Boundary layer thickness, accelerating flow.

  1. May 19, 2009 #1
    Hello,

    You've all probably seen the classic Blasius solution concerning the thickness of a boundary over a flat plate. This problem though assumes that the free stream velocity is constant.

    http://www.see.ed.ac.uk/~johnc/teaching/fluidmechanics4/2003-04/fluids9/2-dboundary.html

    I am currently faced with a problem where the free stream velocity is increasing as you go down the plate, so I cannot use the Blasius solutions.

    I was wondering if anyone out there knows anything about this subject and if they could reference me to some material concerning this topic.

    Thanks
     
  2. jcsd
  3. May 20, 2009 #2

    minger

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    It sounds to me like you have a Falkner-Skan Wedge flow. Basically this is a similarity solution (as the flat plate boundary layer). Similarity is achieved by the variable [tex]\eta = Cyx^a[/tex], which is consistent with a power-law freestream velocity distrubtion:
    [tex]U(x) = Kx^m\,\,\,; m=2a+1[/tex]
    The exponent m may be termed the power-law parameter. do some blah blah blah, and the common form of the Falkner-Skan equation for similar flows is:
    [tex]f''' + ff'' + \beta(1-f'^2) = 0[/tex]
    Where
    [tex]\beta = \frac{2m}{1+m}[/tex]
    The boundary conditions are the same for the flat plate:
    [tex]f(0) = f'(0) = 0; f'(\infty) = 1[/tex]
    Where the parameter [tex]\beta[/tex] is a measure of the pressure gradient, and is positive for positive for a negative or favorable pressure gradient, and negative for an unfavorable pressure gradient; 0 denotes the flat plate.

    I won't type the table out, but you should be able to find a table of solutions online somewhere. Basically they are all non-dimensional, so you'll have to find a reference to dimensionalize them to a real-life problem.
     
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