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Research Papers: Flows in Complex Systems

Vibration-Enhanced Droplet Motion Modes: Simulations of Rocking, Ratcheting, Ratcheting With Breakup, and Ejection

[+] Author and Article Information
Ryan A. Huber

Department of Mechanical and Nuclear
Engineering,
Kansas State University,
Manhattan, KS 66506

Matthew Campbell

Institute for Environmental Research,
Kansas State University,
Manhattan, KS 66506

Nicole Doughramaji

Department of Mechanical and
Nuclear Engineering,
Kansas State University,
Manhattan, KS 66506

Melanie M. Derby

Department of Mechanical and Nuclear
Engineering,
Kansas State University,
Manhattan, KS 66506
e-mail: derbym@ksu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 15, 2018; final manuscript received November 9, 2018; published online January 7, 2019. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 141(7), 071105 (Jan 07, 2019) (13 pages) Paper No: FE-18-1475; doi: 10.1115/1.4042037 History: Received July 15, 2018; Revised November 09, 2018

Power plant water usage is a coupling of the energy–water nexus; this research investigates water droplet motion, with implications for water recovery in cooling towers. Simulations of a 2.6 mm-diameter droplet motion on a hydrophobic, vertical surface were conducted in xflow using the lattice Boltzmann method (LBM). Results were compared to two experimental cases; in the first case, experimental and simulated droplets experienced 30 Hz vibrations (i.e., ±0.1 mm x-direction amplitude, ±0.2 mm y-direction amplitude) and the droplet ratcheted down the surface. In the second case, 100 Hz vibrations (i.e., ±0.8 mm x-direction amplitude, ±0.2 mm y-direction amplitude) caused droplet ejection. Simulations were then conducted for a wide range of frequencies (i.e., 10–100 Hz) and amplitudes (i.e., ±0.018–50 mm), resulting in maximum accelerations of 0.197–1970 m/s2. Under low maximum accelerations (e.g., <7 m/s2), droplets rocked upward and downward in rocking mode, but did not overcome the contact angle hysteresis and, therefore, did not move. As acceleration increased, droplets overcame the contact angle hysteresis and entered ratcheting mode. For vibrations that prompted droplet motion, droplet velocities varied between 10–1000 mm/s. At capillary numbers above approximately 0.0044 and Weber numbers above 3.6, liquid breakup was observed in ratcheting droplets (e.g., the formation of smaller child droplets from the parent droplet). It was noted that both x- and y-direction vibrations were required for droplet ejection.

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Figures

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Fig. 1

Initialized droplet in the domain

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Fig. 2

Experimentally determined (a) receding (60 deg) and (b) advancing (120 deg) contact angles of a 2.6 mm water droplet on a vertical hydrophobic surface

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Fig. 3

Grid independence study using kinetic energy, (left) root-mean-square kinetic energy over 0.03 s and (right) kinetic energy with time

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Fig. 4

Droplet motion of (a) an experimental droplet and (b) simulated droplet at 30 Hz, x-amplitude ±0.1 mm, y-amplitude ±0.2 mm

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Fig. 5

Droplet motion for (a) an experimental droplet and (b) simulated droplet at 100 Hz, x-amplitude ±0.4 mm, y-amplitude ±0.15 mm

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Fig. 6

The 30 Hz simulated droplet motion for (a) x- and y-vibrational forces and (b) only y-vibrational forces (x-amplitude ±0.1 mm, y-amplitude ±0.2 mm)

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Fig. 7

The 100 Hz simulated droplet motion for (a) x- and y-vibrational forces (b) only y-vibrational forces (x-amplitude ±0.4 mm, y-amplitude ±0.15 mm)

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Fig. 8

The 10 Hz simulated droplet (a) velocities for given accelerations and simulations with applied accelerations of (b) 7.11 m/s2 (c) 0.197 m/s2, and (d) 59.2 m/s2 images

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Fig. 9

(a) Velocities of simulated droplets at 30 Hz simulated droplet and accelerations of (b) 59.2 m/s2, (c) 7.11 m/s2, and (d) 178 m/s2

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Fig. 10

The 70 Hz simulated droplet (a) velocities for given accelerations, (b) 197 m/s2 images, (c) 59.2 m/s2 images, and (d) 9.67 m/s2 images

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Fig. 11

The 100 Hz simulated droplet (a) velocities for given accelerations, (b) 197 m/s2 images, (c) 59.2 m/s2 images, and (d) 7.11 m/s2 images

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Fig. 12

Average downward velocities for constant accelerations across different frequencies

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Fig. 13

Strouhal number for constant accelerations across different frequencies

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Fig. 14

Average downward velocities for constant amplitudes across different frequencies

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Fig. 15

Three-dimensional plot of velocity versus amplitude and frequency

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Fig. 16

Capillary numbers for droplet motion modes (i.e., ratchet and breakup) versus nondimensionalized acceleration on vibrating surfaces for f = 10, 30, 70, and 100 Hz

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Fig. 17

Higher Weber numbers associated with the breakup of the liquid droplet; data are for f = 10, 30, 70, and 100 Hz and rocking modes are excluded from the graph

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Fig. 18

Reynolds number calculated based on initial droplet diameter with respect to nondimensionalized acceleration; data are for f = 10, 30, 70, and 100 Hz and rocking modes are excluded from the graph

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