Abstract
The method for geometric modeling of the S-shaped camber line of the profile of an axial compressor blade, which is a compound curve formed from three sections, was developed. Each of these sections is modeled in the natural parameterization using certain laws of curvature distribution along the arc of the modeled curve. The curvature of the input section obeys the linear law and that of the other two obeys the quadratic law of distribution from the length of the proper arc. Sections are connected with ensuring the second order of smoothness which implies the equality of the values of functions, derivatives, and the curvature at the conjugation point. In contrast to existing methods, it is proposed to plot the camber line of the compressor blade profile directly in the cascade of profiles, for which the axial length, stagger angle and its chord are known. In this case, the geometric angles of flow inlet and outlet are used as source data. Giving the S-shape to the camber line of the blade profile will facilitate multi-gradient motion of working medium at the outlet of the cascade of the profile, and therefore reduce energy losses in a compressor. Based on the proposed method, we developed a software code, which, in addition to digital information on the modeled camber line of the compressor blade profile, also displays the obtained results in a graphical form on the screen of a computer monitor. The performed calculation and experimental studies proved the efficiency of the proposed method for modeling camber lines of the profiles of axial compressor blades. This method can be useful to the organizations involved in designing axial compressors for gas turbine engines
Highlights
Axial compressors are widely used in the constructive schemes of aviation, marine and locomotive turbine engines
We developed the method for geometric modeling the S-shaped camber lines of the profiles of plane cross-sections of axial compressors blades in the form of a curve composed of three sections
Each section is represented in natural parameterization and applying the laws of curvature distribution depending on the length of the proper arc
Summary
Axial compressors are widely used in the constructive schemes of aviation, marine and locomotive turbine engines. In order to enhance the efficiency of a compressor, the measures related to the change of the geometry blades are applied: lean and sweep [1], wing sweep [2], windage [3], a change in the configuration of the leading edges [4], the use of profiles with «controllable» diffusivity [5, 6], etc The research in this direction is carried out by introducing these changes of the geometrical shape of the blade edge to the methods of designing these important components of flowthrough parts of axial compressors. At an increase in the velocity of the flow of the working medium, the designers of compressors began to give camber lines S-shaped form, which leads to the so-called «cont rollable» diffusivity It ensures gradient-free motion of working medium at the outlet of inter-blade channels. This leads to the relevance of research towards the development of the methods for the mathematical description of camber lines of the profiles of axial compressor blades of the S-shape type, which will contribute to enhancement of effective indicators of compressor of turbine engines
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