Generic energy approach for the evaluation of the self and coupling added mass coefficients for multiple submerged bodies

This paper presents a straightforward generic energy approach for the evaluation of the self and coupling added mass coefficients of many bodies immersed in a fluid. This method could be applied independently from the body shapes and their number, confinement type, and fluid in motion or at rest. The finite element method is used to compute the potential field by solving the Laplace equation. The kinetic energy is then evaluated by integrating the potential velocity field over the whole fluid domain for different cases in which the bodies are moving separately or together. This novel energy approach is then used to calculate the self and coupling added mass coefficients from the kinetic energies obtained for the different cases aforementioned. This method is first validated against theoretical models for two cylinders immersed in an infinite quiescent fluid and for the case of a cluster of cylinders confined in a cylindrical fluid at rest. Additional applications are discussed as illustration on the use of this new approach. The first consists of a clownfish, representing a randomly shaped object, trapped inside a compressible square enclosure. In the second example, the self and coupling added mass coefficients for two clownfish oscillating in a bowl are evaluated. The energy approach proposed in this study could be easily adopted for any case without the need to integrate the fluid pressure over the bodies' surfaces. The applications of this method would be interesting, for instance, to study the vibration of fuel rods in nuclear reactors and in heat exchangers and steam generator pipes.