Non-Spherical Particle Trajectory Modelling for Ice Crystal Conditions

Aircraft icing is a significant issue for aviation safety. In this paper, recent developments for calculating the trajectory of non-spherical particles are used to determine the trajectory and impingement of ice crystals in aircraft icing scenarios. Two models are used, each formulated from direct numerical simulations, to give the drag, lift and torque correlations for various shaped particles. Previously, within the range of Reynolds number permitted in this study, it was only possible to model the trajectory and full rotational progression of cylindrical particles. The work presented in this paper allows for analysis of a wider range of ice shapes that are commonly seen in icing conditions, capturing the dynamics and behaviours specific to ice crystals. Previous limitations relate to the in ability to account for particle rotation and the dependency of force correlations on the measure of particle sphericity – which are now overcome. The method also provides an opportunity for new analysis – the creation of catch bounds for mixed clouds of particles. The above models are applied to two geometries and compared with drag only cases for spheres and non-spherical particles as parameterized by sphericity. The analysis shows that taking the worstand best-case scenarios provide a range of values for the catch, which can help to understand better the extent over which particles impinge. Hence a catch-limit for a mixed cloud of particles of different shaped particles and different sized particles may be easily gained. The methods are also able to capture rotations and trajectories in three dimensions. Incorporating new methods for modelling the trajectory, rotation and orientation of nonspherical particles into the modelling of aircraft icing opens new avenues for industrial analysis. In turn this may aide several areas of aircraft design related to engine design and flight instrumentation system design as well as informing the aircraft certification process. Introduction From 1997, aircraft icing was on the United States National Transportation Safety Board (NTSB) ‘Most Wanted List’ for safety improvements [1]. Whilst significant improvements have been made throughout the industry in recent years, aircraft icing continues to be a contributory factor in accidents and incidents. Given the hazard posed by ice crystals, aviation regulations were expanded by the Federal Aviation Administration to include ice crystals and account for the threat to air safety. In particular, two chapters on the airworthiness standards for transport planes and aircraft engines (14 CFR 25 and 14 CFR 33, respectively [2]) include: Appendix C – atmospheric icing conditions describing key icing conditions; and Appendix D – mixed phase and ice crystal icing envelope (deep convective clouds) to describe ice crystal icing conditions. Whilst it is vital for aircraft manufacturers to comply with these regulations, presently there are still difficulties in demonstrating compliance, particularly with ice particles – the concern of this paper. With the continued increase in world-wide air travel, aircraft are routinely operating in areas of the world where severe icing conditions are more prevalent. Ice crystal events occur mainly at high altitudes, at cold temperatures and in the neighbourhood of convective cloud systems [3]. Aviation generally has a very good safety record considering the number of flights undertaken every day. However, there is still a need to keep improving this record as the frequency and volume of air travel increases, especially given the catastrophic consequences of severe icing events. (For example, in 2009, aircraft icing contributed to the loss of an Air France Airbus A330 aircraft with all 228 passengers and crew. This was, at least in part, attributed to mis-reading of the airspeed system because of ice crystal impacts and ice formation [4].) In working towards reducing the number of incidents and accidents it is required that capability in modelling techniques is improved in combination with ground testing (icing wind tunnels) and flight testing [5]. There have been two issues which have meant that such work has not previously been performed [6]. The first issue was that knowledge of the detailed physics of the phenomena was missing. This has been addressed to some extent by numerous research programmes around the world (e.g. those conducted by NASA Lewis Research Centre, Official National d’Etudes et de Recherches Aérospatiales (ONERA), CIRA, the HAIC programme and its associated partners). Much of this work has focussed on the detection of ice crystal clouds and the physics of ice accretion. This research forms an important basis for the development of numerical models of ice crystal trajectories and impact behaviours. Whilst these research programmes have had a significant impact on the field of aircraft icing, industrial application requires rapid analysis methods. Hence, the second issue is the integration of the methods into industrial codes. The aeronautical industry requires problems to be solved in a practical time-scale, which often requires simplifying assumptions to be made. This in-turn must be balanced to meet acceptable thresholds of accuracy and realism for use in showing compliance with current flight safety requirements and the necessary certification. Such assumptions can only be made with thorough understanding of the problem and detailed knowledge of the limitations. The ability to predict the behaviour of ice crystals is essential for the certification and improved design of anti-icing systems. The low cost of computational modelling and large amount of data and scenarios that can be analysed makes such modelling a convenient option given the recent technological and computational developments [7]. However, performing large scale simulations for whole aircraft geometries can be very time consuming. Ice crystals are more complex to model compared to droplets in as much as the shape, size and thus trajectory of ice particles can vary greatly. Notably, ice crystals may grow up to 2mm in size and form into a wide range of shapes [8]. The complex ice shapes and increased particle mass thus affect their trajectory and response in the airflow. Particularly, for droplets a spherical or near spherical assumption may be made regarding the particle shape, such that only the drag force needs to be considered. By contrast, it is common for ice particles to take on disc-like or cylindrical shapes, introducing asymmetry and the need to consider the particle’s orientation, rotational evolution, torques and lift forces. Given the complexities, many approaches could be taken. In order to capture the intricacies of the real world physics to potential methods are direct numerical simulation (DNS) [9] or coupled computational fluid simulations (CFS) (e.g. [10]). These can vary in complexity and may be used to fully model the coupled flow-particle systems including the detailed internal and external pressure responses that affect an evolving particle trajectory, the present turbulence and temperature effects. Particularly, they require that the Navier-Stokes equations are solved numerically, and that the spatial and temporal scales of the turbulence are resolved. However, such methods are time consuming, requiring large computational power and effort to produce highly accurate and realistic results that are of little relevance for industrial analysis since only small-time spans can be feasibly modelled [11]. This is an issue when performing ice crystal and impingement modelling for industrial purposes since models for large segments of aircraft, or in some cases whole aircraft, are required. As a result, these coupled, highly physical methods increase the computational intensity required, hence such models are not widely implementable or usable in industry. An alternative however is to use these advanced methods or experimental data to produce approximate methods for the force and torque coefficients. These derived correlations may be used to approximate the resultant behaviour of a particle in a flow. A survey of these methods was carried out in [12]. The authors covered a range of methods that may be used to define and quantify the particle shape and how the force and torque correlations may be calculated. This approach is reasonable in aircraft icing scenarios since the concentration of droplets is small such that they have negligible aerodynamic effect on the freestream flow, and thus particle trajectories may be modelled as an independent, uncoupled system. Of note is the particle’s sphericity a parameter used to define the shape of a particle in relation to how it deviates from that of an ideal sphere [13]. Parameterising particle’s in this way helps to simplify the analysis of different shapes as particles may simply be described by two parameters, by its sphericity and size (diameter). Though, there is a limitation vastly different shaped particles, for which very different responses to the air flow may be expected, may each have the same parameter values, Figure 1. This is partly due to sphericity not accounting for the particle orientation. One method that is widely used is that of [14] [15] in which two forms of sphericity are defined in lengthwise (in the direction of the flow) and crosswise (perpendicular to the flow) directions, adding an orientation to the effective sphericity, however this can prove complicated to calculate in practice. In this paper, drag, lift and torque correlations are used to determine the trajectory and impingement of ice particles in aircraft icing scenarios for various shaped particles. Thus far there are few papers that use such methods to address the scenario of aircraft icing. In this paper the correlations from [7] and [16] are both used. These are both formulated from DNS of the particle progression. In [7] force and torque correlations are given for four specific particle s