Semi-Empirical Modelling of Erosion Phenomena for Ice Crystal Icing Numerical Simulation

The aim of this work is to develop a semi-empirical model for erosion phenomena under ice crystal condition, which is one of the major phenomena for ice crystal accretion. Such a model would be able to calculate the erosion rate caused by impinging ice crystals on accreted ice layer. This model is based on Finnie [1] and Bitter [2] [3] solid/solid collision theory which assumes that metal erosion due to sand impingement is driven by two phenomena: cutting wear and deformation wear. These two phenomena are strongly dependent on the particle density, velocity and shape, as well as on the surface physical properties such as Young modulus, Poisson ratio, surface yield strength and hardness. Moreover, cutting wear is mostly driven by tangential velocity and is more effective for ductile eroded body, whereas deformation wear is driven by normal velocity and is more effective for brittle eroded body. Several researchers based their erosion modelling on these two phenomena such as Hutchings et al. [4] for deformation erosion, or Huang et al. [5] and Arabnejad et al. [6] for cutting and deformation erosion. The main work of this paper is to develop an erosion model for ice crystal impingement based on these two phenomena, and to show its capability to predict accretion shape by simulating experimental cases from the National Research Council of Canada (NRC). NRC’s Currie et al. ice crystal experiments [7] [8] realized in warm aerodynamic conditions, such as the one encountered in high icing severity areas of a turbofan engine, show accretion severity for a large range of liquid water content to total water content. In order to validate the erosion model based on solid/solid collision, this paper presents the simulation of the lower melting rate experiment. Results show fair agreement with experimental data and allow us to propose pertinent further work. Introduction Aircraft icing is studied since the early 20 century, as it is a major weather hazard for aircraft operation. During the 90s, ice crystal icing has been identified [9], and the regulation accordingly modified. The mechanisms involved in ice crystal icing are not fully understood and several ongoing projects such as MUSIC-Haic [10] are still needed to improve the knowledge on ice crystal icing and to build robust modelling tools able to predict the location and the severity of the accretion. A major phenomenon that drives ice crystal icing is the erosion caused by impinging crystals on accreted ice deposits. For now, empirical models are used to calculate the erosion rate as the one proposed by Trontin et al. [11] [12] in Onera’s 2D icing code based on Currie et al. experimentations [8] [7]. These empirical models were developed with few experimental data, and even if they have good agreement with the data used for their calibration, it can’t be assumed that they will be able to predict well ice accretion size and shape for new experimental cases. The objective of this paper is to study if a model backed by solid-solid erosion can be proposed. Such a model should be more reliable for the simulation of new cases. The first part of this paper briefly introduces the existing erosion model implemented in Onera’s 2D icing code IGLOO2D, and highlights the improvements needed. The second part of this paper is dedicated to solid/solid collision theory, which allows us to calculate the volume eroded by the two identified mechanisms: deformation wear and cutting wear. The third part presents simulation results and discussion around them, especially compared to IGLOO2D ones. Finally the last part introduces future work, in particular the particle size and the liquid water dependencies. Onera’s 2D icing code erosion modelling IGLOO2D icing code takes into account the influence of erosion phenomenon on ice shape by calculating an erosion rate which corrects the accretion rate given by mass and energy balance equations (IGLOO2D extended Messinger’s equations are presented in [11]). Erosion means here material loss caused by crystals impact on ice layer. During the framework of High Altitude Ice Crystal project (HAIC) [13] Trontin et al. [11] [12] developed an empirical model based on Currie et al. [8] [7] observations in order to calculate this material loss. This model gives the erosion rate ?̇?er as: ?̇?er = ηer × ?̇?imp (1) Where ?̇?imp is the impacting mass rate and ηer the erosion ratio. HAIC erosion model gives a value of ηer, between 0 and 1, according to: ηer = E ( Vt V0 ) 2 ( αl0 αl0 −min(αl , αl0) ) (1 + (l0k) 2) (2) Where Vt is the tangential impact velocity, αl the wall liquid ratio, and k the wall curvature. E, V0, αl0 and l0 are empirical parameters only calibrated on Currie’s experiment. One can notice that the velocity dependency is linked to the tangential component only, which means that negligible erosion should be predicted for quasinormal impact. Also the curvature term is a numerical correction which reflects the smoothing effect of erosion phenomenon. The new model presented furtherly is aimed at reducing the empiricism of the original one by giving more physical meaning to the adjustable parameters. In addition, it is expected to have a larger domain of validity. Semi-empirical erosion modelling This section presents the semi-empirical erosion model inspired by Finnie [1] and Bitter [2] [3] solid-solid collision theory. According to these authors, erosion phenomenon caused by a solid particle impact on a wall is mainly due to two phenomena: the deformation wear and the cutting wear. For the sake of simplification, and because