Eulerian Method for Ice Accretion on Multiple-Element Airfoil Sections J.M. Hospers and H.W.M. Hoeijmakers IMPACT, Engineering Fluid Dynamics – University of Twente

Outline

 Problem background  Supercooled Large Droplets  Numerical method: Droplerian  Numerical method: Splashing model  Catching efficiency results

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Problem Background

 Supercooled droplets present in clouds  Droplets freeze instantly on impact with aircraft/wing  Added mass  Reduced aerodynamic efficiency  Altered aerodynamic characteristics  Occurs at low altitude (landing situations)  > 50 accidents and incidents, claiming > 800 lives from 1992-2000

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Supercooled Large Droplets

 Normal icing conditions:  D ≤ 50 μm

 Heavily researched, protection measures available  SLD icing conditions  50 μm ≤ D ≤ 1000 μm (or even bigger)  Relatively rare but dangerous  Splashing/rebound and breakup become important  EU-EXTICE project aims to improve SLD modeling

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Numerical Method

 Flow calculation (air and droplets, Lagrangian or Eulerian)  Catching efficiency β = non-dimensional mass flux on airfoil surface  Messinger Model (thermodynamic balance)  Ice thickness → New geometry  Possibly iterate the above steps

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Droplerian

 Eulerian method based on a similar Lagrangian code  Conservation equations for droplet phase  Droplets experience only gravity and drag  One-way-coupling, droplet distribution does not alter the flow ∂  . αρ u =0  αρ d  ∇ d d ∂t

α: liquid volume fraction

∂  . αρ u u =αρ f  αρ d  u d  ∇ g d d d d drag α  ρ d − ρ a   ∂t f drag =

 C A D 1 = ρa ∣u −u d∣  u − ud  D d ρd V d 2 ρd V d C Re 18 μ = D d 2 a  u −u d  24 d eq ρd

β  s =−

αρ d  u d . n  U ∞ LWC

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results

 Potential-flow solution (obtained from panel-method)  4616 elements, 400 surface elements  2D NACA-23012 airfoil with experimental data from Papadakis et al.1  2.5° AoA, U∞ = 78.23 m/s, T∞ = 299 K  20 μm and 236 μm MVD, LWC = 2.5 g/m3

[1]Papadakis et al., NASA/TM-2007-213961 (2007) Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results without Splashing

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Results without Splashing

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Results without Splashing

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Splashing Model

 Trujillo1





M splashed =0.8⋅ 1−exp [ −0.85  K y −K y ,crit  ]

 [

2



] 

∣u0∣ 1 N= 0.0437 K −K c , dry −44.92 22 u0⋅n

   

u ⋅t ⋅t u =0.850.0025 arctan 0 u0⋅n u0⋅t u ⋅t ⋅ u n =0.120.002 arctan 0 u0⋅ n u0⋅n

K, Kc,dry, Ky, Ky,crit, splashing parameter, function of Oh and We

 Habashi/Honsek2

 

M splashed =

3.8 ⋅ 1−exp [ −0.85  K y −K y ,crit  ] K y



[1]Trujillo et al., Int. J. Engine Res. 1 (2000) [2]Honsek, Habashi and Aubé, J. Aircr. 45 (2008) Second FERMaT-IMPACT meeting, 13-16 October 2009

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Splashing Model

 Airfoil boundary conditions with splashing  Splashing depends on value of K  If K <= Kc all mass is deposited on the surface  If K > Kc part of the mass is deposited, the rest is re-injected  Re-injection in correct droplet bin

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results with Splashing

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Results with Splashing

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Results with Splashing 236 μm MVD

 Bin 1, D = 1.046E-3 m  NO splashing

 WITH splashing

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Results with Splashing 236 μm MVD

 Bin 2, D = 7.632E-4 m  NO splashing

 WITH splashing

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Results with Splashing 236 μm MVD

 Bin 3, D = 7.473E-4 m  NO splashing

 WITH splashing

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Results with Splashing 236 μm MVD

