Theoretical Study of Particle-Laden Flows in Synthetic Turbulence

The dispersion and clustering of inertial particles in turbulent flows present a fundamental challenge in fluid mechanics, with relevance to a wide range of natural and engineering systems, from cloud microphysics to combustion and pollutant dispersion. Simulating this phenomenon requires capturing both the turbulent flow features and the dynamics of an extreme number of particles, which remains computationally prohibitive for direct numerical simulations (DNS) at high Reynolds numbers. Previous research consistently reports that clustering is reduced at both very small and very large Stokes numbers for moderate Reynolds numbers.

To address this limitation, this study employs Kinematic Simulations (KS), coupled with a Lagrangian particle tracking algorithm as an alternative framework. In KS, the velocity field is represented as a sum of divergence-free Fourier modes with a turbulence-like energy spectrum, yielding computational efficiency while preserving key turbulence statistics. A numerical study examined the chaotic dynamics of inertial particles and their effect on particle clustering.
Finally, we examined the effects of time-dependent changes in particle diameter on the system.

Our results show that KS successfully reproduces clustering of particles, in good agreement with trends previously reported in DNS studies. Thus, KS is a practical tool for studying clustering in regimes where DNS is not feasible and for incorporating additional physics (e.g., thermodynamics or phase change). Moreover, when the Stokes number varies dynamically over time, noticeable clusters form, even for low Stokes numbers that would typically exhibit negligible clustering. This suggests that transient effects associated with evolving particle inertia can significantly enhance clustering behavior beyond what would be predicted based solely on a constant Stokes number.