Unsteady flow fields over a circular cylinder are trained and predicted using four different deep learning networks: generative adversarial networks with and without consideration of conservation laws and convolutional neural networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information of flow fields at previous occasions. Predictions of deep learning networks are conducted on flow fields at Reynolds numbers that were not informed during training. Physical loss functions are proposed to explicitly impose information of conservation of mass and momentum to deep learning networks. An adversarial training is applied to extract features of flow dynamics in an unsupervised manner. Effects of the proposed physical loss functions and adversarial training on predicted results are analyzed. Captured and missed flow physics from predictions are also analyzed. Predicted flow fields using deep learning networks are in favorable agreement with flow fields computed by numerical simulations.

The governing equations for large-eddy simulation are derived from the application of a low-pass filter to the Navier–Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter, causing results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operation, and hence the resolved turbulence, from the underlying mesh distribution alleviating some of the grid sensitivities. We investigate the use of explicit filtering in large-eddy simulation in order to obtain numerical solutions that are grid independent. The convergence of simulations using a fixed filter width with varying mesh resolutions to a true large-eddy simulation solution is analyzed for a turbulent channel flow at Reτ=180, 395, and 640. By using explicit filtering, turbulent statistics and energy spectra are shown to be independent of the mesh resolution used.

The tip-leakage flow in a turbomachinery cascade is studied using large-eddy simulation with particular emphasis on understanding the underlying mechanisms for viscous losses in the vicinity of the tip gap. Systematic and detailed analysis of the mean flow field and turbulence statistics has been made in a linear cascade with a moving endwall. Gross features of the tip-leakage vortex, tip-separation vortices, and blade wake have been revealed by investigating their revolutionary trajectories and mean velocity fields. The tip-leakage vortex is identified by regions of significant streamwise velocity deficit and high streamwise and pitchwise vorticity magnitudes. The tip-leakage vortex and the tip-leakage jet which is generated by the pressure difference between the pressure and suction sides of the blade tip are found to produce significant mean velocity gradients along the spanwise direction, leading to the production of vorticity and turbulent kinetic energy. The velocity gradients are the major causes for viscous losses in the cascade endwall region. The present analysis suggests that the endwall viscous losses can be alleviated by changing the direction of the tip-leakage flow such that the associated spanwise derivatives of the mean streamwise and pitchwise velocity components are reduced.

An improvement of the dynamic procedure of Park et al. [Phys. Fluids 18, 125109 (2006)] for closure of the subgrid-scale eddy-viscosity model developed by Vreman [Phys. Fluids 16, 3670 (2004)] is proposed. The model coefficient which is globally constant in space but varies in time is dynamically determined assuming the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation of which utilization was proposed by Park et al. Like the Vreman model with a fixed coefficient and the dynamic-coefficient model of Park et al., the present model predicts zero eddy-viscosity in regions where the vanishing eddy viscosity is theoretically expected. The present dynamic model is especially suitable for large-eddy simulation in complex geometries since it does not require any ad hoc spatial and temporal averaging or clipping of the model coefficient for numerical stabilization and more importantly, requires only a single-level test filter in contrast to the dynamic model of Park et al., which employs two-level test filters.