Investigation of fluid added mass matrix during hydroelastic slamming of wedges

Abstract

The investigation of the fluid added mass (FAM) matrix during the water entry of an elastic structure is crucial for understanding the mechanism of hydroelastic slamming, as it characterizes the fluid–structural interaction process. In this paper, we excavate a model for directly estimating the FAM matrix during hydroelastic slamming and employ this model to study the limitations and optimized values of the relaxation factor for a partitioned coupling solver. Our simulation of hydroelastic slamming couples the Wagner theory with the modal superposition method (MSM), and the FAM matrix is computed using a monolithic coupling scheme. We conduct a series of parametric studies to analyze how the modal number, hydroelasticity, deadrise angle, and structural boundary condition influence the eigenvalues of the FAM matrix. Based on these studies, we then propose an analytical model to directly express the eigenvalues of the FAM matrix, demonstrating their linear relationship with the wetted ratio. Furthermore, we apply this analytical model to analyze the relaxation factor in the partitioned coupling scheme, theoretically explaining its strong connection to the FAM effect. The limitations and optimized values of the relaxation factor are theoretically presented, and these results are verified through our numerical tests.