Effect of Bird Yaw/Pitch Angles on Soft Impact Damage of a Fan Assembly

+is paper presents a numerical investigation of bird attitude angles affecting the soft-impact damage of a full fan assembly. Firstly, considering the geometry of a mallard, a real bird model is established by the Smoothed Particle Hydrodynamics (SPH) method and calibrated with available test data. +en, complying with airworthiness requirements, simulations of a full-bladed fan assembly subjected to a real bird were conducted to determine the critical ingestion parameters (CIP). Furthermore, a real bird with different attitude angles aimed at a full fan assembly was simulated. Results show that attitude angles of the bird produce a significant impact on the effect of the bird strike on rotating blades and would increase the possibility of blade failures, especially for the yaw angle of -45° and the pitch angle of − 60°. It is invaluable for commercial airlines and engine manufactures to provide safe flight and landing by adopting the real bird model with critical yaw and pitch angles in the design for resistance to bird ingestion.


Introduction
Bird strikes have been presenting the main threat to aircrafts since the beginning of aviation history. All available statistics indicate that the bird-strike hazard is increasing dramatically, due to the significant expansion of wild bird populations, as well as, to some extent, because of the steady increase in air transport [1]. erefore, aviation authorities require that all forward facing components need to prove a certain level of bird-strike resistance in certification tests before they are allowed for operational use [2]. However, according to a large number of reported bird-strike incidents, substantial damage to aircraft structures occurs even though the involved energies of the bird did not achieve the aircraft certification standard. It indicates that only taking the mass and impact speed of the bird into account is far from enough.
Initially, early studies were commonly based on theoretical and experimental studies. Wilbeck [3,4] conducted a comprehensive set of experimental studies on bird impacts on various structures regarding different bird sizes, initial velocities, bird substitutes, and oblique impacts. It was found that real birds behave as fluids during impact at velocities larger than 100 m/s, and the impact process consists of four typical phases. In recent times, much effort and significant progress have been done to get better insight into simulating the process of bird-strike events, involving substitute bird models [5,6], numerical methods [7][8][9], and material models [10,11]. It can be concluded that the substitute model with bird shapes, namely, ellipsoid and hemispherical-ended cylinder (aspect ratio of 2), is recommended, associated with material properties of homogenized fluidic materials. e equation of state is used to describe the compressibility characteristics of bird material.
However, the values of Hugoniot pressure obtained from theoretical and experimental results are so far from each other, especially at lower velocities [12]. Meanwhile, the values obtained from numerical results calculated by different authors are in a wide range between the experimental and theoretical values [2,12]. erefore, some scholars shifted the focus to the real bird model. Lakshmi [13] used a multimaterial bird model with a more realistic bird shape to capture a more detailed impact load spectrum. McCallum et al. [14] developed a physically representative bird model of a Canadian goose. e results show that, compared with the traditional model, the physically representative bird model produces a lower Hugoniot pressure and higher magnitude of peak impact force with longer duration. Hedayati et al. [12,15] established a real bird model based on the mallard CT-scan image data. ey found that the numerical results of the realistic bird model are closer to the available experimental results than those in the case of the traditional model. Bird strikes are the major factor of blade damage for aircraft engines [16]. It is worth noting that, in a large number of incidents, the involved bird energy was lower than the magnitude of impact energy in certification, whereas aircraft structures can be substantially damaged [17]. In a typical field-event of the bird strike, it is common to observe a single bird coming into contact with multiple blades with respect to arbitrary attitude angle. Projectile yaw during impact would result in a variation in the impact loading history [4]. On that point, several research works have been done to capture the amount of damage imposed on blades due to bird impact, considering bird orientation or pitch/yaw angles [18][19][20]. e results reveal that bird orientation has a significant effect on the impact force. However, with respect to a realistic bird shape, not only is the bird attitude far more complicated, but also the effect of bird orientation on rotating blades during the bird strike is different for yaw and pitch angles. Moreover, it is difficult and complicated to record attitude angles of bird both in physical tests and in a field-event of bird strikes. e highpressure gas cannon is not capable of firing a real bird or a substitute bird with arbitrary yaw/pitch angle. Biologically inspired motion modelling and control algorithms [21][22][23][24][25] may seem like a good choice to determine the bird attitude, which is urgent to study. Attitude angles in our research are assumed in a wide range from 0°to 60°. e study presented in this paper aims to focus on attitude angels of a realistic bird affecting soft impact damage of jet engine blades. Considering the shape of a real mallard in a published literature [12], a new bird model was established using the SPH approach and validated against the latest published experimental results [26]. To determine the influence of bird orientation on the blade damage, the realistic bird model with various attitude angles targeted at a fan assembly has been developed. e simulations were performed based on Magic Cubic-II of Shanghai Supercomputer Centre, using LS-DYNA FE code. Figure 1 shows the main stages and the pressure profile of a typical bird-strike process, a normal impact of a flat cylinder on a rigid plate. At the moment of impact in Figure 1, the bird material is rapidly decelerated, and a shock wave is initiated at the bird-target interface, resulting in a sharp rise in pressure. e shockwave pressure exceeds the strength of bird material to a large extent. Consequently, as the shockwave propagates through the bird body in Figure 1, it rapidly breaks the internal bonds of birds, generating a transition from a solid towards a fluid phase. e bird material is transitioned to a fluid-like medium. e high-pressure gradient across the free surface of bird and the surrounding air forces out shocked material radially [27]. is behavior is known as shock release. With the propagation of release waves towards the center of the bird, the pressure of the bird material gradually decays to the fluid pressure. As the bird strike progresses in Figure 1, the bird material is progressively forced out of the original bird volume and spreads outwards nonlinearly. With the bird tail approaching the target, the bird-strike pressure decays to zero. Figure 1 shows the pressure at the center of the impact. e shockwave pressure (Hugoniot pressure, P H ) at the initial impact (see Figure 1) is determined by [28]

