Effect of base cavities on the stability of the wake behind slender blunt-based axisymmetric bodies

We extend our previous research on the instability properties of the laminar incompressible flow of density ρ and viscosity μ, which develops behind a cylindrical body with a rounded nose and length-to-diameter ratio L/D = 2, aligned with a free-stream of velocity w_∞ [E. Sanmiguel-Rojas et al., Phys. Fluids 21, 114102 (2009); P. Bohorquez et al., J. Fluid Mech. 676, 110 (2011)]. In particular, we analyze the effects of a cylindrical base cavity of length h and diameter D_c on both critical Reynolds number, Re_c = ρw_∞D/μ, and drag coefficient, C_D, combining experiments, three-dimensional direct numerical simulations, and global linear stability analyses. The direct numerical simulations and the global stability results predict with precision the stabilizing effect of the cavity on the stationary, three-dimensional bifurcation in the wake as h/D increases. In fact, it is shown that, for a given value of D_c/D, the critical Reynolds number for the steady bifurcation, Re_cs, increases monotonically as h/D increases, reaching an asymptotic value which depends on D_c/D, at h/D ≈ 0.7. Likewise, for a fixed value of h/D, we have studied the effect of the cavity diameter D_c/D on the critical Reynolds number. No effect on Re_cs is observed over the range $0≤Dc/D≲0.6$⁠, but Re_cs shows a monotonic growth for $0.6≲Dc/D<1$⁠. On the other hand, for steady flows, the drag coefficient decreases with the length of the cavity reaching an asymptotic minimum for $h/D>rsim0.5$ and D_c/D → 1. Similar behavior with the cavity length has been observed experimentally and numerically for the second, oscillatory bifurcation, and its associated critical Reynolds number, Re_co.