No presente trabalho foi implementado um modelo matemático para simular o sistema antigelo eletrotérmico de um aerofólio. Por meio do programa ONERA2D simulou-se o escoamento potencial completo com velocidade 44,7 m/s (100 mph) e 89,4 m/s (200 mph) em torno de um aerofólio perfil NACA0012 de corda 0,914 m (3 pés) com ângulo de ataque de 0°, e calculou-se a eficiência de coleta local de gotículas de água com diâmetro mediano volumétrico de 20 μm. Foram simuladas quatro condições de teste com diferentes distribuições de fluxo de calor nos aquecedores elétricos do sistema antigelo. O modelo previu a distribuição de temperaturas na superfície sólida do aerofólio e no filme de água líquida, e as distribuições de fluxo de água líquida sobre a superfície do aerofólio (\"runback water\") e de coeficiente de transferência de calor por convecção de calor entre a superfície do aerofólio e o escoamento gasoso. Os resultados da simulação obtidos com o modelo foram comparados com resultados experimentais da NASA e os resultados numéricos dos programas LEWICE/ANTICE (EUA) e CANICE (Canada). Para as regiões molhadas pelo filme de água líquida, obteve-se um desvio máximo de temperatura de 2,6°C entre os resultados do presente modelo e o resultados experimentais. Para as regiões secas, onde não existe o filme de água líquida sobre a superfície do aerofólio, obteve-se um desvio de máximo de temperatura de 8°C. As previsões para distribuição de vazão de \"runback\", posição do término do filme de água líquida foram comparadas com os resultados do programa LEWICE/ANTICE. O modelo desenvolvido simula com adequada aproximação os efeitos da transferência de calor e de massa por convecção entre a superfície não-isotérmica do aerofólio ou do filme de água líquida e o escoamento gasoso, bem como os efeitos da transição entre o escoamento laminar e o turbulento na camada limite dinâmica e térmica e ainda a influência do escoamento do filme de água líquida sobre o desempenho do sistema de antigelo do aerofólio. / An electro-thermal anti-ice system was simulated with a mathematical model developed in the present work. A 44.7 m/s (100 mph) and 89.4 m/s (200 mph) full potential flow around a 0.914 m (3 ft) chord NACA0012 airfoil with 0° angle of attack and the local water catch efficiency of 20 μm median volumetric diameter droplets impingement were calculated by the numerical code ONERA2D. Four test conditions were simulated with four different heat flux distributions of the anti-ice system according to the experimental work developed at NASA. The model predicted distributions of solid surface and liquid water film temperatures, runback water flow and convection heat transfer coefficient between airfoil or water surface and gaseous flow. The simulated results obtained by the mathematical model developed were compared to NASA experimental results and the ones predicted by the numerical codes LEWICE/ANTICE (US) and CANICE (Canada). For the regions wetted by the water film, the present model provided 2.6°C maximum temperature deviations between the predicted results and experimental data. For the dry regions, where there is no liquid water on the airfoil surface, an 8°C maximum temperature deviation was obtained. The runback flow and water film ending point position were compared to LEWICE/ANTICE numerical results. The developed model predicts adequately the convection heat and mass transfer effects between the non-isothermal airfoil or liquid water film surface and the gaseous flow, as well the effects of laminar to turbulent flow transition within dynamic and thermal boundary layer and the influence of the liquid water film flow on the anti-ice system performance.

No presente trabalho foi implementado um modelo matemático para simular o sistema antigelo eletrotérmico de um aerofólio. Por meio do programa ONERA2D simulou-se o escoamento potencial completo com velocidade 44,7 m/s (100 mph) e 89,4 m/s (200 mph) em torno de um aerofólio perfil NACA0012 de corda 0,914 m (3 pés) com ângulo de ataque de 0°, e calculou-se a eficiência de coleta local de gotículas de água com diâmetro mediano volumétrico de 20 μm. Foram simuladas quatro condições de teste com diferentes distribuições de fluxo de calor nos aquecedores elétricos do sistema antigelo. O modelo previu a distribuição de temperaturas na superfície sólida do aerofólio e no filme de água líquida, e as distribuições de fluxo de água líquida sobre a superfície do aerofólio (\"runback water\") e de coeficiente de transferência de calor por convecção de calor entre a superfície do aerofólio e o escoamento gasoso. Os resultados da simulação obtidos com o modelo foram comparados com resultados experimentais da NASA e os resultados numéricos dos programas LEWICE/ANTICE (EUA) e CANICE (Canada). Para as regiões molhadas pelo filme de água líquida, obteve-se um desvio máximo de temperatura de 2,6°C entre os resultados do presente modelo e o resultados experimentais. Para as regiões secas, onde não existe o filme de água líquida sobre a superfície do aerofólio, obteve-se um desvio de máximo de temperatura de 8°C. As previsões para distribuição de vazão de \"runback\", posição do término do filme de água líquida foram comparadas com os resultados do programa LEWICE/ANTICE. O