pitch angle in bird strike numerical simulation using SPH method

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Effect of arbitrary yaw/pitch angle in bird strike numerical simulation using SPH method

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Zhuo Zhang, Liang Li ∗ , Dingguo Zhang School of Science, Nanjing University of Science and Technology, Nanjing 210094, PR China

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a r t i c l e

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a b s t r a c t

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Article history: Received 14 June 2018 Accepted 9 August 2018 Available online xxxx

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Keywords: Bird strike Bird model Attitude angle Rotating engine blades SPH

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The influences of arbitrary attitude angles on bird strike on a fixed rigid flat plate and a rotary jet-engine fan are studied. A verified real bird model and a hemispherical-ended cylinder substitute bird model are modeled by using the smoothed particle hydrodynamics (SPH) method. Since birds can strike aircraft engine from any orientations, simulations of bird models striking a rigid flat plate at random attitude angles are first done as a validation test. Results show that different attitude angles of bird model have distinct effect on the response of bird strike. As the attitude angle increases, the peak impact force becomes larger and the bird model loses more energy. By considering the rotation of the jet-engine fan ignored before, the impact behavior of real bird models striking on rotating engine blades from arbitrary attitude angles is investigated. Effects of the attitude angle on the most concerned impact force, kinetic energy and von Mises stress of blade roots are discussed. It is concluded that considering attitude angles of real bird and rotation of the jet-engine fan in bird strike simulation has practical significance on structural tolerant design. © 2018 Elsevier Masson SAS. All rights reserved.

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1. Introduction

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Bird strike has threatened aircraft’s safety all the time since aeroplane was invented in 1903. About 90% of aircraft accidents were reported to be caused by bird strike, although aircraft faced the risk of many foreign object damage (FOD) [1]. Furthermore, according to the Federal Aviation Administration (FAA) statistics, aircraft engines were most frequently impacted component in bird strike accident [2]. When flying birds impact an aircraft engine in the sky and hit compressor blades, it will cause large plastic deformation or local bulging, and even lead to the rupture of blades which will result in an imbalance of the rotor or deteriorating the aerodynamic performance of the engine. It is estimated that bird strike costs the aviation industry more than 600 million dollars every year [3]. To manage the risk of bird strike accidents, researchers have done a lot of relevant experiments and theoretical studies. In the study of early bird collisions, Barber et al. [4,5] and Wilbeck [4–6] advocated that a hemispherical-ended cylinder with approximate mass could be used as the bird substitute model. They compared birds with different species, weights, and initial velocities striking on a rigid panel, and noted that in case of high speed,

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*

Corresponding author. E-mail address: [email protected] (L. Li).

https://doi.org/10.1016/j.ast.2018.08.010 1270-9638/© 2018 Elsevier Masson SAS. All rights reserved.

bird material behaved like fluid material. They provided references and made important contributions for future research work. Lavoie et al. [7] impacted gelatin birds on rigid targets and confirmed that the deformation of bird model did behavior like fluid and numerical simulation results correlated well with experiment data. Moreover, they listed the modeling procedure of the gelatin birds. Frederik et al. [8] set bird impact experiments on a rigid plate, wedge and splitter target respectively, and proved that the rigid target could still be valuable in bird strike research. However, the experimental verifications are not only time consuming, but also expensive and hard to control related influencing factors. In recent decades, with the rapid development of numerical methods and computer technology, numerical simulation has been a time-saving and precise method to study bird strike problems widely since 1980s. Meguid et al. [1] compared namely, bird shape and length to diameter aspect ratio by using the finite element (FE) method, found that the initial contact area between the bird and the target had significance effects on peak force while aspect ratio of bird had little influence on impact force. Nishikawa et al. [9] used a contact algorithm based on Lagrange multiplier method to predict appropriate impact force, this method solved the severe contact-induced deformation due to a large contact force and highly deformable projectile. Previous studies usually adopted the lagrangian formulation to model bird strike. Due to element instability, refining mesh elements and narrowing the time step method had to be used to alleviate the problem [10]. To solve this problem,

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Fig. 1. Substitute bird models: (a) Hemispherical-ended cylinder; (b) Straight-ended cylinder; (c) Ellipsoid and (d) Circular.