 Bin 4, D = 7.158E-4 m  NO splashing

 WITH splashing

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Results with Splashing 236 μm MVD

 Bin 5, D = 6.454E-4 m  NO splashing

 WITH splashing

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Results with Splashing 236 μm MVD

 Bin 6, D = 5.084E-4 m  NO splashing

 WITH splashing

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results with Splashing 236 μm MVD

 Bin 7, D = 2.985E-4 m  NO splashing

 WITH splashing

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results with Splashing

 Bin 8, D = 1.354E-4 m  NO splashing

 WITH splashing

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results with Splashing 236 μm MVD

 Bin 9, D = 6.365E-5 m  NO splashing

 WITH splashing

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Results with Splashing 236 μm MVD

 Bin 10, D = 16.25E-6 m  NO splashing

 WITH splashing

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Conclusions

 Catching efficiency 

Using 10 droplet bins improves matching with experimental results



Splashing improves matching with experimental results



Under-prediction near leading edge



Over-prediction downstream of leading edge



Effect of splashing only visible in droplet bins with smallest diameter

 Possible causes for differences with experimental results 

Rebound of droplets



Breakup of droplets



Deformation of droplets



Excluded flow effects (viscosity of surrounding air, two-way-coupling)

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Questions?

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Future Work

 Add specific SLD relations for droplet drag (due to deformation of droplets)  Add rebound model  Add breakup model  Improve existing models  Perform test cases to compare with experimental data  Catching efficiencies  Ice-accretion shapes

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2DFOIL-ICE

 Implemented  Multidisperse droplet distributions  Perform serial simulations of individual droplet bins  Splashing model  Re-injection of secondary droplets difficult  Accurate simulations for single-element airfoils  For multi-element airfoils a more accurate flow model is needed  Further improvement for SLD conditions is needed

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Droplerian

 Implemented  Multidisperse droplet distributions (Same as 2DFOIL-ICE)  Splashing model (Same as 2DFOIL-ICE)  Results can be compared with Lagrangian (2DFOIL-ICE) results as initial verification method

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results with Splashing

 Habashi/Honsek splashing model added  Secondary droplets added to droplet bin representing diameter closest to average secondary diameter from Habashi/Honsek model  Droplet bins are calculated serially, from largest to smallest  Smaller droplet bins can include splashed/secondary droplets  Allows re-impingement of secondary droplets

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results without Splashing

 2DFOIL-ICE  400 elements on airfoil  Droplerian  4616 elements (triangle)  400 surface elements (same as 2DFOIL-ICE)  JST-scheme

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2DFOIL-ICE

 Potential-Flow-Model (panel-method)  One-way-coupling, droplet distribution does not alter the flow  Lagrangian droplet tracking  Catching efficiency:

=

dy ds

 Messinger Model (thermodynamic balance), provides the mass of water that freezes

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Droplerian

 Any available flow model can be used (flow is used as input)  One-way-coupling, droplet distribution does not alter the flow  Droplet distribution calculated on a grid (Eulerian method)  Messinger model (same as 2DFOIL-ICE)  Icing shape (same as 2DFOIL-ICE) Advantages:  Possibility to include higher accuracy flow models  Entire droplet-flow-field available (instead of trajectories)  Splashing/re-injection can be implemented as BC  Easily extended to 3D

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Splashing Model

 Based on empirical Trujillo model  Mass-loss coefficient  Velocity of secondary droplets after splashing event  Number (and size) of secondary droplets  Habashi calibrated this model for SLD conditions  Altered mass-loss  Secondary droplets are injected into a smaller droplet class

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results without Splashing

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Results without Splashing

LWC kg/m3

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Intermediate Conclusions

 Over-prediction of catching efficiency  Over-prediction slightly reduced by using multiple droplet bins  Possible causes for over-prediction  Splashing  Rebound  Breakup  Droplet deformation  Excluded flow effects (viscosity, two-way-coupling)

Second FERMaT-IMPACT meeting, 13-16 October 2009

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Results with Splashing

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