Computational fluid dynamics compatible transition modeling using an amplification factor transport equation

A new laminar-turbulent transition model for low-turbulence external aerodynamic applications is presented that incorporates linear stability theory in a manner compatible with modern computational fluid dynamics solvers. The model uses a new transport equation that describes the growth of the maximum Tollmien-Schlichting instability amplitude in the presence of a boundary layer. To avoid the need for integration paths and nonlocal operations, a locally defined nondimensional pressure-gradient parameter is used that serves as an estimator of the integral boundary-layer properties. The model has been implemented into the OVERFLOW 2.2f solver. Comparisons of predictions using the new model with high-quality wind-tunnel measurements of airfoil section characteristics confirm the predictive qualities of the model, as well as its improvement over the current state of the art in computational fluid dynamics transition modeling at approximately half the computational expense.