ON THE STUDY OF AN TWO-DIMENSIONAL AIRFOIL USING SHAPE MEMORY ALLOY (SMA)

1. ON THE STUDY OF AN TWO-DIMENSIONAL AIRFOIL USING SHAPE MEMORY ALLOY (SMA) Vinícius Piccirillo 1, Luiz Carlos Sandoval Goes 2 , José Manoel Balthazar 3 1 ITA – Tecnologial Institute of Aeronautics, São José dos Campos, Brazil, pcmec@ita.br 2 ITA – Tecnologial Institute of Aeronautics, São José dos Campos, Brazil, goes@ita.br 3 UNESP – Sao Paulo University, Rio Claro, Brazil, jmbaltha@rc.unesp.br BACKGROUND RESULTS Aeroelasticity is the dynamic interaction of structural, inertial, and aerodynamic forces. Conventional methods of examining aeroelastic behavior have relied on a linear approximation of the governing equations which describe both the flow field and the structure. The nonlinear aeroelastic systems may exhibit nonlinear dynamic response characteristics such as limit cycle oscillations (LCOs), internal resonances, and chaotic motion, (Lee, et.al., 1999). The flutter phenomena is a very special case in the aeroelasticity study, many authors dedicates years of its research in the resolution of this kind of problem. Trying to get positive answers in this study, we decide to make a simple application of intelligent material in a typical wing section, in order to study which would be the effect of this material in this kind of phenomena. The chosen material had been Shape Memory Alloys. We use the V-g method to calculated the flutter velocity. In V-g method, the unsteady aerodynamics formulated by Wagner is used. The flutter speed calculated using V-g method is about 2.55 or 15 m/s. The figure below show the V-g method and the time history for the flutter velocity. In this case we are not even considering the inclusion of the SMA torsional tube. PURPOSE A theoretical simulation study of the nonlinear response of a two degree of freedom typical airfoil section using a Shape Memory Alloy (SMA) is presented. The model is integrated into a numerical solution of the aeroelastic nonlinear dynamic system that results from the inclusion of Shape Memory Alloy components in a dynamic structural system. In the present investigation, concentrated the SMA nonlinearities in the airfoil pitch. The goal is to use the SMA torsional tube to suppress flutter and to maintain stability system. The numerical results show the present SMA element can be used to alleviate the dynamic response, especially for the plunge and pitch responses. Figure 4: Typical time series showing the linear flutter phenomenon for V = 15 m/s In the next simulation we included the SMA torsional tube. The figure 5 shows the variation of radius r versus the maximum amplitude of Pitch considering the flutter speed, ie V = 15 m / s. Thus we get that the best value for the radius is r = 0006 m. The figure 6 show the response in the time history considering the flutter velocity and SMA tube. Figure 1: Wing Model with SMA torcional tube MATERIALS AND METHODS Figure 6: Tube radius vs maximal picth amplitude for V=15 m/s Figure 7: Time history for V=15 m/s SMA CONSTITUTIVE MODEL: To describe the behavior of the shape memory alloy, the assumed phase transformation kinetics constitutive model is adopted. The shear stress–shear strain relation is expressed by the following equation: AEROELASTIC MODELING: The linear equation of motion of the aeroelastic system is When SMA is outside the phase transformation region, the third equation in Eq. (5) can be simplified as During the phase transformation from Austenite to Martensite, and during the phase transformation from Martensite to Austenite, Figure 2: Pseudo elastic effect: shear stress – strain relation Table 1: System parameters of two-dimensional typical section model The response of the system at critical flutter velocities is affected by the nonlinear pitch stiffness. The system response does not grow exponentially when the flutter velocity is reached; rather LCOs occur. The next figs shows the aeroelastic responses with the two different LCOs when the speed is 20 m/s Figure 9: LCO motion in plung Figure 10: SMA Behavior Figure 8: LCO motion in pitch CONCLUSIONS The results for both structurally linear and non-linear cases are compared to show the effects on flutter boundary. The detailed of the aeroelastic SMA system responses of limit-cycle oscillations are also presented to show the vibration characteristics. The response of the system when introduce the SMA element affected the critical flutter velocities, where the system response show a LCO behavior. Of the analysis and simulations can be seen that by introducing the SMA torsional tube the flutter speed change from 15 m/s to approximately 23.5 m/s so that means an increase of around 55% BIBLIOGRAPHY Dessi, D., Mastroddi, F., 2008, “A Nonlinear Analysis of Stability and Gust Response of Aeroelastic System”, Journal of Fluids and Structures, Vol. 24, pp. 436 – 445. Lee, B.H.K., Price, S.J., Wong, Y.S., 1999, “Nonlinear Aeroelastic Analysis of Airfoil: Bifurcations and Chaos”, Progress in Aeroespace Science, Vol. 35, pp. 205 – 334. Poirel, D.C., Price, S.J., 2001, “Structurally Nonlinear Fluttering Airfoil in Turbulent Flow”. AIAA Journal 39, Vol. 10, pp.1960–1968. Tang, D., Henry, J.K., Dowell, E.H., 2000. “Nonlinear Aeroelastic Response of Delta Wing to Periodic Gust”, Journal of Aircraft 37 Vol. 1, pp. 155–164. Tang, D., Dowell, E.H., 2002. “Experimental and Theoretical Study of Gust Response for High-Aspect-Ratio Wing”. AIAA Journal 40, Vol. 3, pp. 419–429. Fung, Y.C., 1969, “An Introduction to the Theory of Aeroelasticity”, Dover, New York, pp.498.