Machine learning-based prediction of centerline pressure decay in supersonic jets

Abstract

Understanding the evolution of centerline pressure in underexpanded supersonic jets is essential for characterizing mixing, shock-cell structure, and the influence of nozzle modifications such as tabs and corrugations. Although extensive experimental datasets exist, their use in predictive modeling remains limited. This work develops a machine learning (ML) surrogate to predict the centerline pressure ratio ( p / p ₀ ) directly from operating and geometric parameters. The prediction is formulated as a pointwise regression problem, in which the pressure ratio at a given axial location X / D is modeled as a locally conditioned response to the nozzle pressure ratio (NPR), aspect ratio, nozzle configuration, and axial distance. This formulation enables prediction directly on the native experimental measurement grid without interpolation, while retaining the dominant effects of shock-cell dynamics on the overall decay behaviour. Beyond predictive accuracy, the pointwise formulation enables an examination of the limits of local conditioning, wherein systematic discrepancies between predictions and measurements are interpreted as indications of flow behaviour that cannot be represented within a purely local surrogate framework. The methodology is demonstrated using a curated dataset covering three aspect ratios, five nozzle configurations, and NPRs ranging from 4 to 8. Across grouped leave-one-file-out (LOFO) evaluation, the multilayer perceptron (MLP) yielded the lowest prediction error among the tested surrogates, while the largest residuals remained concentrated in the first shock-cell region. Using the corrected LOFO statistics, the MLP reduced the root-mean-square error (RMSE) by 24 % relative to polynomial regression and by 12 % relative to gradient boosting.