The development of a reliable subgrid-scale (SGS) model for large-eddy simulation (LES) is of great importance for many scientific and engineering applications. Recently, deep learning approaches have been tested for this purpose using high-fidelity data such as direct numerical simulation (DNS) in a supervised learning process. However, such data are generally not available in practice. Deep reinforcement learning (DRL) using only limited target statistics can be an alternative algorithm in which the training and testing of the model are conducted in the same LES environment. The DRL of turbulence modeling remains challenging owing to its chaotic nature, high dimensionality of the action space, and large computational cost. In the present study, we propose a physics-constrained DRL framework that can develop a deep neural network (DNN)-based SGS model for the LES of turbulent channel flow. The DRL models that produce the SGS stress were trained based on the local gradient of the filtered velocities. The developed SGS model automatically satisfies the reflectional invariance and wall boundary conditions without an extra training process so that DRL can quickly find the optimal policy. Furthermore, direct accumulation of reward, spatially and temporally correlated exploration, and the pre-training process are applied for the efficient and effective learning. In various environments, our DRL could discover SGS models that produce the viscous and Reynolds stress statistics perfectly consistent with the filtered DNS. By comparing various statistics obtained by the trained models and conventional SGS models, we present a possible interpretation of better performance of the DRL model.
We use the recently developed Macroscopic Forcing Method [Mani and Park, Physical Review Fluids, 6:054607, 2021] to compute the scale-dependent eddy diffusivity characterizing ensemble-averaged scalar and momentum transport in incompressible homogeneous isotropic turbulence. For scales larger than the energy containing eddies, eddy diffusivity is found to be constant and consistent with the Boussinesq approximation. However for small scales eddy diffusivity is found to vanish inversely proportional to the wavenumber. Behavior at all scales is reasonably captured by a non-local eddy diffusivity…
In isotropic helical turbulence, a new single helical model is suggested for large eddy simulation. Based on the Kolmogrov's hypotheses, the helical model is proposed according to the balance of helicity dissipation and the average of helicity flux across the inertial range, and the helical model is a kind of eddy viscosity model. The coefficient of the helical model is constant and can be also determined dynamically. Numerical simulations of forced and decaying isotropic helical turbulence demonstrate that the helical model predicts the energy and helicity evolution well. The statistical char…
An analysis of the turbulence-radiation interaction in the framework of large eddy simulation (LES) is presented. Direct numerical simulation (DNS) of statistical steady forced homogeneous isotropic turbulence is used to evaluate the relevance of the unclosed terms of the filtered radiative transfer equation (RTE) and to study the influence of parameters like the optical thickness and the turbulence intensity. LES without subgrid-scale models of the filtered RTE has also been investigated. Neglecting the subgrid-scale fluctuations of radiation has proved to be an accurate assumption in various…
This work presents a converged framework of Machine-Learning Assisted Turbulence Modeling (MLATM). Our objective is to develop a turbulence model directly learning from high fidelity data (DNS/LES) with eddy-viscosity hypothesis induced. First, the target machine-learning quantity is discussed in order to avoid the ill-conditioning problem of RANS equations. Then, the novel framework to build the turbulence model using the prior estimation of traditional models is demonstrated. A close-loop computational chain is designed to ensure the convergence of result. Besides, reasonable non-dimensional…
We describe and compare two time-periodic flows embedded in Large Eddy Simulation (LES) of turbulence in a three-dimensional, periodic domain subject to constant external forcing. One of these flows models the regeneration of large-scale structures that was observed in this geometry by Yasuda et al. ({\sl Fluid Dyn. Res.} {\bf 46}, 061413, 2014), who used a smaller LES filter length and thus obtained a greater separation of scales of coherent motion. We speculate on the feasibility of modelling the regenerative dynamics with time-periodic solutions in such a flow, which may require novel techn…
A simple variant of recycling and rescaling method to generate inflow turbulence using unstructured grid CFD codes is presented. The method has been validated on large eddy simulation of spatially developing flat plate turbulent boundary layer. The proposed rescaling algorithm is based on the momentum thickness which is more robust and essentially obviates the need of finding the edge of the turbulent boundary layer in unstructured grid codes. Extension of this algorithm to hybrid RANS/LES type of approaches and for wall-bounded turbomachinery flows is also discussed. Results from annular diff…
For the constant-stress layer of wall turbulence, two-point correlations of velocity fluctuations are studied theoretically by using the attached-eddy hypothesis, i.e., a phenomenological model of a random superposition of energy-containing eddies that are attached to the wall. While the previous studies had invoked additional assumptions, we focus on the minimum assumptions of the hypothesis to derive its most general forms of the correlation functions. They would allow us to use or assess the hypothesis without any effect of those additional assumptions. We also study the energy spectra and …
