Abstract: Based on the linear stability theory, the e^N method is one of the most reliable transition prediction techniques for aerospace vehicles. However, the complexity of traditional linear stability theory increases the difficulty in its application to the flows over complex aerodynamic configurations. With the rapid development of the local-variable-based transition model in recent years, modeling the process of the traditional linear stability theory, that is, transforming the linear stability theory analysis into a CFD problem, has become a research hotspot. The key idea is to analyze the linear stability of a large number of similarity solutions of laminar boundary layers, followed by obtaining the relationship between the envelope of the amplification factor and the characteristic variables of the mean laminar flow. After that, the amplification factor transport model using the integral characteristics of the transport equation is constructed. The non-local variables in the model are solved locally and the new transport equations are coupled with the turbulence model to form a new transition-turbulence transport model. Verifications show that the current developed streamwise N_TS transport model and crossflow N_CF transport model have achieved high prediction accuracy in a wide range of numerical examples, despite improvements yet to be made in some aspects.

Key words: linear stability theory, transition model, turbulence model, amplification factor, e^N method