On the use of recurrent neural networks for predictions of turbulent flows
Swedish e-Science Research Centre (SeRC)（瑞典电子科学研究中心）
Luca Guastoni, Prem A. Srinivasan, Hossein Azizpour, Philipp Schlatter, Ricardo Vinuesa
备注：
Conference paper presented at 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11) at Southampton, UK, July 30 to August 2, 2019
In this paper, the prediction capabilities of recurrent neural networks are assessed in the low-order model of near-wall turbulence by Moehlis {\it et al.} (New J. Phys. {\bf 6}, 56, 2004). Our results show that it is possible to obtain excellent predictions of the turbulence statistics and the dynamic behavior of the flow with properly trained long short-term memory (LSTM) networks, leading to relative errors in the mean and the fluctuations below $1\%$. We also observe that using a loss function based only on the instantaneous predictions of the flow may not lead to the best predictions in terms of turbulence statistics, and it is necessary to define a stopping criterion based on the computed statistics. Furthermore, more sophisticated loss functions, including not only the instantaneous predictions but also the averaged behavior of the flow, may lead to much faster neural network training.
In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow fields given the solution of a computationally inexpensive but inaccurate low-fidelity solver. The resulting surrogate is able to generate physically accurate turbulent realizations at a computational cost magnitudes lower than that of a high-fidelity simulation. The deep generative model developed is a conditional invertible neural network, built with normal…
Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neural network methods allow higher dimensional input features to be considered without compromising the efficiency and accuracy of the traditional data driven models. Neural network methods proposed earlier follow a cumbersome methodology of predicting…
Direct Numerical Simulation of turbulent Taylor-Couette flow
本文描述了完全湍流状态下Taylor-Couette流动的直接数值模拟（DNS）。数值方法扩展了Quadrio和Luchini（Eur. J. Mech. B / Fluids，v.21，pp.413--427，2002），并且基于使用混合空间离散化（均匀方向上的谱方案，以及径向方向上的四阶、紧凑显式有限差分方案）的并行计算机代码。本文首次用DNS方法模拟了湍流状态下的Taylor-Couette流动。统计量的计算，以补充现有的实验信息，以期比较它的平面，压力驱动的湍流在相同的雷诺数值。平面流和曲壁流之间的流量统计差异的主要来源是由于曲率效应产生的大规模旋转结构的存在。
This paper proposes a new data assimilation method for recovering high fidelity turbulent flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion (POD-Inversion) data assimilation method. Aiming at the flows including shock wave discontinuities or separated flows at high angle of attack, the proposed method can reconstruct high-fidelity turbulent flow field combining with experimental distributed force coefficients. We firstly perform the POD analysis to the turbulent eddy viscosity fields computed by SA model and…
We present data driven kinematic models for the motion of bubbles in high-Re turbulent fluid flows based on recurrent neural networks with long-short term memory enhancements. The models extend empirical relations, such as Maxey-Riley (MR) and its variants, whose applicability is limited when either the bubble size is large or the flow is very complex. The recurrent neural networks are trained on the trajectories of bubbles obtained by Direct Numerical Simulations (DNS) of the Navier Stokes equations for a two-component incompressible flow model. Long short term memory components exploit the t…
In the first part of this study, we compared the performances of two categories of no-slip boundary treatments, i.e., the interpolated bounce-back schemes and the immersed boundary methods in a series of laminar flow simulations within the lattice Boltzmann method. In this second part, these boundary treatments are further compared in the simulations of turbulent flows with complex geometry to provide a next-level assessment of these schemes. Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent f…
Technische Universität Ilmenau（伊尔默瑙工业大学）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；New York University（纽约大学）
A combined convolutional autoencoder-recurrent neural network machine learning model is presented to analyse and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh-Bénard convection flow at Prandtl number ${\rm Pr}=7$ and Rayleigh number ${\rm Ra}=10^7$. Two recurrent neural networks are applied for the temporal advancement of flow data in the reduced latent data space, a reservoir computing model in the form of an echo state network and a recurrent gated unit. Thereby, the present work exploits the modular combination…
One of the most enigmatic science question concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number as the ratio of particle diffusivity and turbulent eddy viscosity. Using direct acoustic measurement of turbulent particle flux profile, and two-phase flow turbulence-resolving numerical simulation, it is demonstrated that turbulent dispersion of particles is reduced rather than enhanced when predicted with existing literature model. The explanation lies in the misleading assumption of settling velocity in quiescent water to estimate …
We investigate the spatio-temporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale $l_{0}$. Using controlled laboratory experiments, an exponential decay as a function of distance is observed with a decay rate which depends on the flow properties. The same law is observed in two different flows indicating that it can be a generic property of turbulent flows.
