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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
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
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
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
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
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
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
11/02/2013   8




VTT creates business from
technology

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Huttunen saara

  • 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. 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. 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. 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. 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. 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. 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. 11/02/2013 8 VTT creates business from technology