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In this paper, we establish Zhang and Fei’s substitute bird model [17] considering geometric characteristics of a flying canvasback in numerical simulations. Note that the rotation of the jet-engine fan in the above-mentioned literatures was ignored, and only limited attitude angles were studied, those results may not reflect the actual situation. To this end, this work will make up such deficiency. This paper is organized as follows: Hugoniot pressure and stagnation pressure are introduced in section 2; material parameters and geometric parameters of a SPH real bird model are given in section 3.1 and section 3.2, respectively; a rigid plat round plate target is constructed in section 3.3; a jet engine fan is modeled and meshed in section 3.4, material parameters as well as equation of state (EOS) parameters of the jet engine fan are given in section 3.5; the traditional cylinder substituted bird model and SPH real bird model with arbitrary attitude angle impacting on the rigid plate are simulated and discussed in section 4.1; simulations of the traditional cylinder substituted bird model and SPH real bird model with arbitrary attitude angles impacting on rotating blades are performed in section 4.2; some conclusions are drawn in section 5.

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Fig. 2. Schematic of the pitch/yaw angle.

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ρ1 V sh = ρ2 ( V sh − V p )

(1)

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(2)

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2 = P 2 + ρ2 ( V sh − V p )2 P 1 + ρ1 V sh

where ρ1 and ρ2 are the particles densities of material before and after impact, respectively; P 1 and P 2 are the pressures of material before and after impact, respectively; V sh is the shock velocity in the fluid; V p is the velocity of the particles behind the shock and is equal to the initial velocity. Combine Eq. (1) and Eq. (2), the pressure is found to be:

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According to Wilbeck’s [6] theory, in case of a cylinder impact on a rigid plate, the flow across a shock can be considered one-dimensional and adiabatic, irreversible. In this situation, the equation of conservation of mass (continuity) and momentum may be written as:

(3)

Hugoniot pressure is given by Eq. (3), which is also the pressure in shock region. Thus, Eq. (3) becomes:

P H = ρ1 V sh V p

(4)

As for how to obtain the shock velocity, Hedayati et al. [13] had explained in detail. In the steady-state condition, since the bird material flows in streamlines, the stagnation pressure is given by Eq. (5) according to Bernoulli’s equation:

P stag =

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P 2 − P 1 = ρ1 V sh V p

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nowadays more researchers use arbitrary Lagrange–Euler (ALE) [3, 7,11,12] and smoothed particle hydrodynamics (SPH) [7,8,13–18] method in bird strike problems [13]. Jenq et al. [19] simulated the soft model bird projectile striking a flat rigid panel according to Wilbeck’s report in ALE methods, results corresponded well with experiment data. Many researchers investigated the impact responses of composite materials sandwich panels in recent years [20–24]. To date, researchers have made a lot of efforts to discuss appropriate bird model shape [13]. McCarthy et al. [25] used a hemispherical-ended cylinder with a length-to- diameter ratio of two as bird substitute model, which was also adopted by many other researchers frequently. Liu and Li [15] modeled the straight-ended cylinder, which has quite fewer applications than the hemispherical-ended cylinder. Besides, ellipsoid geometry also appeared in some literatures such as Meguid et al. [1] and Reza and Ziaei-Rad [14]. Liu et al. [26] compared the circular model with experiment data. In general, there are four commonly used models: hemispherical-ended cylinder, straight-ended cylinder, ellipsoid and circular, as shown in Fig. 1. In addition, Hedayati and Ziaei-Rad [27] constructed a real geometry bird model with more consistent simulation results with experiments. McCallum et al. [28] established a new model including eight body parts and accounts for variations in density and material strength, which had a longer impact duration and higher peak impact force. Zhang and Fei [17] considered the bird may impact from any orientation: head side, tail side, bottom side and wing side and they proved that bird geometry and impact orientation had important influence on bird strike accidents. In the period of a bird strike accident, it is possible that the bird impacts the engine from any orientation and any part of the bird may strike on the aircraft firstly [17]. As for impact orientation angles, several studies have revealed that the peak pressure produced by a bird model hitting the rigid plate from the bottom is about three times that from the head. It should be noticed that in many accidents, the energy of bird impact released was lower than that standard currently requires, however, it did cause serious damage continuously in reality [29]. In other words, only considering bird mass and impact speed is not enough to ensure flight safety, further studies are still necessary to consider more factors. Therefore, here we define the pitch/yaw angle between the bird’s axis direction and the speed direction as the attitude angle α in Fig. 2.

