roll wave existence. Asymptotic formulae for nonlinear stability of roll waves of small and maximal amplitudes are derived. Numerical calculation reveals that for a Newtonian fluid, as the bottom inclination decreases downwardly the amplitude of admissible waves diminishes, and the stability domain reduces until it disappears. These results remain valid for a slightly non-Newtonian fluid. For highly non-Newtonian fluid, an inversion in the nature of stability is observed.cf201

Validation of robust SPH schemes for fully compressible multiphase flows

The present study examines the ability of the SPH number-density scheme to treat multiphase problems of the fully compressible regime. The number-density scheme is extended to the fully compressible regime, using the standard variational SPH framework and incorporate artificial diffusion coming from a generic formula. Aiming at robust schemes, we adopt the differential form of mass conservation. The performance of this scheme is studied with the help of two benchmark tests. It is shown that the standard variational framework of SPH may treat multiphase processes in the fully compressible regime, without reverting to non-standard formulations. The SPH solutions are compared to solutions coming from the Arbitrary Lagrangian Eulerian method and are validated against exact solutions

Nonlinear Stability of Roll Waves Down an Inclined Falling Film

The present work is concerned with surface instabilities of non-Newtonian liquid films, usually called roll waves (RW). A thin liquid film in which the shear stress is modeled as a power-law is considered to study the stability of nonlinear roll waves down inclined plane walls. In the long wave approximation, depth-integrated continuity and momentum equations are derived by applying Karman#39s momentum integral method. As the linearized instability analysis of uniform flow only provides a diagnosis of instability, the modulation equations for wave series are derived and a stability criterion depending on two parameters (integro-differential expression) is obtained. The main difficulty to establish the stability domain is due of the presence of singularities near infinitesimal and maximal amplitudes. Numerical calculations are performed using asymptotic formulas near the singularities. The stability diagrams are presented for some values of the flow parameters. They reveal that there are situations wherein at critical values of the flow parameters, where the waves disappear. For the prediction and control of the free-surface profile, it is one of the main reasons for carrying out research in this area, as RW are generally an undesirable phenomenon

Numerical Simulation of Interfacial Waves in Two Layers of Immiscible Fluids

This work is dedicated to the numerical simulation of two-phase flow (gas/liquid) stratified between two parallel planes and inclined relative to the horizontal. In this context, we have chosen to use a code for solving both the Navier-Stokes equations and the constitutive equations of viscoelastic fluid with finite volume (Gilflow) corresponding to a single phase flow of viscoelastic fluid confined between two horizontal plane walls. The two-phase flow model was here implemented successfully, by application of the quotVolume of Fluidquot method (VOF). The transport of the interface is solved by using the transport equation of the VOF function. Both methods: Hirt-VOF and PLIC-VOF are tested for a two-phase flow in an unsteady stratified flow regime (gas/liquid). To illustrate this numerical simulation, the configuration (gas / liquid) stratified is here presented

Numerical and experimental investigations of water hammers in nuclear industry

In nuclear and petroleum industries, supply pipes are often exposed to high pressure loading which can cause to the structure high strains, plasticity and even, in the worst scenario, failure. Fast Hydraulic Transient phenomena such as Water Hammers (WHs) are of this type. It generates a pressure wave that propagates in the pipe causing high stress. Such phenomena are of the order of few msecs and numerical simulation can offer a better understanding and an accurate evaluation of the dynamic complex phenomenon including fluid-structure interaction, multi-phase flow, cavitation … For the last decades, the modeling of phase change taking into account the cavitation effects has been at the centre of many industrial applications (chemical engineering, mechanical engineering, …) and has a direct impact on the industry as it might cause damages to the installation (pumps, propellers, control valves, …). In this paper, numerical simulation using FSI algorithm and One-Fluid Cavitation models ("Cut-Off" and "HEM (Homogeneous Equilibrium Model) Phase-Change" introduced by Saurel et al. [1]) of WHs including cavitation effects is presented