Turbulence Modeling in the Age of Data Duraisamy, Karthik; Iaccarino, Gianluca; Xiao, Heng
Annual review of fluid mechanics,
01/2019, Volume:
51, Issue:
1
Journal Article
Peer reviewed
Open access
Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier-Stokes (RANS) ...equations. In the past few years, with the availability of large and diverse data sets, researchers have begun to explore methods to systematically inform turbulence models with data, with the goal of quantifying and reducing model uncertainties. This review surveys recent developments in bounding uncertainties in RANS models via physical constraints, in adopting statistical inference to characterize model coefficients and estimate discrepancy, and in using machine learning to improve turbulence models. Key principles, achievements, and challenges are discussed. A central perspective advocated in this review is that by exploiting foundational knowledge in turbulence modeling and physical constraints, researchers can use data-driven approaches to yield useful predictive models.
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 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 projection onto a Gaussian distribution to categorize areas that may require dissipation. If our learning determines that closure is necessary, an upwinded scheme is utilized for computing the non-linear Jacobian. In contrast, if it is determined that closure is unnecessary, a symmetric and second-order accurate energy and enstrophy preserving Arakawa scheme is utilized instead. This results in a closure framework that precludes the specification of any model-form for the small scale contributions of turbulence but deploys an appropriate numerical dissipation from explicit closure driven hypotheses. This methodology is deployed for the Kraichnan turbulence test-case and assessed through various statistical quantities such as angle-averaged kinetic energy spectra and vorticity structure functions. Our framework thus establishes a link between the use of explicit LES ideologies for closure and numerical dissipation-based modeling of turbulence leading to improved statistical fidelity of a posteriori simulations.
•An ML classifier determines the numerical scheme for the advective term.•The classifier is trained based on the subgrid closure modeling requirements.•The classifier is dynamic in space and time and links explicit and implicit LES.
A large amount of published data show that particles with diameter above 10% of the turbulence integral length scale (D/l>0.1) tend to increase the turbulent kinetic energy of the carrier fluid above ...the single-phase value, and smaller particles tend to suppress it. We attempted to remove limitations in earlier modeling efforts for solids on the coupling between the particles and turbulence, and better fits to the turbulence modulation amplitude as function of D/l was achieved for a number of data sets. Explicit algebraic forms of the full model were derived using asymptotic analysis, and these are general enough for application to emulsions, bubbles and solids in bulk regions of multiphase turbulent flow.
Rigorous particle-kinetic theory was used to derive the work exchanged between the particles and the fluid due to both drag and added mass forces, where the latter is essential for low or moderate particle/fluid density ratios, enabling a well justified model also for emulsions and bubbles. A novel sub-model for turbulence production by vortex shedding due to turbulence-generated slip velocity was incorporated, where earlier models took the slip velocity as an input parameter. The correct asymptotic limit of vanishing turbulence modulation for small tracer particles was also provided, giving better fit to the data for small particles.
We found that turbulence augmentation for large diameter solids is due to vortex shedding, and turbulence suppression for small diameters is due to mainly to turbulent drag forces and extra fluid dissipation – a conclusion that agrees with earlier models for solids, despite their possible shortcomings. An important finding is that the mechanisms for turbulence suppression for bubbles and emulsion droplets are similar to those of solids, but with the addition of added mass scaling factors. Another important observation is that augmentation may not occur at all for bubbles or emulsion droplets since the larger diameters require moderate turbulence levels to prevent breakup, so that vortex shedding may be insignificant.
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•Solids with diameter above 10% of the turbulence integral length scale increases turbulence.•Bubbles and emulsion droplets may not induce turbulence enhancement by vortex shedding.•Model imitations on coupling between the particles and the turbulence were removed.•Explicit algebraic forms for homogeneous turbulent shear flow were derived.•Improved fits to measured turbulence modulation for varying diameter were achieved.
