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  1. 1. Differential boundary layer model for wind turbine blade icing code TURBICE™ Winterwind 2013, 12th – 13th of February, Östersund Saara Huttunen VTT Technical Research Centre of Finland
  2. 2. 11/02/2013 2 Motivation for differential boundary layer model  Velocity distribution within the boundary layer can be calculated instead of approximate distribution used by integral methods.  More accurate heat flux analysis via Reynolds analogy  More advanced heat and mass transfer analysis  More accurate ice accretion simulation y 𝑈∞ y 𝑈∞ u dy δ u dy δ dx x dx x differential method integral method
  3. 3. 11/02/2013 3 Main features of the model (1/2)  Differential boundary layer equations solved by Keller’s box method 𝜕𝑢 𝜕𝑢 1 𝑑𝑝 𝜕2 𝑢 𝜕 ′ ′ 𝑢 + 𝑣 =− + 𝜈 2− 𝑢 𝑣 𝜕𝑠 𝜕𝑦 𝜌 𝑑𝑠 𝜕𝑦 𝜕𝑦 𝑦) 𝑢𝑒  Grid scaling in normal direction ( 𝜂 = 2𝜈𝑠 to account for large gradients 𝑘𝑛 𝜂 P4 P1 𝜂𝑗 𝜂𝑗 𝜂 𝑗−1/2 ℎ𝑗 𝜂 𝑗−1 𝜂 𝑗−1 P3 P2 𝑠 𝑛−1 𝑠𝑛 𝑠 𝑠 𝑛−1 𝑠 𝑛−1/2 𝑠 𝑛 grid and cell description – Keller’s box method
  4. 4. 11/02/2013 4 Main features of the model (2/2)  Zero-equation algebraic turbulence model with two layer structure: inner viscous region, outer inviscid region 𝜕𝑢 𝜈𝑡 𝑖 = 𝑙2 𝛾 𝜕𝑦 𝑡𝑟 𝜈𝑡 𝑜 = 0.0168𝑅𝑒0.5 𝜂 𝑒 − 𝑓 𝜂 𝑒 𝑠 𝛾 𝑡𝑟 𝛾ν  Michel and laminar separation transition criteria  Local heat transfer coefficient from local Stanton number for forced convective heat transfer 1 𝑆𝑡 𝑙 = 𝑐 𝑃𝑟 1/3 2 𝑓 𝑐 𝑓 /2 𝑆𝑡 𝑡 = 1 + 12.8 𝑃𝑟 0.68 − 1 𝑐 𝑓 /2
  5. 5. 11/02/2013 5 theory, smooth surface (White, F.M. 2004, Equation 6-78) 0,01 Flat plate results new model, smooth surface new model, ks = 0.0001 m new model, ks = 0.00025 m new model, ks = 0.0005 m experimental, ks = 0.0005 m (Mills, A.F. et al. 1983)  Fully turbulent flow over smooth experimental, ks = 0.00025 m (Mills, A.F. et al. 1983) 0,008 experimental, ks = 0.0001 m (Mills, A.F. et al. 1983) and rough flat plates  𝑅𝑒 = 5 × 106 , 𝛼 = 0° 0,006  Mixing length (𝑙) modified for roughness effects following Cf Cebeci (2004) 𝑙 = κ 𝑦 + ∆𝑦 1 − 𝑒 − 𝑦+∆𝑦 /𝐴 0,004 𝜈 + ∆𝑦 = 0.9 𝑘 + − 𝑘 + 𝑒 −𝑘 𝑠 /6 𝑠 𝑠 𝑢𝜏  Typical equivalent sand grain 0,002 roughness height (𝑘 𝑠) for rime ice is 0.4 … 1.0 mm 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 s/c
  6. 6. 11/02/2013 6 900 NACA 0012 results new model TURBICE 800  Smooth NACA 0012 airfoil 700  𝑅𝑒 = 1 × 106 , 𝛼 = 0° 600  Heat transfer coefficient (ℎ)on the leading edge is higher than with the 500 current integral boundary layer h method on TURBICE 400  Experimental references required 300 for comparison  Initial conditions will be examined 200 in detail 100 0 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 s/c
  7. 7. 11/02/2013 7 Future work  Checking inconsistencies and fine tuning the model  Implementation of an inverse method to include separation bubble simulation  Roughness model – Evaluating scope of experimental methods, testing different roughness models  Testing different transition criteria  Implementation of the boundary layer model into TURBICE
  8. 8. 11/02/2013 8 VTT creates business from technology

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