Preferential concentration of heavy inertial particles using the two-fluid equations
Preferential concentration describes the tendency of heavy particles to accumulate in certain regions of a turbulent flow. This process has been hypothesized to play a role in particle growth which is of crucial importance in numerous physical and engineering applications. The efficiency of preferential concentration is known to depend on the ratio of the particle stopping time to the turbulent eddy turnover time, which is called the Stokes number. In this thesis, we investigate the role of turbulence on preferential concentration of heavy particles with Stokes number less than unity. We use Direct Numerical Simulations and adopt the two-fluid formalism, where the particulate phase is treated as a continuum. In the first work, we study a two-way coupled system in the particle-induced Rayleigh-Taylor instability, and observe the striking emergence of dense, filamentary particle structures. Most notably, we find that the particle concentration enhancement primarily depends on three properties of the system: the rms fluid velocity, the Stokes number, and the assumed particle diffusivity from the two-fluid equations. Additionally, we note that when preferential concentration is dominant, the probability distribution function of the particle concentration takes on a distinctive form, characterized by an exponential tail whose slope is related to the same three properties listed above. In the second part, we further extend our study to a regime in which turbulence is externally-driven, and verify that the results found in the first study also hold. In the final work, we use a box-counting algorithm to identify and extract key features of the dense particle structures. We find in particular that these structures have a large aspect ratio. We propose an advection-diffusion model to predict their thickness, and find preliminary evidence that suggests that their long dimension depends on the Taylor microscale.