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Computational Modeling of Ice Cracking and Break-up from

Helicopter Blades

Shiping Zhang, Habibollah Fouladi, Wagdi G. HabashiCFD Lab, McGill University, Canada

Rooh KhurramKing Abdullah University of Science and Technology (KAUST), Saudi Arabia

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Introduction

Ice accretion on wings

Business jet with aft-mounted engine

Ice impact on engine blade

Helicopter Hence it is very important to know where and how ice breaks up !

Air crash happened in 1991 in Stockholm due to ice ingestion

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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.

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

Shear Modulus, G N m-2 3.52×109

Poisson’s ratio, υ n/a 0.325

Schematic stress-strain curves I, II, and III denote low-,intermediate-, and high-strain rates

Elastic properties of homogeneous poly-crystalline isotropic ice at -16ºC

• At low strain rate, ice shows ductile behavior due to rheological property

• At high strain rate, for example during crack propagation process, it behaves

as a brittle material

• Tensile strength: 0.7-3.1 MPa (-10ºC )

• Compressive strength: 5-25 Mpa (-10ºC)

• Adhesive strength with aluminum, 0.3-1.6MPa, at -11ºC

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Framework of ice break-up modeling

Airflow Solution Droplet Solution Ice Accretion

Mesh GenerationStress AnalysisCrack Propagation

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Mathematical model of ice under fluid forces

f

f pt

0

uuu T

0f

t

u

0f

fe

e pt

u u Tu q

T T u u u I

The Navier-Stokes equations in conservation form are:

The viscous stress tensor is defined as:

The equations of equilibrium and the motion for the structure are:

2

2

, , ,

0s s ss

ij k k ij i j j i

df

dtu u u

u

Fluid mechanics

Solid mechanics

Interface conditions

,s ft t fs

t t

uu

Crack propagation

Continuous fracture modes

Crack opening sliding tearing

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Crack propagation

Quarter-point elements

Quadrilateral quarter-point elements

Triangle quarter-point element

The standard Lagrange second order shape functions of 1D quadratic element

1

11

2N

22 1N

3

11

2N

2

1

1 1

2 2

n

i ii

r N r al l l a

Standard, polynomial geometry interpolation scheme

22 3 1 1 3 2

1 1

2 2u u u u u u u

Standard, polynomial displacement interpolation scheme

Parametric Space (a) Cartesian Space (b)

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2D crack propagation

Quarter-point elements

The unusual case of ¼-point geometry

Substitute (3) into standard polynomial displacement interpolation scheme

(3)

Differentiating the displacement field, strain in the element

Singular term

1

4a 2 1

r

l

1 1 2 3 1 2 32 2 3 4r rl

u u u u u u u ul l

1 2 3 1 2 3

1 1 12 2 3 4

2

duu u u u u u

dr l rl

Parametric Space (a) Cartesian Space (b)

Unexpected, non-polynomial interpolation

2

1

1 1

2 2

n

i ii

r N r al l l a

Standard, polynomial geometry interpolation scheme

22 3 1 1 3 2

1 1

2 2u u u u u u u

Standard, polynomial displacement interpolation scheme

(2)

(1)

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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

2

42 2

I b d e c

a b c

K v v v vr v

2

42 2

II b d e c

a b c

K u u u ur v

Evaluation of propagation direction

2

12arctan 8

4I I

IIII II

K Ksign K

K K

2 1 3 3sin cos cos cos

2 2 4 2 4 22 2I II

r

K K

r r

The direction of crack is based on the Hoop Stress Criterion

For plain stress, only replace with1

v

v

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2D crack propagation

Benchmark study

30E MPa

0.25v

Plan strain conditionPropagation steps: 32

Problem description

The single edge cracked plate under far field shear loading

reference result [Alshoaibi] present code

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Results of 2D ice break-up from airfoil

Mesh of fluid domain Pressure field

Induced stress distribution 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

• Propagation direction

• Crack growth increment

maxmax

Ii

I

Pa a

P

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3D crack propagation

Validation of 3D crack propagation package

Three point bending test with the initial crack of an inclined plane

45o

)

130L mm10t mm30w mm

9.8E GPa0.33v

Three points bending test, with initial crack of an inclined planewith angle of 45 degree. The load force is applied at the middleof the specimen

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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

3D ice break-up analysis for helicopter blades

Ice accretion Ice shape identification Meshing

Stress analysis Interfacial separation Crack propagation

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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

2cfF Vr

3920kg m 400rpm

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3D ice break-up analysis for helicopter blades

ice-airfoil interface bond breaking

Cut section stress distribution of principal stress 1

• Ice tensile strength: 0.7 to 3.1MPa at -10ºC• Ice-Aluminum interface adhesion strength: 0.3 to 1.6MPa at

-11ºC

1 2| |i i

i

a ac

l

Edge refinement based on the first derivative of interest value is done to capture the interface bond and de-bonded transition zone

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!