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International Journal of Impact Engineering ] (]]]]) ]]]–]]] www.elsevier.com/locate/ijimpeng
FE analysis of geometry effects of an artificial bird striking an aeroengine fan blade S.A. Meguid, R.H. Mao, T.Y. Ng Division of Aerospace Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore Received 9 January 2007; received in revised form 24 April 2007; accepted 27 April 2007
Abstract Bird strike resistance of aeroengines is a strict certification requirement. Apart from costly experimental bird strike tests, explicit numerical modeling techniques have been employed. However, due to the complicated bird geometry, artificial bird models are still not well defined and it is a perennial problem selecting an appropriate representative artificial bird geometry for the simulations. To examine the relative effects of the artificial bird geometry, explicit 3-D finite element analyses are conducted herein using the commercial code LSDYNA. As a validation test, we first studied the nonlinear transient dynamic response of an artificial bird striking a rigid flat target. Following the validation, we studied the impact behavior of an artificial bird impinging a flexible aeroengine fan blade. The study focused on the three most-frequently used configurations in the literature: namely, hemispherical-ended cylinder, straight-ended cylinder, and ellipsoid, at various length-to-diameter aspect ratios. The results show that the initial contact area between the bird and target in the early phase of the impact event would have a significant effect on the peak impact force. The aspect ratio of the bird striking both rigid panel and flexible fan blade was found to have little influence on the normalized impact force and impulse. r 2007 Elsevier Ltd. All rights reserved. Keywords: Bird strike; Artificial bird configuration; Aspect ratio; Rigid panel; Flexible fan blade
1. Introduction Ever since they began to share the sky with the birds a century ago, aircrafts have been perpetually suffering from bird strikes. In fact, about 90% of all foreign object damage (FOD) can be traced to avian origins. Presently, all available evidence suggests that the bird strike hazard is increasing, and this can be attributed to globalization and conservation, which has resulted in the steady increase in air traffic density levels as well as the dramatic expansion of wild bird populations [1], Fig. 1. These strikes pose a real danger to the lives of aircraft crew members and their passengers, and the potential for severe consequences following a strike is becoming more and more significant. This is because modern jet airliners are carrying more and more passengers, and it is well known that even minor damage due to FOD can easily lead to a catastrophic chain Corresponding author. Tel.: +65 67904040; fax: +65 67913502.
E-mail address: [email protected] (S.A. Meguid).
of events. It is conservatively estimated by the International Birdstrike Research Group [2] that collisions between aircraft and birds cost the aviation industry worldwide over US$1.2 billion each year. As a result, certification authorities require that all exposed aircraft components must be tested to prove their capability to withstand the most adverse impact loading. Special attention has always been given to the aeroengine, which, alongside being the most vulnerable aircraft component or system to bird strikes, is also the only power plant of a jet airliner. The fan blade is the first component of an aeroengine that comes in contact with the bird in a bird strike event, and the resulting plastic deformation and fracture of the fan blade may lead to partial or total loss of thrust, as well as possible containment failure which is strictly prohibited by aviation regulatory authorities, such as the FAA [3]. In fact, even a minor damage to fan blades may introduce engine unbalance. In the 1970s, the validation of the structural integrity and resistance to bird strike of aircraft components was
0734-743X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2007.04.008 Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Across D E F I Iad L L/D m P PTH s
normalized impact pressure, Pad ¼ ðF =Across Þ=PTH s T normalized time, T ¼ t=T 0 ¼ t=ðL=w_ 0 Þ T0 nominal impact duration, T 0 ¼ L=w_ 0 ðsÞ t time (s) u,v,w displacements in X, Y, and Z directions (m) w_ 0 initial velocity of bird, w_ 0 ¼ 225 m/s X,Y,Z cartesian coordinates (m) sij stress tensor (Pa) e_ij strain rate tensor (s1) r instantaneous mass density of bird (kg/m3) r0 initial mass density of bird, r0 ¼ 934.3 kg/m3 m mass density changing ratio of bird, m ¼ ðr=r0 Þ 1 V Poisson ratio of the fan blade material g kinematic viscosity coefficient of fluidic bird material (m2/s)
Pad
Nomenclature (in SI units) average cross-sectional area of bird, Across ¼ m=r0 L ðm2 Þ diameter of bird (m) Young’s modulus of the blade material (Pa) impact or contact force between bird and target (N) between bird and target, I ¼ Rimpulse 1 F dt ðN sÞ 0 normalized impulse, I ad ¼ I=m w_ 0 length of bird (m) aspect ratio (or length-to-diameter ratio) of bird geometry mass of bird, m ¼ 1.82 kg pressure (Pa) theoretical stagnation pressure, pTH ¼ s 2 ð1=2Þr0 w_ 0 ðPaÞ
solely dependent on experiments. It was established by Barber et al. [4] that the loads generated by a high-speed impacting bird were adequately duplicated by representing the bird as a circular cylinder with the same mass, density, and compressibility as the bird tissue. Shortly thereafter, Wilbeck [5] noted the fact that, in case of high-speed impact, the response of the bird is similar to that of a fluid (such as water) where the strength of the bird material is extremely small compared with the impact loads. In addition, high-speed photography was employed by Gao and Li [6] and Teichman and Tardos [7] to record the evolution of the bird torso and the large deformations of the targets such as aeroengine fan blades, through which the fluidic property hypothesis of the bird tissue under
high-speed impact scenarios was further strengthened. These experimental tests, however, are very expensive, time-consuming and difficult to perform. Besides, due to the extremely high velocities and energies involved, the experimental registration of the impact parameters can often prove difficult and complex. With the development of advanced numerical techniques and the advent of high-performance computing, numerical simulations have been more widely used since the 1980s to evaluate the impact capability of different aircraft components. Explicit nonlinear finite element (FE) codes, which are available in several high-end commercial FE solvers, have been used to treat this class of problems. An accurate numerical model can reveal a significant amount of useful
Fig. 1. Bird-strike frequency in recent years in the USA [1]. Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Fig. 2. The three configurations considered for the artificial bird model: (a) straight-ended cylinder, (b) hemispherical-ended cylinder, and (c) ellipsoid.