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed in the convective coordinate frame based on the mean flow, successfully incorporating the convective integration in generally covariant manner.
University of Cambridge（剑桥大学）；Delft University of Technology（代尔夫特理工大学）；Imperial College London（帝国理工学院）；The Alan Turing Institute（艾伦·图灵研究所）
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state for a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live (i.e., it is a numerical approximation of the turbulent attractor). The latent space is found by a series of …
Self-organized large-scale flow structures occur in a wide range of turbulent flows. Yet, their emergence, dynamics, and interplay with small-scale turbulence are not well understood. Here, we investigate such self-organized turbulent superstructures in three-dimensional turbulent Kolmogorov flow with large-scale drag. Through extensive simulations, we uncover their low-dimensional dynamics featuring transitions between several stable and meta-stable large-scale structures as a function of the damping parameter. The main dissipation mechanism for the turbulent superstructures is the generation…
Scaling of turbulent wall-bounded flows is revealed in the gradient structures, for each of the Reynolds stress components. Within the dissipation structure, an asymmetrical order exists, that we can deploy to unify the scaling and transport dynamics within and across these flows. There are subtle differences in the outer boundary conditions between channel and flat-plate boundary-layer flows, which modify the turbulence structure far from the wall. The self-similarity exhibited in the dissipation structures and corresponding transport dynamics establish capabilities and encompassing knowledge…
Something as simple as Couette and Poiseuille onedimensional flow of a newtonian fluid between infinite parallel walls provides an illuminating example of the contrasting physics of laminar and turbulent flow: the difference between their mean velocity profiles has in one regime the opposite sign than in the other. This easily verifiable but yet unnoticed behaviour implies that the physical mechanisms of laminar and turbulent transport are even more fundamentally different than ordinarily presumed.
In this paper, we discuss selected adjoint approaches for the turbulent flow control. In particular, we focus on the application of adjoint solvers for the scope of noise reduction, in which flow solutions are obtained by large eddy and direct numerical simulations. Optimization results obtained with round and plane jet configurations are presented. The results indicate that using large control horizons poses a serious problem for the control of turbulent flows due to existence of very large sensitivity values with respect to control parameters. Typically these sensitivities grow in time and l…
Flows within porous media play important roles in many scientific and industrial systems. However, the case wherein such flows become turbulent has not been completely understood, particularly, from a mathematical viewpoint. In this study, the $k-\varepsilon$ model (the variable $k$ denotes the turbulent kinetic energy per unit mass and $\varepsilon$ the dissipation rate for the turbulent kinetic energy), which has been widely used for the usual turbulent flow in a clear fluid, was applied to a turbulent flow through porous media. If a homogeneous, averaged flow and homogeneous isotropic turbu…
This review focuses on Direct numerical simulations (DNS) of turbulent flows laden with droplets or bubbles. DNS of these flows are more challenging than those of flows laden with solid particles due to the surface deformation in the former. The classification of the discussed numerical methods is based on whether the initial diameter of the bubble/droplet is smaller or larger than the Kolmogorov length scale, and whether the instantaneous surface deformation is fully resolved or obtained via a phenomenological model. Numerical methods that account for the breakup of single droplet/bubble as w…
Annular Couette flow is the flow between two coaxial cylinders driven by the axial translation of the inner cylinder. It is investigated using direct numerical simulation in long domains, with an emphasis on the laminar-turbulent coexistence regime found for marginally low values of the Reynolds number. Three distinct flow regimes are demonstrated as the radius ratio $η$ is decreased from 0.8 to 0.5 and finally to 0.1. The high-$η$ regime features helically-shaped turbulent patches coexisting with laminar flow, as in planar shear flows. The moderate-$η$ regime does not feature any marked lamin…
We use machine learning to perform super-resolution analysis of grossly under-resolved turbulent flow field data to reconstruct the high-resolution flow field. Two machine-learning models are developed; namely the convolutional neural network (CNN) and the hybrid Downsampled Skip-Connection Multi-Scale (DSC/MS) models. These machine-learning models are applied to two-dimensional cylinder wake as a preliminary test and show remarkable ability to reconstruct laminar flow from low-resolution flow field data. We further assess the performance of these models for two-dimensional homogeneous turbule…
