Mean flow reconstruction of turbulent flows from sparse measurements using physics-informed neural networks
File(s)
Author(s)
Patel, Yusuf
Type
Thesis
Abstract
Optimal aerodynamic design is guided by numerical simulation and experimental methods. For flows of engineering interest, numerical simulation is characterised by a trade-off between accuracy and tractability, whilst experimental methods are restricted by the inability to measure all spatio-temporal scales associated with turbulent dynamics. In this thesis, data assimilation (DA) methods, specifically Physics-Informed Neural Networks (PINNs), are explored, to augment low-fidelity numerical approaches (Reynolds-Averaged Navier-Stokes (RANS) equations) with sparse high-fidelity experimental data to accurately reconstruct turbulent flows.
Firstly, PINNs are benchmarked for mean-flow reconstruction using sparse mean velocity measurements against variational-DA. The PINN-DA-SA outperforms adjoint-based variational-DA, attributed to discretisation and regularisation errors in the variational formulation. Introducing an empirical closure model (Spalart-Allmaras) and corrective forcing with turbulence-model augmented PINNs, increase reconstruction accuracy in high velocity gradient and separation regions.
Secondly, a hierarchical PINN approach is proposed for constraining the flow physics with equations that systematically interpolate between direct numerical simulation of the Navier-Stokes (high-fidelity; resolved spectrum) and RANS (low-fidelity; modelled spectrum). We introduce PINNs constrained by the Navier-Stokes expressed in the frequency domain (Harmonic-Balanced Navier-Stokes (HBNS) equations) to resolve low-frequency harmonics and infer residual closure terms, without empirical turbulence models errors. PINN-DA-HBNS accurately reconstructs mean flow and predicts the skin-friction coefficient of the laminar circular cylinder better than RANS-constrained PINNs. Furthermore, use of PINN-DA is extended by building a neural network-based HBNS closure model, mapping low-frequency resolved quantities to residual closures.
Finally, the PINN-DA formulations are used to reconstruct a turbulent, axisymmetric bluff body wake from sparse experimental velocity data. Misaligned velocity measurements significantly affect flow reconstruction accuracy, leading to the proposal of transformation-embedded PINNs, to correct spatially-misaligned measurements. Using transformation-embedded PINN-DA, the bluff body wake flow is accurately reconstructed from sparse velocity measurements, and pressure is inferred away from the wall, where it cannot be measured non-intrusively.
Firstly, PINNs are benchmarked for mean-flow reconstruction using sparse mean velocity measurements against variational-DA. The PINN-DA-SA outperforms adjoint-based variational-DA, attributed to discretisation and regularisation errors in the variational formulation. Introducing an empirical closure model (Spalart-Allmaras) and corrective forcing with turbulence-model augmented PINNs, increase reconstruction accuracy in high velocity gradient and separation regions.
Secondly, a hierarchical PINN approach is proposed for constraining the flow physics with equations that systematically interpolate between direct numerical simulation of the Navier-Stokes (high-fidelity; resolved spectrum) and RANS (low-fidelity; modelled spectrum). We introduce PINNs constrained by the Navier-Stokes expressed in the frequency domain (Harmonic-Balanced Navier-Stokes (HBNS) equations) to resolve low-frequency harmonics and infer residual closure terms, without empirical turbulence models errors. PINN-DA-HBNS accurately reconstructs mean flow and predicts the skin-friction coefficient of the laminar circular cylinder better than RANS-constrained PINNs. Furthermore, use of PINN-DA is extended by building a neural network-based HBNS closure model, mapping low-frequency resolved quantities to residual closures.
Finally, the PINN-DA formulations are used to reconstruct a turbulent, axisymmetric bluff body wake from sparse experimental velocity data. Misaligned velocity measurements significantly affect flow reconstruction accuracy, leading to the proposal of transformation-embedded PINNs, to correct spatially-misaligned measurements. Using transformation-embedded PINN-DA, the bluff body wake flow is accurately reconstructed from sparse velocity measurements, and pressure is inferred away from the wall, where it cannot be measured non-intrusively.
Version
Open Access
Date Issued
2024-08-12
Date Awarded
2025-03-01
License URL
Advisor
Rigas, Georgios
Publisher Department
Department of Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)