The first stage in any aircraft icing issue is to determine whether there is an accretion or not, and how serious it is. The second stage is to use icing codes to analyse the water droplet trajectories, collection efficiency and any resulting growth of ice on the surface [52]. Significant experiments and flight test were carried out between 1940 and 1960s which laid the foundation for most of the ice accretion codes in use today. However, significant progress in theoretical studies of aircraft ice accretion was not achieved until the advent of computer age during the late 1970s [23]. Prominent among the early con- cepts of modern anti-icing systems includes the works of Johnson [53] and Hardy [54] in 1940 and 1946 respectively. Johnson described the effects of wing loading, aircraft icing and associated aspects into modern transport design whereas Hardy developed one
of the modern concept for protection of aircraft against ice for the Defence Evaluation and Research Agency (DERA)1. Around the same time, a dimensionless droplet size distribution was established by Langmuir and Blogett [55] which introduced the use of natural-icing cloud measurements in analysis of aircraft icing. These developments led to further studies on aircraft encounter with super-cooled water droplets in flight. The earlier experimental works on droplets impingement were pioneered by Lewis [56] in 1955 and, Von Glahn [57] and Gelder [58] in 1956. However, the fundamental principle of mass and energy balance calculation method used for aircraft icing analysis was founded by Bernard Messinger [12] in 1953. The Messinger’s model [12] (see section 2.4.4 for further details) utilised convection, sensible heating, evaporation/sublimation, kinetic energy, and viscosity terms in the conservation energy equation to find the equilibrium temperature of an unheated icing surface. In the Messinger model, the heat transfer coefficient and the rate of water catch are the two essential parameters for computing the fraction of the non-freezing water and the balance temperature. The key parame- ters affecting the water collection efficiency are droplet size, angle of attack, chord, and flow speed. However, where the flow speed exceeds Mach 0.3, compressibility effects are normally considered significant. Thus, one of the major limitations of the Messinger model is that it applies to non-compressible flows alone in its original form.
To mitigate the shortfall of the classical Messinger model, in 1983, Cansdale and Gents [59] extended Messingers model to cover compressible flows and water local concentra- tion. Another fundamental limitation of the Messinger model is that the ice and water layers are isothermal, and so conduction through these layers cannot be accounted for. The substrate is assumed insulated which removes conduction through the substrate which is far from ideal. For this reason, the Messinger model would always predict a
lower rate of ice accretion than occurs in practice. In 2001, Myers [60] developed both two and three-dimensional mathematical models for describing ice growth due to su- percooled fluid impacting on a solid substrate. With this, the Messinger method was improved by the addition of an energy source at the substrate. Similarly, ¨Ozgen and Canibek [61] in 2009 developed an extended version of the Messinger model suitable for the runback mass estimation. In 2013, Ryosuke [62] compared the two approaches and came to the conclusion that the extended Messinger model is far more superior to the original Messinger model in simulating glaze icing. In addition to the works credited to the early individual researchers, some major icing research centres have contributed to the analysis and understanding of the cause and effects of aircraft icing through devel- opment of several icing codes and standards. Major research agencies involved in the development of the foundation of icing simulations codes in use today are discussed in the succeeding sections.
The Lewis Research Center in the US, and the DERA in the UK [23] were the first con- tributors in the resurgence of aircraft-icing analysis based on computer icing modelling and simulation. During the International Workshop in Aircraft Icing in July 1978, USA, participants observed that the expanding private aircraft fleet wanted all weather capa- bility for their expensive investment; military and civilian helicopters needed rotor-blade ice protection and the large transport aircraft sought more energy efficient systems. It became clear that it was time to apply modern computers and instrumentation to the icing problem. The new icing program began with three NASA-funded study contracts to develop computer codes that would: a) predict water droplet collection on aircraft surfaces, b) model the ice build-up on aircraft surfaces, and c) provide design tools for various ice-protection systems [63]. French research establishment, Office National d’Etudes et de Recherches A´erospatiales (ONERA) joined in the 1980s. Italy, Spain,
Germany and Canada joined in many collaborative researches in the 1990s which saw to the development of icing codes that are use by aircraft manufacturers today.
Computer based aircraft-icing analysis have transformed the certification process of air- craft for flight into known icing conditions. The ability to analyse cases with the use of computers has reduced the number of experiments and flight tests where they are now predominantly used for the verification and validation phase - thereby inevitably reduc- ing the certification costs. In more recent years, computer icing codes have allowed the analysis of many complex icing problems that were hitherto hard or impossible to anal- yse using rig and flight test. Presently, aircraft anti-icing analysis and certifications are performed by a combination of computational simulations, icing tunnel experiments and flight tests using tanker, Gent [23]. A combination of the above tools is not always ap- plicable on the entire Appendix C icing envelope, due to inherent individual deficiencies associated with each method. In many instances, numerical modelling makes possible the study of some processes which might be difficult or economically unprofitable with a direct experiment. Icing analysis using computer codes also eliminates experimental assumptions and measurement errors.
Despite the enormous advantages of icing analysis using computers, icing codes have 3 major shortfalls. First, the mathematical equations that govern their operation do not reflect all physical processes of a natural process. Secondly, instability of numerical calculations and inaccurate discretisation sometimes affects their results [64]. Nonethe- less, computational simulations are important for analysing icing encounter worst case scenarios and estimating ice accretion rate and patterns. They are fast and cost effective tool for aircraft icing analysis. Computational simulations could be used to determine temperature distribution over the surface vis-`a-vis heating requirements.