Statistics – Applications
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt........12z&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF TORONTO (CANADA), 1994.Source: Dissertation Abstracts International, Volume: 56-07, Section: B, pa
Statistics
Applications
1
Scientific paper
The convective heat and mass transfer of hailstone models has been investigated experimentally in a temperature - and velocity-controlled, closed-circuit wind tunnel. The models used were smooth spherical and spheroidal particles with major axis diameters of 2 and 3 cm and aspect ratios (alpha) of 0.5, 0.67 and 1.0, and rough spherical particles with diameter of 2 cm and surface roughness (beta) of 0, 2. 3.5, 5.5, 8 and 11%. These models were forced to gyrate at a spin frequency (f_3) of 9.5 Hz and a nutation/precession frequency (f_0) of -14 Hz for spheroids and -9.5 Hz for spheres, to rotate at rates (f_1 ) of 0, 5, 10, 15 and 22 Hz, or were suspended in fixed positions. The initial temperature of a typical particle was {~ -}6 ^circ C. The air temperature was set to -15, -19 or -21^circ C. The air speed varied from 6.6 to 24 m s^ {-1}, corresponding to Reynolds numbers of 1.1 times 10^4 <= Re <= 5.2 times 10^4. The surface temperatures of the models were remotely scanned with an "AGEMA 800" Thermal Imaging System to within +/- 0.13 ^circ C during cooling in the airflow. A numerical model was developed to calculate the time-evolution of the temperature distribution, the heat conduction within the particle, and the surface heat flux. Then, the latitude-dependent, Nu_ φ, and the overall Nusselt number, overlineΝ were determined. The results indicated that the heat and mass transfer of a hailstone is non-homogeneous, non-isotropic and latitude -dependent. Both Nuphi and overlineΝ were found to be functions of Re, alpha and beta. overline Ν can be expressed in exponential or linear form for the range of Re considered. This is the first time overlineΝ vs. Re relationships have been established for rotating and gyrating particles. overlineΝ for smooth spherical particles is approximately 30% larger than that predicted by expanded Ranz and Marshall expressions commonly used in hail studies. Spheroidal particles produce overlineΝ up to 40% higher than for spheres with the same diameter, while a rough surface causes an increase of overlineΝ of up to 100% as beta increases from 0 to 11%. It was also found that the fall mode of the particles significantly influences the variation of Nu_φ but yields little difference in overlineΝ. This difference underlines the importance of the motion pattern on the heat and mass transfer of falling hailstones. The experiments also showed that rotation rate has no influence on heat transfer for 5 <= f_1 <= 22 Hz. The results will help to better interpret growth experiments with artificial hailstones and improve the parameterization of computer models of hail growth. They may also be useful in engineering applications.
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