Analysis of Sensitivities and Error Propagation in Heat and Mass Transfer of Spheroidal Hailstones Using Spreadsheets

View More View Less
  • 1 Deportment of Physics, University of Toronto, Toronto, Ontario, Canada
© Get Permissions
Restricted access

Abstract

In conformity with experimental results the heat transfer of gyrating spherical hailstones is divided into two parts. One takes place over a normally wet but supercooled equatorial region of limited roughness, whiles the other occurs over a rough, dry polar zone which is at a substantially lower temperature than the equatorial region. The sensitivity of this complex heat transfer is studied by establishing the response of the heat transfer to changes of 15 individual parameters relative to the results of a single hailstone growth experiment.

The propagation of errors in individually setting the icing conditions of a laboratory experiment is somewhat different from the sensitivity study. Both sensitivity and error hierarchies are given and conclusions are made about measurement accuracies. The measurements for the case at hand suggest that treating hailstones as smooth, nonrotating particles underestimates the heat transfer by a factor as high as two. For the treatment of a whole dataset containing many hailstone growth experiments, roughness may no longer be considered as a single-valued quantity since it seems to vary with hailstone latitude and icing conditions.

The tool used, the “spreadsheet,” is ideal to assess the complex heat budget. It serves to indicate potential problems before large experimental series are launched.

Abstract

In conformity with experimental results the heat transfer of gyrating spherical hailstones is divided into two parts. One takes place over a normally wet but supercooled equatorial region of limited roughness, whiles the other occurs over a rough, dry polar zone which is at a substantially lower temperature than the equatorial region. The sensitivity of this complex heat transfer is studied by establishing the response of the heat transfer to changes of 15 individual parameters relative to the results of a single hailstone growth experiment.

The propagation of errors in individually setting the icing conditions of a laboratory experiment is somewhat different from the sensitivity study. Both sensitivity and error hierarchies are given and conclusions are made about measurement accuracies. The measurements for the case at hand suggest that treating hailstones as smooth, nonrotating particles underestimates the heat transfer by a factor as high as two. For the treatment of a whole dataset containing many hailstone growth experiments, roughness may no longer be considered as a single-valued quantity since it seems to vary with hailstone latitude and icing conditions.

The tool used, the “spreadsheet,” is ideal to assess the complex heat budget. It serves to indicate potential problems before large experimental series are launched.

Save