The diffusion of slightly buoyant diesel oil droplets in isotropic turbulence is studied using high speed in-line digital holographic cinematography. Diesel fuel droplets with specific gravity 0.85 are injected into a 50×50×70 mm3 sample volume located at the central portion of a nearly isotropic turbulence facility. The turbulence in the sample volume is fully characterized using 2D PIV. Probability density functions of the Lagrangian droplet velocity are very close to a Gaussian distribution, which justifies the use of Taylor’s  model to calculate diffusion parameters. Similar to Friedman & Katz  data, our current results confirm that the mean rise velocity of diesel droplets becomes higher than the quiescent rise velocity at high turbulence levels. For most of the present droplet sizes and turbulence level, the rms of the horizontal droplet velocity fluctuations exceeds that of the horizontal fluid velocity fluctuations. The rms values of the vertical droplet velocity fluctuations are higher than those of the fluid only for the highest turbulence level. The droplet to fluid velocity rms ratio in both directions increases with turbulence level, but decreases with increasing droplet size. Assuming Fickian diffusion, Lagrangian auto-correlation functions of 22,000 droplet tracks are used for calculating the diffusion coefficient as functions of droplet size and turbulence level. Using all the data, we show that the diffusion coefficient scaled by quiescent rise velocity and the turbulence integral length scale is a monotonically increasing function of the turbulence level normalized by the droplet quiescent rise velocity.
Lagrangian Motion of Slightly Buoyant Droplets and Fluid Particles in Isotropic Turbulence
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Gopalan, B, Malkiel, E, & Katz, J. "Lagrangian Motion of Slightly Buoyant Droplets and Fluid Particles in Isotropic Turbulence." Proceedings of the ASME/JSME 2007 5th Joint Fluids Engineering Conference. Volume 2: Fora, Parts A and B. San Diego, California, USA. July 30–August 2, 2007. pp. 477-484. ASME. https://doi.org/10.1115/FEDSM2007-37538
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