The research work is carried out for deflagration and detonation combustion processes at different equivalence ratios of hydrogen–air mixtures in a pulse detonation combustor (PDC). Furthermore, the U-shape channel curvature radius and thickness effect on detonation wave propagation are also investigated. This numerical simulation has been done using a SIMPLE algorithm with the finite volume discretization method and laminar finite rate chemistry for volumetric reaction in the Ansys Fluent platform. The numerical result shows that the U-bend radius of R = 3.5 cm can enhance the faster deflagration-to-detonation transition. So far, the fully developed detonation wave was found near the curvature area of the detonation tube having a width of W = 8 cm. This enhanced detonation wave velocity reaches 2775 m/s, which is higher than the C-J detonation velocity. Furthermore, the entropy generation has been analyzed in two modes of the combustion process. The entropy generation number of 0.76 and 0.7 is obtained from the deflagration and detonation combustion processes. However, the entropy production rate is less in the detonation combustion process, but thermal entropy generation is more in the deflagration combustion process with a magnitude of 3.5 kJ/kg K for an equivalence ratio of φ = 1.5. A combustion efficiency of 78% is found in the detonation combustion process, which is comparatively higher than the deflagration process.