Experimental Closure of the Heat and Mass Transfer Theory of Spheroidal Hailstones

Abstract

Hailstone growth experiments were performed in a vertical icing wind tunnel using 2-cm oblate ice spheroids (axis ratio of 0.67) mounted on a gyrator system. The liquid water content ranged from 1 to 5 g m?3, air temperature from ?21° to ?3°C, air speed from 9 to 24 m s?1, and air pressure from 40 to 100 kPa. Icing time, ice and water mass of the hailstone deposit, and final major and minor axis diameters were measured to determine the accretion of supercooled droplets from the air flow. An infrared imaging system was used to measure local and mean hailstone surface temperatures. These experiments allowed calculation of the last two unknowns in the heat and mass transfer equations for spheroidal hailstones: the net collection efficiency, Enet = 0.59 K0.15 (over a Stokes parameter range of 6 ≤ K ≤ 18), and the Nusselt number, Nu = 0.15 Re0.69 (over a Reynolds number range of 13 000 ≤ Re ≤ 50 000, that is, freely falling hailstones with diameters of ?1 to ?3 cm). The net collection efficiency results are consistent with previous investigations. The Nusselt number for spheroids, a measure of heat transfer by convection and conduction, with its built-in shape, ?, and roughness factor, ?, is 45%?65% larger than Nu for smooth spheres and 25%?45% larger than Nu for rough, melting spherical hailstones. Approximately 20% of the increase is due to particle shape and the remainder to roughness. These results can be used to improve computer models of convective storms. In addition, the fourfold increase in Nusselt number with increasing liquid water content previously reported is attributed in this study to uncertainties caused by a combination of shape change, shedding, and low ice fraction at air temperatures close to 0°C.