Computational Modeling of Ice Cracking and Break-up from Helicopter Blades

1. Computational Modeling of Ice Cracking and Break-up from Helicopter Blades Shiping Zhang, HabibollahFouladi, Wagdi G. Habashi CFD Lab, McGill University, Canada RoohKhurram King Abdullah University of Science and Technology (KAUST), Saudi Arabia

2. Introduction Ice impact on engine blade Ice accretion on wings Hence it is very important to know where and how ice breaks up ! Helicopter Business jet with aft-mounted engine Air crash happened in 1991 in Stockholm due to ice ingestion

3. 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

4. Mechanical properties of ice • 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 Elastic properties of homogeneous poly-crystalline isotropic ice at -16ºC Schematic stress-strain curves I, II, and III denote low-,intermediate-, and high-strain rates

5. Framework of ice break-up modeling Droplet Solution Ice Accretion Airflow Solution Mesh Generation Crack Propagation Stress Analysis

6. Mathematical model of ice under fluid forces Fluid mechanics The Navier-Stokes equations in conservation form are: The viscous stress tensor is defined as: Solid mechanics The equations of equilibrium and the motion for the structure are: Interface conditions

7. Crack propagation Continuous fracturemodes Crack opening sliding tearing

8. Crack propagation Quarter-point elements The standard Lagrange second order shape functions of 1D quadratic element Standard, polynomial displacement interpolation scheme Quadrilateral quarter-point elements Triangle quarter-point element Standard, polynomial geometry interpolation scheme Parametric Space (a) Cartesian Space (b)

9. 2D crack propagation Quarter-point elements Standard, polynomial displacement interpolation scheme Parametric Space (a) Cartesian Space (b) (1) Standard, polynomial geometry interpolation scheme (2) The unusual case of ¼-point geometry (3) Substitute (3) into standard polynomial displacement interpolation scheme Unexpected, non-polynomial interpolation Differentiating the displacement field, strain in the element Singular term

10. 2D crack propagation Quarter-point elements P1 distribution of quarter-point element P1 distribution of normal quadratic element

11. 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

12. 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

13. 2D crack propagation Evaluation of stress intensity factor (SIF) Displacement correlation method is adopted for extracting SIF’s from local field information For plain stress, only replace n with Evaluation of propagation direction The direction of crack is based on the Hoop Stress Criterion

14. 2D crack propagation Benchmark study The single edge cracked plate under far field shear loading reference result [Alshoaibi] present code Problem description Plan strain condition Propagation steps: 32

15. Results of 2D ice break-up from airfoil Mesh of fluid domain Pressure field Induced stress distribution Induced stress and crack

16. 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)

17. Results of 2D ice break-up from airfoil Comparison with Franc 2D Franc 2D’s result In-house Code’s result

18. 3D crack propagation Tracking 3D crackpropagationfronts • 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

19. 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

20. 3D crack propagation Validation of 3D crack propagation package 3D out of plane crack propagation

21. 3D crack propagation Validation of 3D crack propagation package Top view of reference results Top view of in-house code results

22. 3D ice break-up analysis for helicopter blades Meshing Ice accretion Ice shape identification Crack propagation Stress analysis Interfacial separation

23. 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 • Iceshape 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

24. 3D ice break-up analysis for helicopter blades ice-airfoilinterfacebondbreaking • 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 Cut section stress distribution of principal stress 1 Mesh adaptation Bond separation

25. 3D ice break-up analysis for helicopter blades Crack initiationandpropagation Evolution of crack (left) and principal stress 1 (right) during the interface bond breaking and crack propagation process Figure 14. Crack propagation process

26. 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 25

27. 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

28. Thank you!