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

Abstract

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.

Semi-empirical Erosion Model with Particle Size and Liquid Water Content Effects for Ice Crystal Icing Simulations

“…This expression differs from the one established by Charton et al [2] and recalled in table (Tab. 1).…”

“…This section presents a summary of the semi-empirical model described by Charton et al [2] based on Finnie and Bitter solid/solid collision theory and adapted for ICI context. There is broad consensus in the community [10] [11] [12] [13] that erosion is driven by two main phenomena: cutting wear and deformation wear.…”

“…In the case of non spherical particle, as it is in ICI context, Arabnejad et al [12] correct the hypothesis of spherical particles using the sharpness factor . Charton et al [2] proposed an expression for based on the observations of Arabnejad et al [12].…”

“…A major phenomenon that drives ICI is the erosion caused by the impingement of ice crystals on accreted ice deposits. The present work pursues prior research efforts [2] to derive a semi-empirical erosion model for ICI simulation tools which improves well known limitations of models based on classic solid/solid collision theory [3] [4] [5] in the ICI context. It appears that in glaciated conditions, i.e.…”

“…This paper is organized as follows: Part III briefly summarizes the principles of the standard erosion models of Finnie and Bitter and the erosion model proposed by the authors during prior work [2]. Part IV rewrites the particle momentum equations without the simplifying assumption of a constant depth-to-width area of contact ratio during impact in order to predict more accurate ice shapes.…”