Dynamic mode decomposition of inertial particle caustics in Taylor\u2013Green flow

Omstavan Samant,Jaya Kumar Alageshan,Animesh Kuley,Sarveshwar Sharma

doi:10.1038/s41598-021-89953-3

Omstavan Samant, Jaya Kumar Alageshan + Show 2 more

Open Access

https://doi.org/10.1038/s41598-021-89953-3

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Abstract

Inertial particles advected by a background flow can show complex structures. We consider inertial particles in a 2D Taylor–Green (TG) flow and characterize particle dynamics as a function of the particle’s Stokes number using dynamic mode decomposition (DMD) method from particle image velocimetry (PIV) like-data. We observe the formation of caustic structures and analyze them using DMD to (a) determine the Stokes number of the particles, and (b) estimate the particle Stokes number composition. Our analysis in this idealized flow will provide useful insight to analyze inertial particles in more complex or turbulent flows. We propose that the DMD technique can be used to perform similar analysis on an experimental system.

Highlights

Inertial particles advected by a background flow can show complex structures
In “Observations” we show the formation of caustic structures and analyze them using dynamic mode decomposition (DMD) method in “Analysis” and demonstrate how we extract the caustic wavefronts from the DMD mode
We study the dynamics of inertial particles in a Taylor–Green flow with periodic boundary conditions in 2D

Summary

Results

The G x is obtained from the DMD as described in “Analysis” by simulating mono-disperse Stokes number particle systems to generate the plots in Fig. 4a which shows G x as a function of St. The alignment of the peaks in G x along a curve indicates a systematic dependence of the location of wavefront on the Stokes number. We find that the prominence of the wavefront has a systematic dependence on the initial concentration of the corresponding Stokes number particles and from Fig. 6b we find that on a log–log plot the relation is linear, with a slope approximately equal to −1 This implies that in a bi-disperse system the ratio of the prominence is inversely related to the ratio of initial concentrations. We can use this relation to predict the concentration of various Stokes number particles in a system

Conclusions

A Validity of particle dynamics

B DMD algorithm