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Standard models such as HIFiRE-5 and HyTRV are used in the validation of hypersonic three-dimensional boundary layer transition. Hypersonic crossflow transition correction is proposed in the C-γ-Reθ transition model based on the original γ-Reθ transition model. In this study, the C-γ-Reθ transition model is applied to transition simulation of HIFiRE-5 and HyTRV under flight test and wind tunnel test conditions. For the flight test of HIFiRE-5, transition prediction is conducted under the conditions including eight typical altitudes and one attitude angle, the results of the C-γ-Reθ transition model are consistent with the heat-flux measurements, and the transition modes on the surface of HIFiRE-5 are compared. For the quiet/noise wind tunnel test of HIFiRE-5, the C-γ-Reθ transition model can accurately calculate the transition front shape and the transition onset location, and the results coincide with the temperature difference measurements. For the noise wind tunnel test of HyTRV, the C-γ-Reθ transition model calculation results of the upper and lower surfaces match with the infrared thermogram measurements under the conditions involving various Reynolds numbers and Mach numbers, and the ability to predict boundary layer transition in the crossflow mode is verified. Its prediction precision of the transition onset location and the transition front shape is on par with the eN method based on LST. As shown in the numerical simulation results, for each of the flight test and the quiet/noise wind tunnel test, the C-γ-Reθ transition model maintains high prediction reliability, and has achieved hypersonic three-dimensional boundary layer transition prediction for typical standard models.