Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session X39: Turbulence Modeling II |
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Chair: Ian Jacobi, Technion Room: 355 E |
Tuesday, November 26, 2024 8:00AM - 8:13AM |
X39.00001: Reynolds stress decay modeling informed by anisotropically forced homogeneous turbulence Omkar Shende, Ty Homan, Ali Mani The Reynolds-averaged Navier-Stokes equations are popular for predicting complex turbulent flows due to their computational affordability and ability to estimate quantities of engineering interest. These equations, however, require proper closure models to treat unclosed terms. Here, we consider the terms responsible for decay of the Reynolds stresses in the six Reynolds stress transport equations. Using anisotropic forcing of the momentum equations, we access states of turbulence anisotropy traditionally not probed in a triply periodic domain and then perform robust selection of model forms and model coefficients to capture the decay terms. Our optimal model extends to cubic terms when expressed in terms of the principal coordinate Reynolds stresses. We demonstrate improved accuracy in predicting simulation data compared to extant models from the literature. |
Tuesday, November 26, 2024 8:13AM - 8:26AM |
X39.00002: Assessment of confinement effects on decay terms of Reynolds-stress transport equations Makrand A Khanwale, Ali Mani The Reynolds stress transport equations provide a valuable framework for developing second-order closure models for the unclosed terms in Reynolds-averaged Navier-Stokes equations. In this work, we specifically focus on the unclosed terms associated with the decay of Reynolds stresses. To study these terms in isolation, we consider a canonical setup of forced turbulence with walls encompassing a wide range of turbulence anisotropies. In this setting, only the decay of the Reynolds-stress terms needs to be closed due to the absence of mean velocity gradients. However, due to the confinement effect of the walls, the decay rate of Reynolds stress and its anisotropy is modified. We present a systematic study of these modifications by analyzing the exact Reynolds-stress equations for various volumetrically forced high-fidelity simulations. |
Tuesday, November 26, 2024 8:26AM - 8:39AM |
X39.00003: Assessment of anisotropy in the decay term of the dissipation equation for Reynolds stress transport models Rozie Zangeneh, Omkar Shende, Ali Mani In a recent study, Homan et al. (DFD-A43.00005, 2023) showed that states of turbulence anisotropy can be accessed in a triply periodic domain using the volumetric forcing scheme of Dhandapani et al. 2019. Using their simulation data, they proposed a new model for the decay terms of the Reynolds stress transport (RST) equations. However, their model assumes the kinetic energy dissipation rate as a given time resolved quantity. In this study, we build on the same methodology by examining the decay rate of the dissipation field itself. For homogeneous flows and in the absence of mean velocity gradients, dissipation decay is the only active closure. Based on our assessment, we identify anisotropies that should be included in the dissipation decay under such conditions. |
Tuesday, November 26, 2024 8:39AM - 8:52AM |
X39.00004: Non-linear structure-based modeling of the rapid pressure strain rate correlation using machine learning Sahil Kommalapati, Sigfried W Haering, Robert D Moser Modeling the rapid pressure strain rate (RPSR) correlation in the Reynolds Stress Transport Equations is a fundamental challenge for developing Reynolds Stress closures in Reynolds Averaged Navier Stokes (RANS) simulations. Earlier attempts have seen limited success, which is hypothesized to be due to missing model dependencies. Kassinos et al. [1] proposed using an extended set of dependencies consisting of the dimensionality and stropholysis structure tensors in addition to the Reynolds stress, and derived a linear model for the RPSR correlation in terms of them, which still exhibited deficiencies. In this work, new nonlinear closure models are developed in terms of the structure tensors. The coefficients appearing in the models are learned as a function of the structure tensor invariants using machine learning trained on a broad ensemble of rapidly distorted turbulence (RDT) simulations. An in-depth analysis of the original linear model and the new nonlinear models is carried out. This development is the first step towards showing that the structure tensors provide a sufficiently rich statistical description of turbulence to enable the modeling of complex turbulent flows. |
