  Ice crystal icing (ICI) in aircraft engines is a major threat to flight
safety. Due to the complex thermodynamic and phase-change conditions involved
in ICI, rigorous modelling of the accretion process remains limited. The
present study proposes a novel modelling approach based on the
physically-observed mixed-phase nature of the accretion layers. The
mathematical model, which is derived from the enthalpy change after accretion
(the enthalpy model), is compared to an existing pure-phase layer model (the
three-layer model). Scaling laws and asymptotic solutions are developed for
both models. The onset of ice accretion, the icing layer thickness, and solid
ice fraction within the layer are determined by a set of non-dimensional
parameters including the Peclet number, the Stefan number, the Biot number, the
Melt Ratio, and the evaporative rate. Thresholds for freezing and non-freezing
conditions are developed. The asymptotic solutions presents good agreement with
numerical solutions at low Peclet numbers. Both the asymptotic and numerical
solutions show that, when compared to the three-layer model, the enthalpy model
presents a thicker icing layer and a thicker water layer above the substrate
due to mixed-phased features and modified Stefan conditions. Modelling in terms
of the enthalpy poses significant advantages in the development of numerical
methods to complex three-dimensional geometrical and flow configurations. These
results improve understanding of the accretion process and provide a novel,
rigorous mathematical framework for accurate modelling of ICI.
