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Boundary layer thickness, accelerating flow. 
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#1
May1909, 04:18 PM

P: 20

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/teach...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
May2009, 08:07 AM

Sci Advisor
P: 1,498

It sounds to me like you have a FalknerSkan 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 powerlaw freestream velocity distrubtion:
[tex]U(x) = Kx^m\,\,\,; m=2a+1[/tex] The exponent m may be termed the powerlaw parameter. do some blah blah blah, and the common form of the FalknerSkan equation for similar flows is: [tex]f''' + ff'' + \beta(1f'^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 nondimensional, so you'll have to find a reference to dimensionalize them to a reallife problem. 


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