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2. Theoretical background

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3. Simulation model

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3.1. SPH bird material model

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When a bird strikes the engine at high speed, the bird material behaves like fluid, and its nonuniformity and inhomogeneity become increasingly negligible, which is practically a homogeneous fluid impinging the target [7]. In order to accurately model the hydrodynamic response, hydrodynamics fluidic material is used in this paper and a linear Mie–Grüneisen equation of state (EOS) that describes the relationship between shock velocity and pressure [30] for the bird model is adopted.

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Fig. 3. The SPH flying bird model [18].

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σi j = − P δi j + 2ργ e˙ i j

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where ρ is the material density; C is the intercept of the v s − v p curve; S 1 , S 2 and S 3 are the coefficients of the slope of the v s − v p curve; γ0 is the Grüneisen gamma; a is the first order volume correction to γ0 ; and μ = ρ /ρ0 − 1. For bird material model, C = 1483 m/s and ρ = 934 kg/m3 are selected and other parameters are assigned to be 0.

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3.2. Geometry of the SPH bird model

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As shown in Fig. 3, a bird with realistic geometry refers to the model in Ref. [17] is established by using the SPH method. The bird weights 1.0 kg and has a length of 0.316 m and wing span of 0.487 m. The geometry dimensions of the substitute model are specified in Ref. [17]. The real bird model is discretized with 16866 SPH particles.

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3.3. Rigid flat plate target model mesh

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A rigid round plate with a radius of 0.4 m and a thickness of 0.02 m fixing at all edges is built, as shown in Fig. 4. The meshed target plate composes of 2880 solid elements and 3980 nodes.

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3.4. Blades model mesh

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A jet-engine fan comprises of 18 identical spaced blades and a hub section are chose in the present simulation [16]. Dynamic relaxation is applied to pre-stress the fan model. 3D solid elements are used to mesh all fan blades, with 9604 elements and 19008 nodes to provide sufficient converged results. The whole meshed blades and the hub section are shown in Fig. 5. The hub section is treated as rigid by using 2-D shell elements and is applied a constant rotating angular velocity.

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3.5. Blades material model

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The jet-engine fan blades are typically assumed to be made of titanium alloy Ti-6Al-4V. To simulate the bird strike process accurately, the Johnson–Cook viscoplasticity material model is used. The Johnson–Cook constitutive relation can be expressed as:

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Fig. 4. A meshed rigid plate.

Mie–Grüneisen EOS for compressed materials is [31]:

ρ0 C 2 μ[1 + (1 − γ20 )μ − 2a μ2 ]

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The constitutive material law of hydrodynamics fluidic materials is:

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Fig. 5. Whole blades and the hub section.

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Table 1 Grüneisen EOS parameters for Ti-6Al-4V [26].

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where A, B, C , n and m are constants; εe is the effective plastic p strain; ε˙ ∗ = εe /˙ε0 is a dimensionless strain rate; ε˙ 0 is a userdefined reference strain rate; T ∗m = ( T − T r )/( T m − T r ) is the homologous temperature. The specific parameters can be found from Ref. [16]. The parameters of Mie–Grüneisen EOS for Ti-6Al-4V are listed in Table 1 [32].

