Realizing highly efficient supersonic combustion is critical for the development of scramjets. The ground test data of scramjet combustors are both expensive and difficult to be measured, thus high-fidelity numerical simulation becomes a necessary way for supersonic combustion research. By aid of the in-house developed compressible reacting flow solver AstroFoam, the hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation (RANS/LES) turbulence modeling framework based on Improved Delayed Detached Eddy Simulation (IDDES) and the Partially Stirred Reactor (PaSR) turbulent combustion model are used for the study of HyShot II scramjet tested in the high enthalpy shock tunnel in Göttingen (HEG). A detailed mechanism of H2/Air combustion with 9 species and 19 elementary reactions is used. The predicted static pressure distribution agrees well with experimental data. Typical flow structures of jet in supersonic cross flow including the evolvement of S-shaped structure to-shaped structure are captured. Based on the distribution of temperature and OH mass fraction, the flow field can be divided into three zones: the mixing zone, the ignition zone and the turbulent combustion zone. Analysis of the cross-sections in the ignition zone along the streamwise direction reveals that the initial emergence OH reactant lies mainly in the shear layer, and the Kelvin-Helmholtz instability is the underlying stimulation of the ignition.