Mach number effects on vortex shedding of a square cylinder and thick symmetrical airfoil arranged in tandem

Abstract

An experimental study was done to elucidate the Mach number effects on vortex shedding of a square cylinder (side length D = 20 mm) and thick symmetrical airfoil (NACA 0018, chord length 20 mm) arranged in tandem , at free stream Mach numbers between 0.1526 and 0.9081, and at free stream Reynolds numbers (based on the side length D ) between 0.702 x 10 5 and 4.188 x 10 5 . The spacing ratio of the central distance, L , between the square cylinder and the airfoil to the side length, D , of the square cylinder was varied from 1.125 to 5.5. It was found that the regular vortex shedding is not suppressed by steady shock waves in the local supersonic flow regions; the periodic vortex shedding is still present, irrespective of the appearance of the shock waves. When the spacing ratio is fixed, the Strouhal number behind the square cylinder is almost constant up to the critical Mach number of about 0.70, but it increases rapidly with further increase of the Mach number. However, once the shock waves are formed on both sides of the vortex formation region, various frequency components, other than the vortex shedding frequency appear; the spectral peaks lower than those of the vortex shedding frequency were identified as frequencies of an acoustic-feedback oscillation and the resonance of the wind tunnel structural system. With increasing the Mach number, the formation region becomes small and asymmetric, and the separating shear layers become wavy. These changes result in an increase of the scale and strength of the vortices and thus enhance the vortex shedding process. However, when the Mach number exceeds the critical value, the streamwise length of the formation region increases suddenly and becomes long enough to enclose the downstream airfoil. Under this circumstance, the formation region is almost symmetrical with respect to the wake axis, and shock waves are formed on the upper and lower separating shear layers. The shock waves are almost normal to the wake axis at M = 0.7512 and 0.8215, but incline to the downstream direction at M = 0.9081. Acoustic waves travelling upstream have been observed most clearly when the vortex shed from the square cylinder hits the leading edge of the airfoil at a Mach number of about 0.63, which is close to, but slightly smaller than the critical value. The mean pressure and the amplitude of the pressure fluctuations in the test section decreases and increases, respectively, with increasing the Mach number. However, the amplitude of the pressure fluctuations decreases suddenly when the steady shock waves are formed on the upper and lower separating shear layers.