Modeling and Analysis Thin Wall Film Formation with Integrated Discrete and Continuous Phase Simulation Approach

Abstract

Water film will be initiated and formed under the continuous impingement of incoming supercooled droplets, and directly affect the ice formation, which is always vital for the performance and safety of aero-engine. A hybrid algorithm integrating Discrete Phase Model (DPM) and Volume of Fluid (VOF) was established to simulate all the stages from droplet initiation to the film well-formed which can make the numerical simulation of icing more realistic and accurate. The transformation criterion from the particle to liquid volume fraction and the distribution of source terms has been improved compared with similar previous approaches. Three verification cases, namely single droplet train impact, staggered droplets impact and two glycerine-solution droplet impact, were conducted to verify the mass conservation and the applicability to both the sparse and dense two-phase flow. The results showed that the relative error of mass transformation is no more than 0.5%. The comparison between simulation and experiment result demonstrated that the hybrid algorithm has the ability to simulate the flow behaviour of droplets accurately. The thin water film formation on a typical wing of NACA0012 airfoil was then analysed, the results of which illustrated that the integrated algorithm could successfully capture the characteristics of liquid film formation and motion. INTRODUCTION Liquid film will form under the continuous impingement of droplets in many industry fields, such as ice accretion process (Rothmayer et al., 2002) (Moore, et al.,2017) on the engine inlet vane or nosecone, fuel spray process inside combustion chamber (Pan et al., 2019), or thin liquid films on steam turbine airfoils (Rossi et al., 2017). It has very important influences on the system operation and flight safety. Icing is always vital for the performance and safety of aero-engine, during the icing process inside aero-engine, the water film will be initiated and formed under the continuous impingement of incoming supercooled droplets, and then flow under the shear force from the mainstream. Thus, calculating the flow pattern accurately after the droplet impingement is of great significance as well as the basis of subsequent ice shape calculation. The formation of wall film during the impingement process has been modelled and investigated with different methods, although the classic Messinger model for icing simulation does not consider the water film flow on the ice layer. Some researches (Myers and Charpin, 2004) (Nakakita et al., 2010) (Cao et al., 2016) (Chauvin et al., 2018) adopted the lubrication equation based on the assumption of continuous and thin liquid film to model the film height, which is validated for the phase where the film has formed well and is unable to consider the initial icing roughness, which has great influence on calculating the shape of ice accurately. The global “equivalent sand grain roughness” whose height does not change with time and space was used to simulate effects of the surface roughness on the flow and heat transfer process. However, it still cannot reproduce the different size of ice beads observed in experiments. In the meantime, beyond the droplet impingement limits, broken of continuous liquid film will happen due to icing or evaporation. Therefore, some other models must be developed to simulate the formation of rivulet and initial roughness, such as the work initiated by Guy (Guy Fortin, et al., 2006) and followed by Li (Li, et al., 2011) and Chang (Chang, et al., 2014), where the roughness prediction model was established after analysing the forced characteristics of water for three different forms of flow, namely water droplets, liquid film and stream. The VOF approach in Eulerian framework could perfectly simulate the liquid water distribution, but the computational cost is extremely high. To balance the requirements of computation capacity and accuracy, a coupled method combined DPM and VOF is brought out to simulate the flow behaviour of super-cooled large droplets after impingement, which has shown some prospects in the field of two-phase flow simulation. Chou et.al (Chou et al. 2015) presented a two-way coupled Eulerian-Lagrangian model to simulate the suspension of fine particles in liquid flows, which demonstrated that the integrated model is capable of revealing the detailed features of particle-laden flows. Zuzio et.al (Zuzio