Tuesday, November 26, 2024 8:52AM - 9:05AM |
X39.00005: Deep neural network framework for modeling pressure hessian tensor in incompressible turbulent flows Deep Shikha, Sawan S Sinha The dynamics of the velocity gradient tensor is crucial in understanding various turbulent nonlinear processes. One of the unclosed terms in the velocity gradient evolution equation for incompressible flows is the anisotropic part of the pressure Hessian tensor. This research introduces a novel approach to model this tensor using machine learning. |
Tuesday, November 26, 2024 9:05AM - 9:18AM |
X39.00006: Prediction of particle trajectories in DNS with machine learning Oanh L Pham, Dimitrios V Papavassiliou The transport of passive particles in turbulent flow can be studied with a combination of Direct Numerical Simulation (DNS) and Lagrangian scalar tracking (LST). While such methods are computationally expensive,1 deep learning has become a promising approach for the prediction of tunrulent flow behavior results for computational savings.2 In the Lagrangian framework, spatial and temporal features are required to construct the particle movement. Long short-term memory (LSTM) and hybrid methods have been used for temporal evolution while training deep neural networks.3 Herein, we use LSTMin combination with artificial neural network (ANN) to generate the trajectories of passive particles. The data was obtained from DNS/LST computations for channel flow at Reτ=300 and 100000 particle trajectores4 divided into 80% for training, 10% for validation and 10% for testing. The performance of the model was investigated at various hyperparameters and the mean square error was chosen as the loss function for fitting procedures. The prediction results were compared with the ground truth values based on the distribution of position and velocity over time. It was found that the LSTM exhibiteed high accuracy predictions at short times. |
Tuesday, November 26, 2024 9:18AM - 9:31AM |
X39.00007: Data-enabled discovery of specific and generalizable turbulence closures Zhongxin Yang, Xianglin Shan, Xiang I. A. Yang, Weiwei Zhang Turbulence closures are critical for the predictive modeling of fluid flows in both natural and engineering contexts. We address this generalizability issue in the context of symbolic regression. A critical aspect of our work is distinguishing between flow physics that is specific to the training data and those that are generalizable, the former of which must be removed or replaced when applying the closure beyond the training dataset. By progressively training on increasingly complex flows, we successively incorporate inner-layer physics, outer-layer physics, and pressure gradient physics into the closures. The resulting models are validated against a wide range of flows, most of which are outside the training dataset, and the results are highly favorable. This work enables the discovery of data-specific and generalizable turbulence closures, addressing the generalizability issue and leading to truly predictive modeling of fluid flows using machine-learning. |
Tuesday, November 26, 2024 9:31AM - 9:44AM |
X39.00008: Differentiable physics for generalizable closure modeling of separated flows Hojin Kim, Romit Maulik The computational modeling of turbulent flows is challenging due to the high computational costs of resolving all spatio-temporal scales. Machine learning (ML) methods have been proposed for constructing turbulence closures which can alleviate these costs by modeling the effects of unresolved structures on resolved quantities. However, several ML-based turbulence models show weak generalization capabilities under varying geometries and their closure requirements. This talk will present results from a differentiable programming framework to learn generalizable closure models. Specifically, our framework involves the training of a graph-neural network (GNN) model for subgrid stresses (SGS), embedded within a finite element (FEM) solver. This is achieved by chaining gradients computed by automatic differentiation for GNNs with the discrete adjoint of the FEM solver and enables the learning of SGS given a fully-resolved flow field. In this research, we leverage the mesh invariant property of GNNs to learn subgrid models for separated flows from different separation physics (i.e., smooth, sharp and for various geometries). Our formulation enables a single GNN-based subgrid closure model that generalizes across different geometries as well as separation phenomena and supports the conclusion that generalizable ML closures may be constructed using the differentiable physics. |
