Wylly, Alexander (1951) A second order solution for an oscillating, two-dimensional, supersonic airfoil. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-03232009-084121
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In this paper a second-order solution, for the forces and moments produced by an oscillating two-dimensional airfoil of arbitrary cross section, has been determined. This solution was obtained by means of an iteration procedure. In the iteration procedure it was necessary to have a linearized solution of simple, closed form which was valid throughout the whole x, y plane. Existing solutions did not satisfy these requirements, thus, it was first necessary to develop a new linearized or first-order velocity potential. This potential was developed as a power series approximation, in frequency, to the exact linearized solution. Six terms of this series were developed and this sixth-order solution shown to be within a few percent of the exact linearized solution for reduced frequencies [...] less than 1.3.
The first two terms of the series approximation were then used in the iteration process to produce the second-order solution in thickness. This solution which is valid to second-order in thickness and frequency has been determined for an oscillating airfoil of general cross section.
The second-order terms were found to have a relatively strong influence on the final solution, particularly for the pitching moment. It will be seen in Section V that in many cases the second-order terms are larger in magnitude than the corresponding first order-terms and thus reverse the tendencies indicated by first-order theory. In particular, it was shown that the theoretical instability predicted by linearized theory for an airfoil of zero thickness is completely eliminated for an airfoil having a thickness ratio as small as three percent.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Engineering and Applied Science|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 January 1951|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||23 Mar 2009|
|Last Modified:||26 Dec 2012 02:35|
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