A wind tunnel investigation on the ventilation coefficients of hailstones

The rate of change of mass of a hailstone by diffusion is affected by its motions. In a stationary pure diffusive case the water vapor distribution around a spherical hailstone is spherically symmetric having rather weak water vapor gradients. However, when a hailstone falls in the air, the flow field and hence the water vapor distribution around the hailstone is asymmetric showing much stronger water vapor gradients which are high at the upstream side and lower at the rear side of the hailstone. When averaged over the whole surface area of the hailstone the mass transfer to or from the falling hailstone surface is always higher compared to a pure diffusive case. This convective enhancement is given by the ventilation coefficient. Thus, to reliably quantify growth or sublimation rates of falling hailstones with models, it is necessary to know their ventilation coefficients. The rate of change of mass is proportional to the rate of change of heat. Therefore, the growth or sublimation of hailstones has not only implications on the humidity of the ambient air but also the vertical temperature profile of the atmosphere and consequently cloud and storm dynamics.

However, there is a lack of experimental studies on the ventilation coefficient of spherical hailstones in the literature. There are just three experimental studies available – all dating back to the 1960’s – which investigate the heat and mass transfer of spherical and oblate hailstones, but all were measured under accretional growth and melting conditions, respectively.

Therefore, experiments in the Mainz vertical wind tunnel were carried out to determine ventilation coefficients of spherical hailstones during sublimation. We investigated stones with diameters between 1 and 3 cm or, equivalently, Reynolds numbers between 10.000 and 45.000. The spherical hailstones were produced by freezing water in moulds and introduced into the wind tunnel. While freely floating at their terminal velocities the hailstones lost mass due to sublimation. The temperature in the tunnel was set to -5°C and relative humidities were rather low, i.e. between 30 % and 50 % with respect to ice, to facilitate sublimation. The mass of the hailstones was measured before and after the wind tunnel measurements from which we calculated the rate of change of mass in the convective case. The recordings of temperature and dew point were used to calculate the rate of change of mass for the pure diffusive case. The ratio of these rates is, by definition, the ventilation coefficient, which was calculated and parameterized as a function of the Reynolds number.