FENSAP-ICE: Analytical Model for Spatial and Temporal Evolution of In-Flight Icing Roughness Giulio Croce * and Erika De Candido † Università di Udine, 33100 Udine, Italy Wagdi G. Habashi ‡ and Jeffrey Munzar § McGill University, Montreal, Quebec H3A 2S6, Canada and Martin S. Aubé, ¶ Guido S. Baruzzi, ** and Cristhian Aliaga †† Newmerical Technologies International, Montreal, Quebec H3A 2M7, Canada DOI: 10.2514/1.47143 Ice roughness, which has a major influence on in-flight icing heat transfer and, hence, ice shapes, is generally input from empirical correlations to numerical simulations. It is given as uniform in space, while sometimes being varied in time. In this paper, a predictive model for roughness evolution in both space and time during in-flight icing is presented. The distribution is determined mathematically via a Lagrangian model that accounts for the stochastic process of bead nucleation, growth, and coalescence into moving droplets and/or rivulets and/or water film. This general model matches well the spatial and temporal roughness distributions observed in icing tunnel experiments and is embedded in FENSAP-ICE, extending its applicability outside the range of airfoil types for which correlations exist. Thus, an additional important step has been taken toward removing another empirical aspect of in-flight icing simulation. Nomenclature g = gravity h = height L = latent heat m = mass flow p = pressure Q h = convective heat flux T = temperature u, v = velocity  = collection efficiency  = viscosity  = density of water  = shear stress I. Introduction I N-FLIGHT icing continues to represent major risks for aircraft safety. When an airplane crosses clouds of supercooled droplets during takeoff, holding, or landing, the impinging droplets may freeze on the exposed surfaces and build up ice around wings, nacelles, tail, empennage, antennas, and several other lifting and nonlifting areas. The accreted ice may alter the aerodynamic performance of the aircraft, interfere with the movement of control surfaces and their effectiveness, block engine inlets, or be shed and damage engines, propellers, or structural components. Computational fluid dynamics (CFD) modeling has emerged as a powerful tool for the prediction of ice shapes and for the simulation and optimization of ice protection systems. However, the simulation of in-flight icing is a very complex multiphysics problem, and several aspects are still far from being well represented. The present paper borrows ideas in a multidisciplinary way from various fields to elucidate one of these issues, namely, the analytical versus empirical evaluation of ice-induced surface roughness, which has an important effect on conjugate heat transfer and, ultimately, on accreted ice shapes. FENSAP-ICE, a 3-D in-flight icing system, serves as the ideal vehicle for the new models developed. Experimental evidence shows that an iced surface is not smooth, but covered by a collection of nearly hemispherical beads with radii of the order of millimeters [1]. Furthermore, because roughness is induced by the ice accretion itself, it is far from being constant in either space or time. In particular, roughness appears at the beginning of ice formation and grows with time until a final distribution is attained asymptotically [2]. Roughness height is also not constant in space but is usually very small around the leading edge and becomes larger further downstream [1,3]. The roughness shape and distribution ought to be intuitively related to the size and evolution of the beads and rivulets formed on the surface by impinging droplets and their interaction with the already accreted layer. Surface roughness affects shear stress and heat transfer [4], which in turn determine the shape and size of the accreted ice layer. Thus, there is a time-varying two-way coupling between roughness buildup and ice accretion. Finally, the liquid water layer on the ice surface affects the effective area exposed to evaporation and, consequently, the evaporative heat flux. The importance of the effective surface fraction exposed to evaporation in heat transfer processes has been clearly demonstrated in different application fields [5,6] and should not be neglected in the simulation of anti- and de-icing systems. The understanding and handling of ice-induced roughness is of crucial importance to obtain accurate and reliable CFD-based ice shapes. Currently, most icing codes provide simplified roughness modeling through the use of empirical correlations. The most widely employed correlation is that of Shin and Bond [7], which gives a Presented as Paper 2009-4126 at the 1st AIAA Atmospheric and Space Environments Conference, San Antonio, TX, 22–25 June 2009; received 11 September 2009; revision received 31 December 2009; accepted for publication 12 January 2010. Copyright © 2010 by W.G. Habashi. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/10 and $10.00 in correspondence with the CCC. * Professor, Department of Mechanical Engineering, Via delle Scienze 208. † Ph.D. Candidate, Department of Mechanical Engineering, Via delle Scienze 208. ‡ Professor, Director of the Computational Fluid Dynamics Laboratory, Department of Mechanical Engineering, 688 Sherbrooke Street West, Fellow AIAA. § Honors Summer Student, Computational Fluid Dynamics Laboratory, Department of Mechanical Engineering, 688 Sherbrooke Street West. ¶ Vice President Operations, 680 Sherbrooke Street West. ** Director of Product Development, 680 Sherbrooke Street West. Member AIAA. †† Chief, Consulting Services, 680 Sherbrooke Street West. JOURNAL OF AIRCRAFT Vol. 47, No. 4, July–August 2010 1283