hw3 - 16.100 Homework Assignment 3 Due Monday September...

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16.100 Homework Assignment # 3 Due: Monday, September 26 th , 9am Problem 1 (70%) Useful reading: Anderson: Section 3.14, 3.16, 4.5, 4.10 nodes where vortices are located X control points where is enforce 0 = n u v v d Γ 2 X Γ 3 V X 0.12c X α Γ 1 c Consider the isosceles triangle airfoil with 12% thickness as shown above. A simple potential flow model for the flow over the triangle is to place point vortices at each of the three nodes and then determine the strengths (i.e. the circulations Γ i ) which satisfy flow tangency at three control points. For this model, let the control points be located at the midpoints of the three edges of the triangle. a) Set-up the 3x3 system of equations that expresses 0 = n u v v at the control points. b) Show that the 3x3 matrix for this system is singular (i.e. it has at least one zero eigenvalue). c) The singularity of the matrix can be removed by applying another condition in addition to flow tangency. Since the solution that is often of interest is attached flow in which the flow leaves the trailing edge smoothly and does not wrap around the trailing edge (i.e. the flow
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