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Flexible all-plastic aircraft models built by additive manufacturing for transonic wind tunnel tests
Aerospace Science and Technology 84 (2019) 237–244
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Flexible all-plastic aircraft models built by additive manufacturing for transonic wind tunnel tests Weijun Zhu a,b,∗ , Xiaoyu Zhang a,b , Dichen Li a a b
State Key Laboratory of Manufacturing Systems Engineering, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China Collaborative Innovation Center of High-End Manufacturing Equipment, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 8 June 2018 Received in revised form 14 October 2018 Accepted 18 October 2018 Available online 23 October 2018 Keywords: Wind tunnel Aerodynamics Additive manufacturing Stereolithography Optimization
a b s t r a c t Wind tunnel testing is considered as a reliable tool, especially for the high-order non-linear aerodynamic problems of large aircraft with high-aspect-ratio wings at transonic speeds. Thanks to its capacity to manufacture complex structures quickly, the introduction of the additive manufacturing (AM) technique into the design and fabrication of testing models can improve the testing performance significantly. However, these AM-built models so far are limited to low-speed testing due to the low strength and modulus of non-metal materials, epoxy resins mostly, used in popular AM processes for aircraft models. The easy-deformation properties are usually considered as the major weakness and many methods are adopted to strengthen the plastic models for high speed tests. Taking advantage of the properties, however, this paper proposes a plastic flexible testing model with a specific pre-deformation that can be deformed into the desired state during wind tunnel tests. To obtain the pre-deformation quantitatively, an optimization formulation was developed based on the coupling of computational fluid dynamics (CFD) and computational structural dynamics (CSD). As a case study, testing models with the DLR (German Aerospace Center) F4 configuration were designed and fabricated by stereolithography (SL), a popular AM process. After the strength calibration, the plastic models were tested in a transonic wind tunnel. All the models performed normally in the harsh condition when the Mach number reached 0.85, and the resulting lift coefficients (C L ) obtained by the plastic models showed good consistence with their metallic counterparts. This indicates that the plastic models of large aircraft made by SL could be used in wind tunnel tests at transonic speeds. However, the all plastic models can only be used in a single combination of testing condition. Further studies should be conduct to extend the scope of application of the models. In conclusion, due to AM’s capacity to manufacture complex structures with low-modulus materials, flexible models could be designed and built quickly in an economic way. The method could be used in the conceptual design for configuration screening of high-aspect-ratio aircraft, and the paper would provide a new test scheme that is fast and reliable for aircraft design. © 2018 Elsevier Masson SAS. All rights reserved.
1. Introduction Large aircraft and other dynamic structures possess highaspect-ratio wings that undergo large deformations under aerodynamic loads [1]. The big aerodynamic deviations between standing and loading states make it difficult and important to accurately predict the aerodynamic performances in different operating states, under large deformation especially, to ensure high security and efficiency of large aircraft. Wind tunnel testing is considered as a reliable tool, especially for the high-order non-linear aerodynamic problems of large aircraft in high subsonic/transonic
*
Corresponding author at: State Key Laboratory of Manufacturing Systems Engineering, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China. E-mail address: [email protected] (W. Zhu). https://doi.org/10.1016/j.ast.2018.10.024 1270-9638/© 2018 Elsevier Masson SAS. All rights reserved.
speeds [2]. The design and fabrication of wind tunnel models is of an important aspect to the quality and cost of data-acquisition during testing, and remarkable researches have and are being conducted to improve the models [3,4]. Among these discussions, the introduction of additive manufacturing (AM) into model fabrication has received much attention [5,6]. Due to its impressive capacity, the technique has attracted aeronautical designers and engineers since the technique was proposed in the 1990s. The feasibility of the new method to build models for aircraft and other dynamic structures [7] has been verified by intensive studies [8,9]. However, materials handled by high-precision AM machines in an economically affordable way are limited to non-metallic materials so far, epoxy-based plastics especially. The application of the method in the fabrication of models operated at high speeds was questioned widely due to their weak mechanical properties, strength, and
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modulus. Generally, the method is limited to handle models with small aspect ratios operated at low speeds. To extend the application range, methods to enhance the material were developed [10,11]. Some efforts were devoted to strengthening the plastic by coating a thin layer of hard metals, such as nickel in the studies of Zhou et al., by electroplating [11,12]. However, it was still not strong enough when the velocity reached the subsonic region or highly reliable data was needed due to over-deformation. Another relatively simple method was commonly adopted in which a plastic shell was supported and strengthened by a metal ‘strongback’ inside [13]. The plastic-metal hybrid models, taking advantage of both traditional and emerging techniques in manufacturing, were developed and discussed by many researches [11,14–16]. Recently, a new AM technique emerged to shape continuous fiber reinforced composites [17–19], which feature a high strength/density ratio. The technique can freeform many lightweight structures with various thermal plastics with high performances, e.g. polyether ether ketone (PEEK) [17]. The technique has promising potential to efficiently build models for wind tunnel testing with high-performance materials. However, the technique is in the very early stages of development and it cannot yet be adopted to directly builds models due to its weaknesses in dimensional precision, stability of material properties, etc. Although pure plastics are weaker than metal, their strength may be adequate since the stresses in wing sections are also reduced sharply as models are scaled down, while low modulus means flexible capacity under loads that make the models act as the real aircraft. Moreover, as proved by previous studies [20], the low modulus can also enable plastic models to possess the internal load-transferring structures like the real aircraft, which is not possible if the model are made only by metals with high moduli. Compared to the metals used to build models, the plastics processed in AM feature higher damping properties, which could contribute to the security of models under unstable airflows during testing. Materials with higher damping could also help to reduce the waiting time for model stabilization to acquire data during position transition of models. Besides, new developments merging computational and experimental tests also provide an opportunity to re-assess and upgrade the traditional tools used in aircraft design. Based on the mentioned progress related to tools for aircraft design, this paper proposes a new way to design and build flexible all-plastic models of large aircraft with the AM technique for use in wind tunnel testing, and further provides a new scheme of experimental tests for aircraft design, especially in the conceptual stage. The paper details the principle and process of the new idea that are then proved by a case study. 2. Materials and method 2.1. Flexible models and materials Rigid models made of materials with high elastic moduli are widely used in wind tunnel testing. Though they are designated as ‘rigid’, deviation of aerodynamic contours occurs due to the ineluctable deformation of models under loads during testing. Thus, as shown in Fig. 1, the deviation between the actual and target contours of rigid models makes it necessary to conduct “deformation correction” to map the acquired data to the target contour. Flexible models could be helpful to reduce the time and risk related with the data correction process. As demonstrated in Fig. 1, the actual contour of the flexible model resulting from the original contour under loads during testing can match the target contour exactly when the original contour of the model has an anticipated deformation from the target contour in the opposed direc-
Fig. 1. Deformation of rigid and flexible models during testing. Table 1 Mechanical properties of materials used in model-fabricating. Properties
Plastic (14120)
Aluminum (7A04)
Density, kg m−3 Young’s modulus E, GPa Poisson ratio ν Tensile strength, MPa Flexural strength, MPa Flexural modulus, GPa Allowable stress (at safety factor of 2), MPa
1120 2.46 0.38 46.0 69.0 2.25 23.0
2780 74.0 0.30 600 N. A. N. A. 300
tion to the aerodynamic loads. Given the complete consistency of the model contours with the target contours, the need for data correction caused by contour deviation could be eliminated. The two prerequisites needed to eliminate contour deviation are manufacturing techniques to build models with precise distribution of stiffness and computational methods capable of obtaining the required pre-deformation of the model from the target contour. Stereolithography (SL), one of the mainstreaming processes in AM technology, features the capacity to build articles of complicated internal and external structures with a UV-curable epoxy-based plastic. A comparison of the mechanical properties of the plastic and aluminum commonly used in aircraft framework is listed in Table 1. The low elastic modulus of the plastic widens the deformation range of the flexible models, which makes it easier to calculate the pre-deformation; additionally, the powerful fabricating capacity can ensure the manufacturability of the designed models in complicated structures with precise stiffness distribution. 2.2. Calculation of the model pre-deformation The design process and the schematic diagram of the new method are demonstrated in Fig. 2. The aim of the process is to obtain the aerodynamic contour of the model for fabrication (defined as the ‘designed contour’ in this paper) that can transform into the ‘target contour’ under aerodynamic loads in a particular operation state (defined as the ‘design point’). The target contour is often a configuration of the aircraft that is expected to have good aerodynamic performance at the design point. As mentioned above, the AM-built plastic models are flexible, so the original contour for fabrication should be pre-deformed downward to a suitable position that can deform upward back to the target contour under aerodynamic loads, which makes it is possible to acquire data for the deformed (target) contour without static aeroelastic and deformation corrections. To obtain the original contour quantitatively, an optimization formulated as equation (1) was set up based on the coupling of computational fluid dynamics (CFD) and computational structural dynamics (CSD).
