Equilibrium Temperature of an Unheated Icing Surface as a Function of Air Speed

The thermal analysis of a heated surface in icing conditions has been extensively treated in the literature. Except for the work of Tribus, however, little has been done on the analysis of an unheated icing surface. This latter analysis is significant in the design of cyclic thermal deicing systems that are attractive for small high-speed aircraft for which thermal anti-icing requirements have become severe. In this paper, a complete analysis of the temperature of an unheated surface in icing conditions is presented for the several significant regimes (i.e., less than 32°F., at 32°F., and above 32°F.) as a function of air speed, altitude, ambient temperature, and liquid water content. The results are presented in graphical form and permit the rapid determination of surface temperature for a wide range of variables. Curves are presented to determine the speeds beyond which no ice accretion will occur. Curves are also presented to indicate the surface temperature and the rate of ice sublimation which takes place when an ice-covered surface emerges into clear air. One significant result of this study is the introduction of a new basic variable referred to as the freezing-fraction, which denotes the proportion of the impinging liquid which freezes in the impingement region. The fact that some of the liquid does not freeze in the impingement region tends to explain the observed variation in ice formation shape with temperature, speed, and water catch. New test data obtained at Mt. Washington, N.H., for stagnation-point surface temperatures of an unheated plastic cylinder in natural and artificial icing conditions are included in the Appendix. These data substantiate the validity of the assumptions made in the theoretical analysis.