{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T06:55:13Z","timestamp":1780642513927,"version":"3.54.1"},"reference-count":27,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T00:00:00Z","timestamp":1664236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2020YFA0712000"],"award-info":[{"award-number":["2020YFA0712000"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["YL2022XFX03"],"award-info":[{"award-number":["YL2022XFX03"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shenyang key laboratory of aircraft icing and ice protection","award":["2020YFA0712000"],"award-info":[{"award-number":["2020YFA0712000"]}]},{"name":"Shenyang key laboratory of aircraft icing and ice protection","award":["YL2022XFX03"],"award-info":[{"award-number":["YL2022XFX03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A 3D icing simulation code is developed in the open-source CFD toolbox OpenFOAM. A hybrid Cartesian\/body-fitted meshing method is used to generate high-quality meshes around complex ice shapes. Steady-state 3D Reynolds-averaged Navier-Stokes (RANS) equations are solved to provide the ensemble-averaged flow around the airfoil. Considering the multi-scale nature of droplet size distribution, and more importantly, to represent the less uniform nature of the Super-cooled Large Droplets (SLD), two droplet tracking methods are realized: the Eulerian method is used to track the small-size droplets (below 50 \u03bcm) for the sake of efficiency; the Lagrangian method with random sampling is used to track the large droplets (above 50 \u03bcm); the heat transfer of the surface overflow is solved on a virtual surface mesh; the ice accumulation is estimated via the Myers model; finally, the final ice shape is predicted by time marching. Limited by the availability of experimental data, validations are performed on 3D simulations of 2D geometries using the Eulerian and Lagrangian methods, respectively. The code proves to be feasible and accurate enough in predicting ice shapes. Finally, an icing simulation result of the M6 wing is presented to illustrate the full 3D capability.<\/jats:p>","DOI":"10.3390\/e24101365","type":"journal-article","created":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T23:12:12Z","timestamp":1664320332000},"page":"1365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Development of a 3D Eulerian\/Lagrangian Aircraft Icing Simulation Solver Based on OpenFOAM"],"prefix":"10.3390","volume":"24","author":[{"given":"Han","family":"Han","sequence":"first","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zifei","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yijun","family":"Ning","sequence":"additional","affiliation":[{"name":"Shenyang Key Laboratory of Aircraft Icing and Ice Protection, Shenyang 110034, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"key":"ref_1","unstructured":"Gent, R., and Hampshire, G. (1991). A review of icing research at the Royal Aerospace Establishment. AGARD CP, 496."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1984","DOI":"10.1175\/1520-0450(2001)040<1984:COAIET>2.0.CO;2","article-title":"Characterizations of aircraft icing environments that include supercooled large drops","volume":"40","author":"Cober","year":"2001","journal-title":"J. Appl. Meteorol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wright, W. (2005, January 10\u201313). Validation results for LEWICE 3.0. Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2005-1243"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Honsek, R., and Habashi, W.G. (2006, January 9\u201312). FENSAP-ICE: Eulerian modeling of droplet impingement in the SLD regime of aircraft icing. Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2006-465"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hedde, T., and Guffond, D. (1993, January 11\u201314). Improvement of the ONERA 3D icing code, comparison with 3D experimental shapes. Proceedings of the 31st Aerospace Sciences Meeting, Reno, NV, USA.","DOI":"10.2514\/6.1993-169"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2712","DOI":"10.2514\/1.J052954","article-title":"High-quality mesh deformation using quaternions for orthogonality preservation","volume":"52","author":"Maruyama","year":"2014","journal-title":"AIAA J."},{"key":"ref_7","first-page":"82","article-title":"Diffusion characteristics of airborne particles with gravitational settling in a convection-dominant indoor flow field","volume":"98","author":"Murakami","year":"1992","journal-title":"ASHRAE Trans."},{"key":"ref_8","first-page":"88","article-title":"Comparison of Diffusion Characteristics of Aerosol Particles in Different Ventilated Rooms by Numerical Method","volume":"110","author":"Zhao","year":"2004","journal-title":"ASHRAE Trans."