{'fraction_non_alphanumeric': 0.01809002944888515, 'fraction_numerical': 0.0016827934371055953, 'mean_word_length': 5.605555555555555, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Robust Design of Transonic Natural Laminar Flow Wings under Environmental and Operational Uncertainties

The introduction of laminar flow configurations is envisioned to provide new opportunities to further reduce aircraft fuel consumption. The robustness of laminar wings is critical, both against instabilities that can unexpectedly trigger transition and against off-design conditions outside the cruise point. However, current inverse design methodologies not only provide suboptimal configurations, but are unable to come up with robust configurations. The objective of this paper is the development and demonstration of a framework for the robust direct design of transonic natural laminar flow wings using state-of-the-art industrial tools such as computational fluid dynamics, linear stability theory and surrogate models. The deterministic optimization problem, which serves as a baseline, searches for the optimum shape that minimizes drag applying a surrogate based optimization strategy. In that case Cross-Flow and Tollmien-Schlichting critical N-Factors are fixed according to calibration data. For the robust approach, uncertainties in these critical N-Factors as well as operational conditions such as Mach number are considered to account for situations that could prematurely trigger transition and thus significantly decrease performance. The surrogate based optimizer is therefore coupled with a surrogate based uncertainty quantification methodology, following a bi-level approach. The objective function shifts towards the expectation of the drag to minimize average fuel consumption, or the 95% quantile to account for extreme events. The framework is able to come up with state-of-the-art natural laminar configurations for a short-haul civil aircraft configuration. The deterministic optimum is able to delay transition till 60% of the wing upper surface where the shock is present but is highly sensitive to small changes in the predefined critical N-Factors, as minor deviations will lead to fully turbulent configuration and hence an increase in drag. The robust configurations are more balanced, as the transition location smoothly moves upstream as the critical N-Factors are reduced. As a direct consequence, obtained pressure profiles are more resistant against instabilities, extending the current design envelope of natural laminar flow wings.