To investigate the relationship of the rotating detonation and tangential instability, series of experiments have been done in a hollow chamber with Laval nozzle. In the present paper, two different ignition methods, named hot-jet and constant-pressure respectively, are adopted to compare the tangential instability and rotating detonation. The results show that, comparing with hot-jet method, when the contraction ratio of the nozzle is small, the realization of rotating detonation by constant pressure method is impossible. Three different combustion patterns have been found and characteristics of pressure oscillations have been discussed. When the contraction ratio is 10 and 12, the intrinsic frequencies of the test mode have been computed. Based on the pressure oscillations and the dominant frequency, the results are compared with the intrinsic frequency of combustion instability. The results show a good coincidence with each other. The non-linear tangential instabilities observed in rocket engines may actually be a manifestation of this rotating detonation wave mechanics in the hollow chamber with Laval nozzle. The work shows the possibility of detonation in a hollow chamber with Laval nozzle. It will enrich detonation wave theory and make a contribution to connecting the detonation and tangential instability. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.