Experimental Investigation Of Disks Settling In Quiescent And Turbulent Air
2024-04
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Experimental Investigation Of Disks Settling In Quiescent And Turbulent Air
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2024-04
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We experimentally investigate the settling of millimeter-sized disks in quiescent air and in homogeneous turbulence, as turbulence can have a strong effect on the fall speed of snowflakes and ice crystals. The range of physical parameters is chosen to be relevant to plate crystals settling in the atmosphere: Disks range in diameter from 0.3 to 3 mm, with diameter-to-thickness aspect ratios of χ = 5 − 60, inertia ratios of I∗ ≈ O(1), and Reynolds numbers from Re = 10 − 663. Both solid and perforated disk geometries are considered, with area ratios in the range AR = 0.73 − 1. Velocity fluctuations of the turbulence are comparable to the disk terminal velocities. Thousands of trajectories are captured and reconstructed for each disk type by planar high-speed imaging, using the method developed by Baker & Coletti (J. Fluid Mech., vol. 943, 2022, A27). This allows for statistical analysis of the translational dynamics in 2D and the rotational dynamics in 3D.
In quiescent air, most disks either fall straight vertically with their maximum projected area normal to gravity or tumble while drifting laterally at an angle <20°. Two of the three disk sizes considered exhibit bimodal behavior, with both non-tumbling and tumbling modes occurring with significant probabilities, which stresses the need for a statistical characterization of the process. The smaller disks (1 mm in diameter, Re = 96) have stronger tendency to tumble than the larger disks (3 mm in diameter, Re = 360), at odds with the diffused notion that Re = 100 is a threshold below which falling disks remain horizontal. Larger fall speeds (and thus smaller drag coefficients) are found with respect to existing correlations based on experiments in liquids, demonstrating the role of the density ratio in setting the vertical velocity. The data supports a simple scaling of the rotational frequency based on the equilibrium between drag and gravity, which remains to be tested in further studies where disk thickness and density ratio are varied.
Air turbulence reduces the disk terminal velocities by up to 35%, with the largest diameters most significantly influenced, which is primarily attributed to drag nonlinearity. This is evidenced by large lateral excursions of the trajectories, which correlate with cross-flow-induced drag enhancement as previously reported for falling spheres and rising bubbles. As the turbulent intensity is increased, flat-falling behavior is progressively eliminated and tumbling becomes prevalent. The rotation rates of the tumbling disks, however, remain similar to those displayed in still air. This is due to their large moment of inertia compared to the surrounding fluid, in stark contrast with studies conducted in water. In fact, the observed reduction of settling velocity is opposite to previous findings on disks falling in turbulent water. This emphasizes the importance of the solid-to-fluid density ratio in analogous experiments that aim to mimic the behavior of frozen hydrometeors.
The velocities estimated by the empirical model of Heymsfield & Westbrook (2010) for both the solid and perforated geometries match quite well with the measured velocities in quiescent air, with an average error of < 20%. This model consistently underestimates the terminal velocities, but is an improvement on the estimates from Bohm (1989). The perforated disk geometries experience a velocity reduction due to the turbulence, of similar magnitude to the solid disk. A stabilizing effect due to the perforations is present for the four quadrant and single hole geometries, which manifests as a larger percentage of steady falling trajectories than for the solid. This result is robust in quiescent air and homogeneous turbulence. In turn, lateral motion induced by the turbulent forcing is less than for the solid disk. A distinct bimodality is present for the angular velocity of the solid disk, directly correlated to the falling style. In the perforated case, the tumbling angular velocity measured is half of that for the solid disk, and thus becomes indistinguishable from the angular velocity in a fluttering descent.
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University of Minnesota Ph.D. dissertation. April 2024. Major: Aerospace Engineering and Mechanics. Advisors: Filippo Coletti, Michele Guala. 1 computer file (PDF); xi, 111 pages.
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