In this work, we present a novel data-based approach to turbulence modeling for Large Eddy Simulation (LES) by artificial neural networks. We define the perfect LES formulation including the ...discretization operators and derive the associated perfect closure terms. We then generate training data for these terms from direct numerical simulations of decaying homogeneous isotropic turbulence. We design and train artificial neural networks based on local convolution filters to predict the underlying unknown non-linear mapping from the coarse grid quantities to the closure terms without a priori assumptions. We show that selecting both the coarse grid primitive variables as well as the coarse grid LES operator as input features significantly improves training results. All investigated networks are able to generalize from the data and learn approximations with a cross correlation of up to 47% and even 73% for the inner elements, demonstrating that the perfect closure can indeed be learned from the provided coarse grid data. Since the learned closure terms are approximate, a direct application leads to stability issues. We show how to employ the artificial neural network output to construct stable and accurate models. The best results have been achieved with a data-informed, temporally and spatially adaptive eddy viscosity closure. While further investigations into the generalizability of the approach is warranted, this work thus represents a starting point for further research into data-driven, optimal turbulence models.
•A novel data-based method to derive LES subgrid closure terms through neural networks.•A rigorous framework for definition of ideal/optimal LES and associated closure terms.•Successful approximation of the exact LES closure terms based on coarse grid data only.•A data-driven eddy viscosity closure model.
ABSTRACT
This article reviews the state‐of‐the‐art numerical calculation of wind turbine wake aerodynamics. Different computational fluid dynamics techniques for modeling the rotor and the wake are ...discussed. Regarding rotor modeling, recent advances in the generalized actuator approach and the direct model are discussed, as far as it attributes to the wake description. For the wake, the focus is on the different turbulence models that are employed to study wake effects on downstream turbines.
In computational fluid dynamics simulations of industrial flows, models based on the Reynolds-averaged Navier–Stokes (RANS) equations are expected to play an important role in decades to come. ...However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and structural uncertainties in turbulence models. We review recent literature on data-free (uncertainty propagation) and data-driven (statistical inference) approaches for quantifying and reducing model uncertainties in RANS simulations. Moreover, the fundamentals of uncertainty propagation and Bayesian inference are introduced in the context of RANS model uncertainty quantification. Finally, the literature on uncertainties in scale-resolving simulations is briefly reviewed with particular emphasis on large eddy simulations.
Over the last years, supervised learning (SL) has established itself as the state-of-the-art for data-driven turbulence modeling. In the SL paradigm, models are trained based on a dataset, which is ...typically computed a priori from a high-fidelity solution by applying the respective filter function, which separates the resolved and the unresolved flow scales. For implicitly filtered large eddy simulation (LES), this approach is infeasible, since here, the employed discretization itself acts as an implicit filter function. As a consequence, the exact filter form is generally not known and thus, the corresponding closure terms cannot be computed even if the full solution is available. The reinforcement learning (RL) paradigm can be used to avoid this inconsistency by training not on a previously obtained training dataset, but instead by interacting directly with the dynamical LES environment itself. This allows to incorporate the potentially complex implicit LES filter into the training process by design. In this work, we apply a reinforcement learning framework to find an optimal eddy-viscosity for implicitly filtered large eddy simulations of forced homogeneous isotropic turbulence. For this, we formulate the task of turbulence modeling as an RL task with a policy network based on convolutional neural networks that adapts the eddy-viscosity in LES dynamically in space and time based on the local flow state only. We demonstrate that the trained models can provide long-term stable simulations and that they outperform established analytical models in terms of accuracy. In addition, the models generalize well to other resolutions and discretizations. We thus demonstrate that RL can provide a framework for consistent, accurate and stable turbulence modeling especially for implicitly filtered LES.
•Application of a novel reinforcement learning framework to turbulence modeling.•Novel data-driven turbulence models for implicitly filtered large eddy simulation.•Generalization of trained models to different resolutions and Reynolds numbers.
•We introduce a new universal nonlocal Laplace operator.•The universal operator includes classical and fractional Laplacians as limits.•We propose nonlocal physics-informed neural networks for ...parameter identification.•We illustrate consistency and accuracy, and discover operator-mimicking phenomena.•We apply our algorithm to a fractional wall-bounded turbulence model.
Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multi-fidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(y), which is more suitable for modeling wall-bounded turbulence, e.g. turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.
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