Mach number dependence of Spectral Character of Unsteady Pressure field on Axisymmetric Backward Facing Step: Transonic Flows

Abstract

Abstract The unsteady pressure field over an axisymmetric backward-facing step was investigated experimentally at transonic Mach numbers of 1.05, 1.2, and 1.4. The study was aimed at examining the influence of transonic Mach numbers on the spatio-temporal character of the unsteady pressure field and on the dominant modes/mechanisms driving it. Surface flow visualization, Schlieren, and unsteady pressure measurements were carried out as a part of the experimental investigation. From oil flow visualization and schlieren, the reattachment region was identified, and consequently, the mean reattachment length was estimated. The mean reattachment length shows an increase with the increase in Mach number. The coefficient of mean pressure along the rearbody imitates a classical backward-facing step flow profile and can be divided into three distinct regions. The peak values of the coefficient of mean pressure and the coefficient of rms are seen to decrease with an increase in the freestream Mach number. Conventional spectral analysis reveals that as the Mach number increases, the dominant peak in the spectra shifts to lower frequencies. From the spectra, three dominant fluid dynamic mechanisms depending on the Mach number have been identified. Proper Orthogonal Decomposition (POD) analysis shows that 79–84% of the total energy contribution comes from the first six modes. The temporal dynamics of the POD modes indicate three prominent mechanisms are responsible for the unsteady pressure field. Spectral analysis of POD modes indicates that the spectra are primarily driven by the first three POD modes for M∞=1.05 and the first two modes for M∞=1.2 and 1.4. Moreover, it reveals the presence of three dominant modes, and the freestream Mach number strongly dictates the dominant mode that is driving the pressure field.