The document presents a new differential boundary layer model for the wind turbine icing code TURBICETM. The model solves the differential boundary layer equations using Keller's box method and includes features like grid scaling, a zero-equation turbulence model, and transition criteria. Initial test results on flat plates and airfoils show improved heat transfer predictions compared to the current integral method. Future work includes further model refinement, implementing separation bubble simulation, testing roughness and transition models, and integrating the boundary layer model into TURBICETM.

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

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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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