Evaluation and Validation of the Messinger Freezing Fraction

One of the most important non-dimensional parameters used in ice-accretion modeling and scaling studies is the freezing fraction defined by the heat-balance analysis of Messinger. For fifty years this parameter has been used to indicate how rapidly freezing takes place when super-cooled water strikes a solid body. The value ranges from 0 (no freezing) to 1 (water freezes immediately on impact), and the magnitude has been shown to play a major role in determining the physical appearance of the accreted ice. Because of its importance to ice shape, this parameter and the physics underlying the expressions used to calculate it have been questioned from time to time. Until now, there has been no strong evidence either validating or casting doubt on the current expressions. This paper presents experimental measurements of the leading-edge thickness of a number of ice shapes for a variety of test conditions with nominal freezing fractions from 0.3 to 1.0. From these thickness measurements, experimental freezing fractions were calculated and compared with values found from the Messinger analysis as applied by Ruff. Within the experimental uncertainty of measuring the leading-edge thickness, agreement of the experimental and analytical freezing fraction was very good. It is also shown that values of analytical freezing fraction were entirely consistent with observed ice shapes at and near rime conditions: At an analytical freezing fraction of unity, experimental ice shapes displayed the classic rime shape, while for conditions producing analytical freezing fractions slightly lower than unity, glaze features started to appear.