Hypersonic Transition Model for Second-Mode Instability

A transition model for second-mode instability is proposed and evaluated. A comprehensive database consisting of 768 boundary-layer solutions for various freestream conditions and geometries is constructed and analyzed using a correlation study. Based on the analysis, the inputs, output, and architecture of the machine-learning model are selected. Additionally, a novel correlation to estimate the onset of second-mode instability is proposed. The model performance is evaluated for different grid resolutions, unit Reynolds numbers, nose-tip bluntnesses, and a case with pressure gradient. Good agreement is obtained with experimental measurements and direct numerical simulation data. Key findings from the correlation analysis include a strong correlation between the local [Formula: see text] ratio (kinematic viscosity over speed of sound) and second-mode growth, indicating larger local growth at lower viscosity and higher speed of sound. The study also indicates that Menter’s local pressure gradient parameter might be sufficient for pressure gradient estimation in two-dimensional and axisymmetric flows. A deep neural network model with local Galilean-invariant inputs is shown to accurately estimate local second-mode growth. Extensive testing confirms the grid independence of the model and its ability to predict transition for different unit Reynolds numbers and nose radii. Excellent agreement with experimental measurements and direct numerical simulation data is also demonstrated for a flared cone geometry at Mach 6.