Soft Impact eory.
in which where ρ 0 is the initial density of the bird. ] S , ] 0 , and ] a represent the speed of shock wave, impact speed of the bird, and sound speed, respectively. z represents bird porosity. C and S 1 are coefficients of the relationship between the shock and particle velocities. e stagnation pressure P S during the liquid impact (see Figure 1) is given by the following equation [28]:

Complexity
where the constant k is 0.5 for an incompressible fluid [27].

2.2.
Loads on Blades during Impact. In a practical fan blade application, the impact progress is far more complex. Figure 2 indicates the bird-slicing action during the impact. e bird is represented as a flat cylinder. As soon as a bird comes into contact with blades, it undergoes cut into several slices by the blade leading edge in the direction of the relative velocity V Relative . Blades subjected to a bird are invariably an "oblique impact" event, consisting of two phases [29]: the bird-slicing action by multiple rotating blades; each individual bird slice travelling along the blade airfoil. us, the impact generates both a slicing-impact load on the blade leading edge and a bird-slice turning load acting on the concave surface, which can be expressed as [29] F Bird− slice � F slicing + F travel . (4) At the moment of the leading edge slicing a bird projectile, it produces a high-intensity shock wave. For the initial impact area on the concave surface is almost a point, the effective load generated by the shock-wave pressure is not significant, and thus its contribution is ignored [29].
us, the slicing-impact load is determined by the slicing stagnation pressure [29].
in which the slicing stagnation pressure is determined by where B a (t) denotes the bird-foot-print area on the blade leading edge. ] impact represents the normal component of the relative velocity V Relative (see Figure 2) on the blade leading edge.

Airworthiness Standards of Aircraft Engines.
Currently, aviation authorities require that all new commercial aero-engines must substantiate physical certification tests before operational use. ese requirements are compiled in the Federal Aviation Regulations (FAR), Chinese Civil Aviation Regulations (CCAR), and the Certification Specifications (CS) of the European Aviation Safety Agency (EASA) [2]. According to airworthiness standards of FAR §33.76 [30], for the inlet throat area 2.37 m 2 of the jet engine presented in this study, it must be substantiated that the fan assembly is subjected to a medium bird of 1.15 kg under FAR §33.76(c) (3), aimed at the most critical location outboard of the primary core flow path [30]. Figure 3 indicates the location of target point on the first exposed rotating stage of the engine. e airfoil height is measured at the leading edge of the blade. e target point for bird ingestion is determined by impact loading on rotating blades, as well as the possibility of blade failures [31].