information to the designer with regard to the mechanisms involved in the high-speed soft body impact event. Having privy to these information prior to conducting experimental tests enables the rapid and economical design of aircraft structures with enhanced impact resistance. In conjunction with the broadened application of numerical techniques to bird strike modeling and simulation, the artificial bird has substituted real birds, mainly for better repeatability and convenience [8]. For all its promise, the reliability of the numerical results is critically dependent on the accurate modeling of the temporal and spatial distribution of the impact force between the bird and target [9,10]. In connection with this, the complex and intricate geometrical configurations of different bird species have perpetually posed a problem for developing a sufficiently simplified and consistent bird model. Many researchers such as Frischbier [11], Langrand et al. [12], McCarthy et al. [13], and Airoldi and Cacchione [14], have simplified the bird torso as a hemisphericalended cylinder. The ellipsoid geometry is also a wellaccepted choice, which has been suggested by the International Birdstrike Research Group [15], and has been used by Guan et al. [16]. Besides these two configurations, the straight-ended cylinder has also been adopted by Brockman and Held [17], but its application remains somewhat infrequent. These three configurations, which are typical of artificial bird geometries, are shown schematically in Fig. 2. Nevertheless, the differences among the impact behaviors associated with these different configurations have not been reported in the open literature. Furthermore, the effect of the length-to-diameter aspect ratio (representing the biometric property of different bird species) is also examined. It has been highly recommended by the International Birdstrike Research Group that the bird model, once standardized, should become the norm for all bird impact testing thereafter [18]. From the simulation viewpoint, standardizing the geometry of the artificial bird model is correspondingly important. Both the bird configuration and aspect ratio have been found to be important parameters that influence the impact response of the target [19]. Thus, the aim of the present investigation is to compare and analyze the numerical results for the abovementioned three different bird configurations, and various aspect ratios will also be considered. The simulation will be carried out using highly accurate Lagrangian-based explicit
nonlinear FE analysis. The flexible fan blade adopted in the present investigation is a typical metallic wide-chord aeroengine fan blade. 2. Finite element modeling in a Lagrangian framework The finite element method (FEM) has been found to be very powerful in the numerical simulation of the crashworthiness and failure analyses [20]. The coupling between the bird and the target can be achieved by a Lagrangian formulation. During high-speed impact, large strain distortions will inevitably occur to the discretized Lagrangian bird, leading to a decrease in solution time-step and possible negative elemental volumes. The excessively distorted elements that possess negative volumes are then eliminated after each time step. However, this automatic elimination procedure usually introduces artificial oscillations in the contact force between the bird and target. Fortunately, the strategy of employing highly refined meshes that encounter element elimination can be used to alleviate this problem [21]. Modern high-performance computing systems can tolerate very small time steps in the order of 109 s or even 101 s, where it used to be 106–107 s, just a few years ago. Thus, by refining the mesh of the Lagrangian bird, the artificial oscillations associated with the impact force can be dramatically reduced. 2.1. Bird properties The bird’s mechanical property actually changes from the low-velocity to the high-velocity regimes. Generally, the mechanical property of typical avian tissues at low speeds is neither uniform nor homogeneous. However, at progressively higher speeds, this nonuniformity and inhomogeneity become increasingly negligible, and the bird can safely be considered as a homogeneous jet of fluid impinging a structure [5]. Thus, the constitutive material law of homogenized fluidic materials can be used: sij ¼ Pdij þ 2rg e_ij .
(1)
There are different hydrodynamic models which have been successfully used to describe the material properties of the bird in compression and among which the most popularly used is the polynomial fitted pressure
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equation: p ¼ C 0 þ C 1 m þ C 2 m2 þ C 3 m3 ,
(2)
where m is the nondimensional mass density changing ratio of the bird tissue earlier defined in the nomenclature. Here, we model the loading from the bird as a pressure pulse on the structure. This is a feasible approach and we can also avoid modeling the bird disintegrating into numerous debris particles. The Brockman compressible modules [17] are employed in the present simulations, whereby 8 C 0 ¼ 0; > > > < C 1 ¼ 2323 MPa; (3) > C 2 ¼ 5026 MPa; > > : C 3 ¼ 15180 MPa: The total mass of the bird is 4 lb (or 1.82 kg), which is presently used as the upper limit of the bird mass criteria in the bird–aircraft strike scenarios [22]. Its initial mass density is set at 934.3 kg/m3, while the initial velocity of the bird is taken to be 225 m/s in the normal Z-direction. Table 1 lists the detailed parameters of three geometries with the commonly used aspect ratio of 2.0:1. Table 2 lists all diameters of hemispherical-ended cylindrical birds with aspect ratios 1.5:1, 2.0:1, and 2.5:1. The bird model is meshed with 3-D 8-node fully integrated solid elements (Solid-164 in LS-DYNA) with a characterized ratio of bird diameter to mesh size of 32, as shown in Fig. 3, which is found to provide efficient simulation runs without compromising on accuracy. In addition, the hourglass energy is found to be well controlled in the present simulation.
DYNA), with 31 nodes in the axial direction and 61 nodes in the radial direction found to provide sufficiently converged results. In addition, the Hughes–Liu formulation was used to eliminate the hourglass modes. The
Fig. 3. Discretized geometries of the three bird configurations used.
2.2. The flexible fan blade A sector of the fan disk, composed of a single blade and a hub section, as shown in Figs. 4(a) and (b), is used in the present simulation. The hub is assumed to be fixed and rigid in comparison with the blade. The deformable blade is discretized using the 2-D shell elements (Shell-163 in LS-
Fig. 4. A schematic diagram of a bird striking a flexible fan blade: (a) isometric view, and (b) top view.
Table 1 Details of the different bird configurations considered (aspect ratio is 2.0:1) Configuration type
Straight-ended cylinder
Hemisphericalended cylinder
Ellipsoid
Length L (m) Diameter D (m)
0.214 0.107
0.228 0.114
0.246 0.123
Table 2 Details of the different bird aspect ratios considered (configuration is hemispherical-ended cylinder) Aspect ratio L/D
1.5:1
2.0:1
2.5:1
Length L (m) Diameter D (m)
0.192 0.128
0.228 0.114
0.260 0.104
Fig. 5. Velocity vectors of the bird at T ¼ 0.05 when impacting a rigid target: (a) side view, and (b) isometric view.
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hourglass coefficient was set to 0.1, quadratic bulk viscosity to 1.5, and linear bulk viscosity to 0.06. Fan blades of modern aeroengines are typically made of titanium alloy Ti–6A1–4V. Due to the high strain rates associated with this problem, the constitutive law used is of the viscoplastic type originally devised by Perzyna [23] sy ðpeff ; _peff Þ ¼ sy ðpeff Þð1 þ ð_peff =CÞ1=p Þ, _peff
(4) sy ðpeff Þ
is the effective plastic strain rate, and is where the initial quasi-static yield stress of the blade material. C and P are strain rate sensitive parameters determined by experiments. The magnitudes of the relevant parameters are listed as follows: 8 > E ¼ 1:14 1011 Pa; > > > > > v ¼ 0:33; > > > sy ðeff Þ ¼ 1:14 10 Pa; > > > > > C ¼ 40:0 s1 ; > > > : P ¼ 5:0:
3. Results and discussion 3.1. Bird striking a rigid panel Fig. 5 shows a typical example of the velocity vectors for the hemispherical-ended cylindrical bird model striking a rigid target at a normalized time J ¼ t/T0 ¼ 0.05. The simulations begin at the instant the traveling bird impinges the target. Both side and isometric views are shown in that figure. It shows that the bird has been deformed, with its right tip contacting the target (Fig. 5(a)). The maximum velocity of the fluidic bird elements, which appears near the frontal surfaces of the bird close to the target, is found to be approximately 123 m/s at this instant of impact. The time histories of the bird impacting a rigid panel for different phases are depicted in Fig. 6. The hydrodynamic fluid-like behavior of the bird can be clearly observed from T ¼ 0.5 onwards. During the impact process, the momentum of the bird will be progressively absorbed by the target; whereas the kinetic energy of the bird will be dissipated in terms of heat, as well as manifested by the elimination of some of the bird elements. Finally, the bird elements, with the umbrella-like configuration, do not possess additional forward momentum, and the impact process is completed at the normalized time T ¼ l. Nevertheless, following this impact event, the bird elements continue to deform and expand outwards. Fig. 7 shows the variation of the normalized impact pressure over time. It is compared with the experimental data from the GARTEUR Bird Strike Group [24] as well as the numerical results of Langrand et al. [12]. It is clearly observed that the present numerical results correspond well with the experimental data. When compared with the
Fig. 6. Deformation history of a bird impacting a rigid target: (a) T ¼ 0, (b) T ¼ 0.25, (c) T ¼ 0.5, (d) T ¼ 0.75, and (e) T ¼ l.
