Program EDDYBL

D .11 . ADDITIONAL TECHNICAL INFORMATION 429D .11 .4 Transformed EquationsThe boundary-layer equations are singular at the leading edge of a body.As noted above, the program uses conventional Levy-Lees variables (~, 71)to remove this singularity . Body oriented physical coordinates (s, n) arerelated to transformed coordinates (~, ij) according todf = Peu,Per2l ds and dii = Pue(ro) j do(D .39)where r o is body radius and subscript e denotes boundary-layer edge .Equivalently, we can write~(S) = sf Pefeper o9 ds0and q(s, n) =where t is the transverse curvature defined bynPe ,ue-77 0 PeI'l, P t. . do (D .40)t = r (D .41)r oThe relations between derivatives in the physical (s, n) and transformed(~, r!) coordinate system are as follows :Cas)na= Peueheroi ( '9~+ C as )n '971)£8n 27 CPe)C19 Peuerot 7The dependent variables are also transformed according to :(D .42)(D .43)U,~ ~(~~ ~l) =T TeTeN, rl) = ~ 2j(D .44)Peue ero [F C as) + Pv~, ]k 2~w (~ 2~ZK( , rl) = u2W(f rl) = u2E ~!) = i4e e eThe transformed equations for the k-w and k-c models can then beexpressed as follows .aF2~a + r~VaV + F = 0 (D .45)