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Tuesday, October 2, 2018 at 12:00pm
Heavy Inertial Particles in Turbulent Flows
Professor Mahdi Esmaily
Sibley School of Mechanical and Aerospace Engineering, Cornell University
Clustering of inertial particles plays a key role in the formation of rain to that of the planets in our early solar system. It has been known for decades that heavy tiny particles in a turbulent flow segregate spatially, forming clusters. The degree of clustering highly depends on the particle relaxation time relative to that of the background flow, viz. the Stokes number. While minimal clustering is observed at very large or small Stokes numbers, clustering is maximized when the two time-scales are comparable and St ≈ 1. This non-monotonic variation, although observed experimentally and reproduced numerically, is yet to be explained theoretically. At the low Stokes number regime, our theoretical knowledge is sufficient for making a quantitative prediction, whereas, for the rest of parameter space, our knowledge is qualitative at its best due to the chaotic and complex behavior of these systems. Filling this gap is the objective of this study. In this talk, I will discuss the underlying mechanisms leading to cluster formation by using a lower dimensional analysis. This analysis explains the non-monotonic behavior of particle clustering versus Stokes number, shows the fundamental response of particles to straining and rotating flows, reveals the existence of a lower bound on the clustering rate, expresses the requirement for trajectory crossing, and predicts the asymptotic variation of the Lyapunov exponents for the full regime of Stokes and Reynolds numbers. Quantitative comparison against direct numerical simulations, including particle-laden isotropic turbulence, confirms these findings.