simulation results reported in the literature, the present result exhibits fewer oscillations than those prevalent in earlier studies, and is clearly more stable. This can be attributed to the fine mesh density used in discretizing the bird geometry. Specifically, we used a bird-to-element length ratio of about 32, compared with 8 used by Stoll and Brockman [25], and Airoldi and Cacchione [14]. The peak value of the pressure from the present simulation is about 20% lower than that of the experimental data, and this difference is probably due to the use of water-compressible modules for the bird’s material model, which underestimates the behavior of a real bird. 3.1.1. Effects of bird configuration Fig. 8(a) shows the impact force variations for different configurations of the bird model. It is found that the straight-ended cylinder reaches its maximum impact force of 7.99 105 N at about 0.049 ms after initial contact, and there is only one dominant peak in its contact force profile. However, there are two quite distinct peaks corresponding to the hemispherical-ended cylinder and ellipsoid models. The hemispherical-ended cylinder reaches its maximum force of 5.27 105 N at 0.054 ms, and its second peak of 3.33 l05 N at 0.134 ms, although this second peak is not as significant as the first one. The ellipsoid model, on the other hand, reaches its first peak of 3.60 105 N at 0.111 ms, and its second peak of 3.78 l05 N at 0.28 ms. Interestingly, this second peak is found to be the maximum magnitude in its force variation time history. Among the three different bird geometries, the maximum impact force for the straight-ended cylindrical bird is the highest. This is because at the instant the three types of bird configurations impinge the rigid target, the straight-ended cylindrical bird has comparatively the largest instantaneous contact area.
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Fig. 7. Variation of normalized impact pressure versus normalized time for a hemispherical-ended cylindrical bird impinging a rigid panel.
Fig. 8. Effect of artificial bird configurations on rigid impact forces and pressures: (a) impact forces, and (b) normalized impact pressures. Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Fig. 9. Effect of aspect ratios of artificial birds on rigid impact forces and pressures: (a) impact forces, and (b) normalized impact pressures.
This also explains why there is only one significant peak in its force variation, and it is because all the elements of this bird model will decelerate immediately and dramatically once it impacts the target. However, this situation is quite different for the hemispherical-ended cylinder and ellipsoidal birds. Since the bird in the high-speed impact scenarios behaves as a liquid, the shear stress between the bird’s elements flowing on neighboring streamlines, compared with the local high pressure, is comparatively negligible. This has been experimentally observed by Barber et al. [4], Wilbeck [5] and Gao and Li [6]. The present investigation treats the bird hydro-dynamically, and neglects the fluidic viscous effect of the bird tissue. Therefore, for the hemispherical-ended cylinder and ellipsoidal birds, only the elements directly downstream of those in contact with the target will experience the dramatic deceleration, whereas the other elements will not decelerate significantly until their frontal elements come into contact with the
target. Thus, when impact progresses for the hemispherical-ended cylinder or ellipsoidal birds, the contact forces decrease after the initial peaks, but will increase again, leading to their respective second peaks. This second peak is quite distinct in the ellipsoidal case, but rather less pronounced in the hemispherical-ended cylindrical bird case. In the ellipsoid model, the contact area reaches its maximum value somewhat late into the impact event. It occurs at approximately the midpoint of the entire impact duration, which explains the presence of its second peak. The normalized impact pressure evolutions for the three bird configurations are plotted in Fig. 8(b). It should be noted that because the cross-sectional areas vary along the geometrical axes of the hemispherical-ended cylinder and the ellipsoid models, the normalization is based on their respective averaged cross-sectional areas. The maximum normalized impact pressure is found to be 3.73 at T ¼ 0.055 for the straight-ended cylinder, 2.61 at
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Fig. 10. Effect of aspect ratios of artificial birds on rigid impact impulse.
T ¼ 0.053 for the hemispherical-ended cylinder, and 2.00 at T ¼ 0.27 for the ellipsoid model. Thus, the maximum impact pressure for the straight-ended cylinder impact case is about 43% higher than the hemispherical-ended cylinder case, and the latter is about 30% higher than the ellipsoid case. 3.1.2. Effects of bird aspect ratio In this section, the 4 lb bird with mass density 934.3 kg/m was simulated at different aspect ratios of 1.5:1, 2.0:1, and 2.5:1. We selected the hemispherical-ended cylinder geometry for the simulations. The impact force evolutions are plotted in Fig. 9(a). Due to its largest cross-sectional areas, the model with 1.5:1 aspect ratio has a maximum impact force of 6.57 l05 N, and it drops to zero first at 0.62 ms. The peak impact forces for the 2.0:1 and 2.5:1 cases are 5.27 l05 and 4.62 l05 N, respectively. This is due to the variance in their respective cross-sectional areas. Fig. 9(b) shows that the peak values for the three cases are much the same after normalization, being 2.75 for aspect ratio 1.5:1, 2.62 for aspect ratio 2.0:1, and 2.61 for aspect ratio 2.5:1. Thus, we note that the aspect ratio does not affect the normalized maximum impact pressure significantly. The impulses for the three aspect ratios are shown in Fig. 10. It is found that the impulse, after normalization, is 0.29 for the aspect ratio 1.5:1, 0.23 for the aspect ratio 2.0:1, and 0.26 for the aspect ratio 2.5:1. 3.2. Bird striking a fan blade In these simulations, the bird impacts the fan blade at a height of 85% radius of the blade from the hub. Due to the flexibility of the fan blade, the impact duration will be longer than the nominal impact time T0 ¼ L/w0. For example, for the hemispherical-ended cylindrical bird, its impact with the fan blade is completed at normalized time
Fig. 11. Deformation history for a hemispherical-ended cylindrical bird impinging a flexible fan blade: (a) T ¼ 0, (b) T ¼ 0.25, (c) T ¼ 0.5, (d) T ¼ 0.75, (e) T ¼ l, and (f) T ¼ 1.34.
T ¼ 1.34. The time histories of the impact process at different phases are shown in Fig. 11. The deformation of the blade when the impact force finally vanishes is also shown in Fig. 11(f). Nevertheless, both the bird and the blade will continue deforming even after the impact force vanishes. However, in the present investigation, only the major bird–blade coupled effects are of interest, and we terminate the simulation when the impact force vanishes. 3.2.1. Effects of bird configuration The impact forces between the hemispherical-ended cylindrical bird and the fan blade are shown in Fig. 12.
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Fig. 12. Impact force variations for a hemispherical-ended cylindrical bird (UD ¼ 2.0) striking a flexible fan blade.
Fig. 13. Effect of artificial bird configurations on normalized impact pressure when striking a flexible fan blade.