Tuesday, November 26, 2024 9:44AM - 9:57AM |
X39.00009: Influence of vibrational non-equilibrium on the dynamics of velocity gradients in turbulent flows Sawan S Sinha, Shishir Srivastava In hypersonic turbulent flow fields, air molecules get vibrationally excited. Further, the flow residence time over a hypersonic vehicle may be too small such that the vibrational and the translational modes of internal energy may exist in a temporally evolving non-equilibrium state. This non-equilibrium leads to modified energetics in the flow field that in turn may affect various non-linear processes of turbulence. In this work, our objective is to identify, isolate and examine how the vibrational non-equilibrium phenomenon specifically influences the dynamics of velocity gradients. We perform well-resolved direct numerical simulation (DNS) simulations of decaying isotropic turbulence, including the physics of vibrational non-equilibrium of air molecules. These simulations are performed for a set of initial conditions, wherein the vibrational Damkohler number and the initial ratio of vibrational to translation-rotational energy are used as simulation parameters. We plan to demonstrate how the vibrational non-equilibrium process specifically influences the solenoidal and dilatational aspects of the hypersonic velocity field. Further, we also discuss how the pressure Hessian tensor acts as an intermediary through which the vibrational non-equilibrium shapes the behavior of the velocity gradient field. |
Tuesday, November 26, 2024 9:57AM - 10:10AM |
X39.00010: Fractional Navier-Stokes equations from first principles Pavan Pranjivan Mehta Turbulence is a non-local and multi-scale phenomenon. Resolving all scales implies non-locality is addressed implicitly. However, if spatially or temporally averaged fields are considered for computational feasibility, then addressing non-locality explicitly becomes important as a result of missing information of all scales. Thus it is natural to introduce a fractional or a non-local operator. However, an overwhelming question remains, ”how do we derive a fractional conservation law from first principles?” Thus, in this talk, I shall introduce the recently developed control volume approach in [3] to derive fractional conservation law from first principles. Subsequently, derive the fractional analogue of Reynolds transport theorem [3]. By virtue of this theorem, we derive the ”fractional continuity” and ”fractional Cauchy equations”, which follows conservation of mass and momentum, respectively [3]. The stress tensor of fractional Cauchy equation is treated with a fractional stress-strain relationship (which was developed in [2]) to get to the final form of ”fractional Navier–Stokes equations”. |
Tuesday, November 26, 2024 10:10AM - 10:23AM |
X39.00011: Investigation of turbulent mixing of scalars with arbitrary Schmidt numbers using the stochastic Hierarchical Parcel Swapping Model David O Lignell, Masoomeh Behrang, Alan R Kerstein, Isaac Wheeler, Tommy Starrick, Heiko Schmidt Hierarchical Parcel Swapping (HiPS) is a stochastic model of turbulent mixing. HiPS is based on a binary tree structure consisting of nodes emanating from the top of the tree and terminating in parcels at the base of the tree containing fluid properties. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent mixing is modeled by swapping subtrees at different tree levels. Swaps involving single parcels result in micromixing that changes scalar states. Swaps are implemented as a Poisson process at rates corresponding to level time scales. HiPS is extended to simulation of multiple scalars with arbitrary diffusivities, considering transport in the inertial, viscous-advective, and inertial-diffusive ranges. Fundamental analysis of particle dispersion is presented with comparisons to theoretical results and DNS data in the inertial and viscous ranges. Scalar energy spectra are analysed in the three ranges and reproduce known scaling exponents. Scalar dissipation statistics are analysed and reproduce the experimental and theoretical lognormal distribution with negative skewness represented by a stretched-exponential function. DNS data are used to evaluate empirical coefficients, facilitating quantitative applications. The physical fidelity demonstrated with HiPS suggests its use as a low-cost subgrid model for coarse-grained flow simulation, for which parcel-pair mixing is a common treatment. |
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