Assessment of Amplification Factor Transport Transition Modeling Using Output-Based Mesh Adaptation

A transport model used to predict laminar-to-turbulent boundary-layer transition is utilized alongside an output-based mesh adaptation algorithm to evaluate meshing requirements for transition modeling. The model, called the amplification factor transport transition model, is based on the approximate envelope method from linear stability theory and includes a transport equation that describes the evolution of the envelope amplification factor for streamwise instabilities. The model is coupled with the negative Spalart–Allmaras eddy-viscosity turbulence model, where a new algebraic intermittency closure model is proposed here. Furthermore, various modifications to the transition model to increase the continuity and, hence, improve the nonlinear convergence of the model are presented. The output-based mesh adaptation is used to create a series of optimal meshes, where each mesh minimizes numerical error in drag; this process is then used to assess mesh distribution requirements to achieve asymptotic solutions to the transition model. These mesh convergence studies, using a flat plate and a natural-laminar-flow airfoil, show that achieving asymptotic solutions for the transition model is challenging. In addition, the lack of mesh convergence is traced back to the formulation of the local shape factor. A future effort will pursue a more numerically favorable local shape factor formulation.