e SPH Method.
e SPH method is increasingly used in bird-strike simulations as it has already been proved to be quite capable of simulating high deforming matter with defragmentation [14]. With the SPH technique, the bird was represented as a set of discrete particles, in which the interaction between particles was achieved through a kernel function rather than a structured mesh [12]. e SPH method is recommended in the simulation of the bird-strike process, because of its high stability, low cost, and good correlation with experimental observations in terms of scattering particles [2]. erefore, the SPH approach was adopted to model a real bird of mallard.

Geometry of a Real Bird.
According to the reported bird strike incidents resulting in substantial damage to civil aircraft components in the period 1990-2017 [32], the waterfowl had been the most threatened species for civil aviation safety, accounting for 28% of the total specified species. erefore, the mallard (a typical species of waterfowl) is represented as a general realistic bird model. Since a real bird consists of several internal cavities, bone structures, etc. with complex geometry, the presented bird model can reflect the bird shape to some extent, not exactly the same as the real one. e main geometric characteristics are given as follows: (1) Wilbeck [3] found that bone effect of a bird can be assumed negligible, and thus a uniform density of the real bird model is used; (2) the head is simplified to be an ellipsoid, and the neck was considered as a circular-conical-frustum [19]; (3) geometric parameters of the bird torso were modelled considering the geometry of a real mallard bird in Ref. [12]; (4) the mass of bird wings accounted for 19% of the total mass in accordance with Ref. [14]. e interparticular distance is 2 mm, and the amount of SPH particles is 153,621, as shown in Figure 4.

Bird Material Constitutive Model.
With a general material model for both solids and fluids to describe the fluidic behavior of the bird material, the Cauchy stress tensor is divided into a hydrostatic part and a deviatoric part [16].
in which the hydrostatic pressure P is written as where σ ij represents stress tensor, and s ij represents deviatoric stress tensor. Variable δ ij represents Kronecker delta symbol.
Since the compression of bird material during impact induces a change in the bird density [27], the Mie-Grüneisen equation of state (EOS) was used to reflect the relationship between the pressure and the density [15].
A linear EOS is adopted for the bird material model [26], and equation (9) can be written as where C, S 1 , S 2 , and S 3 are coefficients of the relationship between the shock and particle velocities, and c 0 represents Mie-Grüneisen gamma. a is the first-order volume correction to c 0 . μ represents the relative change in density Porcine gelatine with 10% porosity is used instead of the bird material [26]. Parameters of porcine gelatine can be obtained from Ref. [33]. us, for the developed bird model, parameters are given as follows: ρ 0 � 954 kg/m 3 , C � 1447 m/s, S 1 � 1.77.

Attitude Angle Description.
In this research work, bird attitude was defined based on the Tait-Bryan angles. e Tait-Bryan angles are three angles, named as yaw angle α, pitch angle β, and roll angle c. ey were introduced to describe the orientation of a bird. As shown in Figure 5, a right-handed Cartesian coordinate system was defined in the center of bird gravity, and any bird attitude can be parameterized by three Tait-Bryan angles α, β, and c.
In a field event of the bird strike, it is difficult and complicated to record the Tait-Bryan angles of bird ingestion. Attitude angles of the real bird are assumed in a wide range from 0°to 60°and the orientation of bird based on an individual Tait-Bryan angle was studied at a time. Considering the weight of wings accounting for about 19% bird mass [14], the effect of the roll angle on the slicing action of a bird is relatively small. erefore, bird attitude based on the roll angle was neglected. Yaw angle α and pitch angle β were selected as ±15°, ±30°, ±45°and ±60°, respectively. Figure 6 shows the attitude angles of a realistic bird, where the attitude angle is represented as the angle between the roll axis and the impact velocity.