modelo desenvolvido simula com adequada aproximação os efeitos da transferência de calor e de massa por convecção entre a superfície não-isotérmica do aerofólio ou do filme de água líquida e o escoamento gasoso, bem como os efeitos da transição entre o escoamento laminar e o turbulento na camada limite dinâmica e térmica e ainda a influência do escoamento do filme de água líquida sobre o desempenho do sistema de antigelo do aerofólio. / An electro-thermal anti-ice system was simulated with a mathematical model developed in the present work. A 44.7 m/s (100 mph) and 89.4 m/s (200 mph) full potential flow around a 0.914 m (3 ft) chord NACA0012 airfoil with 0° angle of attack and the local water catch efficiency of 20 μm median volumetric diameter droplets impingement were calculated by the numerical code ONERA2D. Four test conditions were simulated with four different heat flux distributions of the anti-ice system according to the experimental work developed at NASA. The model predicted distributions of solid surface and liquid water film temperatures, runback water flow and convection heat transfer coefficient between airfoil or water surface and gaseous flow. The simulated results obtained by the mathematical model developed were compared to NASA experimental results and the ones predicted by the numerical codes LEWICE/ANTICE (US) and CANICE (Canada). For the regions wetted by the water film, the present model provided 2.6°C maximum temperature deviations between the predicted results and experimental data. For the dry regions, where there is no liquid water on the airfoil surface, an 8°C maximum temperature deviation was obtained. The runback flow and water film ending point position were compared to LEWICE/ANTICE numerical results. The developed model predicts adequately the convection heat and mass transfer effects between the non-isothermal airfoil or liquid water film surface and the gaseous flow, as well the effects of laminar to turbulent flow transition within dynamic and thermal boundary layer and the influence of the liquid water film flow on the anti-ice system performance.

Icing has since long been identified as a serious issue in the aeronautical world. Ice build up, due to the presence of supercooled water droplets in clouds, leads to degradation of aerodynamic and/or air intake performances, among other undesirable consequences. Hence aircraft manufacturers must comply with certifications and regulations regarding flight safety in icing conditions. In order to do so, ice protection systems are used. Due to the multi-physical context within which these systems operate, numerical simulation can be a valuable asset. The present work deals with the numerical modelling of electro-thermal ice protection systems. It is built around the development of three modules. Two of them are dedicated to modelling heat transfer in the system and in the ice block. The other one models the mechanical behaviour of ice and fracture. Hence, the mechanical properties of atmospheric ice are reviewed in order to identify some mechanical parameters relevant to the fracture model. The fracture mechanics numerical method is used to investigate possible ice shedding mechanisms, that is to say the mechanisms leading to the detachement of ice, which are not yet well understood. The final goal of this work is to propose a completely coupled 2nd generation simulation methodology for electro-thermal ice protection systems. Hence the feasibility of a coupled thermal computation with ice shedding prediction based on the developed modules is shown. / Le givrage a depuis longtemps été identifié comme une problématique sérieuse dans le monde aéronautique.L’accrétion de givre, due à la présence de gouttelettes d’eau surfondue dans les nuages, dégrade les performances aérodynamiques et le rendement des entrées d’air parmi d’autres conséquences néfastes. Ainsi, les avionneurs sont sujets à des règles de certifications concernant la capacité à voler en conditions givrantes. Pour se faire, des systèmes de protection contre le givre sont utilisés. En raison de la complexité des phénomènes physiques mis en jeux, la simulation numérique constitue un atout lors de la phase de conception. Ce travail de thèse porte sur la modélisation et la simulation numérique des systèmes électrothermiques de protection contre le givre. Il s’articule autour de trois approches de modélisation, qui ont donné lieu au développement de trois modules. Deux d’entre eux sont dédiés à la simulation du transfert de chaleur dans le système et dans la glace (changement de phase). Le troisième est lié à la modélisation du comportement mécanique du givre atmosphérique avec fissuration. Ainsi, les propriétés mécaniques du givre atmosphérique sont revues de façon à pouvoir identifier les paramètres intervenant dans le modèle de fissuration. Ce modèle est ensuite utilisé pour étudier les mécanismes possibles de détachement du givre, qui ne sont à l’heure actuelle pas encore bien compris. Le but final de ce travail est de proposer une méthodologie de simulation couplée pour les systèmes électrothermiques de protection contre le givre. Ainsi, la faisabilité d’un calcul couplé thermique-fissuration avec prédiction de détachement de givre est présentée.

