PASSIVE MORPHING AIRFOIL WITH HONEYCOMBS. School of Aerospace and Mechanical Engineering, Korea Aerospace University Goyang-City, Republic of Korea

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1 Proceedings of the ASME 2011 International Mechanical Engineering Conference & Exposition IMECE 2011 November 11-17, 2011, Denver, Colorado, USA IMECE PASSIVE MORPHING AIRFOIL WITH HONEYCOMBS Hyeonu Heo 1 Graduate Research Assistant gjgusdn@naver.com Jaehyung Ju 2 Assistant Professor jaehyung.ju@gmail.com Doo-Man Kim 1 Professor dmkim@kau.ac.kr Chang-Soo Jeon 1 Professor csjeon@kau.ac.kr 1 School of Aerospace and Mechanical Engineering, Korea Aerospace University Goyang-City, Republic of Korea 2 Department of Mechanical and Energy Engineering, University of North Texas Denton, Texas 76207, USA ABSTRACT A passive morphing may improve the aerodynamic characteristics through structural shape change by aerodynamic loads during the flight, resulting in improving fuel efficiency. The passive morphing structure should have a capability to be highly deformed while maintaining a sufficient stiffness in bending. Honeycombs may be good for controlling both stiffness and flexibility. This paper investigates a honeycomb airfoil s static deformations through the fluid-structure interaction using computational fluid dynamics and structural finite element analysis. The structural performance will be investigated with varying honeycomb geometries including regular, auxetic and chiral meso-structures. Key Words: Passive morphing airfoil, Honeycomb, Auxetic, Fluid-Structure Interaction (FSI) 1 INTRODUCTION An aircraft s wing needs to accommodate two extreme conditions while landing and being in cruise [1]. In terms of the fuel efficiency, aircraft are required to have a maximum lift coefficient, C L whlile landing and the lift-todrag ratio should be maximized to increase the flight range while being in cruise. These problems have been solved by leading and trailing edge flaps and slats in conventional aircraft. However, these devices have complex mechanisms that consist of thousands of individual parts and heavy actuators to displace and rotate the whole assembly [2]. Recently, aircraft engineers have developed a wing which has a high lift-to-drag ratio in cruise, and a high maximum lift coefficient while landing by changing a shape of airfoils; varying chord-wise, length, and camber thickness [2]. The recent research has focused on a new morphing mechanism that minimizes complexity and requires structural compliance for carrying prescribed aerodynamic loads, which often conflicts with stiffness requirements. Smart materials 1 Copyright 2011 by ASME

2 and structures which use adaptive materials and technologies in the aerospace field, is a possible way to apply the airfoil with morphing concepts []. In order to change aerodynamic characteristics of an airfoil, several researchers have investigated morphing structural concepts with external sources such as temperature, pressure differences and aerodynamic loads [1]. These external sources transform chamber thickness or trailing-edge displacements of the airfoil. For example, the airfoil with actuator using a thin film made of shape memory alloy (SMA) is deformed by varying temperature with altitude [4]. In another method, the shape of the airfoil whose core structure is made of honeycomb is changed by the deference between internal and external pressure of the airfoil [5]. The aerodynamic performance of morphing airfoils were compared with those of conventional airfoils with a plain flap. According to the recent studies, aerospace engineers have attempted to develop Chiral-core airfoils [6,7]. The performance of the airfoil is investigated by computational simulation with fluid-structure interaction (FSI) [6] and experiments [7]. Results of the studies with chiral mesostructures have demonstrated a capability to be highly deformed in bending due to the flexibility of chiral structure in the in-plane direction. Cell walls of a hexagonal honeycomb are known to be a bending-dominated structure, which is good for flexible structure design [8]. In this paper, the airfoils with regular and auxetic honeycombs are designed to have both load carrying capability and flexibility of trailing-edges under aerodynamic loads. Due to the computational complexity of fluid dynamics and structural analysys, the commercial FSI code, ANSYS, is used for numerical computation of deformed airfoils. This paper investigates a displacement of trailingedge through comparison of FSI results between a chiral-core airfoil and airfoils with hexagonal honeycombs. In this paper, we use aerodynamic loads to change the shape of the airfoil.the analyses of this study is organized in three steps. First, a structural analysis on displacement and maximum stress is conductued with an initially designed airfoil for a concentrated load. The maximum deflection of airfils is investigated while checking the elastic regions of the constitutive material, followed by modifying airfoil design that will be validated in FSI. 2 DESIGN OF AIRFOIL The passive morphing airfoil is an effective way to enhance aerodynamic performance of wings by minimizing drag, eliminating the need for flap mechanisms, etc. In this paper, bending compliant cellular meso-structures are introduced to design flexible cellular morphing airfoil structures. Each unit cell is designed to have the same thickness. The corresponding effective moduli are implemented to airfoil. The cellular airfoil structures displacements are compared with one another and the maximum allowable stains are investigated while checking local stress of a constituent material.fsi analysis is employed to investigate structural changes of airfoil configurations by aerodynamic loads during the flight condition. 2.1 Geometry and Properties of Cellular Structure A chiral core is used based on the previous study whose topology is described in [9]. The topology, shown in Figure 1, is composed of circular elements or nodes of equal radius joined by straight ligaments or ribs of equal length. The critical geometric parameters include the distance between the node centers (R), the rib length (L), the angle (φ) between the imaginary line connecting circles centers and a rib, the wall thickness (t), and the angle (θ) defining unit cell s width to height ratio. Figure 1: Unit cell of a chiral configuration and characteristic parameters (L/R = 0.8) In-plane effective moduli of chiral meso-structure are given by [9]: 2 * * t L Exx Eyy ES (1) 2 L r where E S is Young s modulus of a constituent material. The modulus of chiral meso-structure can be altered through variations of geometric parameters such as the ratio of the rib length, L, to the nod radius, R. The previous works have shown the equivalent in-plane Poisson s ratio to be approximately that leads to unique deformation patterns up to a very high in-plane shear modulus [9]. Moreover, the chiral meso-structure is capable of undergoing large displacements while operating in the elastic range of the constitutive material [9]. 2 Copyright 2011 by ASME

