Longitudinal development of flow-separation lines on slender bodies in translation.

This paper examines flow-separation lines on axisymmetric bodies with tapered tails, where the separating flow takes into account the effect of local body radius r(x), incidence angle ψ and the body-length Reynolds number Re_L. The flow is interpreted as a transient problem which relates the longitudinal distance x to time t* = x tan(ψ)/r(x), similar to the approach of Jeans & Holloway (J. Aircraft, vol. 47 (6), 2010, pp. 2177-2183) on scaling separation lines. The windward and leeward sides correspond to the body azimuth angles ⊝ = 0 and 180°, respectively. From China-clay flow visualisation on axisymmetric bodies and from a literature review of slender-body flows, the present study shows three findings. (i) The time scale t* provides a collapse of the separation-line data, ⊝, for incidence angles between 6 and 35°, where the data fall on a power law ⊝ ~ (t*)^k. (ii) The data suggest that the separation rate k is independent of the Reynolds number over the range 2.1 x 10⁶ ⩽Re_L ⩽23 x 10⁶; for a primary separation k₁ ≃ -0.190, and for a secondary separation k₂ ≃ 0.045. (iii) The power-law curve fits trace the primary and secondary lines to a characteristic start time t*_s ≃ 1.5. [ABSTRACT FROM AUTHOR]