Extension to the Messinger model for aircraft icing

A one-dimensional mathematical model is developed describing ice growth due to supercooled fluid impacting on a solid substrate. When rime ice forms, the ice thickness is determined by a simple mass balance. The leading-order temperature profile 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 first-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-dimensional model 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.