Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session D34: Turbulence: Model Analysis via Statistical and Probabilistic Techniques |
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Chair: Micheal Wilczek, Max Planck Institute Room: Oregon Ballroom 203 |
Sunday, November 20, 2016 2:57PM - 3:10PM |
D34.00001: A probability distribution approach to synthetic turbulence time series Michael Sinhuber, Eberhard Bodenschatz, Michael Wilczek The statistical features of turbulence can be described in terms of multi-point probability density functions (PDFs). The complexity of these statistical objects increases rapidly with the number of points. This raises the question of how much information has to be incorporated into statistical models of turbulence to capture essential features such as inertial-range scaling and intermittency. Using high Reynolds number hot-wire data obtained at the Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization, we establish a PDF-based approach on generating synthetic time series that reproduce those features. To do this, we measure three-point conditional PDFs from the experimental data and use an adaption-rejection method to draw random velocities from this distribution to produce synthetic time series. Analyzing these synthetic time series, we find that time series based on even low-dimensional conditional PDFs already capture some essential features of real turbulent flows. [Preview Abstract] |
Sunday, November 20, 2016 3:10PM - 3:23PM |
D34.00002: Non-Gaussian Extension of the Sparse-Direct Interaction Perturbation David Petty, Carlos Pantano An extension of the Sparse Direct-Interaction Perturbation (SDIP) technique is investigated with the objective to predict the theoretical Obukhov-Corrsin constant consistently with experimental observation. This extension involves relaxing the assumption that, in the case of a turbulent passive scalar field, third-order correlations between Non-Direct-Interaction (NDI) fields are identitically zero. This is the leading order term in the traditional SDIP expansion. The theory of invariants and dimensional analysis provide a functional form of the retained third-order correlation, and integrability of its Fourier modes produces constraints on the remaining unknown parameters. To close the approximation, these unknown parameters are determined from direct numerical simulation of actively forced turbulent mixing. The resulting closure is then used to estimate the scalar spectral constant. [Preview Abstract] |
Sunday, November 20, 2016 3:23PM - 3:36PM |
D34.00003: Turbulence Model Discovery with Data-Driven Learning and Optimization Ryan King, Peter Hamlington Data-driven techniques have emerged as a useful tool for model development in applications where first-principles approaches are intractable. In this talk, data-driven multi-task learning techniques are used to discover flow-specific optimal turbulence closure models. We use the recently introduced autonomic closure technique to pose an online supervised learning problem created by test filtering turbulent flows in the self-similar inertial range. The autonomic closure is modified to solve the learning problem for all stress components simultaneously with multi-task learning techniques. The closure is further augmented with a feature extraction step that learns a set of orthogonal modes that are optimal at predicting the turbulent stresses. We demonstrate that these modes can be severely truncated to enable drastic reductions in computational costs without compromising the model accuracy. Furthermore, we discuss the potential universality of the extracted features and implications for reduced order modeling of other turbulent flows. [Preview Abstract] |
Sunday, November 20, 2016 3:36PM - 3:49PM |
D34.00004: Reducing RANS Model Error Using Random Forest Jian-Xun Wang, Jin-Long Wu, Heng Xiao, Julia Ling Reynolds-Averaged Navier-Stokes (RANS) models are still the work-horse tools in the turbulence modeling of industrial flows. However, the model discrepancy due to the inadequacy of modeled Reynolds stresses largely diminishes the reliability of simulation results. In this work we use a physics-informed machine learning approach to improve the RANS modeled Reynolds stresses and propagate them to obtain the mean velocity field. Specifically, the functional forms of Reynolds stress discrepancies with respect to mean flow features are trained based on an offline database of flows with similar characteristics. The random forest model is used to predict Reynolds stress discrepancies in new flows. Then the improved Reynolds stresses are propagated to the velocity field via RANS equations. The effects of expanding the feature space through the use of a complete basis of Galilean tensor invariants are also studied. The flow in a square duct, which is challenging for standard RANS models, is investigated to demonstrate the merit of the proposed approach. The results show that both the Reynolds stresses and the propagated velocity field are improved over the baseline RANS predictions. SAND Number: SAND2016-7437 A [Preview Abstract] |
Sunday, November 20, 2016 3:49PM - 4:02PM |