3 The other cellular structures, considered in this paper, are regular and auxetic honeycombs. Unit cell geometries with regular and auxetic hexagonal honeycombs are shown in Figure 2. Particularly, hexagonal geometries easily controlled with positive to negative Poisson s ratios by changing cell angles. The critical geometric parameters include the cell angle (θ), the cell height (h), the inclined cell length (l), and the wall thickness (t). Figure 2: Unit cell configurations for (a) Regular and (b) Auxetic Honeycombs (θ = 0, θ = -0 ) Auxetic Airfoil Configurations Based on the unit cell geometries in section 2.1, the mesostructures are mapped into an airfoil profile (Eppler 420). The configuration is depicted schematically in Figure. A similar approach is used as the study by Spadoni and Ruzzene [6], when selecting and mapping a chiral honeycomb. L/R is to be 0.8 and two row chiral honeycombs are used as shown in Figure. The wing dimensions are selected from [7]. The chord length, c, the front angle, α, and the rear angle, β are 0.7 m, 8.58 o, 8.0 o, respectively.the chord length, c, is 0.7 m, the angle, α, is 8.58, and the angle, β, of 8.0. The lengths a and b are 11 and 2.5 cm, respectively. The cell wall thickness, t, of honeycomb structures and skins are 0.76 mm. The out-ofplane width of the airfoil is 1.9 cm and the trailing-edge thickness, t D, is 2.54 cm. Cellular material theory (CMT) has been widely used to describe hexagonal honeycombs elastic behavior [11-14]. Inplane effective moduli of honeycombs from CMT are given by [10]: * t cos Exx ES l 2 ( h / l sin )sin (2) * t ( h / l sin ) Eyy ES l cos () Figure : Mapped chiral meso-structure airfoil configuration * t ( h / l sin ) Gxy ES l h l h l 2 ( / ) (1 2 / )cos In this study, each structure is designed to have the same effective modulus of 8.00 MPa in the x and y directions. Dimensions of these structures are shown in Table 1. Aluminum6061 T651 is used as a base material; a Young s modulus(e s ) of 69GPa, a density(ρ) of 2700 kg/m, a Poisson s ratio (ν) of 0., a yield stress(σ y ) of 276MPa [7]. Table 1: Dimensions of honeycomb meso-structures (4) Designed three honeycomb airfoils are shown in Figure 4; airfoils with (a) chiral honeycomb, (b) regular honeycomb, and (c) auxetic honeycomb. The chiral meso-structure and hexagonal honeycombs are known to be able to carry shear loads [6] and potential torsional rigidity [10]. In the proposed design [7], the airfoil lower skin has been cut to maximize deflections of the trailing-edge. In this paper, thickness of honeycombs core was controlled to match the bending stiffness with the chiral airfoil. Each mesostructure is made of the same base material (T651). Type R (mm) L (mm) r (mm) t (mm) Chiral l (mm) h (mm) θ (degree) t (mm) Regular Copyright 2011 by ASME

