Estimation of the Acoustic Field in a Uniform Duct with Mean Flow using Neural Networks

TL;DR

This work tackles the problem of estimating the frequency-domain acoustic field in a uniform duct with mean flow, a scenario common in HVAC, automotive, and aerospace applications. It develops a trial-solution physics-informed neural-network framework to solve the 1-D Helmholtz equation with and without mean flow, handling complex-valued pressure via a real/imag decomposition and a concatenated neural network architecture that also relates pressure to particle velocity. The approach enforces boundary conditions exactly and uses residual-based losses, achieving high accuracy against analytical solutions up to 2000 Hz and validating impedance predictions against 2-D FEM results; mean flow is shown to shift velocity nodes and alter the acoustic impedance. The authors derive a closed-form expression capturing the influence of mean flow, frequency, and boundary conditions on the field, and discuss extending the method beyond 1-D while highlighting PINN-related challenges such as hyperparameter tuning and complex-valued optimization.

Abstract

The study of sound propagation in a uniform duct having a mean flow has many applications, such as in the design of gas turbines, heating, ventilation and air conditioning ducts, automotive intake and exhaust systems, and in the modeling of speech. In this paper, the convective effects of the mean flow on the plane wave acoustic field inside a uniform duct were studied using artificial neural networks. The governing differential equation and the associated boundary conditions form a constrained optimization problem. It is converted to an unconstrained optimization problem and solved by approximating the acoustic field variable to a neural network. The complex-valued acoustic pressure and particle velocity were predicted at different frequencies, and validated against the analytical solution and the finite element models. The effect of the mean flow is studied in terms of the acoustic impedance. A closed-form expression that describes the influence of various factors on the acoustic field is derived.

Figures (8)

• Figure 1: Schematic diagram of a neural network architecture.
• Figure 2: Schematic diagram of the neural network architecture for complex-valued output.
• Figure 3: Schematic diagram of the domain with boundary conditions.
• Figure 4: Acoustic pressure without mean flow at different frequencies: true solution, predicted solution.
• Figure 5: Acoustic pressure with mean flow at different frequencies: true solution, predicted solution.