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 psi 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 (psi)/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 Theta = 0 and 180 degrees, 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, Theta, for incidence angles between 6 and 35 degrees, where the data fall on a power law Theta similar to (t*)(k). (ii) The data suggest that the separation rate k is independent of the Reynolds number over the range 2.1 x 10(6) <= Re-L <= 23 x 10(6); for a primary separation k(1) similar or equal to -0.190, and for a secondary separation k(2) similar or equal to 0.045. (iii) The power-law curve fits trace the primary and secondary lines to a characteristic start time t(s)* similar or equal to 1.5.