Numerical study on the vertical motion of underwater vehicle with air bubbles attached in a gravity field

• The fully nonlinear interaction between moving body, deformable bubble and gravity is simulated.
• A numerical method to study the pressure on the body in a moving coordinate system is proposed.
• The bubble jet will change from inward to oblique and then to upward as Froude number decreases.
• Acceleration of the body has little influence on bubble evolution but important impact on resultant fluid force.

Air bubbles may be injected and attached on the surface of a moving underwater vehicle to enhance its speed. Thus the nonlinear interactions between the moving body at a variable speed and the deformable bubble attached are of importance. In this paper, a body with an air bubble attached at a variable speed is simulated using the boundary-element method together with the potential theory. The motion of the body and deformation of the bubble under the action of gravity are considered in a moving coordinate system fixed on the body. Bernoulli equation and auxiliary function method in this moving coordinate system are adopted to calculate the pressure and fluid force on the body. Convergence study with mesh and time step has been undertaken with good convergence obtained. Simulated results have also been compared with other published numerical results and good agreement achieves. On this basis, the influences of different parameters have been further studied, such as Froude number, cavitation number and body acceleration. It is found that bubble shape and jet direction are influenced by the gravity a lot in the range of parameters considered and various jet patterns may generate such as inward jet, oblique jet or upward jet.