4 .2 Computational Fluid Dynamics Model Figure 4: Mapped Airfoil Configurations with Cellular Core Deisn; (a) Chiral meso-structure, (b) Regular and (c) Auxetic Honeycombs Figure 5 shows the flow field, the mesh type and the boundary conditions. Dimensions of the flow field are sa follows; a horizontal length of 8500 mm and a vertical length is 7000 mm. The fluid region is meshed with tetrahedron shape. Element sizes of the leading-edge and trailing-edge regions are c, where c is the chord length. The inlet velocity is set to be a Mach of 0.45, an angle of attack (AOA) is set to be 2. The relative outlet pressure is assumed to be 0 Pa. Both side faces are symmetric and the interface between the airfoil structure and the flow field is modeld with a no-slip wall. The turbulence model is chosen to be the default k-ε model. The CFX software employs a coupled fully implicit solver using a transient evolution of the flow from the initial conditions. The physical time-steps used in the transient evolution provide a means of controlling the solution procedure. The conservation equations are solved using the finite volume method. Flow variables (velocity, pressure, enthalpy, etc) are defined at the corners of each element, which are located at the centre of each control volume used for solving the conservation equations. Solver convergence is supposed to be achieved when the normalized residual values at the end of an outer iteration fall below a level specified by the user; usually 5.0E-05 or 1.0E-05. NUMERICAL MODEL OF AIRFOIL The analysis of the designed airfoil consists of the two steps. Two structural analyses are used in this study: i) Under a static vertical deflection at the tail tip, bending stiffness and elastic deformation of cellular airfoil structures are investigated. ii) Based on the evaluation under the static bending analysis, FSI is applied when an aerodynamic load is applied on the skin of the cellular airfoil structures..1 Structural Analysis Model The structural analysis consists of a static state analysis. A D structural FE Model is developed to investigate characteristics of the designed airfoil because the FSI method is only possible to analyze with a D solid element. The solid element used in this study is SOLID187 in ANSYS. It is a higher order element that exhibits a quadratic displacement behavior. The element is defined by 10 nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element supports plasticity, hyperelasticity, creep, stress stiffening, large deflection, and large strain capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials, and fully incompressible hyperelastic materials. The boundary conditions are as follows: the leading edge regions are fixed and a concenterated load, P, is applied in the y direction (Figure ). Figure 5: Mesh and boundary conditions of the flow field. Fluid-Structure Interaction Figure 6 shows the flow chart of FSI. The Multi-field solver (MFS) provides an infra-structure for FSI in ANSYS. It couples ANSYS and CFX together without a third party coupling scheme. Coupling settings determine the convergence conditions. The targets are setup in CFX-Pre. Loads/displacements are updated between the ANSYS and CFX solvers. The usual inner loops, named coefficient loops 4 Copyright 2011 by ASME

5 Vertical Load, P [N] in CFX and equilibrium iterations in ANSYS, are used for converging the field within a solver. 4 RESULTS OF DISCUSSION 4.1 Finite Element Analysis of the Airfoils Figure 8 shows the trailing-edge displacement of the proposed airfoil configurations with an applied concentrated load at the location shown in Figure Chiral Regular Auxetic Figure 6: Flow chart of fluid-structure interaction procedure [17] Figure 7 shows the loop iterations of FSI. Field Loop iterations stop when the field reaches its convergence target (or a maximum iterations in CFX). Stagger loop iterations stop when the loads/displacements reach their convergence targets or the maximum number of loops is reached. The individual field solvers and the loads/displacements are converged before starting the next time step. The CFX field loop does not need to be converged every stagger loop Trailing-edge displacement [mm] Figure 8: Load, trailing-edge displacement curve of the airfoil configurations Figure 7: Iteration Loops of fluid-structure interaction [17] In this paper, the maximum iteration numbers are set to be 10-4.The residual target s root mean square (RMS) is set to be10-6 when the simulation is analyzed in ANSYS. 5 Copyright 2011 by ASME

