Effect of Reynolds number on second-mode waves in transitional hypersonic boundary layers

The second-mode instability plays an important role in the natural transition of hypersonic boundary layer. In this paper, the Reynolds number effect on the second-mode waves has been experimentally investigated using the Nanoparticle-tracer based Planar Laser Scattering (NPLS) technique and PCB (R) fast response pressure sensors in Mach 6 quiet wind tunnel. The flow visualization results clearly capture the rope-like second-mode waves and the "quiet zone" before breakdown. The wavelength of second-mode waves is approximately twice the local boundary layer thickness, increasing with the streamwise distance and decreasing with the Reynolds number. The time delays between sensors indicate no significant Reynolds number effect on the propagation velocity of second-mode waves. The average velocity is about 0.82U(e). The characteristic frequencies are collated at different streamwise locations under different Reynolds numbers and show a linear proportion to root Re/v. Based on the growth law of compressible conical boundary layer thickness, the characteristic frequency relation and wavelength relation are derived as a function of Reynolds number and streamwise distance. The theoretical estimation values agree well with the experimental results, which provides the potential feasibility to predict the characteristic frequency and wavelength in other tunnels.