Uniform Asymptotic Solutions for Potential Flow Around a Thin Airfoil and the Electrostatic Potential About a Thin Conductor

1968 ◽  
Vol 16 (1) ◽  
pp. 75-101 ◽  
Author(s):  
James F. Geer ◽  
Joseph B. Keller
Author(s):  
Robert Spall ◽  
Joshua Hodson

Undergraduate required fluid dynamics and elective aerodynamics courses include substantial material on analysis techniques for forces acting on bodies in external flows. These methods include momentum integral analysis, and, for aerodynamic applications, lift computed using circulation and the Kutta-Joukowski theorem. The author presented in a previous FED meeting code development and preliminary classroom results for the implementation of a fully interactive, two-dimensional potential flow solver for flow over both rigid and flexible thin-airfoil (or sail) geometries. The intent of the development was to design a code that could be used as a virtual wind tunnel. The solver was developed in Fortran 90/95 with user interface and graphics routines developed using the high-level plotting library DISLIN for use on Windows-based computers. The analysis code solves the potential flow equations for single or multiple airfoils using a vortex panel method in which the vortex strength varies linearly along the panel and is continuous from one panel to the next. A variety of controls are available to adjust airfoil shapes and angles-of-attack. The user may also specify either rigid thin airfoil shapes, or flexible airfoils in which the final equilibrium shapes are determined by the pressure distribution. Available graphics include velocity vectors, pressure coefficient contours, and streamlines. Lift, axial and normal force coefficients are also output in the form of bar graphs. Several improvements have been implemented in the code, based on early student feedback, to improve its suitability for educational purposes in fluid dynamics and aerodynamics classes. These include pressure plot distributions over the airfoils, the inclusion of standard NACA 4-digit airfoil definitions, the output of velocity and pressure data about a closed contour for use in circulation and momentum integral analysis calculations, and improvements regarding compatibility for use on computers of widely varying screen resolutions. In this work to be presented, recent improvements to the code, and subsequent educational/student learning results based on a series of Qualtrics online student survey questions are presented. These survey questions query the students understanding of a) momentum integral analysis, b) circulation, c) lift calculations using the Kutta-Joukowski theorem, d) airfoil-to-airfoil fluid flow interactions, e) the necessity for attention to details when performing engineering analysis. The code may be downloaded for use by educators and students at other universities.


2012 ◽  
Vol 132 (1) ◽  
pp. 95-100
Author(s):  
Hiroshi Morita ◽  
Ayumu Hatanaka ◽  
Toshiyuki Yokosuka ◽  
Yoshitaka Seki ◽  
Yoshiaki Tsumuraya ◽  
...  

2006 ◽  
Vol 16 (7) ◽  
pp. 763-776 ◽  
Author(s):  
T. Funada ◽  
J. Wang ◽  
Daniel D. Joseph

2014 ◽  
Vol 5 (2) ◽  
pp. 778-789
Author(s):  
Hassan Nouri Al-Obaidi ◽  
Ali A. Rashead Al-Azawy

Current research presents a visual-computational tool to design and investigate round electrostatic lenses in sense of analysis procedure. The finite elements methods is adopted to find the electrostatic potential in the lens region. Laplace’s equation is first replaced by a certain functional which physically represent the electric energy stored in the electric field. This functional is then minimized at each mesh point with respect to the nearest eight ones. This minimization process is proved to be entirely equivalent to solving Laplace’s equation. The requirement that the functional being minimized is then yields a set of nine point equations which inter relate the potentials at adjacent mesh points. Finally this set of equations is solved to find the electrostatic potential at each mesh point in the region of the lens under consideration. The procedure steps mention above are coded to program written in visual basic. Hence an interface tool for analyzing and designing electrostatic lenses has been built up. Designing results proved that the introduced tools has an excellent outputs in comparison with the others written in not visual programming languages. Furthermore it easier for researchers and designer to use such a tool over their counterpart ones.


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