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A Numerical Study on the Ventilation Coefficients of Falling Hailstones

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  • 1 Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin
  • 2 Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin, and Research Center for Environmental Changes, Academia Sinica, Taipei, Taiwan
  • 3 Research Center for Environmental Changes, Academia Sinica, Taipei, Taiwan
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Abstract

The ventilation coefficients that represent the enhancement of mass transfer rate due to the falling motion of spherical hailstones in an atmosphere of 460 hPa and 248 K are computed by numerically solving the unsteady Navier–Stokes equation for airflow past hailstones and the convective diffusion equation for water vapor diffusion around the falling hailstones. The diameters of the hailstones investigated are from 1 to 10 cm, corresponding to Reynolds number from 5935 to 177 148. The calculated ventilation coefficients vary approximately linearly with the hailstone diameter, from about 19 for a 1-cm hailstone to about 208 for a 10-cm hailstone. Empirical formulas for ventilation coefficient variation with hailstone diameter as well as Reynolds and Schmidt numbers are given. Implications of these ventilation coefficients are discussed.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: pwang1@wisc.edu

Abstract

The ventilation coefficients that represent the enhancement of mass transfer rate due to the falling motion of spherical hailstones in an atmosphere of 460 hPa and 248 K are computed by numerically solving the unsteady Navier–Stokes equation for airflow past hailstones and the convective diffusion equation for water vapor diffusion around the falling hailstones. The diameters of the hailstones investigated are from 1 to 10 cm, corresponding to Reynolds number from 5935 to 177 148. The calculated ventilation coefficients vary approximately linearly with the hailstone diameter, from about 19 for a 1-cm hailstone to about 208 for a 10-cm hailstone. Empirical formulas for ventilation coefficient variation with hailstone diameter as well as Reynolds and Schmidt numbers are given. Implications of these ventilation coefficients are discussed.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: pwang1@wisc.edu
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