Wind Tunnel Experiments of Stall Flutter with Structural Nonlinearity Ahmad Faris R.Razaami School of Aerospace Engineering, Universiti Sains Malaysia, Penang, MALAYSIA Norizham Abdul Razak School of Aerospace Engineering, Universiti Sains Malaysia, Penang, MALAYSIA Abstract: The work presented focuses on a wing undergoing stall flutter in the pitch degree of freedom. The objective of the study is to promote the understanding of stall flutter by characterizing the bifurcation behavior of an aeroelactic system with structural nonlinearity. The wing section chosen for this study is NACA 0018 profile applied to a rectangular wing. The stiffness nonlinearity is achieved through nonlinear cam attached to a leaf spring connected to the airfoil s mechanism. The cam is tailored to apply continuous cubic nonlinearity in pitch degree of freedom. Two level of cubic stiffness (soft and stiff) are tested. The tests are carried out at different wind tunnel airspeeds and static angles of attack. The airspeed was varies between 0 m/s and 10 m/s. The measured aeroelastic responses are analyzed and the bifurcation behavior of the system is characterized. Keywords: Limit cycle oscillation, wind tunnel experiment, nonlinear stiffness. 1 INTRODUCTION Aeroelastic phenomena are the phenomena resulting from the mutual interaction of aerodynamic forces, inertia forces and elastic forces on flexible structures. Stall flutter, buffeting, divergence and galloping are examples of aeroelastic phenomena. Stall flutter is a Limit Cycles Oscillation (LCO) caused by the periodic separation of the flow around a wing immersed in a uniform fluid flow.lco of wings and aircraft is an important problem that has received a lot of attention over the decades. Aeroelastic LCO normally associated with flutter. It is assumed that nonlinearities in the structure or the aerodynamic forces lead to limited of the amplitude of oscillations of an unstable system. LCOs occur due to the presence of various sources of nonlinearity, such as structural nonlinearities (Gilliatt, et al., 1997) and aerodynamic nonlinearities. Example of structural nonlinearities is nonlinear stiffness and examples of aerodynamic nonlinearities are flow separation and shock wave motion. Aeroelastic behavior can be affect by nonlinearities in control system. A number of studies of aeroelastic systems with structural nonlinearity involving cubic stiffness were performed (Lee, et al., 1986; O Neil et al., 1998; O Neil et al., 1996; Price et al., 1995). Extensive work regarding stall flutter oscillations was perfomed by Razak, Andrianne and Dimitriadis (2010) with the objective to promote the understanding stall flutter by characterizing the complete bifurcation behavior for the NACA 018 airfoil. The purpose of the present work is to investigate aeroelastic system of stall flutter with nonlinear structural stiffness. Experiments concerning the stall flutter behavior of a wing with NACA 0018 section and the parameters that influence its behavior are detailed. The wing is allowed to oscillate in pitch degree of freedom. The pitch displacement and pressure distribution around the mid span section are measured. 2 EXPERIMENTAL SETUP 2.1 Structural Setup The experimental work was conducted in the Close Loop Wind Tunnel of the Universiti Sains Malaysia. The wind tunnel test involves the development and testing of stall flutter setup with prescribed nonlinear stiffness. The stiffness nonlinearity is achieved through nonlinear can attached to a leaf spring connected to the airfoil s rotation mechanism. The cam is tailored to apply continuous cubic nonlinearity in pitch degree of freedom. The two level of cubic stiffness (soft and stiffness) are tested. The wind tunnel test setup is shown in Figure 1. The leaf spring was made from aluminum plate (20 cm X 4 cm) with thickness 0.05 cm. For this study, there are three plates (A1, A2, A3) with different values of stiffness have been tested. 76
elastic axis and stiffness were also measured in this phase. Table 1. Stiffness for the leaf springs. Plate Pitch Stiffness (Nm/rad) A1 0.8974x³ + 0.3846x² + 0.6456x 0.0031 A2 1.1706x³ + 0.3199x² + 0.7975x 0.0029 A3 4.7065x³ + 1.1795x² + 1.1606x 0.0104 Figure 2.CAD drawing for wind tunnel test setup with nonlinear pitch stiffness. 2.2 Wing The rigid straight rectangular wing was made from aluminum. The skin was made from 0.05 cm aluminum sheet that was wrapped around the aluminum ribs. There are five ribs inside the wing, positioned 12.0 cm apart. The ribs, with thickness of 0.9 cm, were held together by a fiber rod acting as a spar, located at the 40% of the chord. The profile selected for this study was a NACA 0018. The wing has a chord of 20.0 cm and the span is 49.5 cm. For this work, the mass of the wing including the pitching mechanism was 1.16 kg. The wing is instrumented with 16 pressure tappings connected transducers using silicone tubes for capturing the unsteady pressure distribution around the airfoil. The responses are measured using rotation sensor for bifurcation analysis. 