Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 65, Number 13
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session X11: Turbulence: Modeling & Simulations (10:45am  11:30am CST)Interactive On Demand

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X11.00001: Fractional Reynoldsaveraged Navier Stokesequations (fRANS) for modeling of transitionaland turbulent boundary layers Pavan Pranjivan Mehta, Tamer Zaki, Charles Meneveau, George Karniadakis Reynolds averaged NavierStokes (RANS) equations often invoke a local model for the Reynolds stresses, while in reality the correlations between these stresses and the strain rate are nonlocal. In this work, we propose to model the Reynolds stress in terms of the mean velocity using fractional gradients, which are nonlocal operators. We demonstrate mathematically that a single model structure is valid for all regimes of the flow. Also, when nondimensionalized in wall units, there are no additional coefficient to model. Results are presented for modeling statistics from direct numerical simulations of bypass transition from JHTDB, and for analytical expressions of the total shear stress from the literature. The model can match the mean velocity profile in the transitional and fully turbulent regimes. The results demonstrate the mathematical expressivity of the fractional gradient, where a nonlocal physics are properly captured. [Preview Abstract] 

X11.00002: RANS Wall Modelling for Variable Viscosity Turbulence Kazuhiko Suga, Hajime Katashiba, Yusuke Kuwata With a large temperature difference, modification of turbulence characteristics by temperaturedependent fluid properties becomes nonignorable. It is thus clear that the standard logarithmic law of mean velocities cannot be valid in such a case. To provide an alternative wall model, this study modifies the analyticalwall function by introducing a temperaturedependent nearwall layer for the viscosity. The Favre averaged thin boundarylayer equations (TBLEs) for the momentum and the temperature are considered to construct the wallfunction. To take account of the effects of the steep temperaturedependent nearwall viscosity, this study models the viscosity profile as a simple function of the normalized distance from the wall. The TBLEs are, then, integrated inside walladjacent cells to obtain the wall shear stress and the wall heat flux for the wall boundary conditions. The simulated results show that the proposed model successfully contributes to reproducing the skewed mean velocity and temperature profiles by the RANS $k\varepsilon$ model. [Preview Abstract] 

X11.00003: Modeling subgridscale stress by deconvolutional artificial neural networks in large eddy simulation of turbulence Zelong Yuan, Chenyue Xie, Jianchun Wang A deconvolutional artificial neural network (DANN) framework is proposed to model the subgridscale (SGS) stress in large eddy simulation (LES) of turbulence. The filtered velocities at the local spatial stencil geometry are used as input features of the DANN models to recover the unfiltered velocity. The grid width of the DANN models is chosen to be smaller than the filter width, in order to accurately reconstruct the effects of SGS dynamics. The DANN models with reasonable local stencil geometry can predict the SGS stress more accurately than the conventional approximate deconvolution method (ADM) and velocity gradient model (VGM) with high correlation coefficients (larger than 99\%) and low relative errors (less than 15\%) in the \emph{a prior} study. In the \emph{a posteriori} analysis, the DANN model is superior to the implicit large eddy simulation (ILES), the dynamic Smagorinsky model (DSM), and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, various statistics of velocity and the instantaneous coherent structures without increasing the considerable computational cost. Besides, the trained DANN models without any finetuning can predict the velocity statistics and reconstruct SGS energy flux well for different filter widths. These results indicat [Preview Abstract] 

X11.00004: Rapid Spatiotemporal Turbulence Modeling with Convolutional Neural ODEs Varun Shankar, Gavin Portwood, Arvind Mohan, Peetak Mitra, Venkat Viswanathan, David Schmidt Turbulence modeling has remained a difficult challenge in physics and engineering due to the high complexity of its governing equations. Traditional computational fluid dynamics methods such as DNS and LES have made highfidelity simulations possible, however these conventional techniques are limited by their sizable computational requirements and are often unsuitable for engineering applications. Much attention has now been turned towards datadriven deep learning approaches, which can capture the underlying nonlinear dynamics at a significantly reduced computational cost. We propose a deep learning architecture to predict a spatiotemporal solution field based on the neural ODE algorithm. We approximate the dynamics of the velocity field with a convolutional network, which captures local spatial variations, and can be evolved through time using existing numerical methods. This approach exploits a principled formulation of the dynamical system and enables vast speedup. Predictions are evaluated based on a variety of turbulent statistical diagnostics. Network outputs model large scale behavior well, while neglecting some of the smaller scales. Stationarity is observed in the forecasts with minimal kinetic energy losses and predictive capabilities through 2 eddy turnover times. [Preview Abstract] 

