# A Multi-layered Integral Approach to the de-icing process

Heloise Beaugendre, Andres Benoit, François Morency, Martin Parisot

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Heloise Beaugendre, Andres Benoit, François Morency, Martin Parisot. A Multi-layered Integral Approach to the de-icing process. ECCOMAS 2024 - 9th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2024, Jun 2024, Lisbon, Portugal. 10.23967/eccomas.2024.031. [hal-04868484]

HAL Id: hal-04868484

https://inria.hal.science/hal-04868484v1

Submitted on 6 Jan 2025

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# A Multi-layered Integral Approach to the de-icing process

H. Beaugendre<fnref n="1" />,<fnref n="2" />, A. Benoit<fnref n="2" />, F. Morency<fnref n="3" /> and M. Parisot<fnref n="2" />

**Keywords:** *Shallow water in-flight icing/de-icing model, Multi layered integral approach*

The modification of the shallow water icing model to handle de-icing phenomenon is the main focus of this study. As stated in the original model [1], the runback water is modeled utilizing a lubrication assumption for the water film velocity profile. A constant film temperature $T_f$ is then calculated under the thin-film hypothesis. Unlike the simplified icing model, the temperature field within the ice layer $T_i(t, z)$ is no longer assumed to be constant. Instead, a temperature profile is utilized, enabling the generation of a static film on the wall when a heat conduction source term from a resistance is present [2]. A Temperature profile $T_s(t, z)$ is also used in the static film layer if the model predicts the occurrence of this state. In the energy equation for both the solid ice and liquid portion of the static water film, transverse transfers are not considered, a 1D heat equation is then resolved. An integral approach and proper boundary conditions are used to close the problem. The validity of the integral method deteriorates as the thickness over which vertical integration is performed increases. To avoid this problem, a multi-layer approach is proposed. The thickness of the ice block is then divided into three layers of identical thickness. The purpose of this study is to offer a straightforward and robust method suitable for conducting industrial test cases. The model will first be introduced, followed by a description of the numerical approach. Subsequently, validation test cases will be conducted. Realistic de-icing scenarios will then be designed to evaluate the model [3]. Additionally, non-uniform roughness effects will be examined.

## REFERENCES

[1] Y. Bourgault, H. Beaugendre et W. G. Habashi. Development of a shallow-water icing model in FENSAP-ICE. *Journal of Aircraft*, **37**(4):640-646, 2000.

[2] R. Chauvin, L. Bennani, P. Trontin et P. Villedieu. An implicit time marching Galerkin method for the simulation of icing phenomena with a triple layer model. *Finite Elements in Analysis and Design*, **150**:20-33, 2018.

[3] L. Bennani, P. Trontin et E. Radenac. Numerical simulation of an electro-thermal ice protection system in anti-icing and de-icing mode. *Aerospace*, **10**(1), 2023.

<footnote n="1">¹ Bordeaux University, INRIA, CNRS, Bordeaux INP, IMB, UMR 5251, Talence, France;</footnote>

<footnote n="2">² Project team Cardamom, Centre Inria de l'Université de Bordeaux;</footnote>

<footnote n="3">³Mechanical Engineering Department, École de Technologie Supérieure, Montréal, Canada;</footnote>

<footnote>E-mail: heloise.beaugendre@math.u-bordeaux.fr; andres.benoit@inria.fr;</footnote>

<footnote>francois.morency@etsmtl.ca; martin.parisot@inria.fr</footnote>