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**Shiping Zhang, Habibollah Fouladi, Wagdi G. Habashi**

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 Good morning everyone, thank you Dr XXXXXX for the introduction. The work that I am going to present today is the outcome of a collaborative research between KAUST and Professor Habashi’s group at McGill. This research is mainly the outcome of Shiping’s thesis work. Unfortunately he is not here to present this work because, right after his thesis defense, he flew to China for his engagement.

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**Introduction Hence it is very important to know**

Ice accretion on wings Ice impact on engine blade Hence it is very important to know where and how ice breaks up ! Helicopter In-flight icing is big threat to the safety of the flight. Traditionally, researchers are focus on the effect of lift, drag, weight and thrust, however, ice shedding is another key hazard of in-flight icing. This picture shows a business jet with an aft-mounted engine. It can be seen that if the shedding ice from the nose of fuselage or the root of wings flies into the engine, it can lead to catastrophic disaster. This picture shows an wind tunnel experiment test of ice ingestion. Ice shedding is even bigger threat to helicopters, as ice shedding can cause severe vibrations. The severity of these vibrations has been documented [4] by test pilots engaged in conducting natural icing studies with helicopters. Their reports identify numerous occasions where in-flight icing tests have been aborted because of main rotor blade icing and subsequent asymmetrical shedding which caused vibrations so severe that it became all but impossible to read the instrument panel [4]. [4] Inflight Icing and the Helicopter, Helicopter Safety, Vol.16,No.6, 11/12, 1990 Business jet with aft-mounted engine Air crash happened in 1991 in Stockholm due to ice ingestion 1 1

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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), 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. Describe the experiments: take a look at the papers No direct 2D ice break up analysis considering fracture analysis has been done No 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 2 2

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**Mechanical properties of ice**

Property Units Value Young’s modulus, E N m-2 9.33×109 Bulk modulus, B 8.90×109 Shear Modulus, G 3.52×109 Poisson’s ratio, υ n/a 0.325 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: MPa (-10ºC ) Compressive strength: 5-25 Mpa (-10ºC) Adhesive strength with aluminum, MPa, at -11ºC Elastic properties of homogeneous poly-crystalline isotropic ice at -16ºC This slide will make a brief review about the mechanical properties of ice. An important property of ice is that under low strain load, ice shows ductile behaviour, while under high strain load, for example, crack propagation process, it behaves as brittle materials. This means we can use linear elastic fracture mechanics to analysis the crack propagation process in ice. In terms of cohesive strength of ice, we can see that tensile strength is much lower than compressive strength, which means ice is more likely to break under tension instead of compression. To analysis ice shedding, the adhesive strength between ice and airfoil is very important. Currently, most wings and helicopter blades are made of aluminum. And from literature review, the adhesive strength between ice and aluminum is from 0.3MPa to 1.6 MPa at minus 11 degrees Schematic stress-strain curves I, II, and III denote low-,intermediate-, and high-strain rates 3

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**Framework of ice break-up modeling**

Airflow Solution Droplet Solution Ice Accretion This slide provides a synthetic description of the overall ice break up modeling and its integration with in ice accretion modeling Airflow and droplet solution is employed by the ice accretion model to predict the ice shape. The final ice shape for the given aerodynamic and icing conditions is the input to the ice break up modeling framework. First, an automatic mesh is generated inside the solid domain i.e. inside the ice. Next the stress analysis in performed by applying the given fluid forces at the fluid-ice interface. Based on the principle stresses, judgement of crack initiation is made. For the given stress field, if the crack starts propagating, then this cycle is repeated, till the crack stops propagating or the ice breaks. In the multi-step ice accretion setting, this process is repeated until the total ice accretion time is reached. Mesh Generation Crack Propagation Stress Analysis 4

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**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: The fluid domain is represented by Omega f, Omega s is the solid domain. The fluid-structure interface is represented by gama i. The solid domain, which is the ice, has two BC.s namely, Dirichlet BCs which is at the interface between ice and airfoil, and Newman BCs which is at the interface between ice and airflow. The Newman BC.s comes from the flow solution. Navier-Stroke equations describe the fluid behavior. Equilibrium equation and structure motion equation describe the solid mechanics. Cauchy stress tensor for linear isotropic material is shown here. While at the interface, traction equilibrium and velocity compatibility have to satisfied. Interface conditions 5

