Computational Modeling of Ice Cracking and
Break-up from Helicopter Blades
Shiping Zhang, Habibollah Fouladi, Wagdi G. Habashi
CFD Lab, McGill University, Canada
Rooh Khurram
King Abdullah University of Science and Technology (KAUST), Saudi Arabia
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Introduction
Ice accretion on wings
Ice impact on engine blade
Hence it is very important to know
where and how ice breaks up !
Business jet with aft-mounted engine
Helicopter
Air crash happened in 1991 in Stockholm due to ice ingestion
1
Background
• Scavuzzo, University of Akron, experiments on impact ice
mechanical properties and qualitative analysis for 2D ice
break up
R.J. Scavuzzo, M.L. Chu, C. J. Kellackey, Impact ice stresses in
rotating airfoils, J. Aircraft, 28(1991), 450-455
• Brouwers, The Pennsylvania State University, developed
a quasi-3D model on ice shedding for helicopter blades
E. W. Brouwers, J. L. Palacios, E. C. Smith, A. A. Peterson, The
experimental investigation of a rotor hover icing model with
shedding, AHS 66th Annual Forum and Technology Display, Phoenix,
USA, 2010.
Most previous research on ice shedding are qualitative 2D analyses,
and no fully 3D ice break up analyses have been done.
The object of this study is thus to develop 2D and 3D simulation tools
to quantitatively predict where and how ice breaks.
2
Mechanical properties of ice
Property
Units
Value
Young’s modulus, E
N m-2
9.33×109
Bulk modulus, B
N m-2
8.90×109
• At high strain rate, for example during
crack propagation process, it behaves
as a brittle material
Shear Modulus, G
N m-2
3.52×109
Poisson’s ratio, υ
n/a
0.325
• Tensile strength: 0.7-3.1 MPa (-10ºC )
Elastic properties of homogeneous poly-crystalline isotropic ice at -16ºC
• At low strain rate, ice shows ductile
behavior due to rheological property
• Compressive strength: 5-25 Mpa (-10ºC)
• Adhesive strength with aluminum, 0.31.6MPa, at -11ºC
Schematic stress-strain curves I, II, and III denote low-,intermediate, and high-strain rates
Framework of ice break-up modeling
Airflow Solution
Crack Propagation
Droplet Solution
Stress Analysis
Ice Accretion
Mesh Generation
4
Mathematical model of ice under fluid forces
Fluid mechanics
The Navier-Stokes equations in conservation form are:
 f
     u  0
t
   f u
t
   f e
t
     f uu   p    T  0
    f eu     pu    Tu    q  0
The viscous stress tensor is defined as:

T    u    u 
T
    u I
Solid mechanics
The equations of equilibrium and the motion for the structure are:
 d 2 us

  2  f s     s  0
 dt

 ij  uk ,k ij    ui , j  u j ,i 
s
Interface conditions
us u f
ts  t f ,

t
t
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Crack propagation
Continuous fracture modes
Crack opening
sliding
tearing
Crack propagation
Quarter-point elements
The standard Lagrange second order shape functions of
1D quadratic element
1
N1     1
2
N 2  1   2 
1
N 3     1
2
Standard, polynomial displacement interpolation scheme
Quadrilateral quarter-point
1
1

u  u2    u3  u1    2   u1  u3   u2 
elements
2
2


Triangle quarter-point
element
Standard, polynomial geometry interpolation scheme
1
1

r   Ni  ri  al   l  l 2   a 
2
2

i 1
n
Parametric Space (a)
Cartesian Space (b)
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2D crack propagation
Quarter-point elements
Standard, polynomial displacement interpolation scheme
1
1

(1)
u  u2    u3  u1    2   u1  u3   u2 
2
2

Parametric Space (a)
Cartesian Space (b)
Standard, polynomial geometry interpolation scheme
1
1

r   Ni  ri  al   l  l 2   a 
2
2 
i 1
n
(2)
The unusual case of ¼-point geometry
a
1
4
 2
r
1
l
(3)
Substitute (3) into standard polynomial displacement interpolation scheme
r
rl
Unexpected, non-polynomial interpolation
u  u1  2  u1  2u2  u3     3u1  4u2  u3  
l
l
Differentiating the displacement field, strain in the element

du
1 1
1
 2  u1  2u2  u3     3u1  4u2  u3  
dr
l 2
rl
Singular term
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2D crack propagation
Quarter-point elements
P1 distribution of quarter-point element
P1 distribution of normal quadratic element
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2D crack propagation
Quarter-point elements
P1 distribution in the vicinity of crack tip of
quarter-point elements
P1 distribution in the vicinity of crack tip of normal
quadratic elements
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2D crack propagation
Quarter-point elements
Principal stress I distribution in 3D of quarter-point element
Principal stress I distribution in 3D of normal quadratic element
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2D crack propagation
Evaluation of stress intensity factor (SIF)
Displacement correlation method is adopted for extracting SIF’s from local field information
KI 
K II 
 2
ra b c  2  2v 
 2
ra b c  2  2v 
 4  vb  vd   ve  vc 
 4  ub  ud   ue  uc 
v
For plain stress, only replace n with 1  v
Evaluation of propagation direction
The direction of crack is based on the Hoop Stress Criterion
KI
K II  1


