Abstract
This chapter discusses the models of the physics of the water impingement and ice formation mechanisms. Body discretization, external flow and temperature field, and body wetness have been analysed. The contents give the fundamentals of the design of anti-icing or de-icing systems. The icing process is described from the thermo-fluid-dynamic point of view. The aim is not to detail the ice growing process, but to give methods to determine the water mass flow captured by the aerodynamic profile, the impingement limits and the heat flows involved in the process on the surface, as ice prevention systems are designed to keep the surface reasonably clean of ice. To this aim the general theory for droplet trajectory includes the fixed cylinder case, the collision efficiency calculation for profiles at zero and other than zero AoAs. Calculation of the difference between translating and rotating blade on impinging water is presented and discussed. A numerical example for the profile of the Tjærborg wind turbine rotor is given. Finally, some relevant conclusions applied to wind turbines are drawn. The chapter analyses the water mass balance at the surface, and the thermo-fluid-dynamic processes at the iced surface by the concept of freezing fraction. Thus with the help of energy and mass conservation equations the problem of ice accretion and anti-ice design is presented and solved.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A rigorous analysis reveals that the isoentropic coefficient \(\varepsilon \) within the boundary layer is an equivalent coefficient, taking into account that the viscous layer is formed on dry air, vapour and water. This means that it should be computed as weighted average of the mixture components in the volume according to the following:
$$\begin{aligned} c_{p,eq} = \frac{\displaystyle \sum m_i c_i}{\displaystyle \sum m_i} = \frac{c_{p,air}+\displaystyle \frac{m_{vap}}{m_{\textit{air}}}c_{p,vap}+\displaystyle \frac{m_{w}}{m_{\textit{air}}}c_{w}}{1+\displaystyle \frac{m_{vap}}{m_{\textit{air}}}+ \displaystyle \frac{m_{w}}{m_{\textit{air}}}} \end{aligned}$$(4.6)After substituting the numerical values, it results that \(c_{p,eq}\sim c_{p,\textit{air}}\), so the specific heat of air at constant pressure and hence \(\varepsilon \) will be used for the following analysis within the boundary layer.
- 2.
Another definition (for numerical implementation purposes) considers the fraction of the total liquid entering the control volume that freezes within the control volume.
References
Messinger BL (1953) Equilibrium temperature of an unheated icing surface as a function of air speed. J Aeronaut Sci 20(1):29–42
MacArthur CD (1983) Numerical simulation of airfoils ice accretion. AIAA paper 83:0112
Wright WB (2002) User manual for the NASA green ice accretion code LEWICE-version 2.2.2. NASA Langley Research Center, NASA/CR-2002-211793
Wright WB (1995) Users manual for the improved NASA Lewis ice accretion code LEWICE 1.6. NASA Langley Research Center, NASA CR198355
Hedde T, Guffond D (1995) ONERA Three-dimensional icing model. AIAA J 33(6):1038–1045
Tran P, Brahimi MT, Paraschivoiu I, Pueyo A, Tezok F (1995) Ice accretion on aircraft wings with thermodynamic effects. AIAA J 32(2):444–446
Baruzzi GS, Habashi WG, Guvremont G, Hafez MM (1995) A second order finite element method for the solution of the transonic Euler and Navier-Stokes equations. Int J Numer Methods Fluids 20:671–693
Bourgault Y, Habashi WG, Dompierre J, Baruzzi GS (1999) A finite element method study of Eulerian droplets impingement models. Int J Numer Methods Fluids 29:429–449
Beaugendre H, Morency F, Habashi WG (2003) FENSAP-ICEs three-dimensional in-flight ice accretion module. J Aircr 40(2):239–247
Croce G, Beaugendre H, Habashi WG (2002) CHT3D: FENSAP-ICE conjugate heat transfer computations with droplet impingement and runback effects. AIAA paper 2002-0386
Lozowski EP, Stallabrass JR, Hearty PF (1983) The icing of an unheated, nonrotating cylinder. Part I: a simulation model. J Clim Appl Meteorol 22:2053–2074
Finstad KJ, Lozowski EP, Makkonen L (1988) On the median volume diameter approximation for droplet collision efficiency. J Atmos Sci 45(24):4008–4012
