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## Section: New Results

### Modelling of icing and de-icing of aircrafts

• Participants: Héloïse Beaugendre, Mathieu Colin and Francois Morency

• Corresponding member: Héloïse Beaugendre

In-flight icing on an aircrafts surface can be a major hazard in aeronautics's safety. Numerical simulations of ice accretion on aircraft is a common procedure to anticipate ice formation when flying in a supercooled water droplets cloud. Numerical simulations bring a better understanding of ice accretion phenomena, performance degradations and lead to even more efficient thermal de-icing systems designs. Such simulations imply modelling the phase change of water and the mass and energy transfers. The Messinger model developed in the 1950 is still used today as a reliable basis for new models development. This model estimates the ice growth rate using mass and energy balances coupled to a runback water flow. The main parameter introduced with this approach is the freezing fraction, denoting the fraction of incoming water that effectively freezes on the airfoil.

In-flight ice accretion code predictions depend on heat loss over rough surfaces. The equivalent sand grain roughness models the friction coefficient, but an additional model is needed for heat transfer prediction. The turbulent Prandtl number correction and the sublayer Stanton-based models are commonly used. This year, both models have been used with the Spalart-Allmaras turbulence model to predict heat transfer over rough surfaces typical of ice accretion. The objective here is to compare the results of the two models. First, the sublayer Stanton-based model is rewritten in the context of a turbulent Prandtl number correction formulation. Then, the two models are implemented in the open source software, SU2, and then verified and validated for flow over rough flat plates, airfoils, and wings. The two models' predictions evolve differently with the local Reynolds number, but are always within the experimental $20%$ error margin. The paper related to those developments are under revision.

In the work [17], the objective is to model an ice accretion on an airfoil using a Messinger-based approach and to make a sensitivity analysis of roughness models on the ice shape. The test case is performed on a 2D NACA0012 airfoil. A typical test case on a NACA0012 airfoil under icing conditions is run and confronted with the literature for verification prior to further investigations. Ice blocks profiles comparisons will highlight the differences implied by the choice of the roughness correction, which impact the heat transfer coefficient.

Numerical simulation of separated flow around an iced airfoil is still a challenge. Predictions of post-stall aerodynamic performance by RANS models are unsatisfactory. Recent hybrid RANS/LES methods, based on modified DDES models, have shown promising results for separated flow. However, questions still arise about the best compromise between computation time and accuracy for the unsteady 3D simulations. The span width of the domain and the best grid practice to obtain accurate results still has to be investigated, especially taking into account the recent method improvements. A recent method such as shear-layer adapted DDES should give acceptable flow prediction with a relatively coarse mesh. In the paper [18], we further study the effects of span width length on predicted aerodynamic coefficients and on the pressure coefficient. The study is done using the open-source software SU2. The backward facing step and a stalled NACA0012 is used to validate the numerical results. Then, the numerical flow around an iced Model 5-6 is studied, especially the flow within the separation bubble behind the ice. The accuracy of the CFD results is discussed and a recommendation is made about the span width of the computation domain and the grid size.

In order to spare time and resources while increasing the results' accuracy of the stalled wing configuration's aerodynamic coefficients, the following study [16] offers a parametric grid study for the DDES model. For three different grid refinements, characteristics of lift and eddy phenomena are presented and compared to determine, for an infinite wing, the best compromise between time and resources' consumption, and results's accuracy. Using the open software SU2 6.1 (Stanford University Unstructured), we generate three different types of grid refinements around an airfoil, developed spanwise to obtain a straight wing. On the same stalled configuration for each mesh, CFD solutions are ran with the DDES model, and the raw data are post processed with the open software ParaView 5.6. We then compare the aerodynamic coefficients' distributions obtained by the three mesh. The general modelling of vortex shedding's topology and turbulence viscosity are compared with the literature to ensure the right rendering of vortex structures. Chordwise pressure and friction coefficients' distributions as well as the spanwiselift coefficient are also compared. We conclude with the optimum mesh in term of results and resources' consumption.