Air Entrainment Mechanisms from Artificial Supercavities: Insight based on numerical simulations

Using multiphase computational simulations based on the Navier-Stokes equations, we examine the internal gaseous flows of artificially ventilated supercavities. These simulations indicate that air shear layers that develop on the cavity-wall (the air-liquid interface surrounding the cavity) are an important mechanism of air entrainment. This corroborates previous theory developed for toroidal cavities, and indicates that similar mechanisms occur in twin-vortex cavities and cavities closing on bodies. The importance of these shear layers on the cavity behavior potentially impacts computational simulations, experiments, and design-level models. Lastly, a more inclusive, semi-empirical air entrainment model is presented that attempts to accommodate the observed processes. INTRODUCTION Concept high-speed underwater vehicles surrounded by a ventilated gaseous supercavity (supercavitating vehicles) are potentially advantageous compared to fully wetted vehicles of similar mission. The primary benefit of supercavitation is drag reduction, which is thought to enable very high-speed vehicles. The benefit of ventilation versus vaporous cavitation is cavity stability. Stable cavities of course are also important. Buffeting, surface damage, large-scale vehicle vibrations and other negative consequences typically result from vaporous cavitation. With an artificially inflated cavity, the absence of a condensing gas alleviates this effect. Unfortunately, with such a vehicle, a supply or source of air must be carried onboard, introducing the gas economy problem. The gas economy problem presents the question of how much air must be carried to satisfy a given supercavitating vehicle mission. In this paper, an assessment of models and dynamics of the cavity air, which directly affects the amount of air to be carried, is performed. In a supercavitating vehicle, the hull form is typically designed for the cavitating flow conditions. This is analogous to supersonic aircraft, and their designs are specific to supersonic flight. Thus, the hull-form should be designed to be enclosed by a gaseous supercavity at supercavitation conditions of interest. Adequately enclosing the vehicle within the supercavity minimizes the viscous-drag and prevents cavity destabilization. Furthermore, design of vehicle subcomponents, propulsion, lifting surfaces, etc. require a predictive understanding of the precise supercavity shape. Geometric restrictions create the need for design-level models to approximate the cavity location, and an understanding of the controlling parameters that affect it. Supercavitating vehicle operation depends on an ability to supply air sufficient to fill the cavity. This problem may be reduced to ascertaining the amount of air entrained by the cavity, for given cavity conditions, size, vehicle speed, etc. Obviously this is equivalent to knowing the needed air supply rate to sustain a steady cavity and directly corresponds to air storage requirements. A characteristic feature of the supercavity is the cavity-closure type Typically they are classified as either twinor toroidal-vortex cavities. Cavity-closure mode influences cavity stability and also appears related to the dominant mechanisms of air entrainment. In this work, computational fluid dynamics (CFD) is used to investigate the physical processes of air entrainment. Such a method, if successful, can provide the information needed for analysis and visualization without difficulties associated with physical observation of supercavities. Of course, in any framework other than direct numerical simulation, it is necessary that CFD-discovered phenomena must be validated experimentally. Using CFD solutions, we deduce mechanisms of air entrainment. In particular, evidence appears that corroborates theory, presented by Spurk [1], tying air-entrainment to cavitywall shear layers. The original work by Spurk [1] was limited to toroidal-vortex closing cavities. Although not surprising, the reviewed CFD solutions display evidence that the cavity-shear layers are also a primary mechanism of the air-entrainment from twin-vortex-closing cavities. Using such observations, an improved form of modeling the air-entrainment rate is proposed. Finally, this mechanism may not conform with the conventional viewpoint on supercavity air entrainment. BACKGROUND Theory developed for modeling supercavities, cavityclosure modes, and the impact these closure modes have on the physical mechanisms of air entrainment is reviewed. The viewpoint and all investigations are restricted to horizontal supercavities driven behind an axisymmetric cavitator. Therefore buoyancy is considered and acts perpendicular to the free stream velocity. It is also known that the quality of the cavity interface may have a strong effect on the amount of air entrained. In this effort we restrict our consideration to cavities that separate rather cleanly from a cavitator and interfaces that, over the majority of the cavity length, appear laminar or nearly