The present study focuses on the long-term behavior of low-enthalpy M=7 flows over double wedges that have a fixed fore angle of 30 degrees and aft angles ranging from 45 degrees to 60 degrees. Although there are numerical and experimental studies available in the literature, they mostly consider the short-term behavior of such flows. In one of those studies, Durna et al. (Phys. Fluids 28:096101, 2016) foresee the presence of an aft angle threshold for transition from steady flow to complex shock-boundary layer interactions. The present study investigates the presence of periodicity by performing computations up to 50 times the duration of the previous study. Our analyses show that beyond a threshold value of 47 degrees, the flows become time-periodic. We are able to describe complex interaction mechanisms of the periodic flow by utilizing the density gradients, shock locations, separation angle, and distributions of the pressure and heat flux over the wedge surfaces. The computational results show that as the aft angle is increased, the period of the flow shortens, and the duration, when the transmitted shock impinges on the wedge surface, decreases.