minimize
f (x).
(1)
Herein, the objective function f (x) was defined as the summary error of the contour deviation between the obtained and target
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Table 2 Testing and aerodynamic parameters at the design point. Parameter
Value
Mach numbera Ma Angle of attackb α , ◦ Yaw angle β , ◦ Roll angle γ , ◦ Reynolds number Re Total pressure P 0 , kPa Static pressure P , kPa Dynamic pressure P q , kPa
0.6, 0.85 −2, −1, 0, 1, 2 0 0 4.3 × 105 101 79.6 20.0
a b
Only Ma = 0.6 is at the design point. Only α = 0◦ is at the design point.
Fig. 2. Design process (a) and schematic diagram (b) to obtain the designed contour.
contours. In theory, the error calculation should take into account all the deformations of all the nodes in the contour mesh, but the task would be so complicated that it would not be feasible [21]. As depicted in Fig. 2(b), this paper adopted a simple method. Only the deformations that predominantly influence aerodynamic properties at crucial nodes were calculated, which included the translation deformation along the z axis of the model coordinate and the rotation deformation around the torsion center in several sections of the wing (indicated as the ith n section in the paper). In summary, the simplified objective function is expressed as equation (2).
f (x) = αθ
n i
| θ i | + α z
n
|zi |.
Fig. 3. The wing contour obtained from the optimization and contours nearby.
(2)
i
The variation vector x defining a particular original contour that is ready for the error calculation was determined in a similar way to the objective function. As mentioned, the original contours were obtained from the target contours by pre-deformation. Like the error between the obtained and target contours, difference exists between the original contour and the target contour. Similarly, the original contour can be defined by the contour deviation from the target, which is expressed by the variation vector x as equation (3).
x = ( z1 , z2 , . . . , zn , θ1 , θ2 , . . . , θn ).
(3)
2.3. Design of the flexible models The F4 is a simplified wing-fuselage geometry with an aspect ratio of 9.5, which indicative of large aircraft, and it is widely used as a standard to verify CFD codes for aerodynamic performance [22]. Plastic F4 models with fuselage length of 0.298 m and span length of 0.293 m were designed according to above procedure. A tight coupling computation of CFD/CSD was performed to solve the unsteady fluid Navier–Stokes equation and the structural static equilibrium equation [23]. During the coupling, the virtual surface method [24] was employed to transfer fluid/structure interference data. The testing and aerodynamic parameters at the design point are listed in Table 2.
Fig. 4. The model structure.
The F4 model contour adopted in reference [22] was defined as the target contour. Following the process mentioned above, the designed contour was obtained as indicated with No. 3 in Fig. 3. Other contours with over-deformation (No. 1 and No. 2) and under-deformation (No. 4 and No. 5) around the optimized contour (No. 3) were designated for comparison. The external geometries of the models were defined by the designed contour obtained above, while internal structures were designed according to the balance used in the tests. As demonstrated in Fig. 4, a metal sleeve was inserted into the model fuselage to act as the joint between the plastic model and the metal balance. 2.4. Model calibration To ensure the safety of the designed model, the calibration of strength/stiffness and resonance clearance was conducted numerically. The resistance performance of the model in different states was investigated in combination with CFD and CSD. For calibration of resonance clearance, the first Eigen frequency of the model– balance–support system was calculated via finite element analysis (FEA) and compared with the peak frequency of the wind in tunnel.
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Fig. 5. Strength calibration of plastic models.
Fig. 6. Fabricating of the plastic models.
As summarized in Table 2, the incoming pressure, temperature, velocity, and other fluid-field parameters were given according to the test states. After computations, the pressure and velocity fields on the model (demonstrated in Fig. 5(a)) were abstracted and transported to the subsequent CSD as the aerodynamic loads on the model structure. Based on the CFD analysis, a CSD study on the hybrid model was implemented to calibrate its strength and stiffness. Fig. 5(b) demonstrates the distributions of the stress and deformation on both the metal core and the plastic shell. The maximum Von Mises equivalent stresses and deformations are highlighted in Fig. 5(b). Giving a safety factor of 2, the allowable strength listed in Table 1 for the plastic is 23.0 MPa. It is obvious that the maximal Von Mises equivalent stresses were smaller than the allowable strength, which made it clear that the hybrid model was safe in all the testing conditions.
Fig. 7. The assembled model installed in the tunnel.
2.5. Model fabrication After the design procedure, the models were fabricated based on stereolithography (SPS600B apparatus from Shaanxi Hengtong intelligent machines Co., Ltd, Xi’an, China). The fuselage axis was selected as the fabricating orientation, as shown in Fig. 6(a). Other parameters of the apparatus remained default to ensure the material properties were stable. The model was then built automatically in SPS600B with SOMOS 14120 (DSM Co., Ltd, Heerlen, Netherlands). After washing off the excess resin, the plastic models (shown in Fig. 6(b)) were treated by post-curing for 50 minutes and sandpapering to obtain the desired material properties (as listed in Table 1) and surface roughness (Ra = 1.4 μm in the case). 2.6. Model testing As shown in Fig. 7, the assembled hybrid model was installed onto the support in the tunnel upside down. A six-component balance was inserted between the model and the support, from which force data was acquired during testing. The models were all tested in a transonic wind tunnel with the testing section of
Fig. 8. Measurement setup of the model fabrication accuracy.