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4. Simulation results

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4.1. SPH bird striking on a rigid plate

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To verify the accuracy of the real bird model, a traditional hemispherical-ended cylinder substituted bird model is built in Fig. 6. Figs. 7(a)–(b) show the traditional cylinder substituted bird model before and after a vertical impact (corresponding to α = 0◦ ), respectively. Figs. 7(c)–(d) show the real bird model before and after a head side impact (corresponding to α = 0◦ ). It has already been proved that the time history of the impact pressure obtained

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Fig. 6. The hemispherical-ended cylinder model.

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from Ref. [18] agrees quite well with the experimental data when the hemispherical-ended cylinder substituted bird model strikes the rigid target vertically. As it can be seen from Fig. 7(b) and Fig. 7(d), similar results are observed between the two different models. Figs. 7(e)–(h) show the SPH bird model before impact with arbitrary attitude angles selected as 22.5◦ , 45◦ , 67.5◦ and 90◦ (Bottom side in Ref. [18]), respectively. Fig. 8 shows time histories of the impact force of the SPH model with different attitude angles and the hemispherical-ended cylinder substitute bird model with the vertical impact. It is found that the peak impact force obtained from the traditional model is 286.7 kN at about 0.05 ms after initial contact. It also can be perceived that the peak impact force of the real bird model reaches 234.2 kN at 1.55 ms. The peak impact forces of the bird model

with attitude angles of 22.5◦ , 45◦ , 67.5◦ and 90◦ are 259.9 kN at 1.43 ms, 268.1 kN at 1.18 ms, 287.1 kN at 0.82 ms, 685.2 kN at 0.40 ms, respectively. Obviously, the peak impact force increases as the attitude angle increases. The difference between the minimum and maximum contact forces is 421.1 kN and the difference percentage is about 65.8%. This is because as the attitude angle increases, larger contact area causes the increase of impact force suddenly. It can also be found in Fig. 8 that the larger the attitude angle is, the earlier peak impact force occurs. Fig. 9 shows the time histories of the impact force of the SPH model with different attitude angles and the hemispherical-ended cylinder substitute bird model with the vertical impact. The initial kinetic energy is 6.45 kJ. After contacts with rigid plates, the kinetic energy of traditional model becomes 2.51 kJ, and the percentage of energy loss is 61.1%. While the bird model with attitude angles of 0◦ , 22.5◦ , 45◦ , 67.5◦ and 90◦ are 3.37 kJ, 2.61 kJ, 2.06 kJ, 1.70 kJ and 1.01 kJ, respectively; the percentage of energy loss is 47.75%, 59.53%, 68.06%, 73.64% and 84.19%, respectively. It is found that as the attitude angle increases, the bird model loses more energy. The simulation results of the traditional model and the real bird model are approximate, thus identify rationality of the real bird model.

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4.2. SPH bird impacting on rotating blades

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In this section, the jet engine with a hub section and 18 blades in section 3.4 is used to do the following simulations. Fig. 10 shows

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Fig. 7. Schematics of the Hemispherical-ended cylinder substituted bird model (a) before and (b) after a vertical impact; the SPH bird models (c) before and (d) after a vertical impact; and the SPH bird models with (e) α = 22.5◦ , (f) α = 45◦ , (g) α = 67.5◦ and (h) α = 90◦ , respectively.

