Extension to the Messinger Model for Aircraft Icing

A one-dimensionalmathematical model is developed describing ice growth due to supercooled uid impacting on a solid substrate. When rime ice forms, the ice thickness is determined by a simple mass balance. The leading-order temperature pro le through the ice is then obtained as a function of time, the ambient conditions, and the ice thickness. When glaze ice forms, the energy equation and mass balance are combined to provide a single rst-order nonlinear differential equation for the ice thickness, which is solved numerically.Once the ice thickness is obtained, the water height and the temperatures in the layers may be calculated. The method for extending the one-dimensionalmodel to two and three dimensions is described. Ice growth rates and freezing fractions predicted by the current method are compared with the Messinger model. The Messinger model is shown to be a limiting case of the present method. Nomenclature B.t / = ice layer thickness,m Bg = ice thickness at which glaze rst appears, mOB = height scale, m c = speci c heat, J/kg K e = saturation vapor pressure (temperature dependent), Pa e0 = vapor pressure constant, Pa/K