In this work, we propose a single formula for the law of the wall, which is dubbed as the logarithmic-exponential (LOG-EXP) formula, for predicting the mean velocity profile in different regions near the wall. And then a feedforward neural network (FNN), whose inputs and training data are based on this new formula, is trained for the wall-modelled large-eddy simulation (WMLES) of turbulent channel flows. The direct numerical simulation (DNS) data of turbulent channel flows is used to evaluate the performance of both the formula and the FNN. Compared with the Werner-Wengle (WW) model for the WM…
In large eddy simulation of atmospheric boundary layer flows over wind farms, wall-layer models are generally imposed for the surface fluxes without considering the spatial variability of the surface roughness. In this study, we consider the near-surface model in conjunction with square of the velocity gradient tensor to model the adaptive dissipation of turbulence production. The surface roughness is incorporated through Monin-Obhukhov similarity theory for the computational cells immediately adjacent to the Earth's surface. The underlying proposed near-surface model captures the significant …
Jin (Phys. Fluids, vol. 31, 2019, p. 125102) proposed a new turbulence simulation method which shows better performance than other classic turbulence models. It is composed of a small-eddy-dissipation mixing length (SED-ML) model for calculating the reference solution and a parameter extension method for correcting the solution. The mechanism of this method is more deeply analyzed in this study to find out how to develop a turbulence model with a high accuracy and a low computational cost. The turbulent channel flows with Re_tau=821 and 2003 and decaying homogenous and isotropic turbulence are…
We use laser-Doppler velocimetry (LDV) experiments and Reynolds-averaged Navier--Stokes (RANS) simulations to study the characteristic flow patterns downstream of a standardized clockwise swirl disturbance generator. After quantifying the impact of the mesh size, we evaluate the potential of various eddy-viscosity turbulence models in providing reasonable approximations with respect to the experimental reference. The choice of turbulent models reflects current industry practice. Our results suggest that models from the $k$-$ε$ family are more accurate in predicting swirling flows than models f…
The inner-outer interaction model (Marusic, Mathis & Hutchins, Science, vol. 329, 2010, 193-196) and the attached-eddy model (Townsend, Cambridge University Press, 1976) are two fundamental models describing the multi-scale turbulence interactions and the organization of energy-containing motions in the logarithmic region of high-Reynolds number wall-bounded turbulence, respectively. In this paper, by coupling the additive description with the attached-eddy model, the generation process of streamwise wall-shear fluctuations, resulting from wall-attached eddies, is portrayed. Then, by resorting…
Wall-models are essential for enabling large-eddy simulations (LESs) of realistic problems at high Reynolds numbers. The present study is focused on approaches that directly model the wall shear stress, specifically on filling the gap between models based on wall-normal ordinary differential equations (ODEs) that assume equilibrium and models based on full partial differential equations (PDEs) that do not. We develop ideas for how to incorporate non-equilibrium effects (most importantly, strong pressure-gradient effects) in the wall-model while still solving only wall-normal ODEs. We test thes…
We present a spatio-temporal analysis of a statistically stationary rotating turbulence experiment, aiming to extract a signature of inertial waves, and to determine the scales and frequencies at which they can be detected. The analysis uses two-point spatial correlations of the temporal Fourier transform of velocity fields obtained from time-resolved stereoscopic particle image velocimetry measurements in the rotating frame. We quantify the degree of anisotropy of turbulence as a function of frequency and spatial scale. We show that this space-time-dependent anisotropy is well described by th…
In this article, we utilize machine learning to dynamically determine if a point on the computational grid requires implicit numerical dissipation for large eddy simulation (LES). The decision making process is learnt through \emph{a priori} training on quantities derived from direct numerical simulation (DNS) data. In particular, we compute eddy-viscosities obtained through the coarse graining of DNS quantities and utilize their distribution to categorize areas that require dissipation. If our learning determines that closure is necessary, an upwinded scheme is utilized for computing the non-…
We discuss the role of particular velocity field configurations -- instantons, for short -- which are supposed to dominate the flow during the occurrence of extreme turbulent circulation events. Instanton equations, devised for the stochastic hydrodynamic setup of homogeneous and isotropic turbulence, are applied to the interpretation of direct numerical simulation results. We are able in this way to model the time evolution of extreme circulation events for a broad range of scales, through the combined use of eddy viscosity phenomenology and exact creeping instantons. While this approach work…
We put forth a dynamic modeling framework for sub-grid parametrization of large eddy simulation of turbulent flows based upon the use of the approximate deconvolution procedure to compute the Smagorinsky constant self-adaptively from the resolved flow quantities. Our numerical assessments for solving the Burgers turbulence problem shows that the proposed approach could be used as a viable tool to address the turbulence closure problem due to its flexibility.