Since the geometry of the blade is curved, the impact forces are resolved into the X, Y, and Z directions. However, it can be seen from this figure that the impact force in the Zdirection is dominant, because the initial velocity of the bird is in the Z-direction. Henceforth, only the results in the Z-direction will be shown in the following results. There are multiple peaks in the impact force evolution, which is due to the coupling between the bird and the flexible blade. The blade, upon being impacted by the bird, accelerates in the same direction as the bird’s initial velocity, i.e., the Z-direction. When this happens, the frontal elements of the bird which are in close contact with the blade would expand and their high pressures would thus decrease. Therefore, the total impact force would also decrease dramatically. Consequently, with the lowered impact force from the bird, the bending of the blade would decelerate, and as a result the contact between the bird and the blade becomes intense once more. The impact force between the bird and blade would increase again. The
whole procedure will repeat several times before the impact force eventually vanishes. The normalized impact pressures between the birds and fan blade are shown in Fig. 13 for all the three bird configurations. The dominant peaks are 1.75 at T ¼ 0.094, 1.35 at T ¼ 0.189, and 0.77 at T ¼ 0.32 for the straightended cylindrical bird, and 1.62 at T ¼ 0.06, 1.78 at T ¼ 0.16, and 1.46 at T ¼ 0.45 for the hemispherical-ended cylindrical bird. For the ellipsoidal bird, the peaks are 0.79 at T ¼ 0.06, 1.53 at T ¼ 0.16, and 1.34 at T ¼ 0.39. From Fig. 13, we can observe that the normalized impact pressure variation profiles for the three bird configurations are quite different from the preceding rigid impact cases. This is especially so for the straight-ended cylindrical bird, which no longer possesses the highest peak impact pressure value among the three bird configurations. As there is an attack angle of 601 between the bird trajectory and the blade, as shown in Fig. 4(b), the initial contact area between the straight-ended cylindrical bird and the blade is
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not as large as the rigid panel case. Thus, the initial contact force between the bird and target is also significantly reduced. More importantly, the blade is not rigid but flexible, and the maximum impact force between the straight-ended cylindrical bird and blade is found to be only 47% of the rigid impact case. Similar conclusions have been reached by Shimamura et al. [10] that the target’s flexibility strongly influences the impact force between the bird and target. The impact force between the hemispherical-ended cylindrical bird and blade is about 68% of the former rigid impact case, and correspondingly 76% for the ellipsoidal bird model. Comparing the three geometries, it is noted that the ellipsoidal bird model has a maximum impact force, which is lower than the other two configurations by about 15%.
It is also interesting to note that all the three types of bird configurations have three significant peaks within their variations of the impact forces. This is mainly because the bird mass and density are similar for the three configurations. By varying the mechanical properties of either the bird or the blade, including their masses, densities and/or other properties, it can be expected that the number of significant peaks for the impact force may change as well. The normalized impulse between the bird and blade is shown in Fig. 14. The momentum of the bird is transmitted to the fan blade over the duration of the impact process. However, only 24.4%, 37.5%, and 40.2% of the initial momentum of the bird are finally transmitted to the blade in the Z-direction, for the straight-ended cylinder, hemispherical-ended cylinder, and ellipsoidal bird, respectively.
Fig. 14. Effect of artificial bird configurations on normalized impulse when striking a flexible fan blade.
Fig. 15. Effect of aspect ratios of artificial birds on normalized impact pressure when striking a flexible fan blade. Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Fig. 16. Effect of aspect ratios of artificial birds on normalized impulse when striking a flexible fan blade.
The present simulation has been successful in suppressing the stairway profiles of the impulse accumulation, which was frequently observed in earlier results, such as Stoll and Brockman [25], and Langrand et al. [12]. 3.2.2. Effects of bird aspect ratio Fig. 15 illustrates the evolution of the normalized impact pressure between the fan blade and hemispherical-ended cylindrical birds with three different aspect ratios of 1.5:1, 2.0:1, and 2.5:1. Since their configurations are similar, their evolution histories are also found to be moderately comparable. For all of the cases considered, there are three significant peaks within their impact profiles, and all of them reach their respective maximum values at the second peak, at magnitudes of 1.66 for aspect ratio 1.5:1, 1.78 for aspect ratio 2.0:1, and 1.70 for aspect ratio 2.5:1. The relative differences are less than 7%. Next, the normalized impulse variations for the three aspect ratios are shown in Fig. 16. It can be seen that the impulse evolutions are quite similar as well. Within the normalized time T ¼ 0–0.6, the impulse increases in an almost linear manner. The rate of increase in the impulse plateaus levels off after T ¼ 0.6. When the impact force reaches zero, we note that 34%, 37%, and 32% of the initial momentum of the bird has been transmitted to the fan blade, for the three respective aspect ratios. Thus, we can draw from this study that the aspect ratio does not have significant effects on the normalized impact pressure and impulse results. 4. Conclusions Bird strikes pose one of the most dangerous threats to the safety of modern aircrafts. Bird strike tests are costly but necessary. However, it is also highly desirable to develop accurate predictive numerical tools to assess the bird impact resistance of aeroengine components. In this respect, the geometrical modeling of the artificial bird is very important, though a widely accepted standardized
bird model has not been realized yet. To address this, three different frequently used configurations and aspect ratios, representing diverse biometric bird species, have been examined in the present investigation. It is found from this study that the initial contact area between the bird and target in the early phase of the impact event would have a significant effect on the peak impact force value. For the bird model impacting a rigid target, the maximum impact force for the case of a straight-ended cylindrical bird is about 43% higher than that of a hemispherical-ended cylindrical bird, which in turn is 30% higher than that of an ellipsoidal bird. On the other hand, the impact force profile is also found to be highly dependent on the deformation of the fan blade. Due to the flexibility of the curved fan blade, the maximum impact forces from the straight-ended cylinder, hemispherical-ended cylinder, and ellipsoidal bird models impacting the presently studied fan blade would be respectively reduced by 53%, 32%, and 24%, when compared with their corresponding rigid impacts. The present numerical simulations also reveal that the length-to-diameter aspect ratio of the bird striking both a rigid panel and a flexible fan blade has little influence on the results, especially the normalized impact pressure and impulse. Acknowledgements The authors would like to thanks DSO laboratories, Singapore for their kind supports to the present investigation. References [1] /http://wildlife.pr.erau.edu/database/S. [2] Allan JR. The costs of birdstrikes and birdstrike prevention. In: Clarke L, editor. Human conflicts with wildlife: economic considerations. Fort Collins: US Department of Agriculture; 2002. p. 147–53. [3] Federal Aviation Administration, Federal Aviation Regulation Part 33, Section 33.94,1984.
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[4] Barber JP, Taylor HR, Wilbeck JS. Bird impact forces and pressures on rigid and compliant targets. University of Dayton Research Institute, Technical Report AFFDL-TR-77-60, Dayton, OH, 1978. [5] Wilbeck JS. Impact behavior of low strength projectiles. Air Force Materials Lab, Air Force Wright Aeronautical Labs, Report no. AFML-TR-77-134, Wright-Patterson Air Force Base, OH, 1977. [6] Gao DP, Li QH. Analytical and experimental investigation of bird impact on blades. J Aerospace Power 1990;5(4):335–8. [7] Teichman HC, Tadros RN. Analytical & experimental simulation of fan blade behavior & damage under bird impact. J Eng Gas Turb Power***** 1991;113:582–94. [8] Wilbeck JS, Rand JL. The development of a substitute bird model. ASME Paper ASME 81-GT-23, Gas turbine conference and products show. Houston, TX, 1981. [9] Chen W, Guan YP, Gao DP. Numerical simulation of the transient response of blade due to bird impact. Acta Aeronaut Astronaut Sinica 2003;24(6):531–3. [10] Shimamura K, Shibue T, Grosch D. Numerical simulation of bird strike damage on jet engine fan blade. ASME Press Vess Pip Div 2004;485(Part 1):161–6. [11] Frischbier J. Bird strike capability of a transonic fan blisk. In: Proceedings of the ASME Turboexpo 1997, Orlando, FL, 2–5 June 1997. [12] Langrand B, Bayart AS, Chauveau Y, Deletombe E. Assessment of multi-physics FE methods for bird strike modelling—application to a metallic riveted airframe. Int J Crashworth 2002;7(4):415–28. [13] McCarthy MA, Xiao JR, McCarthy CT, Kamoulakos A, Ramos J, Gallard JP, et al. Modelling of bird strike on an aircraft wing leading edge made from fiber metal laminates—part 2: Modeling of impact with SPH bird model. Appl Compos Mater 2004;11(5):317–40. [14] Airoldi A, Cacchione B. Modelling of impact forces and pressures in Lagrangian bird strike analyses. Int J Impact Eng 2006;32:1651–77.