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1016\/j.buildenv.2004.09.018","article-title":"Numerical study of the transport of droplets or particles generated by respiratory system indoors","volume":"40","author":"Zhao","year":"2005","journal-title":"Build. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1111\/j.1600-0668.2005.00373.x","article-title":"Using large eddy simulation to study particle motions in a room","volume":"15","author":"Beghein","year":"2005","journal-title":"Indoor Air"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5236","DOI":"10.1016\/j.atmosenv.2006.05.086","article-title":"Comparison of the Eulerian and Lagrangian methods for predicting particle transport in enclosed spaces","volume":"41","author":"Zhang","year":"2007","journal-title":"Atmos. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"29","DOI":"10.2514\/8.2520","article-title":"Equilibrium temperature of an unheated icing surface as a function of air speed","volume":"20","author":"Messinger","year":"1953","journal-title":"J. Aeronaut. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"211","DOI":"10.2514\/2.1312","article-title":"Extension to the Messinger model for aircraft icing","volume":"39","author":"Myers","year":"2001","journal-title":"AIAA J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1002\/cnm.1128","article-title":"Particle tracking in unstructured, arbitrary polyhedral meshes for use in CFD and molecular dynamics","volume":"25","author":"Macpherson","year":"2009","journal-title":"Commun. Numer. Methods Eng."},{"key":"ref_15","first-page":"1","article-title":"OpenFOAM: A C++ library for complex physics simulations","volume":"Volume 1000","author":"Jasak","year":"2007","journal-title":"International Workshop on Coupled Methods in Numerical Dynamics"},{"key":"ref_16","unstructured":"Gisen, D. (October, January 29). Generation of a 3D mesh using snappyHexMesh featuring anisotropic refinement and near-wall layers. Proceedings of the 11th International Conference on Hydroscience & Engineering, ICHE 2014, Hamburg, Germany."},{"key":"ref_17","unstructured":"McCroskey, W.J. (1987). A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil, National Aeronautics and Space Administration. Technical Report."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Patankar, S.V. (2018). Numerical Heat Transfer and Fluid Flow, CRC Press.","DOI":"10.1201\/9781482234213"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Spalart, P., and Allmaras, S. (1992, January 6\u20139). A one-equation turbulence model for aerodynamic flows. Proceedings of the 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.1992-439"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.2514\/3.12149","article-title":"Two-equation eddy-viscosity turbulence models for engineering applications","volume":"32","author":"Menter","year":"1994","journal-title":"AIAA J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bourgault, Y., Habashi, W., Dompierre, J., Boutanios, Z., and Di Bartolomeo, W. (1997, January 6\u20139). An Eulerian approach to supercooled droplets impingement calculations. Proceedings of the 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.1997-176"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wirogo, S., and Srirambhatla, S. (2003, January 6\u20139). An Eulerian method to calculate the collection efficiency on two and three dimensional bodies. Proceedings of the 41st Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2003-1073"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"DeGennaro, A.M. (2016). Uncertainty Quantification for Airfoil Icing. [Ph.D. Thesis, Princeton University].","DOI":"10.2514\/6.2015-3383"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"107853","DOI":"10.1016\/j.cpc.2021.107853","article-title":"picFoam: An OpenFOAM based electrostatic Particle-in-Cell solver","volume":"262","author":"Groll","year":"2021","journal-title":"Comput. Phys. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Bai, C., and Gosman, A. (1995). Development of methodology for spray impingement simulation. SAE Trans., 550\u2013568.","DOI":"10.4271\/950283"},{"key":"ref_26","unstructured":"Shin, J., and Bond, T.H. (1992). Experimental and Computational Ice Shapes and Resulting Drag Increase for a NACA 0012 Airfoil, California State Univ.. The Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wright, W., and Potapczuk, M. (2004, January 5\u20139). Semi-empirical modelling of SLD physics. Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2004-412"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1365\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:40:04Z","timestamp":1760143204000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,27]]},"references-count":27,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["e24101365"],"URL":"https:\/\/doi.org\/10.3390\/e24101365","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,27]]}}}