Novel Framework for the Robust Optimization of the Heat Flux Distribution for an Electro-Thermal Ice Protection System and Airfoil Performance Analysis

We present a framework for the robust optimization of the heat flux distribution for an anti-ice electro-thermal ice protection system (AI-ETIPS) and iced airfoil performance analysis under uncertain conditions. The considered uncertainty regards a lack of knowledge concerning the characteristics of the cloud i.e. the liquid water content and the median volume diameter of water droplets, and the accuracy of measuring devices i.e., the static temperature probe, uncertain parameters are modeled as uniform random variables. A forward uncertainty propagation analysis is carried out using a Monte Carlo approach. The optimization framework relies on a gradient-free algorithm (Mesh Adaptive Direct Search) and three different problem formulations are considered in this work. Two bi-objective deterministic optimizations aim to minimize power consumption and either minimize ice formations or the iced airfoil drag coefficient. A robust optimization formulation was also considered aiming to maximize the statistical frequency of the fully evaporative operating regime for fixed power consumption. The framework is applied to a reference test case, revealing the potential to improve the evaporation efficiency of the baseline design, increasing flight safety even at non-nominal conditions. We also conducted a preliminary examination of the impact of run-back ice formations on airfoil performance during a brief ice encounter in uncertain cloud conditions to understand how the rate of ice accretion relates to an airfoil performance metric, such as the drag coefficient. The analysis found that reducing the rate of ice build-up may not necessarily diminish the detrimental effects on aerodynamic performance, except when the rate is very low. Further studies are ongoing to explore airfoil performance degradation in more detail and to reduce the optimization framework computational cost.