0.6 m × 0.6 m (FL-21 tunnel in State Key Laboratory of Aerodynamics, Mianyang, China). 3. Results and discussion 3.1. Model fabrication 3.1.1. Fabrication precision In order to verify the dimensional accuracy of the SL-fabricated plastic models, several feature sizes of the model were measured, as shown in Fig. 8. These feature sizes have a significant impact on the aerodynamic characteristics of the models, can represent the fabrication accuracy of the SL process, and are easy to measure through the vernier caliper.
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Table 3 Results of the model fabrication accuracy.
Designed (mm) Fabricated (mean, mm) Error (mean, mm) Error (%)
Spanwise length
Fuselage length
Chord lengthwing root
Chord lengthwing tip
144.35 144.60 0.25 0.17%
149.10 148.88 −0.22 −0.15%
7.65 7.60 −0.05 −0.61%
25.43 25.32 −0.11 −0.43%
The comparison of measured values and design values of the feature sizes are shown in Table 3. In general, the dimensional deviations of the plastic models conform to the accuracy parameter of the SL equipment provider, that is, when feature sizes are less than 100 mm, the deviations are ±0.1 mm, and when feature sizes are larger than 100 mm, the deviations are ±0.1%. However, feature sizes of the plastic models herein greater than 100 mm, such as the spanwise length and the fuselage length, have deviations greater than 0.1%. The main reason may be the fabrication orientation and supporting method used to fabricate the models. In order to ensure the dimensional accuracy and surface quality of the main aerodynamic components (wings) of the models, the fuselage direction was adopted to fabricate the models by SL, as shown in Fig. 6(b). When the models were fabricated in this direction, the models themselves had fewer support points and required more auxiliary support structures. This can cause instability of the models during SL process, which could affect the dimensional accuracy to a certain extent. 3.1.2. Stiffness of materials Material stiffness is the key parameter to determine the predeformation of the flexible aircraft. The property fluctuation of material stiffness was assessed by comparing the tested and calculated deformations of the all-plastic parts built by SL under a given loading condition. A wing box (depicted in Fig. 9) was selected
Fig. 9. The wing box selected for the stiffness calibration.
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as the objective since wing boxes are the typical loading-bearing components of aircraft. A non-contact optical testing system (XJTUSD, Xi’an, China) was adopted to acquire the deformation of the wing box. The Cartesian coordinates of the wing box on selected points were measured and the deformation was calculated by comparing the values before and after loading. The configurations for physical testing and simulating computing (FEM) are depicted in Fig. 10. The same loading condition was brought to both the physical and simulating models, in which concentrated Z-direction forces of 20 N were applied to the tip of the wing box. The same loading condition was brought to both the physical and simulating wing boxes, in which concentrated Z-direction forces of 20 N were applied to the tip of the wing box. As shown in Fig. 11, the deformations of the physical and simulating models were very consistent. The maximum error of 3.4% means the property fluctuation of material stiffness is very small and acceptable for the model design. The main factors causing the difference in deformation include testing operation errors, dimensional deviations or material property deviations. According to the above dimensional accuracy measurement, the fabrication error of the plastic model processed by SL is about 0.1%. Deviations in material properties, especially variations in the elastic modulus of the material, may be the main factors contributing to this deformation difference. Because of the layering of materials caused by layer-by-layer processing, the material properties of the parts processed by AM techniques are highly correlated with the fabrication orientation, such as Selective Laser Sintering (SLS) process [25], Fused Deposition Modeling (FDM) process [26]. However, due to the chemical bonding rather than the physical bonding principle, the SL process used in this paper has a weak correlation between material properties and fabrication orientation (as shown in Fig. 12), which is about 4.2% [27] that is close to the above deformation difference of 3.4%.
3.1.3. Economic issue As mentioned above, the all-plastic model was feasible to be used in wind tunnel testing and could be an alternative of metal models. In the section, the economic issue of the all plastic model over metal ones will be further studied. Items for comparison are listed in Table 4. The number of processes of AM process is 4, which included stereolithography building, removing of supports and uncured resin, post-curing and sanding. For the machining process, however, the number is about 20, which mainly due to segmentation of metal models into parts. In the sense of Dimensional accuracy, the two technologies are roughly equivalent, the AM being slightly better. While, AM has significant advantages for time and cost to fabricate models.
Fig. 10. The calibration configuration for the material stiffness.
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Fig. 11. The deformations under 20 N loads.
Fig. 12. Effect of fabrication orientation on elastic modulus of materials [27].
Table 4 The economic comparison of model fabrication methods. Item
Additive manufacturing
Machining
Number of processes Dimensional accuracy (mm) Time (h) Cost (RMB)
4 0.1–0.5 10 2000
∼20 0.05–0.25 500 50000
3.2. Model testing All the models performed normally and were not damaged during tests, even in the harsh conditions when Ma = 0.85, AOA = 0◦ and Ma = 0.6, AOA = 2◦ , which indicated that the plastic models of large aircraft made by SL could be used in wind tunnel tests at transonic speeds. As shown in Fig. 13(b), no permanent deformation the plastic models As shown in Fig. 13(b), there is no obvious residual deformation on the plastic model after unloading when the test finished. This observation is easy to understand if the following factors are considered. On the one hand, the plastic used in the model is a typical brittle material that featured a two-stage stress–strain curve: recoverable elastic deformation and brittle fracture. The material does not exhibit obvious plastic characteristics and is not easy to produce residual deformation. On the other hand, the typical temperature of the wind tunnel test is lower than room temperature, which further increases the brittleness of the material while limits its plasticity, thereby further reducing the residual deformation of the material. Curves of the lift (C L ) and drag (C D ) coefficients relative to the angle of attack (α ) at Mach number of 0.6 are shown in Fig. 14. The data denoted as No. 1, No. 2, No. 3, No. 4 and No. 5 were obtained from the plastic models that were designed and fabricated in the current work, while the data marked NLR, ONERA, and DRA were from metal models test in the three European wind tunnels. The metal models are four times bigger than their plastic counterparts. All the data obtained had been treated with static aeroelastic and deformation corrections.