X11.00005: A neuralnetworkbased subgridscale model for LES of turbulent channel flow Jonghwan Park, Haecheon Choi A neuralnetworkbased subgridscale model is developed for a turbulent channel flow at \textit{Re}$_{\tau } \quad =$ 180, and \textit{a priori} and \textit{a posteriori} tests are conducted to investigate the prediction performance of this neural network (NN). In \textit{a priori} test, an NNbased subgridscale (SGS) model with stencils of strain rate or velocity gradient tensor as the input variable provides highest correlation coefficients between the true and predicted SGS stresses. However, these NN models also provide the backscatter, incurring the numerical instability in the actual LES. On the other hand, an NNbased SGS model with a single point of the strain rate tensor as the input shows an excellent prediction performance for the turbulence statistics such as the mean velocity profile and the Reynolds shear stress. The present NN model is applied to a higher Reynolds number (\textit{Re}$_{\tau } \quad =$ 720) with the model trained at \textit{Re}$_{\tau }$ $=$ 180. The results also show good agreements with those of filtered DNS data. When the grid resolutions are different from that of training data, the NNbased SGS model does not work well in LES. This problem is overcome by training the NN with the database obtained with two different filters whose sizes are larger and smaller than the grid sizes used in LES. [Preview Abstract] 

X11.00006: Temporal largeeddy simulation based on direct deconvolution Daniel Oberle, Charles Pruett, Patrick Jenny We propose an approach for Temporal LargeEddy Simulation (TLES) with direct deconvolution. In contrast to previous TLES models like the Temporal Approximate Deconvolution Model (TADM) by Pruett et al., the nonfiltered fields are recovered using a direct deconvolution given by the differential form of the filter operator rather than a truncated series expansion of the inverse filter operator. The closure is obtained by an evolution equation of the temporal residualstress tensor, which is analytically derived from the relation of the filtered and the nonfiltered fields. Thus, the Temporal Direct Deconvolution Model (TDDM) has the advantage of being more accurate and requiring less computational effort relative to the TADM. A secondary regularization term based on selective frequency damping is employed, similar as for TADM. The TDDM was implemented in the spectral element code Nek5000 to simulate different test cases such as homogeneous isotropic turbulence at $Re_{\lambda}$=50 and 190, turbulent channel flow at $Re_{\tau}$=180 and flow over a periodic hill at $Re=$10595. The results demonstrate an improvement compared to the nomodel solutions, while the computational cost is reduced dramatically compared to direct numerical simulation. [Preview Abstract] 
Not Participating 
X11.00007: Resolvent analysis of turbulent mixing layers G S Sidharth Linear resolvent analysis techniques have been successfully used in literature to study coherent structures in turbulent boundary layers and jets. In this work, we carry out resolvent analysis of turbulent mixing layers in selfsimilar coordinates. Two mixing layer configurations — a sheardriven mixing layer and a buoyancydriven mixing layer are considered. The turbulent mean profiles are obtained using largeeddy simulations. The resolvent mode structures in buoyancydriven mixing layer are contrasted with the sheardriven case due to different turbulence production mechanisms. The effect of mean density contrasts in the mixing fluids is also investigated. Using the resolvent framework, an emphasis is made to reconstruct the energetic structures in latetime turbulent fields using the information of the initial perturbation seeds. [Preview Abstract] 

X11.00008: Impacts of Numerical Discretization on Large Eddy Simulation Gopal Yalla, Robert Moser, Todd Oliver In practical Large Eddy Simulation (LES), the filter is often implicitly defined through a projection onto the finitedimensional solution space that is inherent in numerical discretization. Therefore, the interaction between the underlying numerics and the dynamics of the resolved turbulence must be taken into account during the formulation of LES models. However, this interaction is not well understood and is often neglected. Most LES models are developed under the assumptions of homogeneous isotropic resolution, and accurate representation of all scales by the underlying numerics. In this talk, we focus on the effects of resolution inhomogeneity and discretization error on LES. This is examined in the context of homogeneous, isotropic turbulence convecting through an inhomogeneous grid with a range of higher and lower order numerics. A model formulation to correct for such numerical issues is also presented. This model is based on the difference between the numerical second derivative operator and repeated application of the numerical first derivative operator, which acts as a filter for the insufficiently resolved scales of motion. As such, the model is designed to be applicable for a wide range of numerical methods so that it may be broadly and easily adopted. [Preview Abstract] 

