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Master Thesis Report Parameterisation and Reconstruction of the NASA Rotor 67 4.3 Step 3: Fitting the Suction/Pressure side curves of the 2D Pro- file In this section, the fitting algorithm that is used to determine the closest fit of the BSpline curve for the points distributed along the contour of the blade profile will be explained. As previously mentioned, the pressure and suction side curve are constructed using a separate list of distributed points where the curvature is determined by its thickness distribution. This thickness distribution is then directly controlled by the use of a BSpline curve where the control points are the variables. Using such an approach, the user will be able to adjust the thickness distribution of the pressure/suction side curve using a minimum number of variables. In order to ensure a good fit between the pressure/suction curve with the distributed point along the contour of the blade profile, the geometry fitting algorithm was developed. This algorithm is based on the minimisation of error between the distributed points of the actual blade profile and the pressure/suction side curve formulated by the control points which controls the thickness distribution. Using the ’x’ coordinate of the suction/pressure side points, the algorithm searches for the closest ’u’ parameter on the curve. The ’u’ parameter is a normalized coordinate that moves along the BSpline curve. The ’y’ coordinate of the curve is then determined by using the associated ’u’ parameter. The algorithm then computes the differences in ’y’ coordinate between a particular point of interest on the distributed points surrounding the blade contour and the segment of the curve belonging to the asso- ciated ’u’ parameter. An error function is then composed by using the summation of the error along the entire blade contour. The error function is then minimised by using the gradient based optimizer in the Scipy library of python. Both the simplex and sequential least square quadratic programming algorithm is being implemented in the BM. User can decide to use either the mid control points or all the control points for the optimization. In the case that the ’x’ position of the adjacent point is lesser than the current point, the algorithm readjust the value of the starting U parameter so that the associated ’u’ parameter closest to the current ’x’ coordinate can be found. Figure 4.9: Illustration of geometry fitting algorithm method The control points belonging to the leading and trailing edge has to be adjusted manually to obtain a good fit before the optimization algorithm can be applied. An illustration of the blade profile before and after optimization is presented in figure 4.10 and 4.11. Comparing figure 4.10 and 4.11, it can be seen that the pressure and suction side curves exhibits a better fitting at the mid region after the optimization process. The only drawback thus far is that the implementation of using all control points for geometry fitting is not sufficiently robust. 32PDF Image | Aerodynamic Design of the NASA Rotor 67 for Non Uniform Inflow
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