Session G28: Turbulence: DNS and Theory

An examination of effects of finite resolution and sampling uncertainties in large-scale direct numerical simulations of turbulence

Advances in computing power have allowed turbulence simulations to be conducted using massive computational resources of such magnitudes that make rigorous examinations of numerical fidelity in the results ever more important. One common practice in checking for resolution effects is to refine the grid, then integrate over a substantial time period, and compare the results, which will however differ also for reasons of statistical sampling. Another alternative which focuses on local instead of global errors is to begin from the best-resolved simulation available, and progressively filters out high-wavenumber contributions, to identify which features remain and hence may be robust even at more modest resolution. This approach has been applied to the statistics of dissipation and enstrophy in short-time datasets at resolution $16{,}384^3$ for forced isotropic turbulence. In this manner, and using results on the cumulative distribution function, we are also able to separate deterministic errors due to the numerics from errors due to finite statistical sampling.   

Simulations of turbulent compressible flows using periodic boundary conditions: high fidelity on a budget

In direct numerical simulations (DNS) of turbulent flows, it is often prohibitively expensive to simulate complete flow geometries. For example, to study turbulence-flame interactions, one cannot perform a DNS of a full combustor. Usually, a well-selected portion of the domain is chosen, in this particular case the region around the flame front. In this work, we perform a Reynolds decomposition of the velocity field and solve for the fluctuating part only. The resulting equations are the same as the original Navier-Stokes equations, except for turbulence-generating large scale features of the flow such as mean shear, which appear as forcing terms. This approach allows us to achieve high Reynolds numbers and sustained turbulence while keeping the computational cost reasonable. We have already applied this strategy to incompressible flows, but not to compressible ones, where special care has to be taken regarding the energy equation. Implementation of the resulting additional terms in the finite-difference code NGA is discussed and preliminary results are presented. In particular, we look at the budget of turbulent kinetic energy and internal energy. We are considering applying this technique to turbulent premixed flames.   

Reproducing a turbulent jet flow in a 3D periodic box

A triply periodic box is a useful computational geometry to create statistically steady turbulence. It is also convenient to perform a posteriori spectral analysis. However, it is difficult to produce a realistic turbulent flow inside the periodic box. In this current investigation, we aim to develop a method to produce triply periodic DNS whose turbulent properties resemble those of a realistic turbulent flow. The target realistic flow is an axisymmetric turbulent jet on its centerline. The mean velocity information of turbulent jets is applied to the momentum equation in physical space, which results in an anisotropic linear forcing term for a triply periodic box. This new forcing term is derived to replicate the turbulent characteristics of jets in a triply periodic box. Forcing schemes are not new and several have been proposed already for the simulations in spectral space and in physical space. Unfortunately, these methods are rather arbitrary; they prove to sustain the turbulence, but they were not derived to reflect real turbulent flows. In contrast, the new source term successfully reproduces the anisotropy, kinetic energy, and dissipation rate on the centerline of turbulent jets. The spectra of normalized dissipation also compare favorably against experiments.   

Resolution effects and the structure of extreme velocity gradients in high Reynolds number turbulence

It is well known that turbulent flows develop strong velocity gradients, characterized as small-scale intermittency, with these gradients becoming more and more intense with increasing Reynolds number. These extreme gradients play a critical role in applications such as turbulent combustion, cloud physics, but their formation remains to be understood in detail. Using high-resolution direct numerical simulations (DNS) of isotropic turbulence, up to Taylor scale Reynolds number of 1300, we analyze the structure of the velocity gradient tensor, with particular emphasis on the extreme events. We first revisit the effect of small-scale resolution, measured in DNS by $k_{max}\eta$, where $k_{max}$ is maximum wavenumber resolved and $\eta$ is the Kolmogorov length scale. We find that $k_{max}\eta \geq 3$ is required to adequately resolve the structure in the eigenframe of the strain tensor, with lower resolution possibly resulting in spurious observations for the most extreme events. The alignment of vorticity with the intermediate eigenvector of strain is found to be much stronger when conditioned on large gradients, than the overall unconditioned alignment, possibly related to the weakening of the self-amplification of vortex structures when they become more intense.   

