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Unformatted text preview: PROBLEM DESCRIPTION The purpose of this assignment is to analyze the viscous flow over the top surface of an airfoil. Since this task is virtually impossible to do by hand, the use of computers and specially formatted codes are used to perform the necessary calculations. For this problem, the flow over the top surface of a NACA 4412 airfoil is the target of the analysis. Figure 1 below represents the conditions for which the airfoil will be tested. Figure 1 Airfoil Configuration This problem utilizes the Vortex Panel Method applet and the Walz applet available from the Virginia Tech Engineering Applets webpage. The user must first apply the vortex panel method to obtain the velocity distribution over the top surface of the airfoil for an inviscid flow. Once this is obtained, the Walz applet is used to obtain information regarding the boundary layer flow over the airfoil. The vortex panel method consists of six steps outlined below: The airfoil is divided into straight-line panels of a specified number to approximate the shape of the airfoil (a crude representation is shown in figure 2). For a uniform stream at a certain angle of attack, use superposition to locate the distributed potential vorticies on the surface of the airfoil. For each individual panel, a linear variation of circulation per unit length, γ , is used, where the values of γ at the ends of each panel is unknown. There is no flow through the airfoil (solid surface), and thus no flow through the center of each panel. This leads to the conclusion that the velocity component normal to each panel is equal to zero. The previous step provides n-1 equations for the n number of unknowns, so the Kutta Condition is implemented. The Kutta Condition states that the rear stagnation point is located at the trailing edge, providing the final condition for the number of unknowns. The Kutta-Joukowski Theorem is used to calculate the lift per unit span (. To get the total circulation G, the integral of the circulation distribution around the surface of the airfoil must be computed. Figure 2 Vortex Panel Method Airfoil Representation Once the inviscid flow is obtained from the Vortex Panel Method, the Walz code can be used to compute the incompressible laminar boundary layer. The Walz code uses the velocity distribution obtained by the Vortex Panel Method, and through the use of the Thwaites-Walz Integral Method, computes the incompressible laminar boundary layer. INPUT INFORMATION To utilize the Vortex Panel Method applet, the user must input a series of points representing the shape of an airfoil, as well as the angle of attack of the airfoil relative to the free-stream flow. The coordinate points that represent the airfoil should be generated from a program such as Javafoil, however the points used for the NACA 4412 airfoil were adapted from the example problem for the Vortex Panel Method applet from the website. These points are located in table 1 in appendix 1. To use the applet, the user must copy and paste the airfoil...
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This note was uploaded on 01/23/2012 for the course AOE 3044 taught by Professor Schetz,j during the Fall '08 term at Virginia Tech.
- Fall '08