Research of transition criterion for semi-empirical prediction method at specified transonic regime

A transonic wind tunnel transition test is implemented on a fuselage-wing configuration with the sweep angle 35 ^∘ for commercial aircraft. The wide range of angle of attack from −3.69 ^∘ to 3.07 ^∘ assures that with increasing angle of attack, the laminar to turbulent transition dominant factor varies from cross-flow (CF) vortices to Tollmien-Schlichting (TS) waves. With linear stability theory, the limiting N-factors are calibrated based on the pressure distribution by experiment or the Reynolds Averaged Navier-Stokes (RANS) solver using the fixed experimental transition location. The pressure distribution of the RANS solver agrees well with the experiment in general except some small discrepancies, which causes deviation by 0.6 for the limiting TS N-factor. The RANS solver and the stability analysis provide the limiting N-factors of 7.0 and 8.7 for CF-vortices and TS-waves at the two sides, respectively. In the between, the TS value decays with the CF value due to their interaction. Thus, the transition criterion for limiting N-factors is established for the laminar prediction tool of e ^N method at similar transonic wind tunnel. With the transition criterion, the transition location difference for 95% cases between the simulation and the experimental data is lower than 5% chord. The good match illustrates that the transition tool is accurate and robust for engineering applications, and also verifies the reasonability of the limiting N-factors. Therefore, the transition criteria at similar transonic conditions and well-performed e ^N transition tool can be applied for the future laminar wing design.