High-spatial resolution analyses of compressible turbulent boundary layers at Ma \(=\) 4.2

Abstract

High-spatial resolution particle image velocimetry (PIV) and particle tracking velocimetry (PTV) analyses were conducted to investigate the zero-pressure-gradient compressible turbulent boundary layers at Mach 4.2 with \(\textit{Re}_{ \theta } = 2323 - 3220\). The PTV analysis achieves a spatial resolution of O(0.01) mm in the near-wall region to resolve the flow in the viscous sublayer and buffer layer. Several estimation methods have been used to determine the skin friction coefficient based on the streamwise velocity distribution, e.g., the linear relation in the viscous sublayer, the Spalding equation, the logarithmic law, and the wake law. The van Driest \(\textrm{II}\) transformed skin friction coefficients agree well with the Blasius (1913) relation with a deviation less than 5%. The mean and fluctuating streamwise velocities collapse with the law of the wall and the DNS results, when scaled according to van Driest and Morkovin-scaling respectively. Owing to the high-spatial resolution PTV technique, the peaks of the streamwise velocity fluctuations are found at \(\textit{y}^{\mathrm {+}} = 13\) and \(\textit{y}^{\mathrm {*}} = 18\) in inner and semi-local scalings. Furthermore, the convergence of the two-point spatial correlation is improved using an ensemble-averaged method. The inclination angles of the \(\textit{R}_{uu}\) contours are approximately 8\(^{\circ }\) in the logarithmic region and 13\(^{\circ }\) in the wake region, which are different from those observed in incompressible turbulent boundary layers (TBLs). When the wall-normal integral scale is normalized by the characteristic structural length defined by Pirozzoli and Bernardini (2011), a plateau is observed. This indicates that self-similarity of the wall-normal length scale exists for the near-wall structures in CTBLs. Moreover, the uniform velocity zones (UVZs) in CTBLs are also examined. The mean number of UVZs ranges from approximately 1.5to 2 in the friction Reynolds number range of \(\textit{Re}_{\tau }\approx 180 - 230\), in line with the logarithmic increase reported by de Silva et al. (2016). From a statistical perspective, the turbulent/non-turbulent interface (TNTI) appears to primarily modulate the thicknesses of the UVZs, rather than their numbers.