GEOMETRIC MODELING OF THE BLADE AIRFOIL OF AN AXIAL FLOW COMPRESSOR OF THE S-SHAPED FORM
Ключові слова:axial flow compressor, blade airfoil, camber line, S-shape, natural parameterization
A method of geometric modeling of the airfiol of an S-shaped axial flow compressor blade is proposed, which provides the distribution of a well-developed symmetric aerodynamic airfoil along the camber line, which has an inflection point in the outlet region of the modeled airfoil. The camber line of the airfoil is represented by a constructed curve and is formed from two sections. Both sections of the compound curve are modeled in natural parameterization, in which the parameter is the length of the arc of the line, as well as the application of certain laws of curvature distribution. The curvature of the first section obeys a quadratic dependence on the arc length; the second section is modeled using a polynomial dependence of the fifth degree. At the point of joining of the sections, located at the place of the maximum rise of the camber line, the third order of smoothness is provided, which provides for the equality of the values of functions, its derivatives, curvature and derivatives of curvature along the arc length at this point. The coordinates of four points are used as the initial data for modeling the camber line, two of which are located at the leading and trailing points of the modeled curve, the third point is at the place of the maximum rise of the camber line, the fourth point is at the location of the inflection of the curve. At the leading and trailing points, the angles of inclination of the tangents are set, which are determined in the gas-dynamic calculation of the axial flow compressor and take into account the stagger angle of the airfoil. At the point of maximum rise of the line, the angle of inclination of the tangent is zero. At the inflection point of the camber line, which gives the airfoil an S-shape, the angle of inclination of the tangent is not specified, since it is determined during the modeling of the curve. Also, in the process of modeling the sections of the curve, unknown coefficients of the dependences of the distribution of curvature and length of arcs are found. This is done by minimizing the deviation of the intermediate points from the given base points. In the first section, the minimization problem is one-criterion, in the second, it is two-criterion, since the modeled line must pass through the inflection point of the camber line specified by the designer. It is the presence of the bend in the camber line that makes it possible to obtain S-shaped axial flow compressor blade airfoils.
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