In the rapidly growing wind energy market, regions with cold climates are currently in the spotlight owing to their abundance of wind resources. However, the operation of wind turbines in cold climate conditions is challenged by serious icing problems. Ice accretion on the rotor blades of a wind turbine results in a decline in power production, an increase in fatigue loads, and raises health and safety concerns. To mitigate these adverse effects, ice protection systems (IPS) are now widely being employed. These systems mainly rely on costly blade heating techniques, yet their efficiency is limited and they cannot effectively prevent or remove ice build-up under all ambient conditions. In this study, the performance of five identical wind turbines, each equipped with an electrothermal heating IPS, is analyzed over several icing events. All data are collected from an undisclosed wind park located in northern Sweden. Historical wind turbine data is studied to explore the extent of icing-induced losses and IPS activities, as well as the dependence of blade icing and IPS efficiency on meteorological conditions. Based on the results from the analysis, suggestions will be provided on how the control settings of the IPS can be modified to increase the de-icing effectiveness and reduce ice-related production losses. For the purposes of better understanding the performance of the wind turbines and their IPS in icing conditions, an analytic dashboard has been internally developed. To derive quantitative information about the IPS efficiency, a set of standardized metrics is utilized. An internal algorithm has been developed that classifies various forms of ice losses and different status codes of wind turbines. These ice losses and turbine status codes are monitored and analyzed using the analytic dashboard. Statistical analysis indicates that the most substantial source of ice losses is the stoppages caused by blade icing, whereas losses during de-icing operations are relatively insignificant. Results from the IPS performance analysis show that the icing-induced losses are further influenced by the inconsistency in the IPS behavior. The systems have shown to be inefficient even when operating under conditions of wind speed and ambient temperature that fall within their specified operational limits, indicating their dependence on external conditions. In the majority of icing events, a delay in IPS activation was observed, particularly when these events coincided with periods of high wind speeds. Moreover, the heating of the blades is not sufficient, as multiple attempts to melt the accreted ice are often required, yet success is not always achieved. The difficulty in validating whether the blades are free of ice stems from the fact that the heat is emitted only from the blade’s leading edge. The author suggests specific immediate measures to improve the control of the IPS, including changing the threshold values for IPS triggering and adjusting the duration and frequency of ice removal cycles. These measures are confined by constraints tied to Intellectual Property Rights, limiting the extent to which elements in the IPS control settings can be modified by the wind operator. Nevertheless, if these constraints are relaxed, there exists significant untapped potential for further optimizing the control of IPS. / På den snabbt växande vindkraftsmarknaden är regioner med kallt klimat för närvarande i fokus på grund av deras rikliga vindresurser. Driften av vindkraftverk i kalla klimatförhållanden utmanas dock av allvarliga problem med isbildning. Isbildning på vindkraftverkens rotorblad leder till minskad kraftproduktion, ökade utmattningsbelastningar och ger upphov till hälso- och säkerhetsproblem. För att mildra dessa negativa effekter används nu isskyddssystem (IPS) i stor utsträckning. Dessa system är huvudsakligen beroende av kostsamma tekniker för uppvärmning av bladen, men deras effektivitet är begränsad och de kan inte effektivt förhindra eller avlägsna isbildning under alla omgivningsförhållanden. I denna studie analyseras prestandan hos fem identiska vindkraftverk, vart och ett utrustat med en IPS för elektrotermisk uppvärmning, under flera nedisningshändelser. Alla data har samlats in från en icke namngiven vindkraftspark i norra Sverige. Historiska vindturbindata studeras för att undersöka omfattningen av nedisningsinducerade förluster och IPS-aktiviteter, samt beroendet av bladnedisning och IPS-effektivitet på meteorologiska förhållanden. Baserat på resultaten från analysen kommer förslag att ges på hur kontrollinställningarna för IPS kan modifieras för att öka avisningseffektiviteten och minska isrelaterade produktionsförluster. För att bättre förstå hur IPS-utrustade vindkraftverk presterar under isförhållanden har en analysverktyg utvecklats internt. För att få kvantitativ information om IPS-effektiviteten används en uppsättning standardiserade mätvärden. En intern algoritm har utvecklats som klassificerar olika former av isförluster och olika statuskoder för vindturbiner. Dessa isförluster och turbinstatuskoder övervakas och analyseras med hjälp av analysverktyget. Statistisk analys visar att den mest betydande källan till isförluster är de stopp som orsakas av isbildning på bladen, medan förluster under avisning är relativt obetydliga. Resultaten från IPS-prestandaanalysen visar att de isinducerade förlusterna påverkas ytterligare av inkonsekvensen i IPS-beteendet. Systemen har visat sig vara ineffektiva även när de arbetar under förhållanden med vindhastighet och omgivningstemperatur som faller inom deras angivna operativa gränser, vilket visar att de är beroende av yttre förhållanden. Vid de flesta isbildningstillfällen observerades en fördröjning av IPS-aktiveringen, särskilt när dessa händelser sammanföll med perioder med höga vindhastigheter. Vidare är uppvärmningen av bladen inte tillräcklig, eftersom det ofta krävs flera försök att smälta den ackumulerade isen, men man lyckas inte alltid. Svårigheten att avgöra om bladen är fria från is beror på att värmen endast avges från bladets framkant. Studien föreslår specifika omedelbara åtgärder för att förbättra kontrollen av IPS, inklusive ändring av tröskelvärdena för IPS-aktivering och justering av varaktigheten och frekvensen för isborttagningscykler. Dessa åtgärder begränsas av immateriella rättigheter, som begränsar i vilken utsträckning operatören kan ändra IPS-kontrollinställningarna. Om dessa begränsningar lättas finns det dock en betydande outnyttjad potential för ytterligare optimering av kontrollen av IPS.