Hypersonic Transition Model for Second Mode and Crossflow Instabilities

A transition model for second mode and crossflow instabilities was further improved and evaluated with focus on second mode instabilities. A comprehensive database consisting of 768 basic flow calculations for various freestream conditions and geometries was constructed and analyzed using a correlation study. Based on the analysis, the inputs, output, and architecture of the machine learning model were refined. Additionally, a novel correlation to estimate the onset of second mode instability was proposed. The model performance was evaluated for different grid resolutions, unit Reynolds numbers, nosetip bluntnesses, and for a case with pressure gradient, which demonstrate good agreement with experimental measurements and direct numerical simulation data. Key findings from the correlation analysis include a strong correlation between the local /a ratio (kinematic viscosity over speed of sound) and second mode growth, indicating stronger local growth at lower viscosity and higher speed of sound. The study also indicated 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 confirmed 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.