Nonlinear scalar forcing based on a reaction analogy

We present a novel reaction analogy (RA) based forcing method for generating stationary passive scalar fields in incompressible turbulence. The new method can produce more general scalar PDFs (e.g. double-delta) than current methods, while ensuring that scalar fields remain bounded, unlike existent forcing methodologies that can potentially violate naturally existing bounds. Such features are useful for generating initial fields in non-premixed combustion or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived. For large values of the scalar dissipation rate, the method produces statistically steady double-delta scalar PDFs. Gaussian scalar statistics are recovered for small values of the scalar dissipation rate. In contrast, classical forcing methods consistently produce unimodal Gaussian scalar fields. The ability of the new method to produce fully developed scalar fields is discussed using 256$^3$, 512$^3$, and 1024$^3$ periodic box simulations.   

Molecular-Level Simulations of the Turbulent Taylor-Green Flow

The Direct Simulation Monte Carlo (DSMC) method, a statistical, molecular-level technique that provides accurate solutions to the Boltzmann equation, is applied to the turbulent Taylor-Green vortex flow. The goal of this work is to investigate whether DSMC can accurately simulate energy decay in a turbulent flow. If so, then simulating turbulent flows at the molecular level can provide new insights because the energy decay can be examined in detail from molecular to macroscopic length scales, thereby directly linking molecular relaxation processes to macroscopic transport processes. The DSMC simulations are performed on half a million cores of Sequoia, the 17~Pflop platform at Lawrence Livermore National Laboratory, and the kinetic-energy dissipation rate and the energy spectrum are computed directly from the molecular velocities. The DSMC simulations are found to reproduce the Kolmogorov -5/3 law and to agree with corresponding Navier-Stokes simulations obtained using a spectral method. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.   

On the Orientation of Vortical Structures in Homogeneous Turbulent Shear Flows

Direct numerical simulations were performed in order to study the orientation of vortical structures in homogeneous turbulent shear flows with density stratification or system rotation. Inclined structures are observed in the plane of shear and the three-dimensional two-point autocorrelation coefficient of vorticity magnitude is computed to quantify the orientation of the structures. Isosurfaces of the autocorrelation coefficient closely resemble an ellipsoid inclined in the direction of the structures. A least-squares fit of an ellipsoid to the isosurfaces was performed and the major axis was determined. From the major axis, the inclination angle of the structures was computed. For stratified and sheared homogeneous turbulence, the Richardson number $Ri$ was varied. It was observed that both the growth rate of the turbulent kinetic energy and the inclination angle of the structures decrease as $Ri$ is increased. For rotating and sheared homogeneous turbulence, the rotation to shear rate ratio $f/S$ was varied. Again, the growth rate and the inclination angle show a similar dependence on $f/S$. Therefore, the structure of homogeneous turbulent shear flows appears to be directly related to the dynamics of the flows.   

On the Universality of Local Flow-Field Topologies in Turbulent Flows

The local flow patterns observed in an incompressible turbulent flow field can be classified into four distinct topology types based on the invariants of the local velocity gradient tensor. We examine statistics of local flow-field topology and key small-scale mechanisms in turbulence fields at different Reynolds numbers and flow types – forced isotropic turbulence, decaying isotropic turbulence and homogeneous shear turbulence. Direct numerical simulation (DNS) data are used to examine statistics of dissipation-rate, strain-rate, rotation-rate and their evolution conditioned upon the local flow topology. The dominant mechanisms at each topology are identified. The characteristic length scale of each topology is examined. The contributions of each topology towards the fabric of small-scale turbulence and small-scale universality are investigated.   

Scale-by-scale contributions to Lagrangian particle acceleration

Fluctuations on a wide range of scales in both space and time are characteristic of turbulence. Lagrangian particles, advected by the flow, probe these fluctuations along their trajectories. In an effort to isolate the influence of the different scales on Lagrangian statistics, we employ direct numerical simulations (DNS) combined with a filtering approach. Specifically, we study the acceleration statistics of tracers advected in filtered fields to characterize the smallest temporal scales of the flow. Emphasis is put on the acceleration variance as a function of filter scale, along with the scaling properties of the relevant terms of the Navier-Stokes equations. We furthermore discuss scaling ranges for higher-order moments of the tracer acceleration, as well as the influence of the choice of filter on the results. Starting from the Lagrangian tracer acceleration as the short time limit of the Lagrangian velocity increment, we also quantify the influence of filtering on Lagrangian intermittency. Our work complements existing experimental results on intermittency and accelerations of finite-sized, neutrally-buoyant particles: for the passive tracers used in our DNS, feedback effects are neglected such that the spatial averaging effect is cleanly isolated.