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Register a new userInvestigation of nonlocal data-driven methods for subgrid-scale stress modelling in large eddy simulation
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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.
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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.
A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while guaranteeing Galilean invariance by making use of a tensor basis. By modifying a random forest algorithm to accept such a tensor basis, a robust, easy to implement, and easy to train algorithm is created. The algorithm is trained on several flow cases using DNS/LES data, and used to predict the Reynolds stress anisotropy tensor for new, unseen flows. The resulting predictions of turbulence anisotropy are used as a turbulence model within a custom RANS solver. Stabilization of this solver is necessary, and is achieved by a continuation method and a modified $k$-equation. Results are compared to the neural network approach of Ling et al. [J. Fluid Mech, 807(2016):155-166, (2016)]. Results show that the TBRF algorithm is able to accurately predict the anisotropy tensor for various flow cases, with realizable predictions close to the DNS/LES reference data. Corresponding mean flows for a square duct flow case and a backward facing step flow case show good agreement with DNS and experimental data-sets. Overall, these results are seen as a next step towards improved data-driven modelling of turbulence. This creates an opportunity to generate custom turbulence closures for specific classes of flows, limited only by the availability of LES/DNS data.
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.
Cloud cavitation is related to an intrinsic instability where clouds are shed periodically. The shedding process is initiated either by the motion of a liquid re-entrant jet or a condensation shock. Cloud cavitation in nozzles interacts with the flow field in the nozzle, the mass flow and the spray break-up, and causes erosion damage. For nozzle geometries cloud shedding and the associated processes have not yet been studied in detail. In this paper, we investigate the process of cloud cavitation shedding, the re-entrant jet and condensation shocks in a scaled-up generic step nozzle with injection into gas using implicit Large-Eddy Simulations (LES). For modeling of the cavitating liquid we employ a barotropic equilibrium cavitation model, embedded in a homogeneous multi-component mixture model. Full compressibility of all components is taken into account to resolve the effects of collapsing vapor structures. We carry out simulations of two operating points exhibiting different cavitation regimes. The time-resolved, three-dimensional simulation results cover several shedding cycles and provide deeper insight into the flow field. Our results show that at lower cavitation numbers, shedding is initiated by condensation shocks, which has not yet been reported for nozzle flows with a constant cross-section. We analyze the cavitation dynamics and the shedding cycles of both operating points. Based on our observations we propose modifications to established schematics of the cloud shedding process. Additionally, we analyze the near-wall upstream flow in and underneath the vapor sheet and possible driving mechanism behind the formation of the re-entrant jet.
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.
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