3.2.1. Aerodynamics of the plastic models at the design point The No. 3 plastic model was at the design point when Ma = 0.6 and AOA = 0◦ . Table 5 lists C L and C D at the design point obtained from different tunnels. As expected, the C L of the model with the designed contour (denoted as No. 3) was very consistent with the mean value from other tunnels at the design point (0.445 to 0.440, 1.1%). Among all the C L values obtained in the paper, the C L from the No. 3 contour was the biggest, which indicates the target contour possessed the best aerodynamic performance as it was designed [22]. The small error and the good aerodynamic performance of the plastic model at the design point validates the feasibility of the method. The main cause of the deviation of the lift coefficient (1.1%) is the dimensional error of the model (0.2%) and the deviation of material properties (4.2%). In order to further reduce the deviation of the lift coefficient, it is necessary to improve the dimensional accuracy and reduce the material property deviation. Among them, the main measure to reduce the material property deviation is to eliminate the relativity between the fabrication orientation and the material properties. For C D , however, considerable deviations from reported data are observed both in Fig. 14 and Table 4. First, as C D was smaller than C L by an order of magnitude, the influence of C D on the model structures was ignored during the optimization. Another notable reason is the difference of the Reynolds number (Re). The testing Re for the plastic models in the paper, 4.3 × 105 , was much smaller than that of reported tests (3 × 106 ) for metal models [22], which could be one of the main causes of the increased C D in the paper. In addition, the roughness of model surfaces introduced by the layer-additive fabrication fashion of AM could also contribute to the increase of C D [28]. 3.2.2. Aerodynamics of the plastic models at the non-design points Qualitatively, the C L –α curves of the plastic models are nearly linear, like those obtained from metal models [22]. The trends of C D –α curves are also similar between plastic models and metal models. Furthermore, the C L values of the No. 1 and No. 2 models and those of the No. 4 and No. 5 models were closer to each other, which corresponds to the fact that they were from models with under-deformation and over-deformation contours, respectively (as shown in Fig. 3). When the angle of attack increased from −2◦ to 2◦ , the lift coefficient errors of the No. 3 plastic model relative to the metal models were −6.9%, −3.2%, 1.1%, 6.1%, and 15.3%, respectively. The larger the absolute value of the angle of attack, the greater the deviation of the lift coefficient. This is probably due to the unintended deformations of the lift components (mainly the wings) of the all-plastic models. The fact that plastic models have large aerodynamic errors at non-design points indicates that there are limits on the scope of application of such models. Based on the results herein, it is necessary to change plastic models for different testing conditions of
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Fig. 13. Video Screenshots of the plastics models during (a) AOA test and (b) Ma number test.
Fig. 14. Curves of lift (a) and drag (b) coefficients relative to angle of attack at Ma 0.6. Table 5 Comparison of aerodynamic force coefficients at the design point from different tests. Test
CL CD
Plastic models in FL-21 tunnel
Metallic models in other tunnels
1
2
3
4
5
NLR
ONERA
DRA
Mean
0.404 0.0314
0.391 0.0305
0.445 0.0319
0.428 0.0321
0.430 0.0314
0.443 0.0258
0.441 0.0251
0.437 0.0249
0.440 0.0253
AOA and Ma. This is not a big problem from an economic point of view, considering that the processing cost of plastic models is extremely low, as shown in Table 4. However, frequent replacement of models has a significant negative effect on the cost/time and data consistency of the wind tunnel test. Therefore, measures need to be taken to increase the scope of application of a single model. On the one hand, the wings of the plastic models in this paper are in a full-solid structure. In the future research, heterogeneous
structures, such as hollow wing structures and multi-material wing structures, can be used to simulate the force transmission characteristics of real wings. On the other hand, the design point of the model in this paper only considers a single combination of conditions (Ma = 0.6, AOA = 0◦ ). In future research, multiple conditions can be combined as the objective function during the model design, which is potential to improve the scope of application of the model.
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4. Conclusion Plastic models in the DLR-F4 configuration were designed with pre-deformed contours, obtained based on CFD/CSD coupling computation, which can transform to the target contour that interests designers under aerodynamic loads. The models were then fabricated efficiently based on the additive manufacturing technique and tested in a wind tunnel. As the plastic models were undamaged at Mach numbers up to 0.85, which is in the range of the typical cruise speeds for commercial large aircraft, the new method to design and build models can be used in the conceptual design for configuration screening of aircraft of this kind. Furthermore, the cost and time reduction, made by the introduction of AM due to its fabrication flexibility, can potentially improve the R&D efficiency of aircraft. Thanks to the low modulus of its materials and high efficiency of its process, the AM technique not only can help to efficiently build flexible models but also provide a new testing scheme for the conceptual design of aircraft. At this point, the all plastic models can only be used in a single combination of testing condition. Further studies should be conduct to extend the scope of application of the models. Conflict of interest statement The authors declare no competing financial interest. Acknowledgements This work was supported by the National Natural Science Foundation of China, P. R. China [Grant No. 51505457], and the Open Fund of State Key Laboratory of Manufacturing Systems Engineering, P. R. China [Grant No. SKLMS2016013], and the Fundamental Research Funds for the Central Universities, P. R. China. The authors would like to thank Dr. Yan Sun and Dr. Zhengyu Zhang in State Key Laboratory of Aerodynamics, P. R. China for the assistance in model design and wind tunnel testing. We would like to thank LetPub www.letpub.com for providing linguistic assistance during the preparation of this manuscript. References [1] S. Zhou, X.G. Hua, Z.Q. Chen, W. Chen, Experimental investigation of correction factor for VIV amplitude of flexible bridges from an aeroelastic model and its 1:1 section model, Eng. Struct. 141 (2017) 263–271. [2] K. Fujii, Progress and future prospects of CFD in aerospace – wind tunnel and beyond, Prog. Aerosp. Sci. 41 (2005) 455–470. [3] A.C.K. Springer, F. Roberts, Application of rapid prototyping models to transonic wind-tunnel testing, in: 35th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA 97-0988, 1997. [4] G. Timothy, Process improvement for aerodynamic model development, in: AIAA Modeling and Simulation Technologies Conference and Exhibit, AIAA, Honolulu, Hawaii, 2008. [5] A.L. Heyes, D.A.R. Smith, Rapid technique for wind-tunnel model manufacture, J. Aircr. 41 (2004) 413–415. [6] C. Black, K.V. Singh, S. Goodman, A. Altman, R. Kolonay, Design, fabrication and testing of 3D printed wings for rapid evaluation of aeroelastic performance, in:
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[12] Z. Zhou, D. Li, J. Zeng, Z. Zhang, Rapid fabrication of metal-coated composite stereolithography parts, Proc. Inst. Mech. Eng., B J. Eng. Manuf. 221 (2007) 1431–1440. [13] C. Wang, G. Yin, Z. Zhang, S. Wang, T. Zhao, Y. Sun, et al., Design and fabrication of an aircraft static aeroelastic model based on rapid prototyping, Rapid Prototyping J. 21 (2015) 34–42. [14] C. Tyler, Richard J. Schwartz, G. Fleming, S. Fonov, Rapid Prototyping-unmanned Combat Air Vehicle (UCAV)/Sensorcraft, Air Force Research Laboratory, 2008, AFRL-RB-WP-TR-2008-3034. [15] C. Tyler, R.J. Schwartz, G. Fleming, S. Fonov, Directorate AFRLAV, Center LR et al., Rapid Prototyping-Unmanned Combat Air Vehicle (UCAV)/Sensorcraft, Air Force Research Laboratory, 2008. [16] D. Yang, Z. Zhang, Y. Sun, W. Zhu, A preliminary design and manufacturing study of hybrid lightweight high-speed wind-tunnel models, Rapid Prototyping J. 17 (2011) 10. [17] M. Luo, X. Tian, W. Zhu, D. Li, Controllable interlaminar shear strengths and crystallinity of PEEK components by laser assisted material extrusion, J. Mater. Res. (2018). [18] Z. Hou, X. Tian, J. Zhang, D. Li, 3D printed continuous fibre reinforced composite corrugated structure, Compos. Struct. 184 (2018) 1005–1010. [19] W. Hao, Y. Liu, H. Zhou, H. Chen, D. Fang, Preparation and characterization of 3D printed continuous carbon fiber reinforced thermosetting composites, Polym. Test. 65 (2018) 29–34. [20] W.J. Zhu, D.C. Li, Z.Y. Zhang, K. Ren, X.L. Zhao, D.G. Yang, et al., Design and fabrication of stereolithography-based aeroelastic wing models, Rapid Prototyping J. 17 (2011) 298–307. [21] M. French, F.E. Eastep, Aeroelastic model design using parameter identification, J. Aircr. 33 (1996) 198–202. [22] Development AGfAR, A Selection of Experimental Test Cases for the Validation of CFD Codes, Advisory Group for Aerospace Research & Development, Neuillysur-Seine, France, 1994. [23] R. Kamakoti, W. Shyy, Fluid-structure interaction for aeroelastic applications, Prog. Aerosp. Sci. 40 (2004) 535–558. [24] V. Vipperla, T. Victoria, Force and displacement transformations for aerostructure interaction analysis, in: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA, Albany, New York, 2004. [25] B.R. McKnight, J.E. Boyer, P.K. Nardozzo, A. Cortopassi, Design and testing of an additively manufactured advanced hybrid rocket motor propulsion unit for CubeSats (PUC), in: 51st AIAA/SAE/ASEE Joint Propulsion Conference, American Institute of Aeronautics and Astronautics, 2015. [26] K.V. Singh, F. Khan, J. Veta, A.K. Singh, Asme. Influence of printing orientation on the dynamic characteristics and vibration behavior of 3D printed structures, in: Proceedings of the Asme International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2017, vol. 1, Amer Soc Mechanical Engineers, New York, 2017. [27] Inc. F., Validating Isotropy in SLA 3D Printing, Formlabs Inc., 2016. [28] C. Aghanajafi, S. Daneshmand, A.A. Nadooshan, Influence of layer thickness on the design of rapid-prototyped models, J. Aircr. 46 (2009) 981–987.
