On the Turbulence Modelling for an Air Cavity Interface

The use of air lubrication techniques can significantly reduce a ship’s fuel consumption. One of the most promising techniques applicable to ships is the external air cavity technique. An external cavity is created beneath the ship’s hull with the help of a cavitator, which is located directly upstream of an air injection point. The cavitator is extended in the span-wise direction and typically has a rectangular or triangular cross section. It is used to separate the mean water flow from the hull, thereby providing a stable air layer. Air cavity applications are claimed to lead to propulsive power reduction percentages of 10-20% by reducing the ship’s frictional drag (Gorbachev and Amromin (2014), Zverkhovskyi (2014)). However, a complete understanding of the influence that the ship’s hull form has on the relevant twophase flow physics and thereby also on the length and stability of the air cavities is still lacking. This inability to predict the air cavity characteristics hampers the application of air cavity techniques in the shipping industry. Multiphase CFD methods can help us to gain a better understanding of the relevant physics.

The largest challenge in predicting the air cavity characteristics lies in correctly modelling their closure region (Zverkhovskyi et al. (2015), Shiri et al. (2012)). Here, the closure region is defined as the region where the separated air-water flow transforms into a more dispersed flow. Both the re-entrant jet mechanism and the wave pinch-off mechanism are cited as possible mechanisms for air discharge from the cavity in the closure region (e.g. Shiri et al. (2012), Zverkhovskyi (2014), Makiharju (2012)). The re- ¨ entrant jet mechanism is provisionally assumed to be similar to the re-entrant jet mechanism responsible for the break-up of natural sheet cavities. Callenaere et al. (2001) describe the mechanism as follows. In the closure region of a sheet cavity, a region with high adverse pressure gradient is formed. This increase in local pressure forces a thin stream of liquid into the cavity. This thin stream is called the re-entrant jet and it is illustrated in figure 1b. Impingement of this jet with the gas-liquid interface results in a disturbance leading to a portion of the attached cavity being pinched off and transported by the mean flow.

The wave pinch-off mechanism, as illustrated in figure 1c, is governed by waves on the air-water interface. These waves are believed to be formed by turbulence structures interfering with the interface. If the resulting wave amplitudes are of the same magnitude as the cavity thickness, the free surface interface will hit the ship’s bottom and a pocket of air will be shed from the cavity.

This article aims to link the physical modelling of the relevant phenomena to their numerical modelling, with an emphasis on the modelling of the re-entrant jet mechanism with a RaNS turbulence model. The article is based on the available literature in the public domain and on knowledge gained from research projects carried out at Delft University of Technology and at the Maritime Research Institute Netherlands (MARIN).

The numerical solver used for all simulations is ReFRESCO (MARIN (2017)). It is a viscous-flow CFD code that solves multiphase (unsteady) incompressible flows using the RaNS equations. It is complemented with turbulence models, cavitation models and volume-fraction transport equations for different phases. The equations are discretised using a finite-volume approach. Time integration is performed implicitly with first or second-order backward schemes. The implementation is face-based, which facilitates grids with elements consisting of an arbitrary number of faces (hexahedrals, tetrahedrals, prisms, pyramids, etc.) and, if needed, h-refinement (hanging nodes). For turbulence modelling, RaNS/URaNS, SAS (Scale Adaptive Simulation), DES (Detached Eddy Simulation), PANS (Partially Averaged Navier-Stokes) and LES (Large Eddy Simulation) approaches can be used.