A comprehensive review of all relevant experimental data was completed, including recent data for the drag coefficient for a sphere in supersonic and hypersonic flows. The primary characterization parameter included the relative Mach, Knudsen, and Reynolds numbers based on the relative velocity, the sphere diameter, and other parameters. This review of data showed that the previously proposed nexus at a Reynolds number below 45 was not strictly met, and it instead included a weak transonic bump, which was identified numerically for the first time with the present simulations. New continuum-gas and rarefied-gas simulations were conducted and were combined with the expanded experimental dataset to improve the quantitative description of the drag coefficient in this region. The results indicated that a quasi nexus bridges the rarefaction regime and the compressible flow regimes. The comprehensive dataset was then used to develop new empirical models for the drag coefficient that showed improved robustness and accuracy as compared to previous models. These models are limited by the critical Reynolds number associated with boundary-layer transition on the sphere, which was found to increase substantially with the sphere Mach number.

Large-eddy simulations have been conducted to investigate the mechanisms of separated-flow control using a dielectric barrier discharge plasma actuator at a low Reynolds number. In the present study, the mechanisms are classified according to the means of momentum injection to the boundary layer. The separated flow around the NACA 0015 airfoil at a Reynolds number of 63 000 is used as the base flow for separation control. Both normal and burst mode actuations are adopted in separation control. The burst frequency non-dimensionalized by the freestream velocity and the chord length (F⁺) is varied from 0.25 to 25, and we discuss the control mechanism through the comparison of the aerodynamic performance and controlled flow-fields in each normal and burst case. Lift and drag coefficients are significantly improved for the cases of F⁺ = 1, 5, and 15 due to flow reattachment associated with a laminar-separation bubble. Frequency and linear stability analyses indicate that the F⁺ = 5 and 15 cases effectively excite the natural unstable frequency at the separated shear layer, which is caused by the Kelvin-Helmholtz instability. This excitation results in earlier flow reattachment due to earlier turbulent transition. Furthermore, the Reynolds stress decomposition is conducted in order to identify the means of momentum entrainment resulted from large-scale spanwise vortical structure or small-scale turbulent vortices. For the cases with flow reattachment, the large-scale spanwise vortices, which shed from the separated shear layer through plasma actuation, significantly increase the periodic component of the Reynolds stress near the leading edge. These large-scale vortices collapse to small-scale turbulent vortices, and the turbulent component of the Reynolds stress increases around the large-scale vortices. In these cases, although the combination of momentum entrainment by both Reynolds stress components results in flow reattachment, the dominant component is identified as the turbulent component. This indicates that one of the effective control mechanisms for laminar separation is momentum entrainment by turbulent vortices through turbulent transition.