O.B. Nasello

A comparative study on hailstone trajectories using different motion equations, drag coefficients and wind fields

Abstract The growth of hydrometeors to hailstone sizes is simulated by computer. The trajectories are calculated using the results of a three-dimensional cloud model as input. The model simulates the time evolution of the wind, the liquid water content and the air temperature fields in a cubic region of 16 km per side. These fields are recorded and later used in another program that calculates the hail growth and the aerodynamical forces involved. Embryos of 0.25, 0.5 and 1.00 mm of initial radii are released at 676 locations uniformly distributed in a region of 6×6×4 km3 around the updraft center. The trajectories of all the particles are followed all the way to the 0°C altitude. The final radii and residence times in the cloud of all particles are also stored. A systematic study on the changes brought about by the use of different expressions for the drag coefficient and for the equation of motion on both the computed trajectories and on the final size of hailstones is performed. The study includes the location of the most favored regions for the initiation of hail in each case. The effect of using stationary and time dependent fields is also considered in detail. A comparison of the results obtained using a realistic equation of motion and those employing an approximation frequently used by others show the respective final radii differing by up to 30%. It is observed that expressions predicting values for the drag coefficient that are not nearly as scattered as those found in nature can lead to final radii differing by as much as 50%. The use of stationary wind fields can produce an important overestimation of the maximum sizes achieved by hail inside the cloud.

Anisotropic migration of two-dimensional grain boundaries

Abstract Grain boundary migration in two-dimensional samples, when the capillary driving force depends on the grain boundary inclination, is studied. The grain boundary motion equation and the solutions to this equation, specially for samples with the initial geometry proposed by Sun and Bauer, are presented. It is shown that grain boundary velocities depend not only on the free surface energy but also on the second derivative of this energy with the grain boundary inclination. By using a very simple expression for the free surface energy, it is shown that small grain boundary anisotropies can cause important variations in grain boundary velocities.

Surface temperature distribution for ice accreted on a cylindrical collector

Atmospheric icing has been studied by several authors due to its importance in many phenomena where a solid body grows by accretion of supercooled cloud or fog droplets. An important parameter, as for the deposit evolution is the surface temperature, Ts, which determines the deposit density and morphology in dry regime and the transition for dry to wet regime. In the present work an algebraic solution is given for the differential equation representing the equilibrium surface temperature of an ice accretion growing on a fixed cylinder. This solution differs from previous ones because it takes into account the heat flux occurring in a cylinder, due to the temperature gradient created at the surface. It is shown that, for an ice cylinder growing in normal atmospheric conditions, this flux is of the same order of magnitude of that representing the heat exchange with the environment. The proposed mathematical treatment requires the representation of the different heat fluxes in the form of Fourier series, the terms of which are functions of cos (nθ), where θ is the angular distance from the radius through the stagnation point. Special attention is given to the Nusselt number Nu(θ), which affects all heat fluxes related with ventilation. An expression for Nu(θ), valid for an heat conducting cylinder, in the range 4 x 103<Re<2x104, is proposed. Several Ts(θ) curves are given for different environmental conditions and the effects of varying the Stokes and the Reynolds numbers are considered. The results obtained for an isolating, an ice and a Cu collector are compared.

A discussion of mechanisms proposed to explain habit changes of vapor-grown ice crystals

Abstract In the present work, surface kinetics processes that can contribute to the growth behavior of ice crystals from the vapor phase are revised and proposed interpretations of crystal habit changes are discussed. Following the main initial papers on this subject by Hallet, Mason et al. and Kobayashi, relationships are considered between linear growth rate and step velocity. More recent results obtained by Sei and Gonda (SG2) for molecular steps naturally formed on basal and prism surfaces are shown to confirm Hallets interpretation of previous curves obtained for the velocity of giant steps that were artificially formed on basal surfaces only. The different behavior of the condensation coefficient α(T) characterizing growth in pure water vapor, observed by Lamb and Scott for surfaces intersecting a substrate and by Sei and Gonda for free surfaces, is discussed by considering that α is the product of the adsorption and accommodation coefficients β and γ, respectively. It is noted that, as in previous works, β=1 was assumed, the variations of α discussed to interpret crystal habit changes were made to coincide with variations of γ. However, Sei and Gondas results show that in the temperature range where crystal habit changes are observed, values of β(T)≪1 are found. As these depend on surface orientation, they should play an important role in the phenomenon. The dependence of crystal habits on two-dimensional nucleation is also discussed on the basis of measurements carried out by Nelson and Knight of the critical supersaturation σcr on the basal and prism surfaces. A possible relationship between the curves for σcr(T) and those of β(T) derived from Sei and Gondas results is suggested. The mechanisms determining the large anisotropy exhibited by crystals grown in atmospheric conditions are discussed by taking into account that the growth rate curves R(T) on the basal and prism surfaces show a correlation between maximum and minimum values, which are not observed for crystals grown in pure vapor.

