Session F04: Turbulence: Direct Numerical Simulations

On the efficacy of minimal flow units in simulating "healthy" turbulence in plane Poiseuille flows

We present results on a comparison between turbulent channel flows simulated using minimal flow units (MFUs) and extended domains. The goal of the study was to analyze the effect of inherent periodic boundary conditions of MFUs in faithfully capturing turbulent dynamics of plane Poiseuille flow for a range of Reynolds numbers, 200 ≤ Re_τ ≤ 1000. Turbulent statistics of the MFU were compared with those computed in a sub-domain (SD) of an extended domain at the same Reynolds number. The dimensions of the MFU and SD were matched and set such that the artificial periodicity in the MFU was minimized. MFU streamwise and spanwise dimensions were chosen such that “healthy” turbulence, or turbulence which corresponds to a saturated friction Reynolds number and valid mean velocity profile, was achieved. Streamwise and spanwise dimensions of healthy MFUs were found to increase linearly. Statistics of the MFU were in good agreement with SD for each Reynolds number, other than Re_τ = 200. The agreement between MFU and SD dynamics suggest that MFUs may be used to faithfully represent turbulence dynamics up to Re_τ = 1000. The comparison between MFU and SD is extended using quadrant analysis, which further confirms the agreement between MFU and SD dynamics. A diminished log-law region may occur even when the friction Reynolds number is saturated, suggesting that further criterion may need to put in place when using MFUs to simulate higher Reynolds number flows.   

Not Participating

Spatial distribution of various quantities in fluid turbulence is known to be highly-intermittent, especially for small-scales and high-order statistical measurements. Recently it was shown that intermittency emerges within velocity gradients, dissipation and enstrophy in incompessible flows at Taylor Reynolds number (R_λ) of order 10. High-order moments were shown to exhibit scaling at lower-R_λ than low-order moments did, meaning most extreme events exhibit turbulent behavior first. The scaling of velocity gradients at these R_λ has also been shown to be predictive of scaling of velocity differences with respect to scale size in the so-called inertial range (IR). This IR scaling is known to emerge within flows with R_λ  an order magnitude larger than those observed for velocity gradients. In this talk, we use highly resolved direct numerical simulations (DNS) to assess the emergence of scaling in IR for different order moments of velocity differences. The focus is to determine which orders exhibit scaling first and the width of scaling range at each order. We also develop sampling frequency criteria for estimating high-order moments of various quantities to discriminate between various theories that predict similar behavior at low-orders but differ significantly at high-orders.    

Instantaneous cascade dynamics in turbulent flows

The fluctuations of interscale energy transfers. interspace energy transfers, rates of energy change in time, pressure effects and turbulence dissipation, but also their interactions, are studied in Direct Numerical Simulations of statistically stationary periodic turbulence. We use the Kármán-Howarth-Monin-Hill equation and solenoidal/irrotational decompositions as well as a decomposition of the intescale energy transfer rate into a term dominated by local inhomogeneity/spatial intermittency and a term dominated by eddy correlations. The results reveal a picture of fluctuating energy and energy exchanges and dissipation which is very different from the average cascade picture provided by the Kolmogorov theory of statistically stationary homogeneous turbulence.   

Direct Numerical Simulation of Turbulent Separated Flow over the Periodic Hill Geometry at Reh = 19000

We present results from direct numerical simulation (DNS) of incompressible flow over the periodic hill geometry that has, over the years, come to be regarded as a canonical case for turbulent separated flow. In our DNS, the computational domain consisted of 3.2x10⁶ hexahedral elements, with the elements clustered in the near wall region to ensure that the maximum distance of the first grid point from the wall was around 0.1 (in wall units). The incompressible Navier-Stokes equations were evolved using the high-order, spectral element codes, Nek5000, and nekRS, on the IBM Blue Gene/Q (Mira) and on the IBM Power9+NVIDIA (Summit) platforms, respectively. Time advancement was carried out via third-order BDF/extrapolation, with explicit treatment of the nonlinear term and independent system solves for the viscous and pressure updates. In our DNS we represent the flow variables with polymial basis functions of polynomial order p = 7 and p = 9, to demonstrate exponential convergence in p. The DNS mean velocity profiles, velocity correlations, and the locations of the separation/reattachment points,  compare well with data from the ERCOFTAC database. We also present comparisons of DNS and large eddy simulation (LES) at the same Reynolds numbers, to shed light on the sub-grid modeling.    

The Smallest Scales of Turbulence in Gases Are Not Described by the Navier-Stokes Equations

We show that the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations. Energy spectra from Navier-Stokes simulations of turbulent Taylor-Green vortex flow decay exponentially at high wavenumbers, while spectra from corresponding molecular-gas-dynamics simulations grow quadratically due to thermal fluctuations. The quadratic growth begins at length scales much larger than the molecular mean free path, where the Navier-Stokes equations are widely believed to be accurate. Our results show the importance of molecular-level thermal fluctuations and emphasize the need to include them in the Navier-Stokes equations when studying turbulent gas flows.