Numerical Reconstruction of Thermo-Fluid Dynamic Fields from Sparse Pressure Data

Motivation

During the design phase and operational monitoring of thermoacoustic systems, such as combustion chambers in gas turbines, it is crucial to determine the values of quantities of interest (e.g., fluctuations in pressure, velocity, temperature, and heat release) as functions of time at as many spatial locations as possible. Unfortunately, measuring velocity and temperature with high temporal resolution is both expensive and technically challenging. Moreover, measuring the heat release rate requires optical access and costly equipment, which is often impractical during experimental campaigns, especially when the test rig operates at high pressures.
As a result, experimental data often consist solely of pressure time series recorded at a few discrete locations. Unfortunately, such sparse pressure monitoring may be inadequate to effectively control localized high-pressure fluctuations that could damage the system during operation. Furthermore, other quantities of interest, such as velocity, temperature, and heat release, are typically unavailable. These quantities are crucial for evaluating—and potentially controlling—the flame response to flow perturbations, as well as for inferring acoustic boundary conditions, among other applications.

Currently, our group's research focuses on the acoustic reconstruction of thermo-fluid dynamic fields—such as pressure, velocity, and temperature perturbations—using time series of pressure data measured at discrete locations within the system. Five methods are being investigated:

Objectives and Strategy

Currently, our group's research focuses on the acoustic reconstruction of thermo-fluid dynamic fields—such as pressure, velocity, and temperature perturbations—using time series of pressure data measured at discrete locations within the system. Five methods are being investigated:

Fourier Decomposition and Adaptive Multi-Microphone Method: We decompose acoustic signals using Fourier transforms and subsequently implement an adaptive multi-microphone approach for field reconstruction.
Physics-Informed Neural Networks (PINNs): We utilize feed-forward neural networks in combination with cost functions that enforce the fulfillment of the linearized Euler equations, optionally including the heat release rate as a source term. Additional constraints, leveraging prior knowledge of temperature distributions along the combustion chamber, are also incorporated.
Bayesian Methods and Data Assimilation: The extended Kalman filter is applied to the linearized Euler equations to assimilate coefficients characterizing acoustic boundary conditions and temperature profiles within the domain.
Hard-Constrained Neural Networks: A tailored neural network architecture, employing a sinusoidal activation function in the final layer, is used to approximate the transport equations for acoustic waves. The wave number is treated as a spatially varying parameter.
Differential Acoustic Solver: Acoustic wave transport equations are implemented using implicit automatic differentiation via the JAX library, enabling efficient and flexible numerical solutions.