2.3 Test Description The experiments were divided into two phase. The first phase involves determining the natural frequencies of the system in pitch degree of freedom at wind-off conditions using impulse testing for all cases. The system was excited by applying impulses independent of the pitching degree of freedom. The impulses were applied on the leading and trailing edge to induce mainly pitching motion. Several impulses were applied to different points on the wing and the sensor responses were recorded and processed. The results are tabulated in Table 1. The cubic stiffness values shown in Table 1 are obtained by performing cubic fit on the measured data. Other significant parameters such as mass, mass moment of inertia, The second phase of testing involved measurements of the responses at wind-on condition. This series of tests are used to determine the critical airspeeds and the ensuing amplitudes and frequencies of the oscillations. The tests were conducted at various airspeeds for different pitch stiffness values. The wind-off angle of attack is set at 10, 12, 14, 16, 18 and 20. It represents the static equilibrium position of the wing prior to being exposed to the airflow. The airspeed was varied between 0 m/s and 18 m/s. At each set of test parameters (airspeed and stiffness), the system was excited by applying an impulse in pitch mode and the responses were recorded. The recorded time depended on the type of response encountered. Decaying responses only allowed short recording time while LCO responses were recorded for as long as 30 seconds. Once LCO was achieved, no more excitation was applied for higher airspeed cases. The system was allowed to oscillate until certain airspeed was reached where the amplitude was deemed too high to continue. Then the airspeed was reduced gradually until decaying oscillations were reached. 3 RESULTS In this section, the characteristics of the wing s responses and their evolution with airspeed and stiffness will be presented and discussed. 3.1 Responses Figure 2 plots the two typical responses measured for plate A1 at 12 of static angle of attack. The first type was decaying response. An initial impulse is applied to excite the structure and set it in motion. The amplitude of the resulting oscillations decays with time and the motion stops eventually. This behavior indicates loss of energy due to aerodynamic damping. The resulting response is shown in Figure 2(a), measured at 4.6 m/s which are prior to the onset airspeed. At lower airspeed (U < 4.6 m/s), the same effect was observed but with an increased rate of decay. This was caused from lower energy supplied by the airflow which decreases but does not negate the structural damping. 77
were observed the amplitudes were plotted as zeros. For α0 = 10, it can be seen that the first LCO responses are obtained at U = 5.3 m/s with an amplitude of ± 10.2. Increasing airspeed to 8.6 m/s led to jump of amplitude to ± 30.8. This is the maximum airspeed tested for this case since the vibration amplitude was very high. It was decided not to increase the airspeed any further for safety reasons. (a) An increase of 2 in the static angle of attack brings out a significant change in the bifurcation condition. The critical airspeed is lower but the post-critical behavior totally different. The amplitude no longer tends to infinity but it is finite and increases with airspeed. The LCO amplitude is initially low but very quickly jumps to a very high value. Data from the α0 = 14 configuration show that the bifurcation to LCOs occurs at a lower airspeed. Significant oscillation amplitude was observed at airspeed beyond 5.0 m/s. The maximum amplitude measured was ± 25.4. (b) Figure 2. Pitch responses for plate A1 at 12 (a) at v = 4.6 m/s, (b) v = 5.0 m/s. The second type of oscillation observed was the selfsustained limited amplitude oscillation shown in Figure 2 (b), plotting results measured at 5.0 m/s. After the initial perturbation the system quickly settled to constant amplitude of oscillation. Increasing the airspeed resulted in a slight increase in amplitude. The overall dynamic behavior observed for other cases exhibited the same two types of response. In addition, the LCO amplitude was also found to be sensitive to the level of the excitation impulse applied to the system. Results from plate A1 show the system exhibit LCOs at lower airspeeds compare to other plates. 