Abstract
The presented work aims is to develop a numerical computation program to determine the geometrical characteristics of planar thin wall section with constant thickness and make application to airfoils. In the literature, there are exact analytical solutions only for some sections of simple geometries such as circular and rectangular sections. Hence our interest is focused on the search of approximate numerical solutions for more complex sections used in aeronautics. The method used is that the subdivisions of the contour of the section into small infinitesimal segments. The geometric characteristics of a line segment in any given position of the two ends of these nodes can be determined easily. Using the principle of compound surfaces, one can determine the geometric characteristics of the thin-walled section of the airfoil area. The analytic function of the airfoil boundary is obtained using the cubic spline interpolation since it is given in the form of tabulated points. The geometric characteristics of a line segment are approximated by eliminating the results associated with the third power of the thickness. A calculation is made of the error between the approximated and exact formulas for determining a range for application of the approximated formulas.
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Abbreviations
- (x i , y i ):
-
Coordinates of a node
- NS:
-
Number of straight line segments
- NN:
-
Number of nodes on the boundary of the section
- I x , I y :
-
Inertia moments of a straight line segment
- S x , S y :
-
Static moments of a straight line segment
- I xy :
-
Product of inertia of a straight line segment
- L :
-
Segment length and for section
- x G , y G :
-
Coordinates of the center of gravity
- I P :
-
Polar moment of inertia
- \({\eta^{\ast}}\) :
-
Normalized variable
- P, Q :
-
Parameters for the control of mesh points (Stretching function)
- C :
-
Chord of the airfoil
- t :
-
Thickness of the segment and the airfoil
- \({\varepsilon}\) :
-
Relative error
- i :
-
Counter on the nodes and segment
- 12:
-
Segment bounded by the nodes 1 and 2
- G :
-
Center of gravity
References
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Zebbiche, T., Boun-jad, M. & Allali, A. Geometric Characteristics of Thin Wall Sections with Application to Airfoils. Arab J Sci Eng 39, 5917–5927 (2014). https://doi.org/10.1007/s13369-014-1152-1
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DOI: https://doi.org/10.1007/s13369-014-1152-1