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We perform direct numerical simulations of the settling of an ice sphere inan ambient fluid accounting for heat and mass transfer with the aim of studyingin a meteorological context the case of falling graupel in humid air. The studyis motivated by the fact that falling graupels in clouds are heated by thelatent heat released during the accretion of liquid water droplets. They maytherefore be considerably warmer than their surrounding and evaporate watervapor, which mixes with the surrounding air in the wake of the graupel, therebycreating transient zones of supersaturation there. The problem of a fallinggraupel is modeled as that of a heated sphere falling in a quiescent ambientfluid under the action of gravity. The coupling between the temperature andvelocity fields is accounted for by the Boussinesq approximation. This problemcan be parameterized by four parameters: the particle/fluid density ratio, theGalileo number, the Prandtl number, and the Richardson number. A separatescalar transport equation accounts for the vapor transport. Typical cloudconditions involve small temperature differences between the sphere and thesurrounding, yielding relatively small Richardson numbers for both heat andmass transport. We give a special emphasis to the Galileo numbers 150, 170, 200and 300 in order to analyze the specificities of each settling regime. Thequestions addressed in this study are mainly methodological and concern theinfluence of the settling regime and the mobility of the sphere on thestructure of the scalar fields, the possible influence of modest Richardsonnumbers on the structure of the wake, and the possible application of thissimulation framework to the investigation of the saturation in the wake of afalling graupel.

Heat and water vapor transfer in the wake of a falling ice sphere and its implication for secondary ice formation in clouds