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**Crack propagation Continuous fracture modes Crack opening sliding**

In fracture mechanics, there are three different kinds of loading. That is crack opening, sliding and tearing. William expansion gives the theoretical stress field near the crack tip. Suppose the angle theta equals to 0, we can get the stress distribution along the x axis. We can see clearly the stress is singular towards the crack tip. Crack opening sliding tearing 6

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**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 A fundamental difficulty of using finite element method to model linear elastic fracture mechanics is that polynomial basis function for most conventional elements can not represent the singularity of stress and strain around the crack tip. A milestone in the development of using FEM to model LEFM is the advent of quarter point element, which can give exact singular stress and strain around the crack tip. Here I will show briefly how it work. Standard, polynomial geometry interpolation scheme Parametric Space (a) Cartesian Space (b) 7

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**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 8

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**2D crack propagation Quarter-point elements**

This shows the comparison of stress distribution in a test case using normal quadratic element and quarter-point element. These two pictures gives more detailed information about the stress distribution around the crack tip P1 distribution of quarter-point element P1 distribution of normal quadratic element 9

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**P1 distribution in the vicinity of crack tip of quarter-point elements**

2D crack propagation Quarter-point elements This shows the comparison of stress distribution in a test case using normal quadratic element and quarter-point element. These two pictures gives more detailed information about the stress distribution around the crack tip P1 distribution in the vicinity of crack tip of quarter-point elements P1 distribution in the vicinity of crack tip of normal quadratic elements 10

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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 11

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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 For plain stress, only replace n with Evaluation of propagation direction A very important parameter in linear elastic fracture mechanics is SIF, which will be used to calculate the propagation direction The direction of crack is based on the Hoop Stress Criterion 12

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**reference result [Alshoaibi] present code**

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 13

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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 14

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**(quasi-static process, time term is not considered)**

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) 15

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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 16

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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 Describe from paper/thesis Crack growth increment 17

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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 ) In order to validate crack propagation algorithms described before, a bench mark study of 3D out of plain crack propagation is taken here. In this numerical example, a three points bending test of the cracked specimen shown in Fig. is simulated. The case is interesting because the crack is initially inclined with respect to the load direction, which causes a high kink angle at the beginning of the propagation. The crack is subjected to a mixed mode loading condition and a twisted propagation is obtained. The problem has been solved in [53] and the solution reported there is taken as reference. R. Citarella, F.-G. Buchholz, Comparision of crack growth simulation by DBEM and FEM for SEN-specimens undergoing torsion or bending loading, Engineering Fracture Mechanics, 75 (2008), Three point bending test with the initial crack of an inclined plane 18

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**3D crack propagation Validation of 3D crack propagation package**

3D out of plane crack propagation 19

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**3D crack propagation Validation of 3D crack propagation package**

Describe the results Top view of reference results Top view of in-house code results 20

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**3D ice break-up analysis for helicopter blades**

Ice accretion Ice shape identification Meshing Based on the 3D crack propagation package, now we can do the 3D ice break up analysis. The basic steps are as follows: The first step is ice accretion, which is obtained from FENSAP-ICE, the second step is ice shape identification, the third step is meshing, once we get the mesh, then we can do the stress analysis. Then interfacial separation, and finally, crack propagation Stress analysis Interfacial separation Crack propagation 21

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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 22

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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 Cut section stress distribution of principal stress 1 The basic idea here for mesh refinement is adding new nodes to the edge whose first derivative of principal stress over the length of edge has reached a critical value as shown in Where ai1 and ai2 are the value of interest, like principal stress I or shear stress, on node 1 and node 2 of the edge. Del i is the length of the edge. c is the critical value setting by the user. Bond separation Mesh adaptation 23

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**Figure 14. Crack propagation process**

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 Figure 14. Crack propagation process 24

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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 25 25 25

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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 26

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Thank you! 27

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