# The Application of the Lattice Boltzmann Method in the Calculation of the Virtual Mass

## Keywords:

Lattice Boltzmann simulation, added/virtual mass, variable size, various distance, bounce-back boundary condition

## Abstract

Virtual mass is an important quantity in the analysis of the unsteady motion of objects underwater or other fluids or unsteady flow around bodies, for example, the virtual mass effect is important in the inertia of ships, floaters, swimmers’ organs, airplanes, and bubbles. The additional mass resulting from the fluid acting on the structure can be calculated by solving the equation of potential flow around the object. In this paper, a system in which a square object is immersed in a channel of fluid and moves parallel to the wall has been considered. The corresponding virtual mass at a determined distance S from the wall and for the object size D (the side of the square object) is calculated via the Lattice Boltzmann Method. Here, it is tried to change D and S separately and investigate their effects on the virtual mass. According to the simulation results, for the systems in which the distance from the wall is more than four times the object size (S > 4D), the distance does not influence the added mass. Furthermore, the virtual mass rises when the object approaches the wall and experiences its maximum value as it reaches the wall (S → 0). As a result, in this case, the virtual mass is about 75% larger than in the case of S=4D. In addition, the simulations reveal that by increasing the dimensions of the object D the virtual mass increases and vice versa.

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