Parameterizing the fluid forces on limpet shells in unidirectional flow

Abstract

Current parameterizations of the hydrodynamic forces on irregular particles consider some shape dependencies, but lack an explicit dependence on the orientation with respect to the flow. In this paper, we propose a new parameterization of the drag and lift forces acting on whole Limpet shells at arbitrary orientations with respect to the direction of flow through the linear regression of fluid forces against the velocity components in an object frame of reference. The fluid forces were estimated using boundary layer-resolving Reynolds-averaged Navier-Stokes (RANS) simulations. We verified the accuracy of the shear stress transport (SST) \(k-\omega \) turbulence model on flat plates with varying angles of attack, and we achieved coefficients of determination versus existing data of approximately 0.95 for both the drag and lift coefficients. From the linear regression of our simulated force data, we developed a model as a function of 3-dimensional orientations to predict the hydrodynamic forces acting on a Limpet shell with coefficients of determination of 0.80 for normal forces and 0.51 for longitudinal forces.