3.2 Bifurcation Plot Figure 5 shows the bifurcation plot of NACA 0018 self-excited oscillation plotted for different static angles of attack for plate A1. Black squares represent the maximal and minimal variations when the airspeed is increased from zero until LCO is achieved. Meanwhile, blue circles represent the motion when the airspeed is reduced until decaying oscillations were reached. The angles of attack cases shown in the figure are 10, 12, 14, 16, 18 and 20. The bifurcation plot is presented in terms of the maximum and minimum values of oscillating amplitude, where the time derivative of the displacement response in equal to zero. For airspeeds values for which no LCOs Figure 3. Bifurcation plot for plate A1. At α0 = 20, the response is steady until at a critical flight condition, it suddenly becomes oscillatory with enormous amplitude ± 19.8 from amplitude 0 where the measured LCO onset airspeed was 6.3 m/s. All oscillations measured in this research were limited in term of amplitude and self-sustained, suggested that energy was being transferred from the moving fluid into the mechanical system. At airspeed lower than the LCO onset airspeed, the mechanical system loses energy, both to the fluid and to internal damping. At airspeeds higher than the LCO onset condition, the mechanical system absorbs energy from the fluid, 78
such that it can undergo oscillations with limited amplitude. 3.3 The Effect of Weakening Structure Frequency analysis was performed on all measured responses in order to determine if there are any changes occurring with airspeed and pitch stiffness. Figure 4 shows the frequency content of the pitch responses measured for plate A1 and A2 at selected airspeed. It shows the evolution of the frequency content at sub- and post-critical conditions. Red lines represent increasing airspeeds start from zero until certain airspeed was reached where the amplitude was deemed too high to continue. Blue lines represent the airspeeds that reduced gradually until decaying response was reached. (b) From Figure 4 (a), there is no indication of the frequency changes with increasing airspeed. A single 1.9 Hz is observed at airspeed higher than 5.6 m/s. However there are frequency changes in Figure 4 (b). The frequency increases as the airspeed increases. The LCOs appear at 8.6 m/s at 2.2 Hz. At critical airspeed 9.9 m/s, the frequency increase to 2.4 Hz. This is called hardening structure. There are some cases occurred in this study where the stiffness weakened. Figure 4 (c) and (d) show the frequency content for weakening structure. From Figure 4 (c), the frequency decreases as the airspeed increases. The LCOs appear at 5.0 m/s at 1.8 Hz. At critical airspeed 8.0 m/s, the frequency decrease to 1.6 Hz. This is called softening structure. From Figure 4 (d), there is frequency jump from 2.5 Hz to 2.0 Hz because cracked suddenly appeared at airspeed 7.2 m/s. The LCOs appear at 5.0 m/s at 2.4 Hz. (c) (d) Figure 4. Frequency content for (a) plate A1 at 20, (b) plate A2 at 20, (c) plate A1 at 14, (d) plate A3 at 12. (a) 4 CONCLUSIONS The bifurcation behavior of a pitching wing with a NACA 0018 section subjected to various static angles of attack, stiffness values and airspeeds is studied. Stall flutter was observed for all chosen angles of attack. Tests at lower static angles of attack (10, 12 and 14 ) lead higher onset LCO airspeeds, with the LCO amplitudes growing explosively. At higher angles of attack (16, 18 and 20 ), the lower LCO onset condition is followed by a gradual increase of LCO amplitude as airspeed increases. Besides, there is 79
indication of frequency changes with increasing airspeed or variation of the static angles of attack due to the effect of weakening structure. ACKNOWLEDGMENTS The authors gratefully acknowledge Universiti Sains Malaysia for the financial support through research grant 814238. REFERENCES Gilliatt, H. C., Strganac, T. W., and Kurdila, A. J. (1997). Nonlinear aeroelastic response of an airfoil. 35 th Aerospace Sciences Meeting & Exhibit., AIAA- 97-0459. Reno, Nevada. Lee, B. H. K., and LeBlanc, P. (1986). Flutter analysis of two-dimensional airfoil with cubic nonlinear restoring force. Tech. Rep. 25438. O Neil, T., Gilliatt, H., and Strganac, T. (1996). Investigation of aeroelastic response for a system with continuous structural nonlinearities. AIAA Meeting, 96-1390. O Neil, T., and Strganac, T. W. (1998). Aeroelastic response of a rigid wing supported by nonlinear springs. Journal of Aircraft, 35(4), 616-622. Price, S. J., Alighanbari, H., and Lee, B. H. K. (1995). The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities. Journal of Fluids and Structures, (9), 175-193. Razak, N. A., Andrianne, T., and Dimitriadis, G. (2010). Bifurcation analysis of a wing undergoing stall flutter oscillations in a wind tunnel. Proceeding of the International Conference on Noise and Vibration Engineering (ISMA 2010), 201 80