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Computer Problem 4

# Computer Problem 4 - PROBLEM DESCRIPTION The purpose of...

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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 in conjunction with the Walz applet and the Moses 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 for both code methods utilized. Once this is obtained, the Walz and Moses applets can be used to determine boundary layer characteristics over the top of 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

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Once the inviscid flow is obtained from the Vortex Panel Method, the Walz and Moses codes 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, and the Moses code uses the Moses Method to compute the incompressible turbulent 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
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