X11.00009: An Accelerated Macroscopic Forcing Method for Determining Eddy Viscosity Operators Dana Lynn Lansigan, Danah Park, Ali Mani The macroscopic forcing method (MFM) is a statistical technique for determining turbulence closures (Mani and Park (2019), arXiv:1905.08342). Specifically, the method is useful for determining the eddy viscosity operator of turbulent flows. One challenge with this technique is the requirement of multiple highfidelity simulations for a reasonable characterization of the closure operator. Depending on the desired accuracy in details, i.e. relying on the leadingorder moments of the closure operator or requiring assessment of all degrees of freedom, the number of required MFM simulations can vary from one to much larger than 10 for a given configuration. In this work, we present and verify a speed up technique for statistically stationary flows that reduces the cost of MFM by multiple orders of magnitude. As an example, we consider the standard turbulent channel flow and show that full characterization of the eddy diffusivity operator can be achieved by essentially dedicating the cost of a single highfidelity simulation. [Preview Abstract] 

X11.00010: An assessment of LES models using the macroscopic forcing method yasaman shirian, Ali Mani In this work we introduce a new approach to assess the LES models based on contrasting the eddy diffusivity operators obtained from the DNS and LES flow fields. Our analysis is based on the expectation that the mean field momentum obtained from the LES must be the same as the filtered mean field momentum obtained from the DNS. Using the macroscopic forcing method (Park and Mani 2019), we project both the LES and DNS equations onto the RANS space and obtain the respective operators that govern the mean fields of both systems. In this presentation, we consider homogeneous isotropic turbulence as a canonical setting to assess the LES models. We show that while the standard Smagorinsky model performs reasonably at lowwavenumbers when assessed against this criterion, it is overdissipative in the highwavenumbers limit. Inspired by these results we introduce an alternative LES model and demonstrate its superior performance over the entire wavenumber spectrum. [Preview Abstract] 

X11.00011: Dynamic Bridging Paradigm for Coarse Grained Simulations of Turbulent Material Mixing. Fernando Grinstein, Juan Saenz, Rick Rauenzahn, Massimo Germano We focus on simulating the consequences of material interpenetration, hydrodynamical instabilities, and mixing arising from perturbations at shocked material interfaces, as vorticity is introduced by the impulsive loading of shock waves  e.g., as in inertial confinement fusion capsule implosions. Such complex flow physics is capturable with Coarse Grained Simulation  classical and implicit LargeEddy Simulation, where the smallscale flow dynamics is presumed enslaved to the dynamics of the largest scales. Beyond shocks and variabledensity turbulence multiscaleresolution issues, we must address the difficult problem of predicting flow transitions promoted by energy deposited at the material interfacial layers during the shock interface interactions. Transition involves unsteady largescale coherentstructure dynamics resolvable by CGS but not by ReynoldsAveraged NavierStokes modeling based on equilibrium turbulence assumptions and singlepointclosures. We propose a dynamic blended RANS/LES bridging strategy for applications involving variabledensity turbulent mixing applications, and report progress testing its implementation for relevant cases prototyping the shockdriven turbulent mixing applications (Computers and Fluids 2020). [Preview Abstract] 

X11.00012: Transition Modeling for the TaylorGreen Vortex Daniel Israel The exact moment equations that form the basis for most turbulence models are equally valid for nonturbulent flow. Here we are interested in predicting transition of the TaylorGreen vortex (TGV). Conventional $k\varepsilon$ closures include only a destruction term in the dissipation rate equation. However, the transition of the initial delta function spectrum to a broad turbulent spectrum appears as a production of dissipation. The exact dissipation rate equation, $\dot{\varepsilon}=\frac{\varepsilon^{2}}{k}\left(\frac{7}{3\sqrt{15}}SR_{t}^{1/2}+\frac{7}{15}G\right)$, studied extensively by Speziale & Bernard (1992) and Ristorcelli (2003), can have both production and destruction. It turns out that even very simple closures for S and G, namely, setting both to constants, results in qualitatively correct predictions for the TGV transition. Direct numerical simulation data from the entire family of TGV initial conditions further casts light on the role of anisotropy in the transition process, as well as the broader promise and limits of transition modeling. [Preview Abstract] 

X11.00013: A framework for costeffective modeling of nonlocal eddy diffusivities Jessie Liu, Hannah Williams, Ali Mani New techniques, such as the Macroscopic Forcing Method (MFM) (Mani and Park (2019), arXiv:1905.08342), have quantified nonlocality as a missing ingredient in Reynoldsaveraged NavierStokes (RANS) models. In contrast with the commonly used Boussinesq approximation, a purely local approximation, nonlocality allows an unclosed term at a given point to depend on mean field quantities at all points in space and at previous times. However, this dependence also causes implementation of nonlocality to be computationally expensive and impractical for many applications. Using passive scalar transport as an example, we present a framework for costeffective modeling of spatiotemporal nonlocality with extension to inhomogeneous flows. [Preview Abstract] 
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