Using 3D-Printed Analogues to Investigate the Aerodynamics of Complex Ice Particles

The terminal velocity of ice crystals in the atmosphere is a function of their shape, size and mass. Various parameterisations have been proposed to approximate this function (e.g. Mitchell, 1996, J. Atmos. Sci., 53:1710-1723; Heymsfield and Westbrook, 2010, J. Atmos. Sci., 67:2469-2482). However, the accuracy with which these parameterisations are able to predict the terminal velocities of natural ice particles, where there is enormous variability in both shape and Reynolds number, remains unclear. Heymsfield and Westbrook (2010) collated field measurements of falling ice particles and found some cases where the measured velocities differed from the predicted values by a factor as large as two. It is unclear if these differences arise from deficiencies in existing models, or the (unquantified) experimental uncertainties in the field measurements.

In addition to the speeds of the falling particles, preferred orientations and onset of unsteady motions are important characteristics of the sedimentation process, and are crucial to the interpretation/prediction of polarimetric remote-sensing data, as well as our understanding of optical effects like halos and arcs.

Some of the challenges faced during field observations can be avoided in experimental studies of "analogues" falling through liquids. For example, List and Schemenauer (1971) [J. Atmos. Sci., 28:110-115] machined idealised metal models of simple crystals and dropped them in glycerine solutions. Recently, Westbrook and Sephton (2017) [Geophys. Res. Lett., 44, 7994–8001] revived this idea using 3D-printed snowflake analogues to make accurate measurements of the drag coefficient of relatively complex ice particle shapes. The advantage of this approach is that the aerodynamics of complex ice particle geometries can be studied in detail in a controlled laboratory setting. Here, we report on new experimental work that builds upon that preliminary study. In this new experiment snowflake analogues are manufactured using a Stereolithographic (SLA) printer which relies on using focussed ultraviolet light to selectively cure a light-sensitive polymer resin within a bath and then extrudes the model from the resin bath. This approach offers a much superior resolution than the printer utilised by Westbrook and Sephton, and is more suited to the manufacture of smaller, more detailed, and more realistic ice crystal analogues. These analogues are then allowed to sediment through a tall (1.8 metre) column of liquid during which their orientation and projected area are imaged, and settling velocity measured. Subsequently, drag coefficients and Reynolds numbers can be derived, allowing fall speed parameterisations to be tested against accurate data.

The 3D printing technique also enables us to systematically vary the geometric properties of the ice crystal analogues used in order to determine how the particle shape influences both the fall speed of the ice crystal, and its orientation. For example, we can alter the number of bullets, and the angles at which they are separated, on a bullet rosette and deduce how this affects its drag and its orientation. We show that even complex irregular particles such as aggregates have a well-defined preferred orientation in which they fall stably over some range of Reynolds number. We also investigate the influence of riming on the fall dynamics of snowflakes using analogues generated from the Leinonen and Szyrmer (2015) [Earth and Space Science, 2, 346–358] riming model.