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the discretized model for the SPH bird model striking a jet-engine fan, in which the bird is at a height of half radius of the blade from the hub. Figs. 11(a)–(b) show the time histories of the impact force and kinetic energy a jet-engine fan without rotation calculated by the present model and the model in Ref. [18], respectively. Due to the unavoidable modeling difference, there is a delay of the peak impact force and smaller initial kinetic energy of the bird from the present model compared with those of Zhang and Fei [17]. However, the present results are still consistent with those of the reference. The present model can be further used to study a bird strike problem with high speed rotating jet engine. The bird is given an initial velocity of 116 m/s, the blades and the hub are given an initial angular velocity of 418.67 rad/s. Figs. 12(a)–(e) show the models of the SPH bird striking the rotating blades with arbitrary attitude angles selected as 0◦ , 22.5◦ , 45◦ , 67.5◦ and 90◦ , respectively. Fig. 13 shows the schematic of the selected blade tips and root elements to study the deformation of blades. Figs. 14(a)–(e) show effective stress distribution of the blades compacted by the hemispherical-ended cylinder model and the real bird model at different attitude angles, respectively.

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Fig. 8. Time histories of the impact force of the SPH model with different attitude angles and the hemispherical-ended cylinder substitute bird model with the vertical impact.

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Fig. 9. Time histories of the kinetic energy of the SPH model with different attitude angles and the hemispherical-ended cylinder substitute bird model with the vertical impact.

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Fig. 10. Discretized model for a SPH bird model striking rotating blades.

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Fig. 11. Variations of (a) impact force and (b) kinetic energy of bird model striking on static blades.

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Fig. 12. Schematics of bird model striking on blades when (a)

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Fig. 13. Site of nodes N1–N5 and elements E1–E5 on blades.

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Figs. 15(a) and 15(b) show variations of the impact force and kinetic energy of the bird model striking on rotating blades with

= 22.5◦ , (c)

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different attitude angles, respectively. Results of the traditional cylinder model with the vertical impact on rotating blades are also included for comparison purpose. As it is shown in Fig. 15(a), there are several obvious peaks in the impact force curves calculated from the real bird model, while such peaks can not be observed in the results from the traditional model. There are some fluctuations in the kinetic energy curves of the real bird model and the traditional model, which can be observed in Fig. 15(b). This is because the bird models struck many times on different blades during the whole collision process. The peak impact force of the traditional model, whose length is shorter than the bird model, is 16.14 kN at 0.39 ms, and the collision time lasts for 1.64 ms. As for the real bird model, impact force reaches to 68.64 kN at 1.97 ms when α = 0◦ . The real bird model causes stronger impact force than the traditional one. In addition, the peak impact force of the bird model with attitude angles of 22.5◦ , 45◦ , 67.5◦ and 90◦ is 56.07 kN, 55.30 kN, 127.80 kN and 161.62 kN, respectively, and their appearance time is 1.44 ms, 1.77 ms, 1.30 ms and 1.39 ms, respectively. As it can be seen in Fig. 15(b), the kinetic energy of the traditional model before and after the impact is 6.45 kJ and 4.90 kJ, respectively, and the percentage of energy loss is 24.03%. The residue kinetic energy of the real bird model when α = 0◦ is 4.85 kJ, and the percentage of energy loss is 24.81%. For other cases, the residue kinetic energy is 5.00 kJ, 4.84 kJ, 4.69 kJ and

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Fig. 14. Effective stress distribution of the blades after compact: (a) hemispherical-ended cylinder model, (b)

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α = 0◦ , (c) α = 22.5◦ , (d) α = 45◦ , (e) α = 67.5◦ , and (f) α = 90◦ .

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Fig. 15. Variations of (a) impact force and (b) kinetic energy of bird model striking on rotating blades with different attitude angles.

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4.58 kJ, respectively; and the percentage of energy loss is 22.49%,

In order to study the deformation of the blades, variations

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of the Z direction displacement of struck blade tips versus

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that with the attitude angle increases, more kinetic energy dissi-

time are shown in Figs. 16(a)–(f). Six cases are considered: the

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Hemispherical-ended cylinder model when

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It is interesting to note that there are only two blades hit by the traditional model, while there are four or five blades impacted by the real bird model. This is because the real bird model has larger size in length and width, resulting longer contact time and more blade hits. Moreover, more blades may encounter strikes when the rotation speed is higher. When α = 0◦ , The maximum Z dis-

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Fig. 16. Blades tip Z direction displacements: (a) Hemispherical-ended cylinder model; (b) Real bird model when model when α = 45◦ ; (e) Real bird model when α = 67.5◦ ; (f) Real bird model when α = 90◦ .

model at 0◦ ; the real bird model at 22.5◦ ; the real bird model at 45◦ ; the real bird model at 67.5◦ ; the real bird model at 90◦ .