Fan Assembly Model.
e fan assembly consists of 24 equally spaced (15°) wide-chord blades and a fan disc. e fan assembly was modelled with 8-noded solid elements. Bending is the basic mode of load carrying capacity for blades during impact. With a single-point integration at the element centroid, solid elements can carry membrane stresses only [34]. us, blades were assigned 3 layers of solid elements through the thickness. A tied-contact relationship was assumed to represent the attachment between the blade and the fan hub. Fixed boundary constraints of z-displacement direction were defined on the side of the hub component. To restrict nonphysical deformations relevant to zero energy modes, stiffness hourglass control with exact volume integration [34] was applied to the simulation model. Figure 7 shows the finite element model of the fan assembly. e fan assembly consists of 165,200 solid elements with a total of 222,912 nodes.
e minimum element size of the fan assembly model was 0.42 mm at the tip of the blade leading edge, and the corresponding time step for explicit dynamic simulation was 4.06E-8 s. In addition, Figure 7 gives numbers to fan blades during slicing a bird so that it can identify the blade damage in the simulation of the impact on a fully bladed fan rotor.

Blade Material Constitutive Model.
Bird strike events can be described as high strains and high strain rates in short duration with considerable intensity [35]. erefore, the empirical Johnson-Cook relation was selected [36].
in which 4 Complexity where σ y represents the equivalent von Mises stress; ε represents the equivalent plastic strain; and _ ε * represents the normalized equivalent plastic strain rate. e parameters A, B, C, m and n are material constants. T, T melt and T room represent the metal temperature, melting temperature, and room temperature, respectively. Material fracture is determined by a cumulative damage law, a function of mean stress, strain rate, and temperature [36].
in which Complexity where ∆ε is the increment of equivalent plastic strain, and σ * is the mean normalized by the equivalent stress. D 1 , D 2 , D 3 , D 4 and D 5 are damage constants. Failures are assumed to occur when D � 1. e fan assembly is made of titanium alloy Ti-6Al-4V, and material parameters are derived from Ref. [37], as listed in Table 1. In addition, the Mie-Grüneisen EOS (equation (3)) was defined in conjunction with the material constitutive model, and parameters for Ti-6Al-4V are as follows: C � 5.13 × 10 3 m/s, S 1 � 1.028, c 0 � 1.23 and a � 0.17 [35].

Stress Initialization.
e rotating fan assembly undergoes a constant centrifugal force, resulting in significant deformation and initial stresses prior to impact. It is necessary to evaluate the prestress of the rotating components, especially for blades [16]. us, a preload analysis procedure was conducted by assigning rotational velocity of 542 rad/s in an implicit solution. e initial stress of blades assembly is shown in Figure 8.

Bird Model Calibration.
e effect of the high-intensity shock wave on the blade damage can be ignored for the   6 Complexity reason that the initial bird loading area is almost like a point loading [29]. e focus of blade damage analysis needs to be on accurately capturing the steady stagnation pressure phase of impact [27]. us, the stagnation pressure is represented as a criterion to calibrate bird models. Numerical simulation of a normal impact on a rigid plate was established in accordance with the experimental setup in Ref. [26]. A segment sensor was assigned at the center of the plate to extract the impact pressure. e stagnation pressures were estimated by averaging the pressure between T 0 /3 and 2T 0 /3 [26], where T 0 denotes the duration of the bird strike event.
e theoretical curve of the stagnation pressure was determined by equation (3), and test data was derived from Ref. [26], as shown in Figure 9. e numerical results were in a range between theoretical and experimental values. e stagnation pressures captured by simulation of the real bird were in closer agreement with the test data than those in the case of the hemispherical-ended cylinder.

Most Critical Ingestion Parameters.
e critical ingestion parameters are required to be identified for the specified bird ingestion [30]. In this section, simulations of a full fan assembly subjected to a real bird were performed to determine the critical location and ingestion speed under FAR §33.76(c) (1) and FAR §33.76(c) (3).

Most Critical Ingestion Speed.
Complying with FAR §33.76(c)(1), the critical ingestion speed is required to reflect the most severe situation within the range of speeds used for normal flight operations up to 460 m (1,500 feet), but not less than V1 minimum for airplanes [30]. erefore, simulations of the bird ingested at different speeds were performed, aimed at the fan blade height of 80%. Figure 10( As the speed increases, the impact duration becomes shorter. It is also found that the higher the impact speed is, the earlier the peak force occurs. As the normalized sum of effective plastic strains shown in Figure 10(b), the ingestion speed of 65 m/s caused the most severe plastic strain. erefore, 65 m/s was represented as the most critical speed.