6 Load [N] The static analysis is conducted to evaluate the compliance of the three configurations, and to find the maximum displacement of the trailing-edge and the applied concentrated load in the elastic range of the core material. For the airfoil with the chiral meso-structure, the maximum allowing load is 22N. For the regular honeycomb airfoil, the maximum allowing load is 122N. While for the auxetic honeycomb airfoil, the maximum load is 6 N. The maximum allowable deflection of the auxetic honeycomb airfool is 12.4mm. The auxetic honeycomb airfoil is a compliant property compared with the others, when cell walls are designed to be the same. Figure 9 shows von Mises stress distribution of the airfoil configurations which was captured right before the yielding of the constituent material (276MPa). The red indicators of Figure 9 show where the maximum local stress is applied. For of the chiral meso-structure, the maximum stress is applied at the top and front regions of the airfoil (Figure 9(a)). The maximum stresses are applied at middle and bottom points for regular and auxetic honeycomb airfoils, respectively. The stress-strain behavior of the regular honeycomb airfoil is similar to that of the chiral meso-structure airfoil. The auxetic honeycomb airfoil is different compared with others as shown in Figure 10. Under the same deformation the auxetic honeycomb airfoil undertakes a lower local stress than the others as shown in Figure 11. It is the useful characteristics to the passive morphing airfoil that requires large elastic deformation during flight Chiral Regular Auxetic Trailing-edge displacement [mm] Figure 10: Load, trailing-edge displacement curve of the modified airfoil configurations Figure 11 shows von Mises stress distribution of local cell walls of the airfoils at the maximum trailing-edge deflection.the maximum stresses are found on the top and front region for the chiral meso-struture. The maximum local stresses of the regular and auxetic honeycomb airfoils are also found on the top and front region. Figure 9 Von Mises stress distribution of considered configurations (a) Chiral meso-structure, (b) Regular and (c) Auxetic Honeycombs Now, the honeycombs are designed to have the same bending stiffesss by controlling the cell wall thickness, t. When the chiral meso-structure is considered the refrecence structure with a t of 0.76mm, t of the regular and auxetic honeycombs are 1.57 and 2.5mm, respectively so that all configurations have the same bending stiffness as shown in Figure 10.Figure 10 is the trailing-edge displacement of the modified airfoil configurations with an applied concentrated load at the location shown in Figure. Every meso-structure has a local stress level within the elastic range of T Copyright 2011 by ASME

7 Figure 1 shows the imported pressure load to the chiral meso-structure airfoil. The maximum pressure is about 4 MPa on the upper surface of the airfoil. Figure 1: The imported pressure load to the chiral meso-structure airfoil 4. Fluid-Structure Interaction of the Airfoils Figure 11: Von Mises stress distribution of the modified configurations (a) Chiral meso-structure, (b) Regular and (c) Auxetic Honeycombs 4.2 Computational Fluid Dynamics of the Airfoils Figure 12 is the relative pressure contours of the freestream. The reference pressure of fluid domain is 1 atm. The relative pressure affects the pressure load to airfoil. These aerodynamic loads surrounding the airfoil will be transfered to the structural model for FSI analysis. The structural model is analyzed after the fluid dynamics analysis. The structural and fluid dynamics analyses are repeated until the convergence reached the target. The results of the structural analysis are transferred to the fluid dynamics analysis as displacement data. It transforms the mesh of the fluid dynamics analysis. FSI is analyzed through the modified structural model and fluid dynamics model. During the FSI analysis, displacements are evaluated from mesh displacements by the aerodynamics pressure loads. The aerodynamic load results from CFX are transferred to ANSYS as imported pressure loads. The results of structural analysis in ANSYS are updated to the displacements of the CFX mesh. The coupling loop is converged to reach each target of CFX and ANSYS. The number of total iterations is about 2000 and the the number of updates is three to four. Figure 12: The pressure contour around the airfoil 7 Copyright 2011 by ASME

8 demonstrates that there are the other load conditions besides the bending in the actual flow conditions. Figure 14: The deformed shapes of the modified airfoils for FSI analysis (a) Chiral meso-structure, (b) Regular and (c) Auxetic Honeycombs Figure 14 is the deformed shapes of the modified airfoils for the FSI analysis and shows the total mesh displacement. The trailing-edge displacements of the modififed airfoil are as follows: the chiral meso-structure is mm, the regular and auxetic honeycombs are mm and mm respectively. The auxetic honeycomb is a more flexible structure than the other structures when each structure has the same bending stiffness. Even though they have the same bedning stiffness, the results of the FSI analysis are different each other in displacement and local stress of the structures. It Figure 15:Von Mises stress distribution of the modified airfoils for FSI analysis (a) Chiral meso-structure, (b) Regular and (c) Auxetic Honeycombs Figure 15 is the von Mises stress distribution of the modified airfoils. For the chiral meso-structure airfoil, the maximum von Mises stress is 1.8 MPa. For the regular honeycomb airfoil, it is 1.58 MPa. While for the auxetic honeycomb airfoil, the maximum load is 2.16 MPa. The case of chiral meso-structure, the maximum stress is located at the top and front regions of the airfoil. The maximum von-mises stresses of the regular and auxetic honeycomb airfoils are located on the middle and bottom regions, respectively. 8 Copyright 2011 by ASME

