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Master Thesis Report Literature Review the performance of the geometry. Most design of shapes rely on curves. In particular, Beizer and BSpline curves are most suited for shape parameterization [8]. These curves have simple mathematical formulation and their characteristics are strongly coupled to the underlying polygon of control points [8]. Figure 2.13: Camberline Parameterization [7] Figure 2.14: Effect of w on camberline shape [7] The parameterization of a 2D Blade profile begins with the definition of the camberline. This is illustrated in figure 2.13. The camberline can be described by the following parameters; the inlet blade metal angle βin, the exit blade metal angle βout, the axial chord length Cax and finally the stagger angle γ. The leading edge position is first specified by the user. Using the axial chord length and the stagger angle, the trailing edge position can be derived. The intersection of the inlet and outlet line tangential to the inlet and outlet blade metal angle defines the position of the mid control point. For this camberline, the points located at the LE, TE as well as the middle position defines the control points of the beizer curve. Mathematically, the position of the trailing edge point can be derived as follows: xte = xle + Cax (2.41) yte = yle − Cax tan γ (2.42) By adjusting the weight w of the mid control point, the desired curvature of the beizer curve can be obtained. This is illustrated in figure 2.14. The other possibility to construct the camberline curve in the Blade Modeller is to use four control points instead. In this method, the position of the two mid control points are controlled by the t1 and t2 parameter which moves the control points linearly along the inner and outer line tangential to the inlet and outlet blade metal angle. Mathematically, the location of these mid control points can be calculated as shown in equation 2.43 [7]. xp1 = xle + t1(xmid − xle) yp1 = yle + t1(ymid − yle) xp2 = xmid + (1 − t2)(xte − xmid) yp2 = xmid + (1 − t2)(yte − ymid) (2.43a) (2.43b) (2.43c) (2.43d) The parameters t1 and t2 are illustrated in figure 2.15 respectively. Once the camberline is con- structed, the next step is to specify a thickness distribution for both the suction and pressure side 16PDF Image | Aerodynamic Design of the NASA Rotor 67 for Non Uniform Inflow
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