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Aerospace Science and Technology www.elsevier.com/locate/aescte
Flexible all-plastic aircraft models built by additive manufacturing for transonic wind tunnel tests Weijun Zhu a,b,∗ , Xiaoyu Zhang a,b , Dichen Li a a b
State Key Laboratory of Manufacturing Systems Engineering, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China Collaborative Innovation Center of High-End Manufacturing Equipment, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 8 June 2018 Received in revised form 14 October 2018 Accepted 18 October 2018 Available online 23 October 2018 Keywords: Wind tunnel Aerodynamics Additive manufacturing Stereolithography Optimization
a b s t r a c t Wind tunnel testing is considered as a reliable tool, especially for the high-order non-linear aerodynamic problems of large aircraft with high-aspect-ratio wings at transonic speeds. Thanks to its capacity to manufacture complex structures quickly, the introduction of the additive manufacturing (AM) technique into the design and fabrication of testing models can improve the testing performance significantly. However, these AM-built models so far are limited to low-speed testing due to the low strength and modulus of non-metal materials, epoxy resins mostly, used in popular AM processes for aircraft models. The easy-deformation properties are usually considered as the major weakness and many methods are adopted to strengthen the plastic models for high speed tests. Taking advantage of the properties, however, this paper proposes a plastic flexible testing model with a specific pre-deformation that can be deformed into the desired state during wind tunnel tests. To obtain the pre-deformation quantitatively, an optimization formulation was developed based on the coupling of computational fluid dynamics (CFD) and computational structural dynamics (CSD). As a case study, testing models with the DLR (German Aerospace Center) F4 configuration were designed and fabricated by stereolithography (SL), a popular AM process. After the strength calibration, the plastic models were tested in a transonic wind tunnel. All the models performed normally in the harsh condition when the Mach number reached 0.85, and the resulting lift coefficients (C L ) obtained by the plastic models showed good consistence with their metallic counterparts. This indicates that the plastic models of large aircraft made by SL could be used in wind tunnel tests at transonic speeds. However, the all plastic models can only be used in a single combination of testing condition. Further studies should be conduct to extend the scope of application of the models. In conclusion, due to AM’s capacity to manufacture complex structures with low-modulus materials, flexible models could be designed and built quickly in an economic way. The method could be used in the conceptual design for configuration screening of high-aspect-ratio aircraft, and the paper would provide a new test scheme that is fast and reliable for aircraft design. © 2018 Elsevier Masson SAS. All rights reserved.
1. Introduction Large aircraft and other dynamic structures possess highaspect-ratio wings that undergo large deformations under aerodynamic loads [1]. The big aerodynamic deviations between standing and loading states make it difficult and important to accurately predict the aerodynamic performances in different operating states, under large deformation especially, to ensure high security and efficiency of large aircraft. Wind tunnel testing is considered as a reliable tool, especially for the high-order non-linear aerodynamic problems of large aircraft in high subsonic/transonic
*
Corresponding author at: State Key Laboratory of Manufacturing Systems Engineering, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China. E-mail address: [email protected] (W. Zhu). https://doi.org/10.1016/j.ast.2018.10.024 1270-9638/© 2018 Elsevier Masson SAS. All rights reserved.
