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Thwaites correlation for momentum thickness

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Old   September 7, 2001, 07:37
Default Thwaites correlation for momentum thickness
Tim Franke
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can anybody explain what's behind the Thwaites' correlation for determining the momentum thickness ?

Thanks in advance,

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Old   September 16, 2001, 00:49
Default Re: Thwaites correlation for momentum thickness
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Thwaites idea was to see if a single parameter (lambda = big_lambda* (theta/delta)^2, where big_lambda is proportional to dUe/dx) could be used to fit the wall shear stress parameter (tau_wall*theta/(mu*U)) and shape factor (delta_star/theta) by correlating it with a large body of airfoil data. By fitting a linear function to a parameter F = (U*d(theta^2)/dx)/nu vs lambda (ie. F(lambda) = 0.45 - 6.0*lambda), an analytic solution for theta^2/nu was devised, which is the famous Thwaites' integral for theta. With the value of theta, one computes the wall shear stress and displacement thickness from his correlations with lambda. Very clever. In the original paper, the correlations for the wall shear stress and delta_star were given in the form of graphs. Others have given curve fits to these correlations. Thwaites' orginal work is:

"Approximate Calculation of the Laminar Boundary Layer," Aeronautical Quarterly, Vol. 1 pp. 245-280, 1949.

PS. Same response in newsgroup hth, Bob
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