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

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

Modeling turbulent-bounded flow using non-Newtonian viscometric functions

International audienceTurbulent flows of Newtonian fluids have already been compared with non-Newtonian laminar flows. In this paper the analogy between these classes of flows is explored, and a new approach to derive a turbulent model based on a nonlinear constitutive equation is shown. In order to reach this aim, direct numerical simulation databases of turbulent channel flows are used and analyzed in the light of the classical parameters of non-Newtonian constitutive equations. The Reynolds stress tensor is expressed in terms of a set of basis tensors based on a projection of a nonlinear framework. The coefficients of the model are given as functions of the intensity of the mean strain tensor. The apparent turbulent viscosity, the first and second normal stress difference, are presented in function of the shear rate. A turbulent Weissenberg number, based on a characteristic turbulent time ratio of the first normal stress difference to the apparent viscosity is also presented. These material functions, exhibiting a shear-thinning behavior, are fitted with the power law (the Carreau-type) model. The range of the Reynolds number investigated was 180≤Reτ≤2000. One of the advantages of the new algebraic nonlinear power law constitutive equation derived in the paper is that its dependence is only on the mean velocity gradient and can be integrated up to the wall