speeds [2]. The design and fabrication of wind tunnel models is of an important aspect to the quality and cost of data-acquisition during testing, and remarkable researches have and are being conducted to improve the models [3,4]. Among these discussions, the introduction of additive manufacturing (AM) into model fabrication has received much attention [5,6]. Due to its impressive capacity, the technique has attracted aeronautical designers and engineers since the technique was proposed in the 1990s. The feasibility of the new method to build models for aircraft and other dynamic structures [7] has been verified by intensive studies [8,9]. However, materials handled by high-precision AM machines in an economically affordable way are limited to non-metallic materials so far, epoxy-based plastics especially. The application of the method in the fabrication of models operated at high speeds was questioned widely due to their weak mechanical properties, strength, and
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modulus. Generally, the method is limited to handle models with small aspect ratios operated at low speeds. To extend the application range, methods to enhance the material were developed [10,11]. Some efforts were devoted to strengthening the plastic by coating a thin layer of hard metals, such as nickel in the studies of Zhou et al., by electroplating [11,12]. However, it was still not strong enough when the velocity reached the subsonic region or highly reliable data was needed due to over-deformation. Another relatively simple method was commonly adopted in which a plastic shell was supported and strengthened by a metal ‘strongback’ inside [13]. The plastic-metal hybrid models, taking advantage of both traditional and emerging techniques in manufacturing, were developed and discussed by many researches [11,14–16]. Recently, a new AM technique emerged to shape continuous fiber reinforced composites [17–19], which feature a high strength/density ratio. The technique can freeform many lightweight structures with various thermal plastics with high performances, e.g. polyether ether ketone (PEEK) [17]. The technique has promising potential to efficiently build models for wind tunnel testing with high-performance materials. However, the technique is in the very early stages of development and it cannot yet be adopted to directly builds models due to its weaknesses in dimensional precision, stability of material properties, etc. Although pure plastics are weaker than metal, their strength may be adequate since the stresses in wing sections are also reduced sharply as models are scaled down, while low modulus means flexible capacity under loads that make the models act as the real aircraft. Moreover, as proved by previous studies [20], the low modulus can also enable plastic models to possess the internal load-transferring structures like the real aircraft, which is not possible if the model are made only by metals with high moduli. Compared to the metals used to build models, the plastics processed in AM feature higher damping properties, which could contribute to the security of models under unstable airflows during testing. Materials with higher damping could also help to reduce the waiting time for model stabilization to acquire data during position transition of models. Besides, new developments merging computational and experimental tests also provide an opportunity to re-assess and upgrade the traditional tools used in aircraft design. Based on the mentioned progress related to tools for aircraft design, this paper proposes a new way to design and build flexible all-plastic models of large aircraft with the AM technique for use in wind tunnel testing, and further provides a new scheme of experimental tests for aircraft design, especially in the conceptual stage. The paper details the principle and process of the new idea that are then proved by a case study. 2. Materials and method 2.1. Flexible models and materials Rigid models made of materials with high elastic moduli are widely used in wind tunnel testing. Though they are designated as ‘rigid’, deviation of aerodynamic contours occurs due to the ineluctable deformation of models under loads during testing. Thus, as shown in Fig. 1, the deviation between the actual and target contours of rigid models makes it necessary to conduct “deformation correction” to map the acquired data to the target contour. Flexible models could be helpful to reduce the time and risk related with the data correction process. As demonstrated in Fig. 1, the actual contour of the flexible model resulting from the original contour under loads during testing can match the target contour exactly when the original contour of the model has an anticipated deformation from the target contour in the opposed direc-
Fig. 1. Deformation of rigid and flexible models during testing. Table 1 Mechanical properties of materials used in model-fabricating. Properties
Plastic (14120)
Aluminum (7A04)
Density, kg m−3 Young’s modulus E, GPa Poisson ratio ν Tensile strength, MPa Flexural strength, MPa Flexural modulus, GPa Allowable stress (at safety factor of 2), MPa
1120 2.46 0.38 46.0 69.0 2.25 23.0
2780 74.0 0.30 600 N. A. N. A. 300
tion to the aerodynamic loads. Given the complete consistency of the model contours with the target contours, the need for data correction caused by contour deviation could be eliminated. The two prerequisites needed to eliminate contour deviation are manufacturing techniques to build models with precise distribution of stiffness and computational methods capable of obtaining the required pre-deformation of the model from the target contour. Stereolithography (SL), one of the mainstreaming processes in AM technology, features the capacity to build articles of complicated internal and external structures with a UV-curable epoxy-based plastic. A comparison of the mechanical properties of the plastic and aluminum commonly used in aircraft framework is listed in Table 1. The low elastic modulus of the plastic widens the deformation range of the flexible models, which makes it easier to calculate the pre-deformation; additionally, the powerful fabricating capacity can ensure the manufacturability of the designed models in complicated structures with precise stiffness distribution. 2.2. Calculation of the model pre-deformation The design process and the schematic diagram of the new method are demonstrated in Fig. 2. The aim of the process is to obtain the aerodynamic contour of the model for fabrication (defined as the ‘designed contour’ in this paper) that can transform into the ‘target contour’ under aerodynamic loads in a particular operation state (defined as the ‘design point’). The target contour is often a configuration of the aircraft that is expected to have good aerodynamic performance at the design point. As mentioned above, the AM-built plastic models are flexible, so the original contour for fabrication should be pre-deformed downward to a suitable position that can deform upward back to the target contour under aerodynamic loads, which makes it is possible to acquire data for the deformed (target) contour without static aeroelastic and deformation corrections. To obtain the original contour quantitatively, an optimization formulated as equation (1) was set up based on the coupling of computational fluid dynamics (CFD) and computational structural dynamics (CSD).
minimize
f (x).
(1)
Herein, the objective function f (x) was defined as the summary error of the contour deviation between the obtained and target
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Table 2 Testing and aerodynamic parameters at the design point. Parameter
Value
Mach numbera Ma Angle of attackb α , ◦ Yaw angle β , ◦ Roll angle γ , ◦ Reynolds number Re Total pressure P 0 , kPa Static pressure P , kPa Dynamic pressure P q , kPa
0.6, 0.85 −2, −1, 0, 1, 2 0 0 4.3 × 105 101 79.6 20.0
a b
Only Ma = 0.6 is at the design point. Only α = 0◦ is at the design point.
Fig. 2. Design process (a) and schematic diagram (b) to obtain the designed contour.
contours. In theory, the error calculation should take into account all the deformations of all the nodes in the contour mesh, but the task would be so complicated that it would not be feasible [21]. As depicted in Fig. 2(b), this paper adopted a simple method. Only the deformations that predominantly influence aerodynamic properties at crucial nodes were calculated, which included the translation deformation along the z axis of the model coordinate and the rotation deformation around the torsion center in several sections of the wing (indicated as the ith n section in the paper). In summary, the simplified objective function is expressed as equation (2).
f (x) = αθ
n i
| θ i | + α z
n
|zi |.
Fig. 3. The wing contour obtained from the optimization and contours nearby.
(2)
i
The variation vector x defining a particular original contour that is ready for the error calculation was determined in a similar way to the objective function. As mentioned, the original contours were obtained from the target contours by pre-deformation. Like the error between the obtained and target contours, difference exists between the original contour and the target contour. Similarly, the original contour can be defined by the contour deviation from the target, which is expressed by the variation vector x as equation (3).
x = ( z1 , z2 , . . . , zn , θ1 , θ2 , . . . , θn ).
(3)
2.3. Design of the flexible models The F4 is a simplified wing-fuselage geometry with an aspect ratio of 9.5, which indicative of large aircraft, and it is widely used as a standard to verify CFD codes for aerodynamic performance [22]. Plastic F4 models with fuselage length of 0.298 m and span length of 0.293 m were designed according to above procedure. A tight coupling computation of CFD/CSD was performed to solve the unsteady fluid Navier–Stokes equation and the structural static equilibrium equation [23]. During the coupling, the virtual surface method [24] was employed to transfer fluid/structure interference data. The testing and aerodynamic parameters at the design point are listed in Table 2.
Fig. 4. The model structure.
The F4 model contour adopted in reference [22] was defined as the target contour. Following the process mentioned above, the designed contour was obtained as indicated with No. 3 in Fig. 3. Other contours with over-deformation (No. 1 and No. 2) and under-deformation (No. 4 and No. 5) around the optimized contour (No. 3) were designated for comparison. The external geometries of the models were defined by the designed contour obtained above, while internal structures were designed according to the balance used in the tests. As demonstrated in Fig. 4, a metal sleeve was inserted into the model fuselage to act as the joint between the plastic model and the metal balance. 2.4. Model calibration To ensure the safety of the designed model, the calibration of strength/stiffness and resonance clearance was conducted numerically. The resistance performance of the model in different states was investigated in combination with CFD and CSD. For calibration of resonance clearance, the first Eigen frequency of the model– balance–support system was calculated via finite element analysis (FEA) and compared with the peak frequency of the wind in tunnel.
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Fig. 5. Strength calibration of plastic models.
Fig. 6. Fabricating of the plastic models.
