Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L39: Turbulence Modeling II |
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Chair: Christopher White, University of New Hampshire Room: Georgia World Congress Center Ballroom 3/4 |
Monday, November 19, 2018 4:05PM - 4:18PM |
L39.00001: Data-driven fractional order model for drag-reduced wall bounded turbulent flows Zhen Li, Fangying Song, George Em Karniadakis We develop a data-driven fractional-order mathematical model that unifies and generalizes the formulation of drag-reducing mean flow in wall-bounded turbulence with polymer additives. Our model incorporates the nonlocality of complicated interactions between coherent turbulent structures, which is formulated with fractional-order operators applied to stress tensor. The variable fractional order involved in the model is learned from available computational and experimental data obtained from both direct numerical simulations with different micro-rheological models and laser doppler anemometer measurements in pipe flow experiments. Results show that the data-driven fractional-order model uncovers a universal formulation of wall-bounded turbulent flows, which is able to correctly predict the mean velocity profiles of various viscoelastic turbulent flows, valid for a large range of Reynolds numbers and various polymer concentrations. The proposed model provides a convenient way to effectively evaluate the drag-reduction in wall-turbulence and offers new insights to understanding the hidden fluid physics of how polymer additives change the complicated interactions in coherent turbulent structures in wall-bounded flows. |
Monday, November 19, 2018 4:18PM - 4:31PM |
L39.00002: Application of Spectral Proper Orthogonal Decomposition (SPOD) on a Broad Spectrum Statistically Stationary Flowfield Rekesh M Ali, Scott Coder, Scott Murman, Patrick Blonigan Although overshadowed by its space-only counterpart, Spectral Proper Orthogonal Decomposition (SPOD) was incepted many decades ago and can be considered the frequency domain form of Proper Orthogonal Decomposition (POD). Recent work shows that SPOD can reduce flow fields into structures that evolve coherently in time and space. Because of this characteristic, SPOD is a method well suited for statistically stationary flows, data that are random about a mean and do not grow or decay in time. In this work SPOD is applied to a flow field extracted from the surface of a rocket body in transonic flight. All aerodynamic vehicles experience broad spectrum loading in the transonic regime; this is known as "buffet". SPOD is a step in identifying the physics responsible for buffet. Specifically, the extraction of flow features at high energy frequencies within the broad spectrum can be very helpful for reduced order model construction or tool development for flow driven structural analysis. Future applications will push this study even further with the implementation of SPOD on a three-dimensional rotorcraft wake. |
Monday, November 19, 2018 4:31PM - 4:44PM |
L39.00003: A nonlocal algebraic tensor model for Reynolds-stress closures Chao Jiang, Shujin Laima, Hui Li Reynolds-stress closure modeling has been playing a major role in applied computational fluid dynamics and remains a challenging issue in complex shear flows. Here we report a new closure strategy for Reynolds stresses based on two-point correlation, which accounts for nonlocal effects on the anisotropy due to spatial variations in the mean velocity gradient tensor. The present model represents complete anisotropy with tensor coefficients, and provides a prior knowledge for separation of general and universal constants from closure coefficients, holding promise to deduce a real constitutive relationship for Reynolds stresses. These constants represent intrinsic similarities of different turbulent flows. Comparative analysis with prior linear and nonlinear eddy-viscosity models shows that the proposed model is able to capture more physical details of complex turbulent flows. Further detailed tests are made in fully-developed turbulent channel flow where nonlocal effects are expected to be important. This model provides improved predictions for Reynolds stresses and corrects log-layer mismatch. |
Monday, November 19, 2018 4:44PM - 4:57PM |
