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Register a new userInvariant Data-Driven Subgrid Stress Modeling in the Strain-Rate Eigenframe for Large Eddy Simulation
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We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows. The key to our approach is representation of model input and output tensors in the filtered strain rate eigenframe. Provided inputs and outputs are selected and non-dimensionalized in a suitable manner, this yields a model form that is symmetric, Galilean invariant, rotationally invariant, reflectionally invariant, and unit invariant. We use this model form to train a simple and efficient neural network model using only one time step of filtered direct numerical simulation data from a forced homogeneous isotropic turbulence simulation. We demonstrate the accuracy of this model as well as the models ability to generalize to previously unseen filter widths, Reynolds numbers, and flow physics using a priori and a posteriori tests.
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A nonlocal subgrid-scale stress (SGS) model is developed based on the convolution neural network (CNN), a powerful supervised data-driven approach. The CNN is an ideal approach to naturally consider nonlocal spatial information in prediction due to its wide receptive field. The CNN-based models used here only take primitive flow variables as input, then the flow features are automatically extracted without any $priori$ guidance. The nonlocal models trained by direct numerical simulation (DNS) data of a turbulent channel flow at $Re_{tau}=178$ are accessed in both the $priori$ and $posteriori$ test, providing physically reasonable flow statistics (like mean velocity and velocity fluctuations) closing to the DNS results even when extrapolating to a higher Reynolds number $Re_{tau}=600$. In our model, the backscatter is also predicted well and the numerical simulation is stable. The nonlocal models outperform local data-driven models like artificial neural network and some SGS models, e.g. the Smagorinsky model in actual large eddy simulation (LES). The model is also robust since stable solutions can be obtained when examining the grid resolution from one-half to double of the spatial resolution used in training. We also investigate the influence of receptive fields and suggest using the two-point correlation analysis as a quantitative method to guide the design of nonlocal physical models. To facilitate the combination of machine learning (ML) algorithms to computational fluid dynamics (CFD), a novel heterogeneous ML-CFD framework is proposed. The present study provides the effective data-driven nonlocal methods for SGS modelling in the LES of complex anisotropic turbulent flows.
Expressing the evolution equations for the filtered velocity gradient tensor (FVGT) in the strain-rate eigenframe provides an insightful way to disentangle and understand various processes such as strain self-amplification, vortex stretching and tilting, and to consider their properties at different scales in the flow. Using data from Direct Numerical Simulation (DNS) of the forced Navier-Stokes equation, we consider the relative importance of local and non-local terms in the FVGT eigenframe equations across the scales using statistical analysis. The analysis of the eigenframe rotation-rate, that drives vorticity tilting, shows that the anisotropic pressure Hessian plays a key role, with the sub-grid stress making an important contribution outside the dissipation range, and the local spinning due to vorticity making a much smaller contribution. The results also show the striking behavior that the vorticity tilting term remains highly intermittent even at relatively large scales. We derive a generalization of the Lumley triangle that allows us to show that the pressure Hessian has a preference for two-component axisymmetric configurations at small scales, with a transition to a more isotropic state at larger scales. Correlations between the sub-grid stress and other terms in the eigenframe equations are considered, highlighting the coupling between the sub-grid and nonlinear amplification terms, with the sub-grid term playing an important role in regularizing the system. These results provide useful guidelines for improving Lagrangian models of the FVGT, since current models fail to capture a number of subtle features observed in our results.
Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the `Recent Fluid Deformation (RFD) approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the product of the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in Large Eddy Simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other `nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.
This paper presents a numerical investigation of aerodynamic noise generated by a generic side-view mirror mounted on a flat plate using the Stress Blended Eddy Simulation (SBES) coupled with the Ffowcs Williams and Hawkings (FW-H) equation. A grid evaluation study was performed using a standardised side-view mirror with a Reynolds Number (Re) of 5.2 x10^5 based on the diameter of the model. The predictions for hydrodynamic pressure fluctuations on the mirror, the window and the sound emitted at various microphone locations are in good agreement with previously published experimental data. In addition, our numerical results indicate that yawing the mirror closer to the side window results in the flow being attached to the rear of the mirror resulting in an overall reduction in Sound Pressure Level (SPL) at several receiver locations.
We have performed Coherent-vorticity Preserving Large-Eddy simulations of a trefoil knot-shaped vortex, inspired by the experiments of Kleckner and Irvine. The flow parameter space is extended in the present study, including variations of the circulation Reynolds numbers in the range Re = 2000 - 200000, where Re = 20000 is the value used in the experiments. The vortex line corresponding to the trefoil knot is defined using a parametric equation and the Biot-Savart law is employed to initialize the velocity field. The CvP LES computation displays a good qualitative match with the experiment. In particular, the vortex entanglement process is accurately represented as well as the subsequent separation of the main vortex in two distinct structures - a small and a large vortex - with different self-advection speeds that have been quantified. The small vortex propagates faster than the large oscillatory vortex which carries an important amount of vorticity. The advection velocity of the vortex before bursting is found to be independent of the Reynolds number. The low Reynolds number computation leads to a decrease of the separated vortices velocity after bursting, compared to the higher Reynolds computations. The computation of energy spectra emphasizes intense energy transfers from large to small scales during the bursting process. The evolution of volume-averaged enstrophy shows that the bursting leads to the creation of small scales that are sustained a long time in the flow, when a sufficiently large Reynolds number is considered (Re>20000). The low Reynolds number case Re = 2000 hinders the generation of small scales during the bursting process and yields essentially laminar dynamics. The onset of background turbulence due to the entanglement process can be observed at Re = 200000
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