[15] Richard B. The development of a substitute artificial bird by the international Bird strike Research Group for use in aircraft component testing. International Bird Strike Committee ISBC25/ WP-IE3, Amsterdam, 2000. [16] Guan YP, Chen W, Huang ZY. Sliced model for bird impacting blades. J Nanjing Univ Aeronaut Astronaut 2004;36(6):784–6. [17] Brockman RA, Held TW. Explicit finite element method for transparency impact analysis. University of Dayton Research Institute, Technical report WL-TR-91-3006, Dayton, OH, 1991. [18] Bowman DR. International birdstrike research group (IBRG) development of a new artificial bird. ASTM F7.08 2004 transparency technical seminar, Washington DC, 2004. [19] Edge CH, Degrieck J. Derivation of a dummy bird for analysis and test of airframe structures. In: Proceedings of bird strike, 1999. [20] Jones N, Wierzbicki T. Structural crashworthiness and failure. London: Elsevier Science Publishers; 1993. [21] Mao RH, Meguid SA, Ng TY. Finite element modeling of a bird striking an engine fan blade. AIAA J of Aircraft 2006 in press. [22] Paul E. Jet engine certification standards. International Bird Strike Committee ISBC25/WP-IE1, Amsterdam, 2000. [23] Perzyna P. Fundamental problems in viscoplasticity. Advances in applied mechanics, vol. 9. New York: Academic Press; 1966. p. 243–377. [24] Willows M, Driffill B. GARTEUR (Group for Aeronautical Research and Technology in EURope) Bird Strike Group, Round robin work package: Rigid wall phase 1 and task 1, DERA Farnborough, Hants, 1999. [25] Stoll F, Brockman RA. Finite element simulation of high-speed softbody impacts. In: Proceedings of the 1997 38th AIAA/ASME/ASCE/ AHS/ASC structures, structual dynamics and materials conference, Part 1, Kissimmee, FL, 1997. p. 334–44.
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International Journal of Impact Engineering ] (]]]]) ]]]–]]] www.elsevier.com/locate/ijimpeng
FE analysis of geometry effects of an artificial bird striking an aeroengine fan blade S.A. Meguid, R.H. Mao, T.Y. Ng Division of Aerospace Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore Received 9 January 2007; received in revised form 24 April 2007; accepted 27 April 2007
Abstract Bird strike resistance of aeroengines is a strict certification requirement. Apart from costly experimental bird strike tests, explicit numerical modeling techniques have been employed. However, due to the complicated bird geometry, artificial bird models are still not well defined and it is a perennial problem selecting an appropriate representative artificial bird geometry for the simulations. To examine the relative effects of the artificial bird geometry, explicit 3-D finite element analyses are conducted herein using the commercial code LSDYNA. As a validation test, we first studied the nonlinear transient dynamic response of an artificial bird striking a rigid flat target. Following the validation, we studied the impact behavior of an artificial bird impinging a flexible aeroengine fan blade. The study focused on the three most-frequently used configurations in the literature: namely, hemispherical-ended cylinder, straight-ended cylinder, and ellipsoid, at various length-to-diameter aspect ratios. The results show that the initial contact area between the bird and target in the early phase of the impact event would have a significant effect on the peak impact force. The aspect ratio of the bird striking both rigid panel and flexible fan blade was found to have little influence on the normalized impact force and impulse. r 2007 Elsevier Ltd. All rights reserved. Keywords: Bird strike; Artificial bird configuration; Aspect ratio; Rigid panel; Flexible fan blade
1. Introduction Ever since they began to share the sky with the birds a century ago, aircrafts have been perpetually suffering from bird strikes. In fact, about 90% of all foreign object damage (FOD) can be traced to avian origins. Presently, all available evidence suggests that the bird strike hazard is increasing, and this can be attributed to globalization and conservation, which has resulted in the steady increase in air traffic density levels as well as the dramatic expansion of wild bird populations [1], Fig. 1. These strikes pose a real danger to the lives of aircraft crew members and their passengers, and the potential for severe consequences following a strike is becoming more and more significant. This is because modern jet airliners are carrying more and more passengers, and it is well known that even minor damage due to FOD can easily lead to a catastrophic chain Corresponding author. Tel.: +65 67904040; fax: +65 67913502.
E-mail address: [email protected] (S.A. Meguid).
of events. It is conservatively estimated by the International Birdstrike Research Group [2] that collisions between aircraft and birds cost the aviation industry worldwide over US$1.2 billion each year. As a result, certification authorities require that all exposed aircraft components must be tested to prove their capability to withstand the most adverse impact loading. Special attention has always been given to the aeroengine, which, alongside being the most vulnerable aircraft component or system to bird strikes, is also the only power plant of a jet airliner. The fan blade is the first component of an aeroengine that comes in contact with the bird in a bird strike event, and the resulting plastic deformation and fracture of the fan blade may lead to partial or total loss of thrust, as well as possible containment failure which is strictly prohibited by aviation regulatory authorities, such as the FAA [3]. In fact, even a minor damage to fan blades may introduce engine unbalance. In the 1970s, the validation of the structural integrity and resistance to bird strike of aircraft components was
0734-743X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2007.04.008 Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Across D E F I Iad L L/D m P PTH s
normalized impact pressure, Pad ¼ ðF =Across Þ=PTH s T normalized time, T ¼ t=T 0 ¼ t=ðL=w_ 0 Þ T0 nominal impact duration, T 0 ¼ L=w_ 0 ðsÞ t time (s) u,v,w displacements in X, Y, and Z directions (m) w_ 0 initial velocity of bird, w_ 0 ¼ 225 m/s X,Y,Z cartesian coordinates (m) sij stress tensor (Pa) e_ij strain rate tensor (s1) r instantaneous mass density of bird (kg/m3) r0 initial mass density of bird, r0 ¼ 934.3 kg/m3 m mass density changing ratio of bird, m ¼ ðr=r0 Þ 1 V Poisson ratio of the fan blade material g kinematic viscosity coefficient of fluidic bird material (m2/s)
Pad
Nomenclature (in SI units) average cross-sectional area of bird, Across ¼ m=r0 L ðm2 Þ diameter of bird (m) Young’s modulus of the blade material (Pa) impact or contact force between bird and target (N) between bird and target, I ¼ Rimpulse 1 F dt ðN sÞ 0 normalized impulse, I ad ¼ I=m w_ 0 length of bird (m) aspect ratio (or length-to-diameter ratio) of bird geometry mass of bird, m ¼ 1.82 kg pressure (Pa) theoretical stagnation pressure, pTH ¼ s 2 ð1=2Þr0 w_ 0 ðPaÞ
solely dependent on experiments. It was established by Barber et al. [4] that the loads generated by a high-speed impacting bird were adequately duplicated by representing the bird as a circular cylinder with the same mass, density, and compressibility as the bird tissue. Shortly thereafter, Wilbeck [5] noted the fact that, in case of high-speed impact, the response of the bird is similar to that of a fluid (such as water) where the strength of the bird material is extremely small compared with the impact loads. In addition, high-speed photography was employed by Gao and Li [6] and Teichman and Tardos [7] to record the evolution of the bird torso and the large deformations of the targets such as aeroengine fan blades, through which the fluidic property hypothesis of the bird tissue under
high-speed impact scenarios was further strengthened. These experimental tests, however, are very expensive, time-consuming and difficult to perform. Besides, due to the extremely high velocities and energies involved, the experimental registration of the impact parameters can often prove difficult and complex. With the development of advanced numerical techniques and the advent of high-performance computing, numerical simulations have been more widely used since the 1980s to evaluate the impact capability of different aircraft components. Explicit nonlinear finite element (FE) codes, which are available in several high-end commercial FE solvers, have been used to treat this class of problems. An accurate numerical model can reveal a significant amount of useful
Fig. 1. Bird-strike frequency in recent years in the USA [1]. Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Fig. 2. The three configurations considered for the artificial bird model: (a) straight-ended cylinder, (b) hemispherical-ended cylinder, and (c) ellipsoid.
