2016) used a high-speed camera to measure the terminal velocity. More recent experimental studies ( Yu et al. These values were used in the Beard (1976) parameterization of the terminal velocity. Although wind tunnel method might be prone to measurement error due to non-uniform velocity profile in the tunnel, the measured values for larger droplets agreed well with Gunn and Kinzer’s experimental data ( Beard 1976). Instead, they used a wind tunnel with 100% relative humidity to measure the terminal velocity, and their results indeed suggested a slight overestimation of the terminal velocity of the smallest droplets measured by Gunn and Kinzer (1949). Beard and Pruppacher (1969) pointed out that the environmental condition of 50% relative humidity in Gunn and Kinzer’s experiment might have generated considerable errors in the measurement of the terminal velocity, especially for smaller drops, because some water might have evaporated from the drop before its mass was measured. Two electrode detectors that could detect the passing of charged droplets at separate heights were used to calculate the time span, and thus the terminal velocity could be obtained. In their experiment, droplets were electrically charged and allowed to fall freely in a rain tower. The laboratory experiment conducted by Gunn and Kinzer (1949) produced detailed data on the terminal velocity of drops with diameters ranging from 0.0783 to 5.8 mm at a temperature of 20☌ and pressure of 1013 hPa. 2016) on the measurement of the terminal velocity of water drops. There have been numerous experimental reports ( Gunn and Kinzer 1949 Beard and Pruppacher 1969 Yu et al. In atmospheric modeling, the terminal velocity is commonly retrieved from parameterizations via some empirical formulas derived from experimental data. Because the general equation governing the free-falling motion of water drops of even moderate size (on the order of 10 −1 mm) is nonlinear, an analytic solution of the terminal velocity exists only for drops that are small enough (on the order of 1 μm) for the Stokes law to be applicable. An accurate prediction of the terminal velocity is therefore one of the necessary conditions for improving the accuracy of weather and climate simulations. The terminal velocity of raindrops is one of the major factors that determine the rate of removal of liquid water from the atmosphere, which can strongly affect weather predictions ( Parodi and Emanuel 2009 Hagos et al. This constant speed at which drops fall is called the terminal velocity. Due to the existence of the viscosity, they attain a constant falling speed when the gravitational force is balanced by the viscous frictional force. Internal circulation within falling drops is also presented and compared with previous studies.Īll cloud drops and raindrops 1 experience an acceleration toward the ground by the pull of the gravitational force. It is also shown that the falling speed of a small drop is not sensitive to shape oscillation, and the terminal velocity decreases by only less than 1.3% when the axis ratio increases by 12% with reduced surface tension. We propose a new empirical formula that describes the air density dependence of the terminal velocity. Simulations under various atmospheric conditions show that existing empirical parameterizations that account for the air density dependence of the terminal velocity have errors up to 11.8% under the conditions examined in this study. The velocities converge to the analytic Hadamard–Rybczynski solution within 2% for small Reynolds numbers, demonstrating the robustness of our simulations. Simulated terminal fall velocities of free-falling drops at 20☌ and 1013 hPa agree within 3.2% with the previous empirical parameterization (Beard formula), and 4.5% with existing laboratory data in the diameter range between 0.3 and 0.5 mm. In this study, an incompressible two-phase flow direct numerical simulation model is used to calculate the free-falling motion of axisymmetric drops with diameters between 0.025 and 0.5 mm to study the terminal fall velocity. Because these experiments were performed only at typical environmental conditions of 20☌ and 1013 hPa, parameterizations have been introduced to deduce the terminal velocity aloft without rigorous evaluation. Current formulations rely on laboratory experiments made in the 1940s and 1960s. The terminal velocity of cloud drops and raindrops used in numerical model calculations can significantly affect weather predictions.
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