Hydrodynamic force interaction of two fixed spheres in a wall-bounded linear shear flow

We examine the modulations of the drag coefficient C-d and lift coefficient C-l on a spherical particle caused by the presence of a neighboring sphere when positioned in close proximity to a wall. Data are generated through the utilization of a fast and accurate Particle -Resolved Direct Numerical Simulation (PR -DNS) method that relies on the Direction -Splitting algorithm and that was extensively validated in our prior study (Goyal and Wachs, 2023a, 2023b; Morente et al., 2023). We further validate the method in the flow configuration of the present study by comparing them with data published in the literature. We consider three Reynolds numbers Re = 20, Re = 50 and Re = 100, which describe the flow conditions in the vicinity of the wall. The primary sphere is positioned at a distance delta from the wall, while the neighboring sphere is positioned at a constant distance from the primary sphere encompassing all possible angular positions theta. We report the modulations of C-d and C-l compared to a situation without any neighboring sphere as a function of delta, theta and Re. The inclusion of a wall intensifies the influence of the neighboring sphere on the primary sphere and significantly modifies the values of C-d and C-l. We attempt to relate the values of the modulations of C-d and C-l to the modulations in the contours of the pressure and of the spanwise vorticity on the surface of the primary sphere. We take advantage of the periodic nature of C-d and C-l as a function of the relative angular position theta of the neighboring sphere and propose a Fourier Predictive Model (FPM) to effectively represent the data using a finite number of modes in the cosine Fourier series. We show that our FPM is able to estimate the modulations of C-d and C-l excellently with a coefficient of determination R-2 greater than or similar to 0.99 in the parameter space investigated in our study.