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

• Published in: Physics of fluids (1994) Vol. 23; no. 11; pp. 114103 - 114103-11
• Main Authors: Sanmiguel-Rojas, E., Jiménez-González, J. I., Bohorquez, P., Pawlak, G., Martínez-Bazán, C.
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.11.2011
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar flows; Physics; Stability of laminar flows; Laminar flow; Digital simulation; Hydrodynamic instability; Wakes; Slender body; Modelling; Incompressible fluid; Revolving body; Viscous fluids; Axial symmetry; Mesh generation
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3658774

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 , Phys. Fluids 21 , 114102 (2009); P. Bohorquez , 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 ≤ D c / D ≲ 0 . 6 , but Re cs shows a monotonic growth for 0 . 6 ≲ D c / 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 > rsim 0 . 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 .