L39.00004: Part-I: A Fractional Transport Model for Scalar Turbulence Mohsen Zayernouri, Mehdi Samiee, Mark M. Meerschaert The stochastic dynamics of coherent motions in turbulent flows involves with merging and filamentation of coherent vortices, which can induce a variant of non-Markovian random processes in the underlying scalar transport of particles with distinguished features of trappings (memory effects) and long jumps (nonlocal effects). Such anomalies leads to intermittent signals and non-Gaussian statistics, which in turn requires a proper (fractional) mathematical framework for better understanding of such scalar transports. One approach to model heavy-tailed behavior of turbulent mixing of a passive scalar is to derive the fractional scalar transport equation from the Kinetic theory, following the derivation of the fractional Navier-Stokes equations. We propose and derive the scalar transport equation with fractional Laplacian in the context of an isotropic turbulent flow, incorporating Lévy distribution and explore the subsequent impressions of the corresponding fractional exponent on the dynamics of coherent vortices via numerical simulation. |
Monday, November 19, 2018 4:57PM - 5:10PM |
L39.00005: Part-II: A Fractional Subgrid-Scale Model for Turbulent Flows Mehdi Samiee, Mohsen Zayernouri, Mark M. Meerschaert Following the fractional framework of scalar turbulence, we propose another new fractional approach to modeling the subgrid-scale stresses in large eddy simulation (LES) of turbulent flows. This approach is motivated by the derivation of filtered Navier-Stokes equations with fractional Laplacian. The subgrid-scale velocities are then obtained from a fractional derivative of the resolved-scale quantities, in which the fractional exponent depend on the Reynolds number and the filter length. To study the characteristics of the new model, we compare the results of LES of isotropic turbulent flows against DNS data and examine the accuracy of the results. |
Monday, November 19, 2018 5:10PM - 5:23PM |
L39.00006: Two-point spectral model for variable-density homogeneous turbulence Nairita Pal, Susan Kurien, Timothy T Clark, Denis Aslangil, Daniel Livescu We present a study of buoyancy-driven variable-density homogeneous turbulence, using a two-point spectral closure model. We compute the time-evolution of the spectral distribution in wavenumber $k$ of the correlation of density and specific-volume $b(k)$, the mass flux $\bm{a}(k)$, and the turbulent kinetic energy $E(k)$, using a set of coupled equations. Each dynamical variable has two coefficients governing spectral transfer among modes. In addition, the mass flux $\bm{a}(k)$ has two coefficients governing the drag between the two fluids. |
Monday, November 19, 2018 5:23PM - 5:36PM |
L39.00007: Towards Leveraging Machine Learning and Other Statistical Methods To Improve Turbulence Modeling Balu Nadiga, Chiyu Jiang, Daniel Livescu Notwithstanding the on-going explosive growth in computational capabilities, coarse-grained |
Monday, November 19, 2018 5:36PM - 5:49PM |
L39.00008: Spatio-temporal Modeling of High-fidelity Turbulence with Convolutional Long Short-Term Memory Neural Networks Arvind T Mohan, Michael Chertkov, Daniel Livescu A major challenge in machine learning for turbulence is the chaotic, high dimensional and spatio-temporal nature of the data; which can make the learning process ineffective and/or expensive. Previous work [1] had demonstrated the capability of Long Short-Term Memory (LSTM) neural networks to capture temporal dynamics of turbulence. In this work, we extend this capability to modeling spatio-temporal dynamics using the Convolutional LSTM (ConvLSTM) neural network. ConvLSTM augments the traditional architecture of the LSTM cell with a convolutional layer to capture spatial correlations in multidimensional data. We demonstrate the potential of ConvLSTM in learning and predicting the dynamics of a DNS homogeneous isotropic turbulence dataset. We perform statistical tests on the predicted turbulence to quantify the quality of the“learned” physics and develop physics-inspired neural network constraints for improved predictions. Finally, we study the feasibility of this approach for large datasets and explore strategies to increase computational efficiency. [1] https://arxiv.org/abs/1804.09269 |
Monday, November 19, 2018 5:49PM - 6:02PM |
