Abstract
Aerodynamic scientists are interested in geometry definition and possible geometric shapes that would be useful in design. This paper illustrates a simulation of a NACA four digits airfoil blade profile using MATLAB. As airfoil design became more sophisticated, this basic approach has been modified to include additional variables, and suggestions for the chord line length at the root and at the end of the blade. as well as changes in the twisting angle of the blade and its thickness, this helps to reduce the weight of the blade significantly Simulating NACA equations is very useful in obtaining coordinates of airfoil curvature for the whole series of NACA four digits, which is very effective in optimizing blade design. In order to get an optimal operating performance and high efficiency for the airfoil, the blade surface must be smooth and does not suffer any discontinuities or undefined cases, which cause separation of the boundary layer during the airflow, and get as a result great energy losses. Therefore, the conditions for the continuity of the blade was extracted using mathematical analysis, so the air flow does not suffer any interruptions which reduce the efficiency. This enable us to determine the locations of the maximum thickness of the blade sections on the chord along the blade, in addition to specifying conditions for the chord line length at the root and at the end of the blade which keep the blade curvature continuous and doesn’t have any irregular points, which also facilities writing the necessary programs.
Highlights
National advisory committee for aeronautics described airfoil geometry using digits after the word NACA
From equations (28, 29) we find that to avoid the undefined cases, which lead to discontinuities in blade curvature, conditions of smoothness, and continuity of the surface would be given as the following:
It is very effective to choose the values of chord line at the blade root and its end, and the position at the chord line corresponds to maximum thickness from the ranges defined above, in avoiding geometry problems
Summary
National advisory committee for aeronautics described airfoil geometry using digits after the word NACA. To get the optimal geometries and superior aerodynamic performance circle method has been modified and applied on the design of 2D isolated airfoils [5]. Some researchers have applied circle method to a symmetrical airfoil and a non- symmetrical airfoil, to remove their surface curvature and slope- of- curvature discontinuities [9]. Others have applied the prescribed surface curvature distribution blade design method on airfoil E387 to remove the gradient of curvature discontinuities [8]. Two- dimensional direct blade- design method has been developed, which uses a mixture of analytic polynomials and a mapping of a desired curvature distribution on the (x, y) plane to specify the geometry and avoid small slope- of- curvature discontinuities
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