information to the designer with regard to the mechanisms involved in the high-speed soft body impact event. Having privy to these information prior to conducting experimental tests enables the rapid and economical design of aircraft structures with enhanced impact resistance. In conjunction with the broadened application of numerical techniques to bird strike modeling and simulation, the artificial bird has substituted real birds, mainly for better repeatability and convenience [8]. For all its promise, the reliability of the numerical results is critically dependent on the accurate modeling of the temporal and spatial distribution of the impact force between the bird and target [9,10]. In connection with this, the complex and intricate geometrical configurations of different bird species have perpetually posed a problem for developing a sufficiently simplified and consistent bird model. Many researchers such as Frischbier [11], Langrand et al. [12], McCarthy et al. [13], and Airoldi and Cacchione [14], have simplified the bird torso as a hemisphericalended cylinder. The ellipsoid geometry is also a wellaccepted choice, which has been suggested by the International Birdstrike Research Group [15], and has been used by Guan et al. [16]. Besides these two configurations, the straight-ended cylinder has also been adopted by Brockman and Held [17], but its application remains somewhat infrequent. These three configurations, which are typical of artificial bird geometries, are shown schematically in Fig. 2. Nevertheless, the differences among the impact behaviors associated with these different configurations have not been reported in the open literature. Furthermore, the effect of the length-to-diameter aspect ratio (representing the biometric property of different bird species) is also examined. It has been highly recommended by the International Birdstrike Research Group that the bird model, once standardized, should become the norm for all bird impact testing thereafter [18]. From the simulation viewpoint, standardizing the geometry of the artificial bird model is correspondingly important. Both the bird configuration and aspect ratio have been found to be important parameters that influence the impact response of the target [19]. Thus, the aim of the present investigation is to compare and analyze the numerical results for the abovementioned three different bird configurations, and various aspect ratios will also be considered. The simulation will be carried out using highly accurate Lagrangian-based explicit
nonlinear FE analysis. The flexible fan blade adopted in the present investigation is a typical metallic wide-chord aeroengine fan blade. 2. Finite element modeling in a Lagrangian framework The finite element method (FEM) has been found to be very powerful in the numerical simulation of the crashworthiness and failure analyses [20]. The coupling between the bird and the target can be achieved by a Lagrangian formulation. During high-speed impact, large strain distortions will inevitably occur to the discretized Lagrangian bird, leading to a decrease in solution time-step and possible negative elemental volumes. The excessively distorted elements that possess negative volumes are then eliminated after each time step. However, this automatic elimination procedure usually introduces artificial oscillations in the contact force between the bird and target. Fortunately, the strategy of employing highly refined meshes that encounter element elimination can be used to alleviate this problem [21]. Modern high-performance computing systems can tolerate very small time steps in the order of 109 s or even 101 s, where it used to be 106–107 s, just a few years ago. Thus, by refining the mesh of the Lagrangian bird, the artificial oscillations associated with the impact force can be dramatically reduced. 2.1. Bird properties The bird’s mechanical property actually changes from the low-velocity to the high-velocity regimes. Generally, the mechanical property of typical avian tissues at low speeds is neither uniform nor homogeneous. However, at progressively higher speeds, this nonuniformity and inhomogeneity become increasingly negligible, and the bird can safely be considered as a homogeneous jet of fluid impinging a structure [5]. Thus, the constitutive material law of homogenized fluidic materials can be used: sij ¼ Pdij þ 2rg e_ij .
(1)
There are different hydrodynamic models which have been successfully used to describe the material properties of the bird in compression and among which the most popularly used is the polynomial fitted pressure
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equation: p ¼ C 0 þ C 1 m þ C 2 m2 þ C 3 m3 ,
(2)
where m is the nondimensional mass density changing ratio of the bird tissue earlier defined in the nomenclature. Here, we model the loading from the bird as a pressure pulse on the structure. This is a feasible approach and we can also avoid modeling the bird disintegrating into numerous debris particles. The Brockman compressible modules [17] are employed in the present simulations, whereby 8 C 0 ¼ 0; > > > < C 1 ¼ 2323 MPa; (3) > C 2 ¼ 5026 MPa; > > : C 3 ¼ 15180 MPa: The total mass of the bird is 4 lb (or 1.82 kg), which is presently used as the upper limit of the bird mass criteria in the bird–aircraft strike scenarios [22]. Its initial mass density is set at 934.3 kg/m3, while the initial velocity of the bird is taken to be 225 m/s in the normal Z-direction. Table 1 lists the detailed parameters of three geometries with the commonly used aspect ratio of 2.0:1. Table 2 lists all diameters of hemispherical-ended cylindrical birds with aspect ratios 1.5:1, 2.0:1, and 2.5:1. The bird model is meshed with 3-D 8-node fully integrated solid elements (Solid-164 in LS-DYNA) with a characterized ratio of bird diameter to mesh size of 32, as shown in Fig. 3, which is found to provide efficient simulation runs without compromising on accuracy. In addition, the hourglass energy is found to be well controlled in the present simulation.
DYNA), with 31 nodes in the axial direction and 61 nodes in the radial direction found to provide sufficiently converged results. In addition, the Hughes–Liu formulation was used to eliminate the hourglass modes. The
Fig. 3. Discretized geometries of the three bird configurations used.
2.2. The flexible fan blade A sector of the fan disk, composed of a single blade and a hub section, as shown in Figs. 4(a) and (b), is used in the present simulation. The hub is assumed to be fixed and rigid in comparison with the blade. The deformable blade is discretized using the 2-D shell elements (Shell-163 in LS-
Fig. 4. A schematic diagram of a bird striking a flexible fan blade: (a) isometric view, and (b) top view.
Table 1 Details of the different bird configurations considered (aspect ratio is 2.0:1) Configuration type
Straight-ended cylinder
Hemisphericalended cylinder
Ellipsoid
Length L (m) Diameter D (m)
0.214 0.107
0.228 0.114
0.246 0.123
Table 2 Details of the different bird aspect ratios considered (configuration is hemispherical-ended cylinder) Aspect ratio L/D
1.5:1
2.0:1
2.5:1
Length L (m) Diameter D (m)
0.192 0.128
0.228 0.114
0.260 0.104
Fig. 5. Velocity vectors of the bird at T ¼ 0.05 when impacting a rigid target: (a) side view, and (b) isometric view.
