Machine-Learning-Based Amplification Factor Transport Equation for Hypersonic Boundary-Layers

The accurate prediction of laminar-turbulent boundary-layer transition is critical for the design and safe operation of hypersonic flight vehicles. Because of the substantially different transition physics compared to subsonic boundary-layers, low-speed transition models are not suitable and cannot directly be extended to hypersonic flows. Subsonic transition models typically rely on analytical and semi-empirical boundary-layer and transition relations. The development of similar relations for hypersonic flows is either very difficult or simply impossible. This paper explores the feasibility of feed-forward neural networks as an alternative to the analytical and semi-empirical relations. A network was trained with amplification-factor envelopes from linear stability theory analyses for base flows with different streamwise pressure gradients and wall to freestream total temperature ratios. The base flows were obtained by numerical integration of the compressible self-similar boundary-layer equations and validated using solutions of the full Navier-Stokes equations. An inverse method based on the Prandtl-Meyer function is proposed for obtaining the body shape from the pressure gradient. The trained neural network was then implemented into a compressible Reynolds-averaged Navier-Stokes code. Calculations with an amplification-factor transport equation were carried out for a Mach 6 flat-plate boundary layer with two different wall-temperature ratios for a Mach 6 boundary layer with adverse pressure gradient. The amplification factor distributions obtained from the calculations and linear stability analyses are in good agreement.