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Homework Help: Source Panel method for flow pressure distribution over cylinder

  1. Feb 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Develop a source-panel computer program to numerically calculate the potential flow pressure distribution on a right circular cylinder with and without circulation.

    1.) Tabulate and plot your numerical results for the pressure coefficient distribution on the cylinder together with the corresponding exact analytic solution as a function of the angular variable omega, measured clockwise from the negative x-axis to the center of panels, from 0-360 degrees. Tabulate the following results:
    i, omega, q, numerical Cp, theoretical Cp, % error.

    2.) Do your calculations for the following values of circulation: K =[itex]\Gamma/\left(2\pi\right)[/itex] = 0, -1, -2, and -3. For K=0 do your calculations for N=4 and 250. For all other values of K, use only N=250.

    sourcepanelpicture.jpg

    2. Relevant equations
    w=omega
    Theoretical Cp=1-4*sin(w)^2
    w=(360/N)(i-0.5)
    θi= ARCtan((yi+1-yi)/(xi+1-xi))
    ζi=0.5(xi+xi+1)
    ηi=0.5(yi+yi+1)
    yi=sin(wi)
    xi=cos(wi)

    U0sin(θi - α) =(qi)/2 - SUM^{N}_{j=1}qjcij j does NOT equal i
    cij=sin(θi-[itex]\Phi[/itex]ij)/2[itex]\pi[/itex]rijΔS
    rij=[(ζij)2+(ηij)2]1/2
    [itex]\Phiij[/itex]=ARCtan(ηji)/(ζji)
    Sorry but I am making some mistake with the complex symbol program on this forum.

    3. The attempt at a solution

    I have calculated i, ωi, ηi, ζi, xi, yi, θi for N=250. I can't find the j components of those needed.

    Also I'm having trouble finding out the length of each panel. If a square was inside the unit circle, each length would be 1.414 right? But N=250 not 4.
     
    Last edited: Feb 19, 2012
  2. jcsd
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