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hourglass coefficient was set to 0.1, quadratic bulk viscosity to 1.5, and linear bulk viscosity to 0.06. Fan blades of modern aeroengines are typically made of titanium alloy Ti–6A1–4V. Due to the high strain rates associated with this problem, the constitutive law used is of the viscoplastic type originally devised by Perzyna [23] sy ðpeff ; _peff Þ ¼ sy ðpeff Þð1 þ ð_peff =CÞ1=p Þ, _peff
(4) sy ðpeff Þ
is the effective plastic strain rate, and is where the initial quasi-static yield stress of the blade material. C and P are strain rate sensitive parameters determined by experiments. The magnitudes of the relevant parameters are listed as follows: 8 > E ¼ 1:14 1011 Pa; > > > > > v ¼ 0:33; > > >
3. Results and discussion 3.1. Bird striking a rigid panel Fig. 5 shows a typical example of the velocity vectors for the hemispherical-ended cylindrical bird model striking a rigid target at a normalized time J ¼ t/T0 ¼ 0.05. The simulations begin at the instant the traveling bird impinges the target. Both side and isometric views are shown in that figure. It shows that the bird has been deformed, with its right tip contacting the target (Fig. 5(a)). The maximum velocity of the fluidic bird elements, which appears near the frontal surfaces of the bird close to the target, is found to be approximately 123 m/s at this instant of impact. The time histories of the bird impacting a rigid panel for different phases are depicted in Fig. 6. The hydrodynamic fluid-like behavior of the bird can be clearly observed from T ¼ 0.5 onwards. During the impact process, the momentum of the bird will be progressively absorbed by the target; whereas the kinetic energy of the bird will be dissipated in terms of heat, as well as manifested by the elimination of some of the bird elements. Finally, the bird elements, with the umbrella-like configuration, do not possess additional forward momentum, and the impact process is completed at the normalized time T ¼ l. Nevertheless, following this impact event, the bird elements continue to deform and expand outwards. Fig. 7 shows the variation of the normalized impact pressure over time. It is compared with the experimental data from the GARTEUR Bird Strike Group [24] as well as the numerical results of Langrand et al. [12]. It is clearly observed that the present numerical results correspond well with the experimental data. When compared with the
Fig. 6. Deformation history of a bird impacting a rigid target: (a) T ¼ 0, (b) T ¼ 0.25, (c) T ¼ 0.5, (d) T ¼ 0.75, and (e) T ¼ l.
simulation results reported in the literature, the present result exhibits fewer oscillations than those prevalent in earlier studies, and is clearly more stable. This can be attributed to the fine mesh density used in discretizing the bird geometry. Specifically, we used a bird-to-element length ratio of about 32, compared with 8 used by Stoll and Brockman [25], and Airoldi and Cacchione [14]. The peak value of the pressure from the present simulation is about 20% lower than that of the experimental data, and this difference is probably due to the use of water-compressible modules for the bird’s material model, which underestimates the behavior of a real bird. 3.1.1. Effects of bird configuration Fig. 8(a) shows the impact force variations for different configurations of the bird model. It is found that the straight-ended cylinder reaches its maximum impact force of 7.99 105 N at about 0.049 ms after initial contact, and there is only one dominant peak in its contact force profile. However, there are two quite distinct peaks corresponding to the hemispherical-ended cylinder and ellipsoid models. The hemispherical-ended cylinder reaches its maximum force of 5.27 105 N at 0.054 ms, and its second peak of 3.33 l05 N at 0.134 ms, although this second peak is not as significant as the first one. The ellipsoid model, on the other hand, reaches its first peak of 3.60 105 N at 0.111 ms, and its second peak of 3.78 l05 N at 0.28 ms. Interestingly, this second peak is found to be the maximum magnitude in its force variation time history. Among the three different bird geometries, the maximum impact force for the straight-ended cylindrical bird is the highest. This is because at the instant the three types of bird configurations impinge the rigid target, the straight-ended cylindrical bird has comparatively the largest instantaneous contact area.
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Fig. 7. Variation of normalized impact pressure versus normalized time for a hemispherical-ended cylindrical bird impinging a rigid panel.
Fig. 8. Effect of artificial bird configurations on rigid impact forces and pressures: (a) impact forces, and (b) normalized impact pressures. Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Fig. 9. Effect of aspect ratios of artificial birds on rigid impact forces and pressures: (a) impact forces, and (b) normalized impact pressures.
This also explains why there is only one significant peak in its force variation, and it is because all the elements of this bird model will decelerate immediately and dramatically once it impacts the target. However, this situation is quite different for the hemispherical-ended cylinder and ellipsoidal birds. Since the bird in the high-speed impact scenarios behaves as a liquid, the shear stress between the bird’s elements flowing on neighboring streamlines, compared with the local high pressure, is comparatively negligible. This has been experimentally observed by Barber et al. [4], Wilbeck [5] and Gao and Li [6]. The present investigation treats the bird hydro-dynamically, and neglects the fluidic viscous effect of the bird tissue. Therefore, for the hemispherical-ended cylinder and ellipsoidal birds, only the elements directly downstream of those in contact with the target will experience the dramatic deceleration, whereas the other elements will not decelerate significantly until their frontal elements come into contact with the
target. Thus, when impact progresses for the hemispherical-ended cylinder or ellipsoidal birds, the contact forces decrease after the initial peaks, but will increase again, leading to their respective second peaks. This second peak is quite distinct in the ellipsoidal case, but rather less pronounced in the hemispherical-ended cylindrical bird case. In the ellipsoid model, the contact area reaches its maximum value somewhat late into the impact event. It occurs at approximately the midpoint of the entire impact duration, which explains the presence of its second peak. The normalized impact pressure evolutions for the three bird configurations are plotted in Fig. 8(b). It should be noted that because the cross-sectional areas vary along the geometrical axes of the hemispherical-ended cylinder and the ellipsoid models, the normalization is based on their respective averaged cross-sectional areas. The maximum normalized impact pressure is found to be 3.73 at T ¼ 0.055 for the straight-ended cylinder, 2.61 at
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Fig. 10. Effect of aspect ratios of artificial birds on rigid impact impulse.
T ¼ 0.053 for the hemispherical-ended cylinder, and 2.00 at T ¼ 0.27 for the ellipsoid model. Thus, the maximum impact pressure for the straight-ended cylinder impact case is about 43% higher than the hemispherical-ended cylinder case, and the latter is about 30% higher than the ellipsoid case. 3.1.2. Effects of bird aspect ratio In this section, the 4 lb bird with mass density 934.3 kg/m was simulated at different aspect ratios of 1.5:1, 2.0:1, and 2.5:1. We selected the hemispherical-ended cylinder geometry for the simulations. The impact force evolutions are plotted in Fig. 9(a). Due to its largest cross-sectional areas, the model with 1.5:1 aspect ratio has a maximum impact force of 6.57 l05 N, and it drops to zero first at 0.62 ms. The peak impact forces for the 2.0:1 and 2.5:1 cases are 5.27 l05 and 4.62 l05 N, respectively. This is due to the variance in their respective cross-sectional areas. Fig. 9(b) shows that the peak values for the three cases are much the same after normalization, being 2.75 for aspect ratio 1.5:1, 2.62 for aspect ratio 2.0:1, and 2.61 for aspect ratio 2.5:1. Thus, we note that the aspect ratio does not affect the normalized maximum impact pressure significantly. The impulses for the three aspect ratios are shown in Fig. 10. It is found that the impulse, after normalization, is 0.29 for the aspect ratio 1.5:1, 0.23 for the aspect ratio 2.0:1, and 0.26 for the aspect ratio 2.5:1. 3.2. Bird striking a fan blade In these simulations, the bird impacts the fan blade at a height of 85% radius of the blade from the hub. Due to the flexibility of the fan blade, the impact duration will be longer than the nominal impact time T0 ¼ L/w0. For example, for the hemispherical-ended cylindrical bird, its impact with the fan blade is completed at normalized time
Fig. 11. Deformation history for a hemispherical-ended cylindrical bird impinging a flexible fan blade: (a) T ¼ 0, (b) T ¼ 0.25, (c) T ¼ 0.5, (d) T ¼ 0.75, (e) T ¼ l, and (f) T ¼ 1.34.
