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Aerodynamics of a Morphing Airfoil Adam Niksch Senior, Aerospace Engineering Texas A&M University The purpose of this research is to develop a MATLAB model which can calculate the aerodynamics, such as lift, drag, and pressure, on an airfoil as it changes shape. This model needs to be computationally efficient and should have reasonable accuracy. A constant strength doublet panel code, which takes thickness and camber distribution as inputs, is used to model the aerodynamics. This code has the ability for thickness and camber to change, which effectively allows the airfoil to morph. INTRODUCTION/BACKGROUND The purpose of this research is to develop a computational model with which to calculate the aerodynamics on a morphing airfoil. One of the major requirements for this model is that it be computationally efficient. Some error is allowable, but the model must be reasonably accurate and must produce the correct shapes for lift and drag plots. There are many possible ways to implement this model. One way is to use thin airfoil theory. The drawbacks to using thin airfoil theory are the assumptions that must be made, namely that the airfoil must be thin. Another possible approach is to use conformal mapping, which is an exact method using complex variables. A third possibility is to use a panel method. However, high order panel methods can be very computationally inefficient. During this research, both conformal mapping and a doublet panel code were attempted and each had its advantages and disadvantages. The doublet panel code was chosen in the end because it works for both symmetric and asymmetric airfoils without too much modification required. This panel code is able to accurately predict the pressure distribution on any airfoil. The panel code did have some problems, but it proved to be the best option in the end. EXPERIMENTAL SETUP A MATLAB code is developed to model the aerodynamic changes an airfoil would encounter as it changes its shape. This code accepts thickness and camber distribution for the airfoil as inputs, not specified points as in some panel codes. This gives the user the ability to easily change these parameters, which causes the airfoil to morph. This MATLAB code is a powerful tool in that it allows thickness, camber, chord, and angle-of-attack all to vary. If a simple ‘for’ loop were to be placed around the function with all of these parameters varying, the code could simulate morphing the shape of the airfoil using 4 degrees of freedom. The reason this code is so versatile is that it was designed to be a subprogram in a larger reinforcement learning program, which is a branch of artificial intelligence. With the combination of these two programs running, an aircraft will learn how to change the shape of its own airfoil for control purposes rather than use current control mechanisms. One of the assumptions made when writing this code is that the flow is incompressible. This assumption is valid because current interests lie in the realm of micro air vehicles, which fly at speeds less than Mach 0.3.Since the final model uses a panel method to calculate the aerodynamics, it is very sensitive to the grid, or location of the panels, and the number of panels created. The grid must be a sinusoidal spaced grid in the x direction, which puts more points at the trailing edge of the airfoil. This is necessary because many aerodynamic changes occur near the trailing edge. If the number of panels used were to decrease, the accuracy of the model would also decrease. The code also assumes inviscid flow, and thus it is only valid for the linear range of airfoils, or angles-of-attack prior to stall. RESEARCH PLAN Since thin airfoil theory required too many assumptions be placed on the airfoil, it was almost immediately decided not to use that approach. The first attempted model was a MATLAB code which used conformal mapping to calculate the aerodynamics. A symmetric airfoil is modeled and only its thickness is allowed to change. The model produced very accurate results when compared to wind tunnel data in Ref. 1. The basic equations for conformal mapping are listed below in equations 1-3 [3]. However, once camber was integrated into the model, the process became extremely complex and required complicated numerical analysis. Conformal mapping was no longer a feasible approach given the scope of this research and was abandoned. A constant strength doublet panel method replaced conformal mapping as the modeling tool. This code required no changes to be made if the airfoil is asymmetric. Since it is a low order panel method, it is computationally efficient. The equations for the velocity on each panel are listed as equations 4 and 5 [3] where x and z are in the local panel coordinate system. Since these equations require panel coordinates, a transformation from the global coordinate system to the local panel coordinate system must be made. This transformation is listed as equation 6 [3]. The panel code is based on the no penetration condition, which states that the flow cannot cross the solid boundary of the airfoil, thus the velocity normal to the surface is 0 in the global coordinate system. Equation 7 is used to transform the velocities from equations 4 and 5 into the global coordinate system. [3]. Now it is possible to solve for the doublet strengths using equations 4-7. These doublet strengths can be used to find the tangential velocities at each point. Once the tangential velocities are calculated, the pressure coefficient can be calculated using Bernoulli’s equation which, when modified, produces equation 8 [2]. The pressure coefficient can be broken up into normal and axial forces using simple integration. These forces can also further be broken up into lift and drag using simple trigonometry. These equations are listed as equations 9-12. RESULTS The first airfoil to be modeled using the constant strength doublet panel method was a NACA 0012. This airfoil was


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