D34.00005: RANS turbulence model form uncertainty quantification for wind engineering flows Catherine Gorle, Stephanie Zeoli, Laurent Bricteux Reynolds-averaged Navier-Stokes simulations with linear eddy-viscosity turbulence models are commonly used for modeling wind engineering flows, but the use of the results for critical design decisions is hindered by the limited capability of the models to correctly predict bluff body flows. A turbulence model form uncertainty quantification (UQ) method to define confidence intervals for the results could remove this limitation, and promising results were obtained in a previous study of the flow in downtown Oklahoma City. The objective of the present study is to further investigate the validity of these results by considering the simplified test case of the flow around a wall-mounted cube. DNS data is used to determine: 1. whether the marker, which identifies regions that deviate from parallel shear flow, is a good indicator for the regions where the turbulence model fails, and 2. which Reynolds stress perturbations, in terms of the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor, can capture the uncertainty in the flow field. A comparison of confidence intervals obtained with the UQ method and the DNS solution indicates that the uncertainty in the velocity field can be captured correctly in a large portion of the flow field. [Preview Abstract] |
Sunday, November 20, 2016 4:02PM - 4:15PM |
D34.00006: Galerkin POD Model Closure with Triadic Interactions by the Maximum Entropy Method Nicolas H\'erouard, Robert K. Niven, Bernd R. Noack, Markus W. Abel, Michael Schlegel The maximum entropy method of Jaynes provides a method to infer the expected or most probable state of a system, by maximizing the relative entropy subject to physical constraints such as conservation of mass, energy and power. A maximum entropy closure for reduced-order models of fluid flows based on principal orthogonal decomposition (POD) is developed, to infer the probability density function for the POD modal amplitudes. This closure takes into account energy transfers by triadic interactions between modes, by extension of a theoretical model of these interactions in incompressible flow (Noack et al, JNET, 2008). The framework is applied to several incompressible flow systems including the cylinder wake, both at low and high Reynolds number (oscillatory and turbulent flow conditions), with important implications for the triadic structure and power balance (energy cascade) in the system. [Preview Abstract] |
Sunday, November 20, 2016 4:15PM - 4:28PM |
D34.00007: A single-point model from SO(3) decomposition of the axisymmetric mean-flow coupled two-point equations Timothy Clark, Robert Rubinstein, Susan Kurien The fluctuating-pressure-strain correlations present a significant challenge for engineering turbulence models. For incompressible flow, the pressure is an intrinsically two-point quantity (represented as Green's function, integrated over the field), and therefore representing the implied scale-dependence in a one-point model is difficult. The pioneering work of Launder, Reece and Rodi (1975) presented a model that satisfied the tensor symmetries and dimensional consistency with the underlying Green's function solution, and described the assumptions embedded in their one-point model. Among the constraints of such a model is its inability to capture scale-dependent anisotropic flow development. Restricting our attention to the case of axisymmetric mean-field strains, we present a one-point model of the mean-flow couplings, including the pressure-strain terms, starting from a directional (tensorially isotropic) and polarization (tensorially anisotropic and trace-free) representation of the two-point correlation equations, truncated to the lowest order terms. The model results are then compared to simulations performed using arbitrary orders of spherical harmonic functions from which the exact solution may be obtained to desired accuracy. [Preview Abstract] |
Sunday, November 20, 2016 4:28PM - 4:41PM |
D34.00008: Rapid Bayesian Inference for Fluid Flow Modeling and Control Robert K. Niven, Eurika Kaiser, Bernd R. Noack, Louis N. Cattafesta III, Markus W. Abel, Laurent Cordier We give a new framework for rapid Bayesian inference for flow modeling and control, based on Bayes' rule $p(\vec{\theta} | \vec{x}) = p(\vec{x} | \vec{\theta}) p(\vec{\theta}) / p(\vec{x})$, where $p$ is a probability density function, $\vec{x}$ are multivariate data and $\vec{\theta}$ is one model drawn from a continuous model space $\Omega_{\vec{\theta}}$. We thus seek the pdf of the model $\vec{\theta}$, given the data $\vec{x}$. Traditionally, Bayesian inference requires marginalization of the integral $p(\vec{x}) =\int d\vec{\theta}\, p(\vec{x} | \vec{\theta}) p(\vec{\theta})$, which is highly computationally expensive and may not even be feasible. Instead, we propose initial order reduction of the data, such as by k-means clustering, to generate discretized data $c_i$ on a reduced-order data space $C$, followed by Bayesian inference to infer the conditional probability $P(\gamma_m | c_k)$ of the discretized model $\gamma_m$ in a reduced-order model space $\Gamma$. If needed, an inversion to infer $p(\vec{\theta} | \gamma_m)$ can be conducted. The method substantially reduces the computational complexity of Bayesian inference, enabling real-time turbulent modeling and control. We report applications to several turbulent flow and dynamical systems. [Preview Abstract] |
Sunday, November 20, 2016 4:41PM - 4:54PM |
D34.00009: On the statistics of backscatter from sub-grid fluctuations at high Reynolds numbers Michele Buzzicotti, Hussein Aluie, Luca Biferale, Fabio Bonaccorso, Moritz Linkmann We study the effect of different filtering strategies on the statistical properties of the subgrid-scale energy transfer of high Reynolds numbers homogeneous and isotropic turbulence. We focus on the upscale energy transfer (backscatter) from small to large scales. We discuss the extent to which the backscatter statistics depend on the filtering strategy, using either exact projectors on different subsets of Fourier modes or more traditional convolutions with analytical kernels in physical space. We also assess the backscatter contribution from different helical components of the sub-grid fluctuations. [Preview Abstract] |
Sunday, November 20, 2016 4:54PM - 5:07PM |
D34.00010: ABSTRACT WITHDRAWN |
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