T ¼ 1.34. The time histories of the impact process at different phases are shown in Fig. 11. The deformation of the blade when the impact force finally vanishes is also shown in Fig. 11(f). Nevertheless, both the bird and the blade will continue deforming even after the impact force vanishes. However, in the present investigation, only the major bird–blade coupled effects are of interest, and we terminate the simulation when the impact force vanishes. 3.2.1. Effects of bird configuration The impact forces between the hemispherical-ended cylindrical bird and the fan blade are shown in Fig. 12.
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Fig. 12. Impact force variations for a hemispherical-ended cylindrical bird (UD ¼ 2.0) striking a flexible fan blade.
Fig. 13. Effect of artificial bird configurations on normalized impact pressure when striking a flexible fan blade.
Since the geometry of the blade is curved, the impact forces are resolved into the X, Y, and Z directions. However, it can be seen from this figure that the impact force in the Zdirection is dominant, because the initial velocity of the bird is in the Z-direction. Henceforth, only the results in the Z-direction will be shown in the following results. There are multiple peaks in the impact force evolution, which is due to the coupling between the bird and the flexible blade. The blade, upon being impacted by the bird, accelerates in the same direction as the bird’s initial velocity, i.e., the Z-direction. When this happens, the frontal elements of the bird which are in close contact with the blade would expand and their high pressures would thus decrease. Therefore, the total impact force would also decrease dramatically. Consequently, with the lowered impact force from the bird, the bending of the blade would decelerate, and as a result the contact between the bird and the blade becomes intense once more. The impact force between the bird and blade would increase again. The
whole procedure will repeat several times before the impact force eventually vanishes. The normalized impact pressures between the birds and fan blade are shown in Fig. 13 for all the three bird configurations. The dominant peaks are 1.75 at T ¼ 0.094, 1.35 at T ¼ 0.189, and 0.77 at T ¼ 0.32 for the straightended cylindrical bird, and 1.62 at T ¼ 0.06, 1.78 at T ¼ 0.16, and 1.46 at T ¼ 0.45 for the hemispherical-ended cylindrical bird. For the ellipsoidal bird, the peaks are 0.79 at T ¼ 0.06, 1.53 at T ¼ 0.16, and 1.34 at T ¼ 0.39. From Fig. 13, we can observe that the normalized impact pressure variation profiles for the three bird configurations are quite different from the preceding rigid impact cases. This is especially so for the straight-ended cylindrical bird, which no longer possesses the highest peak impact pressure value among the three bird configurations. As there is an attack angle of 601 between the bird trajectory and the blade, as shown in Fig. 4(b), the initial contact area between the straight-ended cylindrical bird and the blade is
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not as large as the rigid panel case. Thus, the initial contact force between the bird and target is also significantly reduced. More importantly, the blade is not rigid but flexible, and the maximum impact force between the straight-ended cylindrical bird and blade is found to be only 47% of the rigid impact case. Similar conclusions have been reached by Shimamura et al. [10] that the target’s flexibility strongly influences the impact force between the bird and target. The impact force between the hemispherical-ended cylindrical bird and blade is about 68% of the former rigid impact case, and correspondingly 76% for the ellipsoidal bird model. Comparing the three geometries, it is noted that the ellipsoidal bird model has a maximum impact force, which is lower than the other two configurations by about 15%.
It is also interesting to note that all the three types of bird configurations have three significant peaks within their variations of the impact forces. This is mainly because the bird mass and density are similar for the three configurations. By varying the mechanical properties of either the bird or the blade, including their masses, densities and/or other properties, it can be expected that the number of significant peaks for the impact force may change as well. The normalized impulse between the bird and blade is shown in Fig. 14. The momentum of the bird is transmitted to the fan blade over the duration of the impact process. However, only 24.4%, 37.5%, and 40.2% of the initial momentum of the bird are finally transmitted to the blade in the Z-direction, for the straight-ended cylinder, hemispherical-ended cylinder, and ellipsoidal bird, respectively.
Fig. 14. Effect of artificial bird configurations on normalized impulse when striking a flexible fan blade.
Fig. 15. Effect of aspect ratios of artificial birds on normalized impact pressure when striking a flexible fan blade. Please cite this article as: Meguid SA, et al. FE analysis of geometry effects of an artificial bird striking an aeroengine fan.... Int J Impact Eng (2007), doi:10.1016/j.ijimpeng.2007.04.008
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Fig. 16. Effect of aspect ratios of artificial birds on normalized impulse when striking a flexible fan blade.
The present simulation has been successful in suppressing the stairway profiles of the impulse accumulation, which was frequently observed in earlier results, such as Stoll and Brockman [25], and Langrand et al. [12]. 3.2.2. Effects of bird aspect ratio Fig. 15 illustrates the evolution of the normalized impact pressure between the fan blade and hemispherical-ended cylindrical birds with three different aspect ratios of 1.5:1, 2.0:1, and 2.5:1. Since their configurations are similar, their evolution histories are also found to be moderately comparable. For all of the cases considered, there are three significant peaks within their impact profiles, and all of them reach their respective maximum values at the second peak, at magnitudes of 1.66 for aspect ratio 1.5:1, 1.78 for aspect ratio 2.0:1, and 1.70 for aspect ratio 2.5:1. The relative differences are less than 7%. Next, the normalized impulse variations for the three aspect ratios are shown in Fig. 16. It can be seen that the impulse evolutions are quite similar as well. Within the normalized time T ¼ 0–0.6, the impulse increases in an almost linear manner. The rate of increase in the impulse plateaus levels off after T ¼ 0.6. When the impact force reaches zero, we note that 34%, 37%, and 32% of the initial momentum of the bird has been transmitted to the fan blade, for the three respective aspect ratios. Thus, we can draw from this study that the aspect ratio does not have significant effects on the normalized impact pressure and impulse results. 4. Conclusions Bird strikes pose one of the most dangerous threats to the safety of modern aircrafts. Bird strike tests are costly but necessary. However, it is also highly desirable to develop accurate predictive numerical tools to assess the bird impact resistance of aeroengine components. In this respect, the geometrical modeling of the artificial bird is very important, though a widely accepted standardized
bird model has not been realized yet. To address this, three different frequently used configurations and aspect ratios, representing diverse biometric bird species, have been examined in the present investigation. It is found from this study that the initial contact area between the bird and target in the early phase of the impact event would have a significant effect on the peak impact force value. For the bird model impacting a rigid target, the maximum impact force for the case of a straight-ended cylindrical bird is about 43% higher than that of a hemispherical-ended cylindrical bird, which in turn is 30% higher than that of an ellipsoidal bird. On the other hand, the impact force profile is also found to be highly dependent on the deformation of the fan blade. Due to the flexibility of the curved fan blade, the maximum impact forces from the straight-ended cylinder, hemispherical-ended cylinder, and ellipsoidal bird models impacting the presently studied fan blade would be respectively reduced by 53%, 32%, and 24%, when compared with their corresponding rigid impacts. The present numerical simulations also reveal that the length-to-diameter aspect ratio of the bird striking both a rigid panel and a flexible fan blade has little influence on the results, especially the normalized impact pressure and impulse. Acknowledgements The authors would like to thanks DSO laboratories, Singapore for their kind supports to the present investigation. References [1] /http://wildlife.pr.erau.edu/database/S. [2] Allan JR. The costs of birdstrikes and birdstrike prevention. In: Clarke L, editor. Human conflicts with wildlife: economic considerations. Fort Collins: US Department of Agriculture; 2002. p. 147–53. [3] Federal Aviation Administration, Federal Aviation Regulation Part 33, Section 33.94,1984.
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