9 5 CONCLUSIONS In this paper, a passive morphing airfoil structural application of honeycomb meso-structures including chiral, hexagonal regular and auxetic confogurations was investigated while maximizing the bending flexilbity of the cellular strictures. The airfoils with the core design were invegated through the static and FSI analyses. Auxetic honeycombs shows not only the highest bending flexibility but a lower local stress than the other structures, when meso-structures are designed to have the same bending stiffness, which shows potential to be used as a passive morphing airfoil structure. As a future work, we will investigate the optimum mesostructures for the passive airfoil application. 6 ACKNOWLEDGEMENTS This work is partially supported by Haneul Project of Korea Ministry of Land, Transport and Maritime Affairs. 7 REFERENCE [1] Ruijgrok, G.J.J., Elements of Airplane Performance, Delft University Press, Delft, The Netherlands, [2] Rudolph, P.K.C., "High-Lift Systems on Commercial Subsonic Airliners," NASA Contractor Report 4746, September, [] McGowan, A.R., Cox, D.E., Lazos, B.S., Waszak, M.R., Raney, D.L., Siochi, E.J. and Pao, P.S., Biologically Inspired Technologies in NASA s Morphing Project, In: Proceedings of SPIE Smart Structures and Materials, March, San Diego, CA, pp1 1, 200. [4] Jin-Ho Roh, Kyung-Seok Kim, and In Lee, Shape Adaptive Airfoil Actuated by a Shape Memory Alloy and its Aerodynamic Characteristics, Mechanics of Advanced Materials and Structures, Vol. 16, Issue, Pages , [5] Roelof Vos and Ron Barrett, Pressure adaptive honeycomb: a new adaptive structure for aerospace applications, Proc. SPIE 7647, 76472B, [6] Spadoni, A and Ruzzene, M, Static Aeroelastic Response of Chiral-core Airfoil, Journal of Intelligent Material Systems and Structures, Vol. 18, pp , [8] Ju, J. Summers, J.D., Ziegert, J. and Fadel, G., Compliant Hexagonal Meso-Structures Having Both High Shear Strength and High Shear Strain, In Proceedings of the ASME International Design Engineering Technical Conferences, DETC , Montreal, Quebec, Canada, [9] Prall, D. and Lakes, R.S., Properties of a Chiral Honeycomb with Poisson s ratio of -1, International Journal of Mechanical Sciences, 9():05 14, [10] Gibson, L. J. and Ashby, M. F., Cellular Solids Structure and Properties, 2nd ed. Cambridge, UK: Cambridge University Press, [11] Masters, I. G. and Evans, K. E., "Models for the Elastic Deformation of Honeycombs," Composite Structures, vol. 5, no. pp , [12] Bezazi, A., Scarpa, F., and Remillat, C., "A Novel Centresymmetric Honeycomb Composite Structure," Composite Structures, vol. 71, no , [1] Balawi, S. and Abot, J. L., "A Refined Model for the Effective in-plane Elastic Moduli of Hexagonal Honeycombs," Composite Structures, vol. 84, no. pp , [14] Gonella, S. and Ruzzene, M., "Homogenization and Equivalent in-plane Properties of Two Dimensional Periodic Lattices," International Journal of Solid and Structures, vol. 45, no. pp , [15] Wang, A. J. and Mcdowell, D. L., "In-Plane Stiffness and Yield Strength of Periodic Metal Honeycombs," Transactions of the ASME Journal of Engineering Materials and Technology, vol. 126, no. pp , [16] E. G. Herbert, W. C. Oliver, and G. M. Pharr, On the measurement of yield strength by spherical indentation, Philos. Mag. 86:, , [17] ANSYS CFX Advanced Training (FSI & Moving Mesh) [7] Spadoni, A and Ruzzene, M, Numerical and experimentral analysis of the static compliance of chiral truss-core airfoils, Journal of mechanics of materials and structures, Vol. 2, No. 5, Copyright 2011 by ASME