Calibration of a γ-Reθγ-Reθ transition model and its validation in low-speed flows with high-order numerical method

Based on the Reynolds-averaged Navier–Stokes (RANS) equations and structured grid technology, the calibration and validation of γ-Reθγ-Reθ transition model is preformed with fifth-order weighted compact nonlinear scheme (WCNS), and the purpose of the present work is to improve the numerical accuracy for aerodynamic characteristics simulation of low-speed flow with transition model on the basis of high-order numerical method study. Firstly, the empirical correlation functions involved in the γ-Reθγ-Reθ transition model are modified and calibrated with experimental data of turbulent flat plates. Then, the grid convergence is studied on NLR-7301 two-element airfoil with the modified empirical correlation. At last, the modified empirical correlation is validated with NLR-7301 two-element airfoil and high-lift trapezoidal wing from transition location, velocity profile in boundary layer, surface pressure coefficient and aerodynamic characteristics. The numerical results illustrate that the numerical accuracy of transition length and skin friction behind transition location are improved with modified empirical correlation function, and obviously increases the numerical accuracy of aerodynamic characteristics prediction for typical transport configurations in low-speed range.