Numerical methods for 3D in-flight ice accretion under uncertainties

In-flight icing is a safety concern that must be addressed by aircraft designers early in the design loop. Regulators require aircraft manufacturers to comply with ever more strict requirements regarding in-flight icing. Most air-worthy vehicles must be certified for operations in icing hazard conditions. It means that aircraft must be equipped with ice protection systems (IPS) or, for smaller planes, at least with detection systems. Smaller general aviation aircraft may not need icing certification but then are not allowed to fly in such conditions. Certification for flight in icing does not always imply continuous operations in icing conditions. For smaller general aviation aircraft, it may be intended to allow for a temporary period of operation in icing conditions long enough to return to safer conditions. Certification requirements cover three main aspects: airframe and systems ice protection, aircraft handling and performances, and powerplant ice protection. All three aspects must be addressed for small and supercooled large droplets (SLD) for liquid icing. Certifications requirements can be proven via testing, usually aided by numerical simulation. Also, IPS design is often performed via numerical simulations due to the more competitive cost than wind tunnel or in-flight testing. Safety and economic concerns led to the blossoming of research activities related to the physics of ice accretion and the development of ice prediction tools. Nowadays, research is focused on ice prediction on three-dimensional configurations that were previously unfeasible due to the computational effort required. This work builds on the available literature and presents robust and efficient tools for the simulation of in-flight icing on three-dimensional geometries. The target application is icing on in-flight fixed-wing vehicles, although most of the presented methods are general enough to be applied, with little to no modifications, to other areas such as icing on unmanned aerial vehicles, rotorcraft and on-ground structural icing, e.g. wind turbines. A Lagrangian iterative algorithm with adaptive mesh refinement (AMR) is presented to efficiently compute the water catch efficiency on two and three-dimensional surfaces for small and larger droplets. Also, Eulerian and mixed Eulerian-Lagrangian methodologies are introduced. The algorithms are thoroughly verified and validated via comparison with experimental data on straight and swept wings. A semi-stochastic model is presented to simulate the ice buildup on a surface. It combines a deterministic Myers-like thermodynamic model with a stochastic model made of a ballistic and a random walk module. The thermodynamic module, which depends on the aerodynamic and droplet fields, is used to compute the freezing fraction on the surface. The freezing fraction is then used as a freezing probability for impinging fluid elements that either freeze at the impact point or move along the iced surface until freezing. The model is used to replicate ice accretion experiments on 3D wings. The predicted ice shapes compare well with the experimental data, even for the single-shot approach employed. A surface reconstruction methodology is also presented for extending the presented approach to multi-step simulations or evaluating the icing effects on aircraft handling and performance. Also, in-flight ice accretion under parametric uncertainty is investigated. An accuracy assessment, achieved by comparing numerical predictions against experimental observations, confirms the computational icing model's robustness and predictiveness. Besides, sensitivity analyses highlight the variance of the targeted outputs to the different uncertain inputs. In rime icing conditions, a predominant role is played by the uncertainty affecting the airfoil angle of attack, the cloud liquid water content, and the mean volume diameter of droplets. In glaze icing conditions, the sensitivity analysis shows that the output variability is due mainly to the ambient temperature uncertainty. Moreover, this work exposes an inherent challenge in approximating the full icing model using standard (linear) polynomial chaos regression techniques. The complexity is related to the approximation of the model behavior in domain regions scarcely affected by ice buildup. In order to mitigate this issue, a nonlinear regression method is proposed and applied.

L’accrescimento di ghiaccio pone un grave problemi alla sicurezza dei velivoli in volo che va considerato fin dalle prime fasi di progetto. Gli enti per la sicurezza impongono norme sempre piu stringenti ai produttori di aeromobili riguardo alla certificazione per il volo in condizioni di ghiaccio. La maggior parte dei velivoli deve essere certificata per operazioni in tali condizioni, tramite l’equipaggiamento di sistemi di protezione da ghiaccio (IPS) o per velivoli piu piccoli di sistemi di rilevazione. I requisiti necessari ad ottenere la certificazione vengono di solito dimostrati tramite esperiementi e simulazioni numeriche, le ultime decisamente piu convenienti dal punto di vista economico. Motivi legati alla sicurezza e al risparmio dei costi, ha portato ad un rapido sviluppo delle attivita di ricerca legate alla simulazione numerica dell’accrescimento di ghiaccio sui velivoli. Oggi giorno la ricerca si concentra sullo sviluppo di tecniche per la simulazione di accresciemnto di ghaiccio su geometrie tridimensionali, cosa che in passato risultava impossibile per via dell’alto costo computazionale. Il lavoro di questa tesi parte dai metodi e dalla ricerca precedente disponibile nella letteratura, e si pone di introdurre una metodologia robusta ed efficiente per la predizione dell’accrescimento di ghiaccio in 3D. Il lavoro di questa tesi introduce metodi robusti per il calcolo della quantita di acqua sottoraffreddata che impatta le superfici di un velivolo in volo. Vengono trattati schemi numerici che utilizzano sia un approccio Lagrangiano che un approccio Euleriano ai Volumi Finiti. Viene presentato inoltre un modello semi stocastico per il calcolo dell’accumulo di ghiaccio sulle superfici. L’approccio combina un modello termodinamico simile a quello di Messinger con una parte stocastica basata su un modello balistico e una random-walk. Il modello viene usato per replicare eperimenti di accrescimento di ghaiccio su ali in galleria del vento fornendo risultati in accordo con i dati. Questo lavoro presenta anche una metodologia per la ricostruzione dell’interfaccia aria-ghiaccio utile per l’implementazione di simulazioni multi-step o per valutare l’effetto della modifica della geoemtria sulle prestazioni del velivolo. Questo lavoro studia inoltre l’effetto delle incertezze delle condizioni operative sulla distribuzione di ghiaccio che si va a formare sui velivoli. Il metodo presentato in questo lavoro permette di propagare le incertezze sperimentali al risultato numerico in modo da poter comparare i valori sperimentali, incerti, con valori numerici che tengono conto di questa incertezza.