A Numerically Tolerant Formulation of the
Amplification Factor Transport Transition Model
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simpson-simpsann-sm-physics-2026-thesis.pdf
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Author(s)
Simpson, Anna M.
Advisor(s)
Galbraith, Marshall C.
Johnson, Steven G.
Date Issued
February 2026
Publisher
Massachusetts Institute of Technology
Abstract
Modeling instabilities behind laminar-to-turbulence transition is an important component of constructing a complete picture of fluid behavior in the boundary layer. The Reynoldsaveraged Navier Stokes (RANS) equations can be used to quickly obtain approximate flow solutions, but closure of these equations requires modeling choices to account for turbulence and transition. While obtaining approximate solutions of fully turbulent flow has been successfully enabled by various models, the incorporation of laminar-to-turbulent transition for RANS still presents modeling and computational challenges. In particular, the Amplification Factor Transport (AFT) model uses a formulation of the local boundary layer shape parameter that leads to numerical challenges, as revealed by the use of adaptive meshing. With this parameterization, asymptotic solutions are not found with unstructured meshes. This work presents an analysis of self-similar parameters for Falkner-Skan wedge flow boundary layer profiles from which a new local shape parameter for AFT is found that is more numerically tolerant. New correlation functions are also developed. Additionally, a derivation is performed of solutions to the AFT equation based on Falkner-Skan profiles. New correlation functions are found and new coefficients are introduced to the AFT equation to calibrate the model to wedge flows based on the integral boundary layer solutions. The model is demonstrated for three wedge flow cases, showing the success of this calibration. The NLF(1)-0416 airfoil is used to highlight outstanding issues with implementing the model on curved geometry. Lastly, avenues for future work and improvements to the model are discussed.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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