A Novel Add-On Tool for Calculating Hydrodynamic Force on Immersed Object Independent of Local Wall Orientation

Hydrodynamic force (HF), resulting from drag, lift, and side forces on immersed objects, plays a critical role in automotive, aerospace, maritime, and wind engineering, as well as in sports. In computational fluid dynamics technique, HF is typically calculated from the resolved velocity gradients and pressure fields through postprocessing. However, this becomes challenging for non-flat objects due to the requirement of local wall orientation information. In this study, we derived a rigorous formulation of HF based on the Reynolds Transport Theorem equation for momentum. The HF acting on the object is calculated solely from surface integrals of velocity gradients and pressure over rectangular planes in proximity to the immersed object, eliminating the need of local wall orientation information. A systematic study has been performed to evaluate the numerical accuracy and convergence of the HF formula using the benchmark case of flow past a sphere at various Reynolds numbers. This formulation can serve as an add-on toolkit for any CFD solvers. We apply it to the volumetric lattice Boltzmann solver and verify its accuracy and convergence. Our work demonstrates that this new approach provides a robust and versatile method for calculating HF, potentially enhancing the precision of simulations in various engineering fields.