A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air

Abstract

SUMMARYThe internal circulation and the shape of water drops falling at terminal velocity in air of 20°C at sea level pressure, and nearly water saturated, were studied by means of a wind tunnel. Drops with an equivalent radius a, smaller than 140 pm had within the experimental error no detectable deformation from spherical shape.Drops of sizes 140 pm < a. < 500 p m were slightly deformed into an oblate spheroid. The deviation of these drops from spherical shape was found to be in fair agreement with that theoretically predicted by Imai (1950) and others. The deformation of drops of sizes 0.5 mm < uo < 4.5 mm was found to be linearly related to the drop size. Such a linear relationship is predicted by the semi-empirical calculations of Savic (1953).By means of a tracer technique it was established that water drops falling at terminal velocity in air have a well developed internal circulation. T h e flow pattern inside a drop was found to be consistent with the flow pattern of the air around the drop and that predicted theoretically by Hadamard (1911) and by Hamielec and Johnson (1962). The surface velocity at the equator of a drop was found to be about 1/100 of the drop's terminal velocity. The experimentally determined internal velocities were compared with those predicted theoretically by McDonald (1954) from boundary layer theory and by Hadamard (1911) based on Stokes flow.

Quantitative estimation of Tropical Rainfall Mapping Mission precipitation radar signals from ground‐based polarimetric radar observations

“…Thus it can be seen that K dp can be reduced by the variance of canting angle distribution, or decreasing the mean axis ratio. The slope of the k-K dp relationship for the Pruppacher and Beard [1970], Beard and Chuang [1987], and Andsager et al [1999] axis ratio models are 1.96 dB deg À1 and 02.24 dB deg À1 , and 2.67 dB deg À1 , respectively. However, whatever is modeled, the resulting values of Z h , Z dr , and K dp should be consistent with observations [Keenan et al, 2001].…”

Assessment of global navigation satellite system (GNSS) radio occultation refractivity under heavy precipitation

“…Raindrops fall following gravity and are flattened due to the air drag, becoming approximately oblate-shaped (e.g., Pruppacher and Beard, 1970;Beard and Chuang, 1987). Here, we do not take into account the canting angle effect (raindrops being tilted by wind), for simplicity and because in this situation its effect is secondary.…”

The multiparameter remote measurement of rainfall

“…The authors note that although the Z discrepancy can be explained on the basis of disdrometer errors, this is not the case with the Z DR estimates. To reduce the bias in radar measured Z DR , the relationship between D and the ratio of minor to major axes of the oblate spheroid is modified so that, in effect, the smaller drops are taken to be more spherical in shape than would be predicted from the equilibrium results of Pruppacher and Beard (1970). This modification reduces the Z DR bias to 0.15 db while having a 53 negligible effect on Zh .…”