Low-frequency wake modulation governs back-side particle deposition on cylinders

We compute particle deposition rates on the back side of a cylinder at Reynolds numbers $\textit{Re}={1685}$ , $6600$ and $10\,000$ using direct numerical simulation and Lagrangian particle tracking. We find that the deposition rates for $\textit{Re}={6600}$ and $10\,000$ are highly variable in time, with differences of up to a factor 27 in deposition rates between alternating low- and high-deposition-rate periods. The deposition-rate fluctuations are found at frequencies lower than the vortex-shedding frequency and therefore require long simulation times to be discovered. Additionally, we find that these fluctuations correlate positively with the drag and negatively with the cylinder base pressure. These observations imply that the back-side deposition process is governed by the low-frequency modulation of the cylinder wake. The high-deposition-rate regime is associated with a shorter wake and a more efficient turbulent transport of particles towards the cylinder surface, where the wake length modulation appears to have a more prominent effect. Consequently, the wake modulation controls the deposition rate but does not significantly affect the deposition mechanism. The back-side deposition has a maximum at Stokes number $St = 0.07$ , as particles of lower Stokes number have too little inertia to deposit effectively and the deposition rate decorrelates from the wake fluctuations for larger Stokes numbers. These results highlight the strong sensitivity of the back-side deposition process to accurate descriptions of the wake turbulence over long enough times. These observations are critical when constructing accurate datasets for data-assisted methods to predict long-term back-side deposition on bluff bodies.