Numerical simulations of air-water flow and rigid-body motion based on two-liquid CLSVOF/IB method and overset mesh

Abstract

For simulating air-water flows with rigid-body motion, the rigid boundary has to be body-fitted and discretized in the traditional dynamic mesh method, which will lead to a severe computational instability due to the mesh deformations when large displacements are involved. A two-liquid CLSVOF/IB (coupled Level Set and Volume of Fluid/Immersed Boundary method) method for directional numerical simulation of air-water flow and water-water mixing with a moving rigid-body is presented in this study, which is based on overset mesh method. In order to make the CLSVOF method applicable to two different cell sizes in overset mesh and background mesh respectively, the formula of the artificial time step size in the re-initialization equation of Level Set (LS) method is improved. A simple and effective IB method suitable for the overset mesh method and the dynamic mesh technique is also implemented. The IB method marks the cells around the rigid-body as forcing cells in the overset mesh, and then an artificial momentum forcing term is introduced into the momentum equation of the fluid to satisfy no-slip boundary condition in fluid-solid interface. The method has been validated with laboratory data, including two-liquid dam-break flow with wet bed and single-liquid water entry problem. The effects of various parameters such as ambient water depth and gate motion on mixing pattern and front propagation of water-water interface are investigated in the dam-break flow problems. The results have good agreement with the published experimental results and emphasize the necessity of considering the gate in numerical simulation of dam-break flow. In the numerical simulation of a free-falling rigid-body impacting the free surface of water, the simulation results, including the computed shape of the air cavity and displacement of free-falling rigid-body, agree well with experimental results.