Integral formulation and simulations of falling and sheared thin films

Amélie Simon (1, 2) , Jean-Marc Hérard (3, 2) , Meryem Marcelet (2)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique
2 EDF R&D STEP - Simulation et Traitement de l'information pour l'Exploitation des systèmes de Production
3 I2M - Institut de Mathématiques de Marseille

In the electricity production, studying liquid films in steam turbines contributes to reduce damages and losses due to wetness. Thin liquid films are created by the deposition of droplets and are highly sheared by surrounding steam. Up to now, no comprehensive and validated model has arisen to describe this phenomenon. Thus, a 2D model based on an integral formulation associated with closure laws is developed to represent this film. Compared to classical Shallow-Water equation, the model takes into account additional effects such as mass transfer, droplet impact, shearing at the free surface, surface tension, pressure gradient and rotation effects. The model properties (hyperbolicity, entropy inequality, linear stability, Galilean and rotational invariance) are examined in order to evaluate the relevance of the model. A 2D code is implemented in the EDF code Code Saturne which relies on finite volume method for unstructured meshes. The model, which degenerates into classical Shallow-Water equations for the case of a falling liquid film on a inclined plane, is validated using the experiment of [Liu and Gollub, 1994] and is compared to reference models ([Ruyer-Quil and Manneville, 2000] and [Lavalle, 2014]). Sheared film under low-pressure steam turbine conditions are simulated and also validated using the experiment of [Hammitt et al., 1981]. Unsteady simulations show that the surface tension effects are of great importance; they also give the main features in the behavior of liquid film under realistic low-pressure steam turbine conditions.

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]

Amélie Simon, Jean-Marc Hérard, Meryem Marcelet. Integral formulation and simulations of falling and sheared thin films. 2017. ⟨hal-01612611⟩