For helical isotropic turbulence, an improved two-term helical subgrid-scale (SGS) model is proposed and four types of dynamic methods are given to do large-eddy simulation (LES), which include the standard dynamic procedure, the least quatratic sum dynamic procedure, the dynamic procedure with single con- straint of helicity dissipation and the dynamic one with dual constraints of energy and helicity dissipation. Tested a priori and a posteriori in both steady and decaying helical isotropic turbulence, the four types of dynamic helical models and the dynamic Smogorinsky model are compared wit…
The generation of initial or inflow synthetic turbulent velocity or scalar fields reproducing statistical characteristics of realistic turbulence is still a challenge. The synthetic eddy method, previously introduced in the context of inflow conditions for large eddy simulations, is based on the assumption that turbulence can be regarded as a superposition of coherent structures. In this paper, a new type of synthetic eddy method is proposed, where the fundamental eddy is constructed by superposing three Hill's vortices, with their axes orthogonal to each other. A distribution of Hill's vortic…
A promising and cost-effective method for numerical simulation of high Re wall-bounded flows is wall-modeled large-eddy simulation. Most wall models are formulated from the Reynolds-averaged Navier-Stokes equations (RANS). These RANS-based wall models are calibrated using mean turbulence data and make no use of the current vast knowledge on turbulent flow structure. Moreover, RANS-based models are limited to predicting the mean velocity profile, and the mean wall shear stress. Using the knowledge of the wall-normal self-similarity of high-$Re_τ$ wall-bounded turbulent flows, we present a coupl…
The predictions of resolvent analysis for turbulent channel flow are evaluated for a friction Reynolds number of Retau = 550. In addition to the standard resolvent operator with kinematic viscosity, a resolvent operator augmented with the Cess eddy viscosity is considered. Adding eddy viscosity significantly alters the low-rank behavior of the resolvent. Regardless of the wave speed selected, the eddy resolvent is low-rank for spanwise wavelengths of ly+ = 80 and ly/h = 3.5 in comparison to the standard resolvent whose low-rank behavior depends on the wave speed. The leading eddy modes have hi…
We investigate the role of the bulk eddy-viscosity variation on the well-known log-layer mismatch problem. An analysis of the mean momentum-balance shows that the modeled stress term close to the wall can dominate because of the bulk eddy-viscosity. Consequently, the momentum-balance equation lacks a degree-of-freedom and the mean velocity conforms to an incorrect profile to satisfy the momentum-balance. We show that zonal enforcement of the target mass flow-rate can be an effective strategy to introduce an additional degree of freedom to the mean momentum-balance, which led to a significant r…
Deconvolutional artificial neural network (DANN) models are developed for subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence. The filtered velocities at different spatial points are used as input features of the DANN models to reconstruct the unfiltered velocity. The grid width of the DANN models is chosen to be smaller than the filter width, in order to accurately model the effects of SGS dynamics. The DANN models can predict the SGS stress more accurately than the conventional approximate deconvolution method (ADM) and velocity gradient model (VGM) in a prior study: the …
Motivated by the need to characterize the spatio-temporal structure of turbulence in wall-bounded flows, we study wavenumber-frequency spectra of the streamwise velocity component based on large-eddy simulation (LES) data. The LES data are used to measure spectra as a function of the two wall-parallel wavenumbers and the frequency in the equilibrium (logarithmic) layer. We then reformulate one of the simplest models that is able to reproduce the observations: the random sweeping model with a Gaussian large-scale fluctuating velocity and with additional mean flow. Comparison with LES data shows…
The original goal of Large Eddy Simulations of fully developed turbulent flows was to accurately describe large-scale flow features ${\bf u}(Δ)$ at the scales $r\geq Δ$ where $Δ$ is a size of computational mesh. The effect of small-scale velocity fluctuations ($r<Δ$) was to be accounted for by effective transport coefficients (subgrid models) in the coarse-grained Navier-Stokes equations. It is shown in this paper that, due to anomalous inertial range scaling (intermittency) of the moments of velocity difference, the existing subgrid models are intrinsically incapable of quantitatively describ…
