The partial wetting is generally defined by a contact angle between the liquid and the surface in the case of a static equilibrium excluding other types of actions such as gravity, inertia, viscosity, etc. When these last effects are no longer negligible, the modeling of two-phase flows governed by capillary forces cannot be reduced to simple geometrical laws on the surface tensions between the phases. The triple line is subject to accelerations that combine in a complex way to fix in time its motion on the surface. The macroscopic approach adopted is based on the representativity of the discrete equation of motion derived from the fundamental law of dynamics expressed in terms of accelerations. The formalism leads to a wave equation whose form corresponds to the two components of a Helmholtz Hodge decomposition, the first to the curl-free and the second to the divergence-free. Like all other contributions, the capillary effects are expressed in two terms of the capillary potential, an energy per unit mass. The longitudinal and transverse surface tensions allow for possible anisotropy effects in the tangent plane at the interface. The assignment of the surface tension values on the triple line related to the contact angle allows to take into account the partial wetting effects in a dynamic context. Two examples illustrate the validity of this approach.
This article states a numerical method of finished differences, making it possible to calculate the variables describing an average flow, no viscous and no heavy, through a mobile wheel of a wind mill with horizontal axis, to deduce its performances from them, by using a grid with irregular steps. Centered space discretization’s diagrams inside the calculation domain and decentered towards the interior for the nodes placed on the borders are used. The temporal discretization uses an explicit diagram with two steps of time, with about two precisions. Calculations are made in two stages: a prediction stage and a correction stage. They preceded to calculations of the three-dimensional flow initial state, realized thereafter in its bypass sections. Boundary conditions are imposed on the borders of the calculation domain. Calculation convergence is ensured by numerical viscosity implicitly introduced by the time discretization’s diagrams. The internal stability is ensured by a constraint on the step of temporal discretization in accordance with CFL condition Initial conditions are calculated while realizing, on the flow bypass sections, characteristic quantities initially imposed in the calculation domain volume.