TY - JOUR
T1 - An enthalpy-based model for the physics of ice-crystal icing
AU - Peters, Timothy
AU - Shelton, Josh
AU - Tang, Hui
AU - Trinh, Philippe H.
N1 - Funding: T.P. acknowledges support from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (EPSRC grant no. EP/S022945/1). J.S. and P.H.T. acknowledge support from EP/V012479/1, and J.S. is additionally supported by EP/W522491/1.
PY - 2024/12/25
Y1 - 2024/12/25
N2 - 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 with 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 Péclet 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 present good agreement with numerical solutions at low Péclet numbers. Both the asymptotic and numerical solutions show that, when compared with 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.
AB - 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 with 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 Péclet 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 present good agreement with numerical solutions at low Péclet numbers. Both the asymptotic and numerical solutions show that, when compared with 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.
KW - Icing
KW - Solidifcation/melting
UR - https://arxiv.org/abs/2403.20071
U2 - 10.1017/jfm.2024.1054
DO - 10.1017/jfm.2024.1054
M3 - Article
SN - 0022-1120
VL - 1001
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - A12
ER -