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α = 0◦ ; (c) Real bird model when α = 22.5◦ ; (d) Real bird

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placement obtained from the traditional model and the real bird model is 3.44 mm on blade 1# and 5.69 mm on blade 3# , respectively. As for other cases, the maximum Z displacement is 4.11 mm on blade 3# , 5.37 mm on blade 4# , 9.07 mm on blade 4# and 13.22 mm on blade 3# , respectively. Figs. 17(a)–(f) show the time histories of the von Mises stress of blade root elements for different cases. It is clearly observed that in every case, the stress of root element changes distinctly once

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the bird hit on a blade; besides, the blade 1 is first struck, resulting other blades being affected. It is also found that there is delay on the significant change of the von Mises stress after the collision occurs. For the impact of the hemispherical-ended model, the maximum von Mises stress of elements E1 and E2 is 333.1 MPa. While for the real bird in other cases, the maximum von Mises stress of blade root element is 1240.3 MPa, which appears in element E2 when α = 90◦ . It is reasonable that the variation range of von Mises stresses of element E1 is always smaller than other cases, because the blade with element E1 is always struck by the

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Fig. 17. Von Mises stresses of blade root elements: (a) Hemispherical-ended cylinder model; (b) Real bird model when bird model when α = 45◦ ; (e) Real bird model when α = 67.5◦ ; (f) Real bird model when α = 90◦ .

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A real bird model is modeled by the SPH method to study the influence of arbitrary attitude angles on bird strike problems. A fixed rigid plate and a jet-engine fan composes of eighteen rotating blades are established as the striking targets. The performance of the bird model striking on a rigid plate with different attitude angles is simulated and verified. The attitude angle and bird geom-

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Conflict of interest statement

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No conflict of interest.

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This research was supported by the grants from the National Natural Science Foundation of China [grant numbers 11502113, 11772158].

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[1] S.A. Meguid, R.H. Mao, T.Y. Ng, FE analysis of geometry effects of an artificial bird striking an aeroengine fan blade, Int. J. Impact Eng. 35 (2008) 487–498. [2] R.A. Dolbeer, S.E. Wright, J. Weller, Wildlife Strikes to Civil Aircraft in the United States 1990–2008, FAA National Wildlife Strike Database, Serial report number 15, September 2009. [3] D.L. York, J.L. Cummings, R.M. Engeman, et al., Hazing and movements of Canada geese near Elmendorf air force base in Anchorage, Alaska, Int. Biodeterior. Biodegrad. 45 (2000) 103–110. [4] J.P. Barber, P.F. Fry, J.M. Klyce, et al., Impact of Soft Bodies on Jet Engine Fan Blades, Technical Report AFML-TR-77-29, University of Dayton Research Institute, OH, 1977. [5] J.P. Barber, H.R. Taylor, J.S. Wilbeck, Bird Impact Forces and Pressures on Rigid and Compliant Targets, Technical Report AFML-TR-77-60, University of Dayton Research Institute, Dayton, OH, 1978. [6] J.S. Wilbeck, Impact Behavior of Low Strength Projectiles, Air Force Materials Laboratory, 1977. [7] M.A. Lavoie, A. Gakwaya, M.N. Ensan, et al., Bird’s substitute tests results and evaluation of available numerical methods, Int. J. Impact Eng. 36 (2009) 1276–1287. [8] F. Allaeys, G. Luyckx, W.V. Paepegem, et al., Characterization of real and substitute birds through experimental and numerical analysis of momentum, average impact force and residual energy in bird strike on three rigid targets: a flat plate, a wedge and a splitter, Int. J. Impact Eng. 99 (2017) 1–13. [9] M. Nishikawa, K. Hemmi, N. Takeda, Finite-element simulation for modeling composite plates subjected to soft-body, high-velocity impact for application to bird-strike problem of composite fan blades, Compos. Struct. 93 (2011) 1416–1423.

