Learning time-averaged turbulent flow field of jet in crossflow from limited observations using physics-informed neural networks

Abstract

Physics-informed neural networks (PINNs) are becoming popular in solving fluid mechanics problems forwardly and inversely. However, under limited observations, the PINNs were found difficult to be applied to solve the inverse problems of three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations. In this study, the classical turbulent case of jet in crossflow (JICF) was representatively adopted into the investigation. The dataset was obtained from a high-fidelity large-eddy simulation. The tensor-basis eddy viscosity ( t-EV) model was imported firstly into the PINNs structure as prior knowledge. Observations of 5 measured planes were preliminarily used to reconstruct the time-averaged turbulent flow field. After embedding the t-EV model, the highest absolute error and the relative L2 error of streamwise velocity were reduced by 11.1% and 31.4%, respectively. To cut down the volume of limited observations, a more effective training dataset containing only two planes and two pairs of lines was determined based on the flow characteristics (e.g., shear layer and counter-rotating vortex pair). Compared with those of 5 planes, the highest absolute error and the relative L2 error of streamwise velocity were further reduced by 30.0% and 6.4%, respectively. The investigation in this study provided the alternative to resolve the inverse problems of three-dimensional RANS equations with limited observations, which extended the deep learning application in fluid mechanics.

Effect of network architecture on physics-informed deep learning of the Reynolds-averaged turbulent flow field around cylinders without training data

“…Increasing errors associated with higher Reynolds numbers were also reported by Sun et al [27] and Harmening et al [6]. Consequently, numerous studies were conducted incorporating measured or simulated training data to support training of the PINN [3,5,8,10,19,21,35,36], while investigations focusing unsupervised physics-informed DL of high Reynolds number flows without training data remain sparse [7].…”

Effect of Network Architecture on Physics-Informed Deep Learning of the Reynolds-Averaged Turbulent Flow Field around Cylinders without Training Data

“…Increasing errors associated with higher Reynolds numbers were also reported by Sun et al [8] and Harmening et al [12]. Consequently, numerous studies were conducted incorporating measured or simulated training data to support training of the PINN [14][15][16][17][18][24][25][26], while investigations focusing unsupervised physics-informed DL of high Reynolds number flows without training data remain sparse [13].…”

Swirling flow field reconstruction and cooling performance analysis based on experimental observations using physics-informed neural networks

“…where u ι , p, and u 0 ι u 0 | represent the mean velocity components, pressure, and Reynolds stress, respectively. Previous study (Huang et al, 2023) has provided the in-depths information about the determination of hyperparameter and MLP structure on solving RANS problems. In this study, 10 hidden layers, each containing 300 neurons is prescribed in MLP structure (Figure 2).…”

“…5 in PINNs couldn't perform well in previous work. Huang et al (2023) designed the t-EV model in consideration of the anisotropy. This model has been validated its capability of wellpredicting jet in crossflow field.…”

“…They found that the velocity components were matched with the experimental results while the Reynolds stress components were poorly estimated. More complex cases of jet in crossflow were investigated by Huang et al (2023), they designed the 2-rank tensor-basis eddy viscosity (t-EV) model to better fit PINNs' structure and represent the anisotropy, effectively improving PINNs' regression. It's found from the above evidence that the investigated case is relatively simple and most of the training datasets are extracted from the clean numerical simulation.…”