 3
3 
sin cos2 
 cos  cos 
2
2
2 4
2 
2 r
2 r  4
2


 KI 
1  KI
  2arctan
 sign  K II  
  8

4  K II
 K II 


 r 
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2D crack propagation
Benchmark study
The single edge cracked plate under far field shear loading
reference result [Alshoaibi]
present code
Problem description
E  30 MPa
v  0.25
Plan strain condition
Propagation steps: 32
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Results of 2D ice break-up from airfoil
Mesh of fluid domain
Induced stress distribution
Pressure field
Induced stress and crack
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Results of 2D ice break-up from airfoil
Crack propagation: Re-meshing (left) P1 stress distribution (right)
(quasi-static process, time term is not considered)
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Results of 2D ice break-up from airfoil
Comparison with Franc 2D
Franc 2D’s result
In-house Code’s result
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3D crack propagation
Tracking 3D crack propagation fronts
• The direction of crack is based on the Principal Stress
Criterion, the crack propagates into the direction normal
to the direction of maximum principal stress
• Calculating maximum principal stress and its direction
T.v = l v
• Propagation direction
Rv = Nv ´ Tv
• Crack growth increment
 P 
ai  amax  I 
 PI max 
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3D crack propagation
Validation of 3D crack propagation package
Three points bending test, with initial crack of an inclined plane
with angle of 45 degree. The load force is applied at the middle
of the specimen
)
Three point bending test with the initial crack of an inclined plane
L  130mm
t  10mm
w  30mm
  45o
E  9.8GPa
v  0.33
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3D crack propagation
Validation of 3D crack propagation package
3D out of plane crack propagation
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3D crack propagation
Validation of 3D crack propagation package
Top view of reference results
Top view of in-house code results
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3D ice break-up analysis for helicopter blades
Ice accretion
Ice shape identification
Stress analysis
Interfacial separation
Meshing
Crack propagation
3D ice break-up analysis for helicopter blades
•Ice accretion
• Caradonna hover test case used for flow solution
• Ambient temperature of -19°C
• Liquid water content (LWC) of 1 g/m3
• Droplet mean value diameter (MVD) of 20 microns
• NACA 0012 airfoil, two untwisted blades
• Time: 120 seconds
•Ice shape identification
• Mesh of iced blade
• Mesh of clean blade
•Meshing
• Closed surface mesh
• Unstructured tetrahedral elements generated by
TetGen
•Stress analysis
• According to reference, the aerodynamic force
could be negligible compared with centrifugal force
Fcf  Vr 2
  920kg m3
  400rpm
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3D ice break-up analysis for helicopter blades
ice-airfoil interface bond breaking
• Ice tensile strength: 0.7 to 3.1MPa at -10ºC
• Ice-Aluminum interface adhesion strength: 0.3 to 1.6MPa at
-11ºC
Edge refinement based on the first derivative of
interest value is done to capture the interface bond
and de-bonded transition zone
|
ai1  ai 2
| c
li
Cut section stress distribution of principal stress 1
Bond separation
Mesh adaptation
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3D ice break-up analysis for helicopter blades
Crack initiation and propagation
Evolution of crack (left) and principal stress 1 (right) during the interface bond breaking and crack propagation process
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Summary
• Employing a fracture mechanics framework, 2D and 3D crack propagation
methodologies were developed
• A thorough validation study of the two approaches is made
• The 2D and 3D crack propagation are integrated seamlessly into FENSAP-ICE,
providing the flow, impingement, ice accretion, mesh generation, stress analysis
and crack propagation automatically, and making it the first to have the capability
to quantitatively simulate and analyze the 2D and 3D ice break-up and shedding
from airplane wings and helicopter blades
• 2D ice break-up from wings of aircraft and 3D ice break-up from helicopter
blades are analyzed for typical flow, icing, and operating conditions. The exact
location of ice initial cracking, the crack propagation and the shed ice shape are
obtained, which could be used in the future for ice shedding and impact analysis
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Future work
•The ice break-up methodology will be coupled with rotor blade vibration
analysis, de-icing, ice shedding trajectory and impact simulations.
•Ice break-up package will be used to predict ice shedding from wind turbine
and power cables
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Thank you!
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