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[20] G.S.E. Bikakis, C.D. Dimou, E.P. Sideridis, Ballistic impact response of fiber– metal laminates and monolithic metal plates consisting of different aluminum alloys, Aerosp. Sci. Technol. 69 (2017) 201–208. [21] A.A. Nia, S. Mokari, M. Zakizadeh, et al., Experimental and numerical investigations of the effect of cellular wired core on the ballistic resistance of sandwich structures, Aerosp. Sci. Technol. 70 (2017) 445–452. [22] M. Sadighia, M.Y. Tooskib, R.C. Alderliestenc, An experimental study on the low velocity impact resistance of fibre metal laminates under successive impacts with reduced energies, Aerosp. Sci. Technol. 67 (2017) 54–61. [23] S.J. Salami, Low velocity impact response of sandwich beams with soft cores and carbon nanotube reinforced face sheets based on extended high order sandwich panel theory, Aerosp. Sci. Technol. 66 (2017) 165–176. [24] X.T. Zhang, R.Q. Wang, J.X. Liu, et al., A numerical method for the ballistic performance prediction of the sandwiched open cell aluminum foam under hypervelocity impact, Aerosp. Sci. Technol. 75 (2018) 254–260. [25] M.A. Mccarthy, J.R. Xiao, N. Petrinic, et al., Modelling of bird strike on an aircraft wing leading edge made from fibre metal laminates – part 1: material modelling, Appl. Compos. Mater. 11 (2004) 295–315. [26] J. Liu, Y.L. Li, X.S. Gao, Bird strike on a flat plate: experiments and numerical simulations, Int. J. Impact Eng. 70 (2014) 21–37. [27] R. Hedayati, S. Ziaei-Rad, Effect of bird geometry and orientation on bird-target impact analysis using SPH method, Int. J. Crashworthiness 17 (2012) 445–459. [28] S. Mccallum, H. Shoji, H. Akiyama, Development of an advanced multi-material bird-strike model using the smoothed particle hydrodynamics method, Int. J. Crashworthiness 18 (2013) 579–597. [29] J.F. Kou, F. Xu, S.H. Ji, et al., Influence of bird yaw/pitch orientation on birdstrike resistance of aircraft structures, Explos. Shock Waves 37 (2017) 937–943. [30] U.A. Dar, W.H. Zhang, Y.J. Xu, FE analysis of dynamic response of aircraft windshield against bird impact, Int. J. Aerosp. Eng. 2013 (2013) 171768. [31] L.S. Inc, LS-DYNA Keyword User’s Manual, VER. 9.71, Livemore, CA, 2014. [32] A. Airoldi, B. Cacchione, Modelling of impact forces and pressures in Lagrangian bird strike analyses, Int. J. Impact Eng. 32 (2006) 1651–1677.

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etry have significant effect on the impact force, the kinetic energy of bird released, and the von Mises stresses of blade roots. As the attitude angle increases, the peak impact force becomes larger and the bird model loses more energy. Compared with the rigid plate impact, the impact force and the energy of the real bird model striking rotating blades are smaller. The rotating blades are more vulnerable to destruction when the attitude angle is 90◦ than other cases. This is because a larger bird slice cut off by rotating blades can cause bigger impact forces and stresses. Effects of both the attitude angle and bird model shape on bird-strike are significant. Therefore, it is essential and helpful to adopt real bird substitute models and investigate attitude angles for bird strike analysis.

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