Most Critical Exposed Location.
To find out the most critical location under FAR §33.76(c)(1), the real bird aimed at different target points on the leading edge of blades was evaluated at a speed of 65 m/s. Figure 11(a)  It can be observed that the impact location of 80% blade height reaches the maximum value of peak impact force. As the blade damage indicated in Figure 11(b), with the single medium bird targeted at the fan blade height of 80%, it occurs to the most  Complexity severe blade plastic strain. As a result, the most critical location for a middle-sized bird should be aimed at 80% of the fan blade height. Figure 12 shows the deformation of bird oriented along the engine axis. As expected, it can be clearly observed that, prior to the impact of the bird torso, the real bird was sliced into more pieces. e orientation of bird has a direct effect on slicing action of fan blades. With respect to different attitudes, the contact area and duration of bird strikes change, resulting in a significant impact on the effect of the bird strike on rotatory blades and the possibility of blade failures. Figure 13 shows the effect of the yaw angle on impact loading history. As shown in Figure 13 Figure 14 shows the effect of pitch angle on the time histories of impact loads. As shown in Figure 14 Figure 15 shows effective plastic strains of a single blade, which undergoes the most severe plastic deformation during impact. Obviously, with the change of the bird attitude angle, the blade undergoes more severe plastic deformation. Especially, as subjected to a real bird with a yaw angle of − 45°or a pitch angle of − 60°, the blade suffers more than twice the magnitude of effective plastic strain compared with a real bird oriented along the engine centerline. It can be concluded that attitude angles would increase the possibility of fan blade failure. Moreover, the yaw angle of bird ingestion has a significant effect on the location of the blade with the most severe plastic deformation.     Figure 16 shows the effective plastic strains of the fan assembly. It can be seen that a "cusp" plastic deformation occurs at the leading edge, and the maximum plastic strain occurred to the impact location. Compared with the plastic deformation of a fan assembly during a normal impact (see Figure 16(a)), subjected to a bird with an attitude angle of α � − 45°and β � − 60°, fan blade failure occurs at the impact location, and the plastic deformation at the root of the fan blade leading edge is more significant, which would increase the risk of a fan blade release event.

Conclusions
Considering a geometric shape similar to what has already been published as a real mallard [12], a real bird model was developed. en, this paper discusses the effect of attitude angles of the realistic bird model on the soft impact damage of a full fan assembly. Besides, the stagnation pressure is represented as a criterion to calibrate the developed bird model. Results show a good correlation with available test data [26].
In accordance with certification requirements, the most critical ingestion parameters for the new bird model were investigated. It is found that the real bird aimed at the fan blade height of 80% with an ingestion speed of 65 m/s produces the most severe damage to the full fan assembly.
Complying with the critical ingestion parameters of the bird, simulations of a full fan assembly subjected to a real bird with respect to various attitude angles reveal that both yaw and pitch angles of the bird have a significant effect on the impact loading history. e blade that undergoes the highest magnitude of effective plastic strain would be confronted with a more plastic deformation than that in the case of a normal impact (attitude angle 0°), even though the impact loading decreases. Especially, as subjected to a real bird with yaw angle of − 45°or pitch angle of − 60°, the blade suffers more than twice the magnitude of effective plastic strain compared with that of attitude angle 0°, and the plastic  Complexity deformation at the root of the leading edge is more significant, which would increase the risk of a fan blade release event.
Moreover, it is invaluable to ensure the safety of commercial airlines and engine manufacture by adopting the realistic bird model with the dangerous attitude angle in the certification of engine designs for resistance to bird strikes, which will provide sufficient resistance in actual bird-strike events. However, attitude angles of the bird were set up based on the assumption in this paper. If the bird attitude could be determined through experiments or control algorithms [38][39][40][41][42], it is of great significance to investigate the effect of bird attitude on soft impact damage, as well as the distribution of flocking bird.

Data Availability
All data included in this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.