Some Numerical Considerations For Prediction Of Laminar Turbulent Transition In Boundary Layers

Disturbances in an incompressible laminar boundary layer can grow over time and lead to the transition to turbulence. This laminar to turbulent process can be computationally expensive for modern CFD solvers and has led to the emergence of streamwise marching techniques that accurately compute the disturbance growth in the laminar and transition regions at a fraction of the cost. The common streamwise marching techniques in slowly evolving shear flows, however, retain some undesirable limitations motivating the development of a novel marching algorithm presented here and known as the Spatial Perturbation Equations (SPE). The SPE couples the marching of boundary layer equations along with the perturbation equations. This coupling results in an accurate capturing of the mean flow distortion for high-amplitude disturbances; which existing methods have under-predicted. The SPE is also able to capture the growth of linear, multi-modal, and nonlinear growth of time-periodic disturbances once the projection operator is introduced to stabilize the marching procedure. The SPE is able to accurately capture the linear evolution of a Tollmien-Schlichting (TS) wave and the multi-modal transient growth for time-periodic disturbances. Nonlinear interaction is also observed for high-magnitude TS waves. For compressible flow, the laminar to turbulent process also has a major impact on many engineering quantities of interest such as surface heating in hypersonic atmospheric flight. In high-speed atmospheric flight, the so called Mack's second mode disturbances are observed as a common route of transition. Capturing the evolution and growth of the mode can be difficult when numerical dissipation from shock capturing techniques are introduced. Linear stability theory (LST) and streamwise marching techniques are used to estimate the growth of the second mode and compare the growth as predicted from direct numerical simulations. However, the choice of inflow conditions and shock-capturing techniques can have a major influence on the predicted growth. The effect of numerical dissipation is examined and explained for various shock-capturing methods and inflow conditions.