Requirements for low density riming and two stage growth on atmospheric particles

Abstract A theoretical study is carried out of the conditions that can be expected to determine low density riming on atmospheric ice particles. Using a growth simulation model, critical liquid water contents L wc and air temperatures T a are calculated, which correspond to a density ρ =0.5 g/cm 3 for rime deposit on ice particles with radii varying from 1 to 10 mm. Their dependence on the used laws for the ice density as a function of Macklins parameter and for the drag coefficient as a function of Reynolds number, is discussed. The evolution of the density and related parameters for free falling particles growing by accretion from initial values of the radius R and density ρ is studied in different environmental conditions. It is shown that the temperature of the deposit T s increases with R , up to the transition to wet growth, represented by T s =0°C. Only for L wc ≥2 g/m 3 the transition from low density ice to wet growth is found to occur rapidly, at a distance from the center R ≤1 cm. This distance is considered to represent the maximum radius of regions where two-stage growth, due to water penetration and freezing into pores of low-density layers, can be responsible for rapid variations of the particle density and consequently of its free-fall speed, which would characterize the effect of hail growth via microphysical recycling.

On the search for a representative drag coefficient law to be used in hail trajectory simulations

A new method to calculate the ice particle drag coefficient used in hailstone trajectory calculations is presented. The method takes into account the high variability of this parameter and also allows for the investigation of the different trajectories that equally initialized embryos may follow within a cloud due to non-deterministic changes in their surface texture. The method is applied in a hail trajectory simulation model. The results are compared with those obtained by means of curves fitted to the drag coefficient going through mean, low and high values. The aim of this work is to investigate the representativity of hail trajectories simulated using these curves for the assessment of the drag coefficient value.

Comments about the drag laws used in hail growth simulations

The values of the drag coefficient (CD), experimentally obtained by different authors for graupels and hailstones, are carefully analyzed, in order to investigate how the numerical simulations of hail trajectories, which markedly depend on the CD values assigned to the growing particle, can be improved. It is found that new measurements of CD should be performed in the whole range of the Reynolds number (Re) of the cloud ice particles. These measurements should be carried out applying the same criterion to define the characteristic variables (particle cross section and dimensions) used to calculate CD and Re. Furthermore, it is found that the CD fitting curves should be expressed as a function not only of Re but also of other parameters which represent the particle surface roughness and the departure from the spherical form. Based on this finding, a plausible definition of these variables and the way to introduce them in a hail trajectory calculation are proposed.

Crystal structure of droplets frozen on an ice substrate after low speed collision

Abstract In the present work, the freezing behaviour, for droplets colliding at terminal free fall speed with an ice substrate, is studied. The study of the crystal structure of singular frozen droplets was carried out using spectra, having 135 and 75 μm mean volume diameter. The results show that the transition temperature T∗, corresponding to a value P = 0.5 of the probability of nucleation of new orientations in the droplets, decreases with the droplet diameter, varying from -18 to -29°C on a prism (1120) substrate, and from -11 to -13°C on a basal substrate. This behaviour is discussed on the basis of the nucleation theory. Small accretions were also grown in a cold room without ventilation, using droplets having 85 μm mean volume diameter. It is shown that, for air and substrate temperatures Ta = -7 and Ts = -3°C respectively, these accretions mostly followed the substrate orientation, although a few crystals with new orientations were formed. The difference existing between these accretions structures and those obtained in icing wind tunnels, at about the same values of Ta and Ts, is pointed out.

An experimental method to study grain boundary diffusivity in anisotropic materials

It has been shown that the theoretical treatment developed by Di Prinzio et al. to study the grain boundary diffusivity in anisotropic material can be experimentally implemented. The method was applied to ice bicrystalline samples. The results obtained show that the diffusivity of tilt boundaries 〈1010〉/21 ° and 〈1010〉/90 ° depends on the grain boundary inclination. As a rule, the authors suggest that when Sun and Bauers method is followed to study grain boundary migration b and F(α) may always be determined; it should be kept in mind that, neither values of the Mγ(β) function nor the mean value of Mγ were obtained; instead Mγeff was found.

CRYSTAL STRUCTURE OF ICE ACCRETED ON AN ICE SUBSTRATE

Thin ice deposits, grown on a prismatic ice substrate and the first layers of large deposits grown about a cylindrical ice collector, are studied. Experiments were performed at 30 m s-1 wind speed and Ta near -20°C. Progressive structural changes in thin accretions with time of water-injection were observed, when the substrate temperature was Ts > -5 ·C. After 60 s injection, which determined a deposit -1 mm thick, the preferred orientation was established and the mean grain area was -0.01 mm 2 . Such structural changes did not appear along the initial layers of thick deposits. These differed mainly from the subsequent zone because of the larger value of the preferred angle between the c-axis and the growth direction. These effects are discussed by considering the nucleation and orientation selection processes which occurred during droplet freezing and the annealing effects that occurred below the growth front. The different c-axis orientations in the initial and main zones are related to the different Ts values during their formation.