When used for the formation of the profile contour of polynomials of degree n (n > 5 for the convex part of the profile, and n > 3 for the concave part) the question arises about the correct choice of the missing n–5 (or n–3) boundary conditions which must be selected on the basis of the requirements of aerodynamic profile perfection.
One of the requirements of building the turbine profiles with good aerodynamic qualities is a gradually changing curvature along the outline of the profile . Unfortunately, the question concerning the nature of the change of curvature along the profile’s surface, is currently not fully understood. Curvature along the profile’s surface, is currently not fully understood.
As a geometric criterion for smooth change of curvature in the lowest range of change in the absence of kinks on the profile, you can take the value of the maximum curvature on the profile contour in the range [xc2,xc1] for the convex and for [xk2,xk1] the concave parts, by selecting the minimum of all possible values at the profile designs with the accepted parameters and restrictions. The requirement for the absence of curvature jumps in the description of the profile contour by power polynomials automatically fulfilled as all the derivatives of the polynomial are continuous functions. Agree to consider determined based on the geometric quality criterion, the missing boundary conditions in the form of derivatives of high orders in points C2, and K2 components of a vector Y ⃗ . For the concave part of the profile vector of
varied parameters Y ⃗ is as follows:
wherein k – the curvature of the profile, and the maximum is searched for in the range [xc2,xc1] on the convex portion of the profile and [xk2,xk1] – on the concave part of the profile using one of the one-dimensional search methods. Read More