L39.00009: A model for passive scalar transport in turbulent channel flow Alireza Ebadi, Juan Carlos Cuevas-Bautista, Christopher White, Gregory Chini, Joseph Klewicki Passive scalar in turbulent boundary layer is transported via the momentum field, which at high Reynolds number is composed of large uniform momentum zones (UMZs) segregated by narrow regions of concentrated vorticity. Recent experimental studies indicate the scalar field is also composed of large uniform scalar zones (USZs) segregated by narrow regions of concentrated scalar gradient. A model that reproduces the fundamental elements of the USZ structure by placing a few concentrated regions of scalar gradient across the boundary layer is presented. The number of concentrated regions of scalar gradient, their most probable location and corresponding scalar quantity in the outer region of the scalar boundary layer (in which the molecular diffusion is negligible) is developed by the analysis of the mean scalar transport equation. An asymptotic length and scalar scaling in the inner region of the boundary layer is explored. Moreover, the combined effects of Re and Pr numbers on the USZ structure is investigated. The numerical results show the model can reproduce the main characteristics of the scalar field up to the fourth statistical moment. Furthermore, in conjugation with the UMZ model developed by the authors, the mode can produce the streamwise velocity-scalar correlation. |
Monday, November 19, 2018 6:02PM - 6:15PM |
L39.00010: Investigating the Mixing-Hydrodynamic Cascade Timescale Ratio in Transient Non-Equilibrium Turbulence Using a Fokker-Planck Equation Approach Juan A Saenz, Raymond Ristorcelli, Jozsef Bakosi We investigate the mixing– hydrodynamic cascade timescale ratio (C_{b2}) in transient, non-equilibrium binary mixing variable density turbulence (VDT). We represent the turbulent flow as a stochastic β-process using a Fokker-Planck equation that evolves a probability density function in time and in bounded mass fraction space. The FPE is integrated to obtain the evolution equation for the density – specific volume covariance (b). This evolution equation for b is compared to the equation obtained from ensemble averaging the Navier-Stokes equations, where the mixing cascade or destruction of b is given by ε_{b}. We use C_{b2} to represent ε_{b} as a linear drag model with a hydrodynamic timescale and a proportionality parameter C_{b2}. The evolution equation for b derived from the FPE is then used to find an expression for timescale ratio C_{b2} as a function of flow statistics, which is then modeled, using a new transient timescale, as an algebraic function of mean flow statistics. Simulations of homogeneous VDT using a Monte Carlo model based on the FPE, and solutions of the BHR equation for b using the new model for C_{b2} are compared with direct numerical simulations at several Atwood numbers, and for different initial conditions. We discuss extensions to in-homogeneous flows. |
Monday, November 19, 2018 6:15PM - 6:28PM |
L39.00011: A uniform momentum zone-vortical fissure model of the turbulent boundary layer Juan Carlos Cuevas-Bautista, Alireza Ebadi, Christopher White, Gregory Chini, Joseph Klewicki Recent studies show evidence that the turbulent boundary layer (TBL) structure at high Reynolds number ($Re_{\tau}$) can be considered like a binary arrangement of large-scale zones of nearly uniform streamwise momentum (UMZ) being segregated by narrow fissures of concentrated vorticity. A simple model to reproduce the statistical dynamics of TBL and channel flow using these two elements is presented. In brief, the UMZs are created by following the edge velocity of the adjacent fissures, while the sharp change in momentum across the fissures scale with the friction velocity $\mathcal{O}$$(u_{\tau})$. The length and velocity scalings of the fissures are informed by the theory. Furthermore, a momentum exchange mechanism is enforced throughout the boundary layer. Then, an ensemble of statistically independent instantaneous velocity profiles is created by allowing the fissures move randomly in the wall normal direction while they exchange momentum with the surrounding fluid. The numerical results shows that the model is able to reproduce the main statistical moments of the streamwise velocity from low to high-moderate $Re_{\tau}$ (e.g. $Re_{\tau}=1000,5000,10000$). Additionally, a dynamical wake mechanism is investigated for accurately modeling the entire domain of the given flow. |
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