As summarized in Table 2, the incoming pressure, temperature, velocity, and other fluid-field parameters were given according to the test states. After computations, the pressure and velocity fields on the model (demonstrated in Fig. 5(a)) were abstracted and transported to the subsequent CSD as the aerodynamic loads on the model structure. Based on the CFD analysis, a CSD study on the hybrid model was implemented to calibrate its strength and stiffness. Fig. 5(b) demonstrates the distributions of the stress and deformation on both the metal core and the plastic shell. The maximum Von Mises equivalent stresses and deformations are highlighted in Fig. 5(b). Giving a safety factor of 2, the allowable strength listed in Table 1 for the plastic is 23.0 MPa. It is obvious that the maximal Von Mises equivalent stresses were smaller than the allowable strength, which made it clear that the hybrid model was safe in all the testing conditions.
Fig. 7. The assembled model installed in the tunnel.
2.5. Model fabrication After the design procedure, the models were fabricated based on stereolithography (SPS600B apparatus from Shaanxi Hengtong intelligent machines Co., Ltd, Xi’an, China). The fuselage axis was selected as the fabricating orientation, as shown in Fig. 6(a). Other parameters of the apparatus remained default to ensure the material properties were stable. The model was then built automatically in SPS600B with SOMOS 14120 (DSM Co., Ltd, Heerlen, Netherlands). After washing off the excess resin, the plastic models (shown in Fig. 6(b)) were treated by post-curing for 50 minutes and sandpapering to obtain the desired material properties (as listed in Table 1) and surface roughness (Ra = 1.4 μm in the case). 2.6. Model testing As shown in Fig. 7, the assembled hybrid model was installed onto the support in the tunnel upside down. A six-component balance was inserted between the model and the support, from which force data was acquired during testing. The models were all tested in a transonic wind tunnel with the testing section of
Fig. 8. Measurement setup of the model fabrication accuracy.
0.6 m × 0.6 m (FL-21 tunnel in State Key Laboratory of Aerodynamics, Mianyang, China). 3. Results and discussion 3.1. Model fabrication 3.1.1. Fabrication precision In order to verify the dimensional accuracy of the SL-fabricated plastic models, several feature sizes of the model were measured, as shown in Fig. 8. These feature sizes have a significant impact on the aerodynamic characteristics of the models, can represent the fabrication accuracy of the SL process, and are easy to measure through the vernier caliper.
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Table 3 Results of the model fabrication accuracy.
Designed (mm) Fabricated (mean, mm) Error (mean, mm) Error (%)
Spanwise length
Fuselage length
Chord lengthwing root
Chord lengthwing tip
144.35 144.60 0.25 0.17%
149.10 148.88 −0.22 −0.15%
7.65 7.60 −0.05 −0.61%
25.43 25.32 −0.11 −0.43%
The comparison of measured values and design values of the feature sizes are shown in Table 3. In general, the dimensional deviations of the plastic models conform to the accuracy parameter of the SL equipment provider, that is, when feature sizes are less than 100 mm, the deviations are ±0.1 mm, and when feature sizes are larger than 100 mm, the deviations are ±0.1%. However, feature sizes of the plastic models herein greater than 100 mm, such as the spanwise length and the fuselage length, have deviations greater than 0.1%. The main reason may be the fabrication orientation and supporting method used to fabricate the models. In order to ensure the dimensional accuracy and surface quality of the main aerodynamic components (wings) of the models, the fuselage direction was adopted to fabricate the models by SL, as shown in Fig. 6(b). When the models were fabricated in this direction, the models themselves had fewer support points and required more auxiliary support structures. This can cause instability of the models during SL process, which could affect the dimensional accuracy to a certain extent. 3.1.2. Stiffness of materials Material stiffness is the key parameter to determine the predeformation of the flexible aircraft. The property fluctuation of material stiffness was assessed by comparing the tested and calculated deformations of the all-plastic parts built by SL under a given loading condition. A wing box (depicted in Fig. 9) was selected
Fig. 9. The wing box selected for the stiffness calibration.
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as the objective since wing boxes are the typical loading-bearing components of aircraft. A non-contact optical testing system (XJTUSD, Xi’an, China) was adopted to acquire the deformation of the wing box. The Cartesian coordinates of the wing box on selected points were measured and the deformation was calculated by comparing the values before and after loading. The configurations for physical testing and simulating computing (FEM) are depicted in Fig. 10. The same loading condition was brought to both the physical and simulating models, in which concentrated Z-direction forces of 20 N were applied to the tip of the wing box. The same loading condition was brought to both the physical and simulating wing boxes, in which concentrated Z-direction forces of 20 N were applied to the tip of the wing box. As shown in Fig. 11, the deformations of the physical and simulating models were very consistent. The maximum error of 3.4% means the property fluctuation of material stiffness is very small and acceptable for the model design. The main factors causing the difference in deformation include testing operation errors, dimensional deviations or material property deviations. According to the above dimensional accuracy measurement, the fabrication error of the plastic model processed by SL is about 0.1%. Deviations in material properties, especially variations in the elastic modulus of the material, may be the main factors contributing to this deformation difference. Because of the layering of materials caused by layer-by-layer processing, the material properties of the parts processed by AM techniques are highly correlated with the fabrication orientation, such as Selective Laser Sintering (SLS) process [25], Fused Deposition Modeling (FDM) process [26]. However, due to the chemical bonding rather than the physical bonding principle, the SL process used in this paper has a weak correlation between material properties and fabrication orientation (as shown in Fig. 12), which is about 4.2% [27] that is close to the above deformation difference of 3.4%.
3.1.3. Economic issue As mentioned above, the all-plastic model was feasible to be used in wind tunnel testing and could be an alternative of metal models. In the section, the economic issue of the all plastic model over metal ones will be further studied. Items for comparison are listed in Table 4. The number of processes of AM process is 4, which included stereolithography building, removing of supports and uncured resin, post-curing and sanding. For the machining process, however, the number is about 20, which mainly due to segmentation of metal models into parts. In the sense of Dimensional accuracy, the two technologies are roughly equivalent, the AM being slightly better. While, AM has significant advantages for time and cost to fabricate models.
Fig. 10. The calibration configuration for the material stiffness.
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Fig. 11. The deformations under 20 N loads.
Fig. 12. Effect of fabrication orientation on elastic modulus of materials [27].
Table 4 The economic comparison of model fabrication methods. Item
Additive manufacturing
Machining
Number of processes Dimensional accuracy (mm) Time (h) Cost (RMB)
4 0.1–0.5 10 2000
∼20 0.05–0.25 500 50000
3.2. Model testing All the models performed normally and were not damaged during tests, even in the harsh conditions when Ma = 0.85, AOA = 0◦ and Ma = 0.6, AOA = 2◦ , which indicated that the plastic models of large aircraft made by SL could be used in wind tunnel tests at transonic speeds. As shown in Fig. 13(b), no permanent deformation the plastic models As shown in Fig. 13(b), there is no obvious residual deformation on the plastic model after unloading when the test finished. This observation is easy to understand if the following factors are considered. On the one hand, the plastic used in the model is a typical brittle material that featured a two-stage stress–strain curve: recoverable elastic deformation and brittle fracture. The material does not exhibit obvious plastic characteristics and is not easy to produce residual deformation. On the other hand, the typical temperature of the wind tunnel test is lower than room temperature, which further increases the brittleness of the material while limits its plasticity, thereby further reducing the residual deformation of the material. Curves of the lift (C L ) and drag (C D ) coefficients relative to the angle of attack (α ) at Mach number of 0.6 are shown in Fig. 14. The data denoted as No. 1, No. 2, No. 3, No. 4 and No. 5 were obtained from the plastic models that were designed and fabricated in the current work, while the data marked NLR, ONERA, and DRA were from metal models test in the three European wind tunnels. The metal models are four times bigger than their plastic counterparts. All the data obtained had been treated with static aeroelastic and deformation corrections.
