The capability of the e N method to predict transition in complex three-dimensional, laminar boundary layers is demonstrated. Flows around inclined prolate spheroids are ideally suited for investigation because they exhibit highly divergent and convergent three-dimensional viscous flows on curved surfaces. The inviscid flowfield is described by the potential theory and the viscous layer by a three-dimensional laminar boundary-layer method. This approach is applied in weak viscous/inviscid interaction regions only, that is, in attached laminar flow regions, and validated by comparison with measured wall pressure and skin friction in magnitude and direction. For the determination of the transition location, the laminar boundary layer is analyzed by the two N factor e N method. Excited Tollmien-Schlichting waves of constant frequencies and stationary crossflow waves of constant wavelength are computed by the local, linear stability theory. Both N factor integrations are executed along 21 streamlines, which regularly cover the surface of the prolate spheroid. First, the values of both N factors at the measured transition locations are calculated, which deliver the stability limit of the prolate spheroid in the considered wind tunnel. Second, based on the knowledge of the stability limit, the transition locations are evaluated. The prolate spheroid with an aspect ratio of 6:1 was tested in two wind tunnels at angles of attack from 0 to 30 deg and Reynolds numbers from 1.5 × × 10 6 to 43 × × 10 6 . The measured transition locations compare remarkably well with computations for all investigated flow cases.
Nomenclaturea = major axis of the prolate spheroid b = minor axis of the prolate spheroid C f t = resultant skin-friction coefficient C p = pressure coefficient L = reference length, 2a N CF = value of N * CF at measured transition N TS = value of N * TS at measured transition N * CF = envelope N factors of unstable crossflow waves N * TS = envelope N factors of unstable Tollmien-Schlichting waves Re = Reynolds number based on freestream conditions and reference length, U ∞ ∞ L/µ ∞ Reδ * c = Reynolds number based on the displacement thickness of the crossflow velocity profile, U e ρ e δ * c /µ e Reδ * s = Reynolds number based on the displacement thickness of the streamwise velocity profile, U e ρ e δ * s /µ e U = velocity component in streamwise direction u = velocity component in ξ direction V = velocity component in crossflow direction v = velocity component in φ direction X, Y, Z = Cartesian coordinates, where X is in direction of the major axis of the prolate spheroid X 0 = absolute value of X coordinate of the stagnation point α = angle of attack α = angle between the velocity components u e and v e γ = local wall shear stress direction relative to a line φ = const = displacement thickness of the crossflow velocity profile, − ∞ 0 V U e dζ δ * s = displacement thickness of the streamwise velocity profile, ∞ 0 1 − U U e dζ λ = angle between the coordinates ξ and φ µ= dynamic viscosity ξ, φ, ζ = orthogonal, surface...