Unsteady vortex flows around a hemisphere—cylinder body with turbulent separation

Abstract

Previous studies have revealed that vortex oscillations exist around slender bodies at low Reynolds numbers where the boundary layers undergo laminar separation. This investigation aims to extend the study to higher Reynolds numbers where the boundary layers exhibit turbulent separation. A hemisphere–cylinder body with a fineness ratio of 24.5 was numerically simulated using detached eddy simulation at angles of attack (AOAs) of 30°–80° and was analyzed using dynamic mode decomposition (DMD). The fineness ratio is the ratio of length to diameter of the cylinder. The Reynolds number based on the cylinder diameter is fixed at Re = 3.0 × 106. The results indicate that, at AOA < 45°, the downstream wake vortices around the slender body exhibit weak oscillations in phase, corresponding to symmetric modes, which is much different from the cases with laminar separation in the previous studies. At AOA > 45°, the vortex flow over the slender body is divided into two parts: forebody vortex oscillations with lower frequencies and shedding of afterbody vortices with higher frequencies. The vortex oscillations produce greater sectional side-force than the vortex shedding, and the associated flow structures are similar to the laminar case, although the separation points in this case are greatly delayed due to turbulent separation. The DMD results at a typical AOA of 50° show that the leading oscillatory mode is antisymmetric, corresponding to alternate vortex oscillation over the forebody; apparent interactions exist between the vortex oscillation and vortex shedding. The vortex shedding region moves forward toward the nose with increasing AOAs. In addition, at the AOAs of 50°–80°, the non-dimensional frequencies for the vortex shedding can be approximately collapsed into a linear relationship with respect to axial location of the afterbody cylinder if the crossflow velocities normal to the cylinder are employed to normalize the frequencies. The vortex-oscillation frequencies, however, are independent of the crossflow velocities, and no suitable scale was found to collapse the data at present.