Numerical analysis of gas bubbles in close proximity to a movable or deformable body

Abstract

The growth and collapse of gaseous bubbles near a movable or deformable body are investigated numerically using the boundary element method and fluid–solid coupling technique. The fluid is treated as inviscid, incompressible and the flow irrotational. The unsteady Bernoulli equation is applied on the bubble surface as one of the boundary conditions of the Laplace’s equation for the potential. Good agreements between the numerical and experimental results demonstrate the robustness and accuracy of the present method. The translation and rotation of the rigid body due to the bubble evolution are captured by solving the six-degrees-of-freedom equations of motion for the rigid body. The fluid–solid coupling is achieved by matching the normal component of the velocity and the pressure at the fluid–solid interface. Compared to a fixed rigid body, the expansion of the bubble is not affected too much but much faster collapsing velocities during the collapsing phase of bubble can be observed when considering the motion of the rigid body. The rigid body is pushed away as the bubble grows and moved toward the bubble as the bubble collapses. The motion of two bubbles near a movable cylinder is also simulated. The large rotation of the cylinder and obvious deformation and distortion for the bubble in close proximity to a curved wall are observed in our codes. Finally, the growth and collapse of bubble near a deformable ellipsoid shell are also simulated using the combination of boundary element method (BEM) and finite element method (FEM) techniques. The oscillations of the ellipsoid shell can be observed during the growth and collapse of bubble, which much differs from the results obtained by only considering effects of a rigidly movable body on the bubble evolution.