Physics-Informed Neural Networks for Nonlinear Pseudoshock Modeling in Duct Flows

Scramjet inlets often struggle with the consequences of supersonic flight. As shock waves interact with thickening boundary layers inside the inlet, instabilities can arise, leading to unstart and a sudden loss of thrust and control.

A common simplification to capture key features of inlet flow dynamics is to model pseudoshocks in backpressured ducts. The Smart-Ortwerth model (2015) does this by predicting the Mach number, pressure ratio, and boundary layer along a duct or inlet.

However, this model relies on estimates of the skin friction coefficient (C_f) and boundary layer thickness (δ), which can introduce significant uncertainty. To improve upon this, we propose a physics-informed neural network (PINN) framework that enhances accuracy by learning nonlinear correction terms based on experimental data and the physical equations in the Smart-Ortwerth model. By embedding the model's governing ODEs into the network's loss function, our approach preserves physical consistency while reducing reliance on uncertain parameters such as C_f or δ.

This hybrid approach brings more reliability into modeling shock-train-dominated duct flows, with the ultimate goal of improving predictive models for the design of high-speed propulsion systems.