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

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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

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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

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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

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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

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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

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