A survey of machine learning wall models for large eddy simulation

This survey investigates wall modeling in large eddy simulations (LES) using data-driven machine learning (ML) techniques. To this end, we implement three ML wall models in an open-source code and compare their performances with the equilibrium wall model in LES of half-channel flow at eleven friction Reynolds numbers between $180$ and $10^{10}$. The three models have ''seen'' flows at only a few Reynolds numbers. We test if these ML wall models can extrapolate to unseen Reynolds numbers. Among the three models, two are supervised ML models, and one is a reinforcement learning ML model. The two supervised ML models are trained against direct numerical simulation (DNS) data, whereas the reinforcement learning ML model is trained in the context of a wall-modeled LES with no access to high-fidelity data. The two supervised ML models capture the law of the wall at both seen and unseen Reynolds numbers--although one model requires re-training and predicts a smaller von K\'arm\'an constant. The reinforcement learning model captures the law of the wall reasonably well but has errors at both low ($Re_\tau<10^3$) and high Reynolds numbers ($Re_\tau>10^6$). In addition to documenting the results, we try to ''understand'' why the ML models behave the way they behave. Analysis shows that the errors of the supervised ML model is a result of the network design and the errors in the reinforcement learning model arise due to the present choice of the ''states'' and the mismatch between the neutral line and the line separating the action map. In all, we see promises in data-driven machine learning models

Statistics of turbulence in the energy-containing range of Taylor-Couette compared to canonical wall-bounded flows

Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva \textit{et al.} (\textit{J. Fluid Mech.}, vol. 823,2017, pp. 498-510) observed that remarkably the \textit{large-scale} (energy-containing range) statistics in canonical wall bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached eddy contributions. By taking the effect of streamwise alignment into account, the attached eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS-framework --- both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high-Reynolds number data are currently available.Comment: accepted in J. Fluid Mec

Log-law recovery through reinforcement-learning wall model for large-eddy simulation

This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number ($Re_\tau = 10^4$) and does not rely on high-fidelity data, as the back-propagation process is based on a reward rather than output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers ($Re_\tau \in [180;10^{10}]$). The effects of varying agents' parameters such as actions range, time-step, and spacing are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws, and for extending this type of ML models to more complex flows in the future.Comment: arXiv admin note: text overlap with arXiv:2211.0361

Extension of the law of the wall exploiting the concepts of strong and weak universality of velocity fluctuations in a channel

This paper explores the universality of the instantaneous velocity profiles in a channel, which, despite the equilibrium nature of a channel flow, are subjected to strong non-equilibrium effects. In the analysis, we employ a one-dimensional scalar variant of the proper orthogonal decomposition (POD) and exploit the concepts of strong and weak universalities. Strong universality requires that all POD modes are universal with respect to the Reynolds number, while weak universality only requires that the first few POD modes are universal. As POD analysis concerns information at more than one location, these universalities are more general than various similarities and universality in the literature concerning single-point flow statistics, e.g., outer layer similarity or universality of the log law. We examine flows at $Re_\tau=$180, 540, 1000, and 5200. Strong universality is observed in the outer layer, and weak universality is found in both the inner layer and the outer part of the logarithmic layer. The presence of weak universality suggests the existence of an extension to the law of the wall (LoW). Here, we propose such an extension based on the results from one-dimensional POD analysis. The usefulness of the LoW extension is assessed by comparing flow reconstructions according to the extended LoW and the equilibrium LoW. We show that the extended LoW provides strikingly accurate flow reconstruction in the wall layer across a wide range of Reynolds numbers, capturing fine-scale motions that are entirely missed by the equilibrium LoW.Comment: 20 pages, 16 figure

Water saturation effects on P-wave anisotropy in synthetic sandstone with aligned fractures

The seismic properties of rocks are known to be sensitive to partial liquid or gas saturation, and to aligned fractures. P-wave anisotropy is widely used for fracture characterization and is known to be sensitive to the saturating fluid. However, studies combining the effect of multiphase saturation and aligned fractures are limited even though such conditions are common in the subsurface. An understanding of the effects of partial liquid or gas saturation on P-wave anisotropy could help improve seismic characterization of fractured, gas bearing reservoirs. Using octagonal-shaped synthetic sandstone samples, one containing aligned penny-shaped fractures and the other without fractures, we examined the influence of water saturation on P-wave anisotropy in fractured rocks. In the fractured rock, the saturation related stiffening effect at higher water saturation values is larger in the direction across the fractures than along the fractures. Consequently, the anisotropy parameter ‘?’ decreases as a result of this fluid stiffening effect. These effects are frequency dependent as a result of wave-induced fluid flow mechanisms. Our observations can be explained by combining a frequency-dependent fractured rock model and a frequency-dependent partial saturation model

Incorporating basic calibrations in existing machine-learned turbulence modeling

This work aims to incorporate basic calibrations of Reynolds-averaged Navier-Stokes (RANS) models as part of machine learning (ML) frameworks. The ML frameworks considered are tensor-basis neural network (TBNN), physics-informed machine learning (PIML), and field inversion & machine learning (FIML) in J. Fluid Mech., 2016, 807, 155-166, Phys. Rev. Fluids, 2017, 2(3), 034603 and J. Comp. Phys., 2016, 305, 758-774, and the baseline RANS models are the one-equation Spalart-Allmaras model, the two-equation $k$-$\omega$ model, and the seven-equation Reynolds stress transport models. ML frameworks are trained against plane channel flow and shear-layer flow data. We compare the ML frameworks and study whether the machine-learned augmentations are detrimental outside the training set. The findings are summarized as follows. The augmentations due to TBNN are detrimental. PIML leads to augmentations that are beneficial inside the training dataset but detrimental outside it. These results are not affected by the baseline RANS model. FIML's augmentations to the two eddy viscosity models, where an inner-layer treatment already exists, are largely neutral. Its augmentation to the seven-equation model, where an inner-layer treatment does not exist, improves the mean flow prediction in a channel. Furthermore, these FIML augmentations are mostly non-detrimental outside the training dataset. In addition to reporting these results, the paper offers physical explanations of the results. Last, we note that the conclusions drawn here are confined to the ML frameworks and the flows considered in this study. More detailed comparative studies and validation & verification studies are needed to account for developments in recent years