1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Modelling a flow past a symmetric body

  1. Oct 18, 2008 #1
    1. The problem statement, all variables and given/known data
    I need to model the streamlines for an incompressible, irrotational flow about various symmetric bodies, starting with an ellipse


    2. Relevant equations
    for a uniform flow in the positive x direction, psi =y
    for a source/sink of strength K at (xn,yn)
    psi = Karctan((y-yn)/(x-xn))
    at any point along the body, there must be no flow across it, and hence psi = 0


    3. The attempt at a solution

    the stream function for the whole flow = Uy+ SUM Knarctan(y/(x-xn)) (no ydisplacement as all sources are on axis)
    this = 0 at each of the control points y(m) (and everywhere else along the surface of the sphere, but a number of control points = to the number of sources should be appropriate)

    hence
    Knpsin(m) - Uy(m) = 0

    and so I should be able to get the strengths from the following matlab code (taking U =1)


    Code (Text):

    n = 10;
    L = 1;
    D = 0.5;
    dx = 2*L/(n+1);
    xs = -L+dx:dx:L-dx;   % uniformly distributed
    xb = -L+dx:dx:L-dx   % uniformly distributed
    %
    % definition of body geometry
    %
       yb = D*sqrt(1-xb.^2./L^2); % ellipse
    %
    % plot control points
    %
    figure
    plot([-L xb L],[0 yb 0],[-L xb L],[0 -yb 0])
    axis equal
    %
    % compute source strengths
    %
    % K = strength
    %
    for i=1:n
        for j=1:n
            a(i,j) = atan(yb(i)./(xb(i)-xs(j)));
        end
        b(i,1) = -yb(i);
    end
    K = a\b
     
    However this, results in all negative values for K, meaning a huge total removal of volume from the system instead of the expected no (or approximately no) change, and hence a set of funky streamlines that look nothing at all like a flow around an ellipse.

    EDIT: realised I made a mistake, should be b(i,1) = yb(i) (not -yb(i)) however this just results in all strengths being positive, so I get what looks like a funky superposition of flows around multiple semi-infinite bodies.
     
    Last edited: Oct 18, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Modelling a flow past a symmetric body
  1. Traffic flow question (Replies: 0)

  2. Time Series Modelling (Replies: 0)

Loading...