3.2.1. Aerodynamics of the plastic models at the design point The No. 3 plastic model was at the design point when Ma = 0.6 and AOA = 0◦ . Table 5 lists C L and C D at the design point obtained from different tunnels. As expected, the C L of the model with the designed contour (denoted as No. 3) was very consistent with the mean value from other tunnels at the design point (0.445 to 0.440, 1.1%). Among all the C L values obtained in the paper, the C L from the No. 3 contour was the biggest, which indicates the target contour possessed the best aerodynamic performance as it was designed [22]. The small error and the good aerodynamic performance of the plastic model at the design point validates the feasibility of the method. The main cause of the deviation of the lift coefficient (1.1%) is the dimensional error of the model (0.2%) and the deviation of material properties (4.2%). In order to further reduce the deviation of the lift coefficient, it is necessary to improve the dimensional accuracy and reduce the material property deviation. Among them, the main measure to reduce the material property deviation is to eliminate the relativity between the fabrication orientation and the material properties. For C D , however, considerable deviations from reported data are observed both in Fig. 14 and Table 4. First, as C D was smaller than C L by an order of magnitude, the influence of C D on the model structures was ignored during the optimization. Another notable reason is the difference of the Reynolds number (Re). The testing Re for the plastic models in the paper, 4.3 × 105 , was much smaller than that of reported tests (3 × 106 ) for metal models [22], which could be one of the main causes of the increased C D in the paper. In addition, the roughness of model surfaces introduced by the layer-additive fabrication fashion of AM could also contribute to the increase of C D [28]. 3.2.2. Aerodynamics of the plastic models at the non-design points Qualitatively, the C L –α curves of the plastic models are nearly linear, like those obtained from metal models [22]. The trends of C D –α curves are also similar between plastic models and metal models. Furthermore, the C L values of the No. 1 and No. 2 models and those of the No. 4 and No. 5 models were closer to each other, which corresponds to the fact that they were from models with under-deformation and over-deformation contours, respectively (as shown in Fig. 3). When the angle of attack increased from −2◦ to 2◦ , the lift coefficient errors of the No. 3 plastic model relative to the metal models were −6.9%, −3.2%, 1.1%, 6.1%, and 15.3%, respectively. The larger the absolute value of the angle of attack, the greater the deviation of the lift coefficient. This is probably due to the unintended deformations of the lift components (mainly the wings) of the all-plastic models. The fact that plastic models have large aerodynamic errors at non-design points indicates that there are limits on the scope of application of such models. Based on the results herein, it is necessary to change plastic models for different testing conditions of
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Fig. 13. Video Screenshots of the plastics models during (a) AOA test and (b) Ma number test.
Fig. 14. Curves of lift (a) and drag (b) coefficients relative to angle of attack at Ma 0.6. Table 5 Comparison of aerodynamic force coefficients at the design point from different tests. Test
CL CD
Plastic models in FL-21 tunnel
Metallic models in other tunnels
1
2
3
4
5
NLR
ONERA
DRA
Mean
0.404 0.0314
0.391 0.0305
0.445 0.0319
0.428 0.0321
0.430 0.0314
0.443 0.0258
0.441 0.0251
0.437 0.0249
0.440 0.0253
AOA and Ma. This is not a big problem from an economic point of view, considering that the processing cost of plastic models is extremely low, as shown in Table 4. However, frequent replacement of models has a significant negative effect on the cost/time and data consistency of the wind tunnel test. Therefore, measures need to be taken to increase the scope of application of a single model. On the one hand, the wings of the plastic models in this paper are in a full-solid structure. In the future research, heterogeneous
structures, such as hollow wing structures and multi-material wing structures, can be used to simulate the force transmission characteristics of real wings. On the other hand, the design point of the model in this paper only considers a single combination of conditions (Ma = 0.6, AOA = 0◦ ). In future research, multiple conditions can be combined as the objective function during the model design, which is potential to improve the scope of application of the model.
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4. Conclusion Plastic models in the DLR-F4 configuration were designed with pre-deformed contours, obtained based on CFD/CSD coupling computation, which can transform to the target contour that interests designers under aerodynamic loads. The models were then fabricated efficiently based on the additive manufacturing technique and tested in a wind tunnel. As the plastic models were undamaged at Mach numbers up to 0.85, which is in the range of the typical cruise speeds for commercial large aircraft, the new method to design and build models can be used in the conceptual design for configuration screening of aircraft of this kind. Furthermore, the cost and time reduction, made by the introduction of AM due to its fabrication flexibility, can potentially improve the R&D efficiency of aircraft. Thanks to the low modulus of its materials and high efficiency of its process, the AM technique not only can help to efficiently build flexible models but also provide a new testing scheme for the conceptual design of aircraft. At this point, the all plastic models can only be used in a single combination of testing condition. Further studies should be conduct to extend the scope of application of the models. Conflict of interest statement The authors declare no competing financial interest. Acknowledgements This work was supported by the National Natural Science Foundation of China, P. R. China [Grant No. 51505457], and the Open Fund of State Key Laboratory of Manufacturing Systems Engineering, P. R. China [Grant No. SKLMS2016013], and the Fundamental Research Funds for the Central Universities, P. R. China. The authors would like to thank Dr. Yan Sun and Dr. Zhengyu Zhang in State Key Laboratory of Aerodynamics, P. R. China for the assistance in model design and wind tunnel testing. We would like to thank LetPub www.letpub.com for providing linguistic assistance during the preparation of this manuscript. References [1] S. Zhou, X.G. Hua, Z.Q. Chen, W. Chen, Experimental investigation of correction factor for VIV amplitude of flexible bridges from an aeroelastic model and its 1:1 section model, Eng. Struct. 141 (2017) 263–271. [2] K. Fujii, Progress and future prospects of CFD in aerospace – wind tunnel and beyond, Prog. Aerosp. Sci. 41 (2005) 455–470. [3] A.C.K. Springer, F. Roberts, Application of rapid prototyping models to transonic wind-tunnel testing, in: 35th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA 97-0988, 1997. [4] G. Timothy, Process improvement for aerodynamic model development, in: AIAA Modeling and Simulation Technologies Conference and Exhibit, AIAA, Honolulu, Hawaii, 2008. [5] A.L. Heyes, D.A.R. Smith, Rapid technique for wind-tunnel model manufacture, J. Aircr. 41 (2004) 413–415. [6] C. Black, K.V. Singh, S. Goodman, A. Altman, R. Kolonay, Design, fabrication and testing of 3D printed wings for rapid evaluation of aeroelastic performance, in:
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