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On the surface of a rotating projectile flying with a supersonic speed, due to the rotational motion, an asymmetric boundary layer transition will occur. This boundary layer distortion caused by the rotation has a significant contribution to the Magnus effect, which will produce a large instability moment and cause flight instability. Therefore, it is of great significance to conduct in-depth research and flow mechanism analysis on the asymmetric boundary layer transition phenomenon on the surface of high-speed rotating projectiles. On the one hand, in supersonic boundary layers, the steamwise flow instability modes are mainly the first mode and the laminar flow separation mode; on the other hand, strong crossflow velocity shear will be generated in the self-rotating state of the projectile and the compressible crossflow instability plays an extremely important role. This paper proposes a physics-informed transition-turbulence model suitable for supersonic/hypersonic boundary layers, which contains physical instability mechanisms and all variables can be solved locally. New time scales for the first mode and crossflow mode are developed. Furthermore, compressibility corrections and cooled wall modifications are performed on the model. Based on this model, we conducted the unsteady simulations of the high-speed rotating straight cone, and carefully compared the mesh sensitivity. In detail, the boundary layer transition characteristics under different Mach numbers, angles of attack, Reynolds numbers and rotational speeds are analyzed through the present transition-turbulence model. Decent agreement with the experiment data verifies that the transition-turbulence model developed by the authors can be applied to predict the asymmetric transition phenomenon on the supersonic flying rotating projectiles with high accuracy. • An improved physics-informed transition-turbulence model for supersonic/hypersonic boundary layers is proposed based on local variables in this paper. • New time scales for the first mode, second mode and crossflow mode are developed and the cooled wall correction is formulated. • When the asymmetric transition phenomenon is considered using the present transition turbulence model, the accuracy of the prediction results has been greatly improved. [ABSTRACT FROM AUTHOR]