Hydrodynamic Force Coefficients for Spherical Shell Fragments: Dependence on the Aspect-Ratio and Flatness

Euler-Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces on individual particles. Currently there are no universal models that can prescribe these forces for both irregularly shaped and arbitrary orientated particles. Here, we use OpenFOAM RANS simulations of steady bottom-boundary layer flow of Reynolds number 12,000 over a series of irregularly shaped spherical shell fragments. These fragments cover a range of elongation and flatness characteristics. This work is an extension of previous modeling efforts to create a predictive hydrodynamic force model for arbitrary rotations of an intact shell. Here, shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while the fragment surface area is held constant to define the overall fragment size. The simulations explicitly resolve the wall boundary layers using O(y+=1) grid spacing at the shell fragment surface and use the SST k-omega turbulence closure model. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.