The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile $U^+$ by using a simple method. The $U^+$ profile is obtained by solving the momentum equation which is written as an ordinary differential equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy $k^+$ function (R. Absi, Analytical solutions for the modeled $k$-equation, ASME J. Appl. Mech. \textbf{75}, 044501, 2008) and the van Driest mixing length equation (E.R. van Driest, On turbulent flow near a wall, J. Aero. Sci. \textbf{23}, 1007, 1956) is used. The parameters …
The present work reports on LES of turbulent reacting flow of the Delft-Jet-in-Hot-Coflow (DJHC) burner, emulating MILD combustion, with transported PDF based combustion models using ANSYS FLUENT 13.0. Two different eddy viscosity models for LES (Dynamic Smagorinsky and Kinetic Energy Transport) along with two solution approaches for PDF transport equation, i.e. Eulerian and Lagrangian, have been used in the present study. Moreover, the effects of chemical kinetics and the micro-mixing models have also been investigated for two different fuel jet Reynolds number (Re = 4,100 and Re = 8,800). Th…
Motivated by the needs of wall modeled Large Eddy Simulation (LES), we introduce fits to numerical solutions of the Reynolds Averaged Navier-Stokes equations in their simplest near-wall, boundary layer approximation including a mixing-length model. We formulate the problem such that independent dimensionless variables are those directly available in LES. We provide practical fits for the dependent variable, fits that encompass a smooth transition between the viscous sublayer and inertial logarithmic layer, and then progress first considering moderate pressure gradients as well as roughness eff…
We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like bluff body call Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (1994). Robustness of the model solutio…
Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such quantities include turbulent kinetic energy for eddy viscosity models and the Reynolds stress tensor (or its anisotropy) in differential stress models. However, such models all have limitations in their robustness and accuracy. Inspired by the successes of machine learning in other scientific fields, researchers have developed data-driven turbulence models. Recently, a nonlocal vector-cloud neural network with embed…
In this paper, we have used renormalized viscosity for performing large eddy simulations (LES) of decaying homogeneous and isotropic turbulence inside a periodic cube on coarse grids ($32^3$, $64^3$ and $128^3$) at initial Taylor Reynolds number ${\mathrm{Re}_λ \approx 315} $. The LES results were compared with direct numerical simulation (DNS) results on $512^3$ grid. We observe good agreement between LES and DNS results on the temporal evolution of turbulence kinetic energy ${E(t)}$, kinetic energy spectrum ${E_{u}(k)}$, kinetic energy flux ${Π_u(k)}$. The isosurfaces of velocity magnitude a…
Large Eddy Simulations of turbulent flows are powerful tools used in many engineering and geophysical settings. Choosing the right value of the free parameters for their subgrid scale models is a crucial task for which the current methods present several shortcomings. Using a technique called nudging we show that Large Eddy Simulations can synchronize to data coming from a high-resolution direct numerical simulation of homogeneous and isotropic turbulence. Furthermore, we found that the degree of synchronization is dependent on the value of the parameters of the subgrid scale models utilized, …
A practical application of universal wall scalings is near-wall turbulence modeling. In this paper, we exploit temperature's semi-local scaling [Patel, Boersma, and Pecnik, {Scalar statistics in variable property turbulent channel flows}, Phys. Rev. Fluids, 2017, 2(8), 084604] and derive an eddy conductivity closure for wall-modeled large-eddy simulation of high-speed flows. We show that while the semi-local scaling does not collapse high-speed direct numerical simulation (DNS) data, the resulting eddy conductivity and the wall model work fairly well. The paper attempts to answer the following…
We conducted WMLES to examine the performance of a simple and widely used ODE-based equilibrium wall model in a spatially-developing 3D TBL inside a bent square duct (Schwarz and Bradshaw 1994) and 3D separated flows behind a skewed bump (Ching et al. 2018a,b; Ching and Eaton 2019). From the square duct simulation, the mean velocity profiles and crossflow angles in the outer region were predicted with high accuracy for all the considered mesh resolutions. Some disagreement was observed in the crossflow angles in the bend region where the non-equilibrium effect is most significant. Also, the si…
We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved large-eddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall ($\sim$ 10 wall units), while still resolving the near-wall region, to present a new path to save the computational cost. Convolutional neural network (CNN) is utilized to estimate a virtual wall-surface velocity from $x-z$ sectional fields near the wall, whose training data are generated by a direct numerical simulation (DNS) at ${\rm Re}_τ=180$. The virtual wall…