Langmuir I, Blodgett KB (1945) A mathematical investigation of water droplet trajectories. General Electric, RL 225 Ad 64354
Dorsch RG, Brun RJ, Gregg JL (1954) Impingement of water droplets on an ellipsoid with fineness ratio 5 in axisymmetric flow. National Advisory Committee for Aeronautics, Technical note NACA-TN-3099
Hacker PT, Brun RJ, Boyd B (1953) Impingement of droplets in \(90^{\circ }\) elbows with potential flow. National Advisory Committee for Aeronautics, Technical note 2999
Langmuir I (1946) Collected works of Irving Langmuir. Pergamon Press 10:348–393
Beard KV, Pruppacher HR (1969) A determination of the terminal velocity and drag of small water droplets by means of a wind tunnel. J Atmos Sci 26:1066–1072
Wang PK, Pruppacher HR (1977) An experimental determination of the efficiency with which aerosol particles are collected by water drops in subsaturated air. J Atmos Sci 34:1664–1669
Anderson DN (2004) Manual of scaling methods. Ohio Aerospace Institute, Brook Park, Ohio, Technical report, NASA/CR-2004-212875
Finstad KJ, Lozowski EP, Gates E (1988) A computational investigation on water particle droplet trajectories. J Atmos Ocean Technol 5:160–170
Wright WB, Potapczuk M (1996) Computational simulation of large droplet icing. FAA International conference on inflight icing, DOT/FAA/AR96/81
Wright WB (1995), Capabilities of LEWICE 1.6 and comparison with experimental data. AHS international icing symposium, Montreal, Canada
Hamed A (1981) Particle dynamics of inlet flow fields with swirling vanes. AIAA paper 81-0001, 19th AIAA aerospace sciences meeting. St. Louis (January 1981)
Farag KA, Bragg MB (1997) Three dimensional droplet trajectory code for propellers of arbitrary geometry. In: Proceeding of 36th AIAA Aerospace Sciences Meeting and Exhibit
Gelder FT, Lewis JP (1951) Comparison of heat transfer from airfoil in natural and icing conditions. NASA Langley Research Center, NACA TN 2480
Al-Khalil KM, Keith TG, De Witt KJ (1993) New concept in Runback water modeling for anti-iced aircraft surfaces. J Aircr 30(1):41–49
Bourgault Y, Beaugendre H, Habashi WG (2000) Development of a shallow-water icing model in FENSAP-ICE. J Aircr 37(4):640–646
Schmidt E, Wenner K (1943) Heat transfer over the circumference of a heated cylinder in transverse flow. NASA Langley Research Center, NACA TM 1050
Martinelli RC, Guibert AG, Morin EH, Boelter LMK (1943) An investigation of aircraft heaters, VIII—a simplified method for the calculation of the unit thermal conductance over wing. NASA Langley Research Center, NACA ARR (WR W-14)
Smith AG, Spalding DB (1958) Heat transfer in a laminar boundary layer with constant fluid proprieties and constant wall temperature. J R Aeronaut Soc 62:60–64
Incropera F, DeWitt D (1996) Fundamentals of heat and mass transfer, 5th ed. Wiley, New York
Tsao JC, Rothmayer AP (2002) Application of triple-deck theory to the prediction of glaze ice roughness formation on an airfoil leading edge. Comput Fluids 31(8):977–1014
Myers TG, Hammond DW (1999) Ice and water film growth from incoming supercooled droplets. Int J Heat Mass Transfer 31(42):2233–2242
Myers TG (2001) Extension to the Messinger model for aircraft icing. AIAA J 39(2):211–218
Oezgen S, Canibek M (2008) Ice accretion simulation on multi-element airfoils using extended Messinger model. J Heat Mass Transfer. doi:10.1007/s00231-008-0430-4
Huang JR, Keith TG Jr, De Witt KJ (1993) Efficient finite element method for aircraft de-icing problems. J Aircr 30(5):695–704
Bourgault Y, Beaugendre H, Habashi WG (2000) Development of a shallow-water icing model in FENSAP-ICE. J Aircr 37(4):640–646
De Witt KJ, Baliga G (1982) Numerical simulation of one-dimensional heat transfer in composite bodies with phase change, NASA CR-165607
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Battisti, L. (2015). Icing Process. In: Wind Turbines in Cold Climates. Green Energy and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-05191-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-05191-8_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05190-1
Online ISBN: 978-3-319-05191-8
eBook Packages: EnergyEnergy (R0)