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Plasma actuators for aeronautics applications

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Plasma actuators for aeronautics applications ( plasma-actuators-aeronautics-applications )

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2 International Journal of Plasma Environmental Science and Technology Vol.2, No.1, MARCH 2008 Thus, if we consider an airplane in motion at a constant velocity and altitude (figure 4), the drag is equal and opposite to the traction due to the propeller moved by the engine and the lift is equal and opposite to the weight due to the gravity. The drag is due to the friction of the air on the airplane body, the wings and the tail. The lift is essentially due to the friction on the wings. Then, it is, important to try to reduce the drag during takeoff and cruise but not for landing and to control the lift, as a higher lift is needed during takeoff than for cruise or landing. Anyway, the shape of the different part of a plane are designed in order to have an aerodynamic profile, which means a drag as small as possible and the appropriate lift for takeoff, cruise and landing. An airplane is made of different parts submitted to air flows. Each of them constitutes an airfoil. with the following formula: ⎛ xx ⎞⎛0.2969 z −0.126 z−0.3516 z2 ⎞ ⎟ ⎝0.2⎠⎜+0.2843z3 −0.1015z4 ⎟ ⎝⎠ y=⎜ ⎟⎜ z is the position along the chord and vary from 0 to 1, y is the half thickness at a given value of z (median line to surface) and xx is the maximum thickness in percentage of the chord. The leading edge is tangent to a cylinder the radius of which r is given by: r = 1.1019 xx 2 (2) Such symmetrical airfoil presents no lift when its median line is parallel to the flow, this is the reason why other airfoils have been performed with a camber of the median line. The simplest asymmetric airfoils are the NACA four digits series, which used the same formula as that used to generate the 00xx symmetric foils, but with the line of mean camber bent. Thus a NACA mpxx has a profile similar to the NACA 00xx but where m is the maximum camber in percentage of the chord and p is the distance from the leading edge of this maximum in tenths of the chord The formula used to compute the mean camber line is given by: (1) traction lift Drag weight Fig. 4. Aerodynamic forces on an airplane in motion. B. Airfoilexample:thewingsofanairplane As the wings are mandatory parts of an airplane, it is important to examine the profile of these airfoils. The wings of an airplane are airfoils which must generate a drag as small as possible and a lift equal to the weight of the plane for a given inclination and velocity. After a lot of studies (Betz [4], Jones [5] ), some profiles of airfoils have been designed to fulfill this purpose. The most known are those proposed by the National Advisory Committee for Aeronautics (NACA). Furthermore, this committee gave a classification of airfoils profiles. One of the most used to design wings is the NACA four-digit series [6]. As an example the profile NACA00xx is related to a profile without camber and xx indicates the value of the maximum thickness in percentage of the width of the wing called usually the chord. We see in figure 5 the profile of a NACA0015 airfoil (the maximum thickness is 15% of the chord). y= m (2px−x2) (3) p2 m (1 − 2 p + 2 p x − x 2 ) (1−p)2 (4) fromx=0tox=p: f r o m x = p t o x = 1 : profile Fig. 6. NACA 2312 profile. Such profile presents a lift even if the z axis is parallel to the air flow (zero angle of attack). Nevertheless, a symmetric airfoil NACA00xx generates a lift for a non null angle of attack (figure 7). Very often experiments are made with a symmetric profile and specially a NACA 0015 (often called just NACA15). y = As an example we can see in figure 6 a NACA 2312 y z y cylinder C tangent to the leading edge maximum thickness z leading edge chord lift drag attack angle of Fig. 5. NACA 00xx profile. The profile of the NACA 00xx is symmetrical regarding the z axis, and the value of y may be computed Fig. 7. Lift and drag on a NACA 0015 profile with attack angle.

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