PT-PINNs: A Parametric Engineering Turbulence Solver based on Physics-Informed Neural Networks

TL;DR

A framework that enhances the ability of PINNs to solve parametric turbulence problems without training datasets from experiments or CFD-Parametric Turbulence PINNs (PT-PINNs) is proposed to improve the accuracy and robustness of this framework.

Abstract

Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to engineering turbulence problems. This study proposes a framework that enhances the ability of PINNs to solve parametric turbulence problems without training datasets from experiments or CFD-Parametric Turbulence PINNs (PT-PINNs)). Two key methods are introduced to improve the accuracy and robustness of this framework. The first is a soft constraint method for turbulent viscosity calculation. The second is a pre-training method based on the conservation of flow rate in the flow field. The effectiveness of PT-PINNs is validated using a three-dimensional backward-facing step (BFS) turbulence problem with two varying parameters (Re = 3000-200000, ER = 1.1-1.5). PT-PINNs produce predictions that closely match experimental data and computational fluid dynamics (CFD) results across various conditions. Moreover, PT-PINNs offer a computational efficiency advantage over traditional CFD methods. The total time required to construct the parametric BFS turbulence model is 39 hours, one-sixteenth of the time required by traditional numerical methods. The inference time for a single-condition prediction is just 40 seconds-only 0.5% of a single CFD computation. These findings highlight the potential of PT-PINNs for future applications in engineering turbulence optimization problems.

Figures (7)

• Figure 1: The framework of the PT-PINNs.a. The configuration of the parametric 3D turbulent BFS problem. b. The flow chart of PT-PINNs. c. The network structure and the training process of PT-PINNs.
• Figure 2: Quantitative comparisons of PT-PINNs' flow field velocity $\mathrm{u}$ and turbulence stress $\mathrm{(u')^2/U_0^2}$ prediction with experimental nadge2014high and CFD results in the recirculation region.a. Velocity u distribution of the section line at x/Xr=0.15, 0.45. 0.6. 0.85 positions in Z=0 Plane. b. Stream-wise variation of maximum turbulent stress $\mathrm{(u')^2/U_0^2}$ under different Reynolds numbers when ER=1.3. The X axis is normalized by mean reattachment length Xr.
• Figure 3: Comparisons of PT-PINNs predictions of streamlines of the recirculation vortex at the Z=0 Plane with experimental nadge2014high and CFD results under different Reynolds numbers and expansion ratios.
• Figure 4: Comparison of PT-PINNs' reattachment length predictions with CFD and experimental results nadge2014high.
• Figure 5: Comparisons of PT-PINNs predictions against CFD results of overall flow fields.