Two-dimensional (2-D) spectra of the streamwise velocity component, measured at friction Reynolds numbers ranging from 2400 to 26000, are used to refine a model for the logarithmic region of turbulent boundary layers. Here, we focus on the attached eddy model (AEM). The conventional AEM assumes the boundary layer to be populated with hierarchies of self-similar wall-attached ($Type\,A$) eddies alone. While $Type\,A$ eddies represent the dominant energetic large-scale motions at high Reynolds numbers, the scales that are not represented by such eddies are observed to carry a significant proport…
Wind-wave interaction involves wind forcing on wave surface and wave effects on the turbulent wind structures, which essentially influences the wind and wave loading on structures. Existing research on wind-wave interaction modeling ignores the inherent strong turbulences of wind. The present study aims to characterize the turbulent airflow over wave surfaces and wave dynamics under wind driving force. A high-fidelity two-phase model is developed to simulate highly turbulent wind-wave fields. Instead of using uniform wind, inherent wind turbulences are prescribed at the inlet boundary using th…
We present first results of an implicit large eddy simulation of the MTU T161 low pressure turbine at a Reynolds number of 90,000 and Mach number of 0.6, both based on isentropic exit conditions, using a high order discontinuous Galerkin method. The aim is to validate the numerical setup with respect to available experimental data. We discuss the steps taken to create realistic inflow boundary conditions in terms of end wall boundary layer thickness and free stream turbulence intensity. This is achieved by tailoring the input distribution of Reynolds stresses and turbulent length scale to a Fo…
High-resolution large-eddy simulation (LES) is exploited to study indoor air turbulence and its effect on the dispersion of respiratory virus-laden aerosols and subsequent transmission risks. The methodology is applied to assess two dissimilar approaches to reduce transmission risks: a strategy to augment the indoor ventilation capacity with portable air purifiers and a strategy to utilize partitioning by exploiting portable space dividers. To substantiate the physical relevance of the LES model, a set of experimental aerosol concentration measurements are carried out, and their results are us…
This work presents a review and perspectives on recent developments in the use of machine learning (ML) to augment Reynolds-averaged Navier--Stokes (RANS) and Large Eddy Simulation (LES) models of turbulent flows. Different approaches of applying supervised learning to represent unclosed terms, model discrepancies and sub-filter scales are discussed in the context of RANS and LES modeling. Particular emphasis is placed on the impact of the training procedure on the consistency of ML augmentations with the underlying physical model. Techniques to promote model-consistent training, and to avoid …
This brief article accompanies a fluid dynamics video presenting the results of a large-eddy simulation of the flow in a realistic left heart. The left heart geometry, from the pulmonary veins to the aortic root, is extracted from medical images and the endocardium movements are reconstructed through image registration. Large-eddy simulations are thus performed in a patient-specific heart model, where the patient-specific movements of the geometry are prescribed. The flow obtained is intermittent, showing both in the left atrium and in the left ventricle turbulent spots correlated to flow dece…
This work presents a feature-rich open-source library for wall-modelled large-eddy simulation (WMLES), which is a turbulence modelling approach that reduces the computational cost of traditional (wall-resolved) LES by introducing special treatment of the inner region of turbulent boundary layers (TBLs). The library is based on OpenFOAM and enhances the general-purpose LES solvers provided by this software with state-of-the-art wall modelling capability. In particular, the included wall models belong to the class of wall-stress models that account for the under-resolved turbulent structures by …
We revise the theory of superfluid turbulence near the absolute zero of temperature and suggest a model with differential approximation for the energy fluxes in the k-space carried by the collective hydrodynamic motions of quantized vortex lines and by their individual uncorrelated motions known as Kelvin waves. The model predicts energy spectra of the hydrodynamic and the Kelvin waves components of the system, which experience a smooth crossover between different regimes of motion over a finite range of scales.
