Session H21: Turbulence: Simulations IV - DNS Application

Direct Numerical Simulations of Turbulent Ekman Layers with Increasing Static Stability: Modifications to the Bulk Structure and Second-Order Statistics

Turbulent Ekman layers, with increasing static stability and Reynolds number, are studied using Direct Numerical Simulations. The highest stability under which continuous turbulence can be sustained is shown to be Reynolds number dependent. The highest Reynolds number flow displays a well-developed inertial range and a logarithmic layer, which is found to obey the Monin-Obukhov similarity theory under non-neutral conditions. The analyses then focus on the budgets of turbulent kinetic energy (TKE), vertical velocity variance, momentum and buoyancy fluxes, and temperature variance. Results indicate that, due to imposed stability, there is damping of vertical motions that leads to a reduction in the turbulent transport of Reynolds stress towards the wall. This reduced transport results in lower production of TKE, which is shown to be more significant than direct buoyant destruction in reducing TKE levels in stable conditions. The reduction in the vertical velocity variance results in significant drops in the production terms in the other second order budgets we study as well. Building on these findings, we conclude by illustrating that the vertical velocity variance is a better parameter to base vertical eddy-diffusivity and viscosity models on than the full TKE.   

Energy dynamics in turbulence generated through concentrated regions of intense kinetic energy

The photo-dissociation of molecules produced by lasers has the capability of ejecting fragments with extremely high velocities, thus creating concentrated regions of very large momentum. It is of fundamental as well as practical interest to determine whether this concentrated momentum is sufficient to generate realistic turbulence. Incompressible direct numerical simulations (DNS) with concentrated sources along ``lines'' are used to represent the photo-dissociation of molecules. The numerical challenges associated with the implementation of strong gradients are presented in a detailed convergence study. A thorough analysis is performed on the different terms of acceleration that determine the evolution of the flow. Our results indicate that pressure and the convective acceleration redistribute most of the momentum both radially and among the components of acceleration. Radial statistics of the different components of velocity, gradients, and accelerations are also related to the time development of the flow and correlated with the eventual emergence of fully developed turbulence. Further results and consequences for particular cases realizable in laboratories will be discussed.   

Modeling of the Gecko's skin microfibrillar structures using the Immersed Boundary method via DNS

There is a current interest in surfaces that mimic the skin of some species (i.e., sharks, dolphins and geckos) in order to achieve drag reduction. The surface considered is based on the microfribrillar structures of a gecko's skin (Aksak et al. 2008). The structures are modeled by means of the immersed boundary method proposed by Fadlun et al. (2000). Direct simulations are performed to predict flow dynamics with a Reynolds number of 7000 based on the height of the channel and centerline velocity. The ratio of the height of the structure with respect to the height of the channel is approximately 0.05. The main motivation is to study how the microfribillar structures affect the momentum transfer from the viscous layer to the outer layer. The surface shows a reduction of the area affected by the shear stress due to the cavities formed by the pattern. As expected, the cavities create a low velocity zone thus decreasing the Reynolds shear stresses. Lambda-2 and Q-criterion were implemented to identify the elongated streamwise vortices. The results show that when compared to a flat channel the microfribillar structures tend to preserve these streamwise vortices instead of bursting into the outer layer which is a source of drag increase.   

DNS of stably stratified Taylor-Green vortex

Stratified flows, flows where density varies in one direction, have wide applications in some of the phenomena occurring in the atmospheric and ocean. Direct numerical simulations (DNS) of transition to turbulence in a stably stratified Boussinesq fluid are presented for the three-dimensional Taylor-Green vortex problem at different stratification and turbulence intensities measured in terms of different Froude (Fr) ($\infty$ and $10^{-2}-10^{-1}$) and Reynolds numbers (Re) (800 and 1600), respectively. Features investigated include temporal variations of the energy spectrum cascade, local Froude numbers, vertical shearing of the velocities, and dissipation of kinetic and potential energy. The results from these simulations demonstrated forward cascade of energy for high Re and revealed the strong anisotropic structure of turbulence and suppression of vertical motion under stratification.   

DNS of helicity-induced stratified turbulent flow

Helical flows undergoing density stratification have wide applications in meteorological phenomena such as dust devils, tornadoes, and hurricanes due to the complexity and disasters caused by them. Direct numerical simulations (DNS) of transition to turbulence in a stably stratified Boussinesq fluid are presented for different rotation and stratification intensities. In order to understand the effect of velocity on the energy cascade, comparisons are made between helicity initiated and non-helical flows. Results show that stratification decelerates the helicity decay and causes velocity and vorticity to align with each other. With respect to the helical and non-helical flow comparisons, the total energy in the presence of stratification decays faster with helicity. In addition, the behavior of length scales were examined by comparing temporal variations of the vertical shearing of velocities. Results showed a growing asymmetry with time in the case of helical flow, while non-helical flow stayed close to begin symmetric.   

New DNS and modeling results for turbulent pipe flow

The near-wall region of turbulent pipe and channel flows (as well as zero-pressure gradient boundary layers)~have been shown to exhibit a very high degree of similarity~in terms of all statistical moments and many other features, while even the mean velocity profile in the two cases exhibits significant differences between in the outer region. The wake part of the profile, i.e. the deviation from~ the log-law, in the outer region is of substantially larger amplitude in pipe flow as compared to channel flow (although weaker than in boundary layer flow). This intriguing feature has been well known but has no simple~ explanation. Model predictions typically give identical results for the two flows. We have analyzed a new set of DNS~ for pipe and channel flows (el Khoury et al. 2013, Flow, Turbulence and Combustion) for friction Reynolds~numbers up to 1000 and~made comparing calculations with differential Reynolds stress models (DRSM). We have strong indications that the key factor behind the difference in mean velocity in the outer region can be coupled to differences~in the turbulent diffusion in this region. This is also supported by DRSM results,~where interesting differences are seen depending on~the~sophistication of modeling the turbulent diffusion coefficient.   

Direct numerical simulation of turbulence in a bent pipe

A series of direct numerical simulations of turbulent flow in a bent pipe is presented. The setup employs periodic (cyclic) boundary conditions in the axial direction, leading to a nominally infinitely long pipe. The discretisation is based on the high-order spectral element method, using the code Nek5000. Four different curvatures, defined as the ratio between pipe radius and coil radius, are considered: $\kappa=0$ (straight), 0.01 (mild curvature), 0.1 and 0.3 (strong curvature), at bulk Reynolds numbers of up to 11700 (corresponding to $Re_\tau=360$ in the straight pipe case). The result show the turbulence-reducing effect of the curvature (similar to rotation), leading close to relaminarisation in the inner side; the outer side, however, remains fully turbulent. Prpoer orthogonal decomposition (POD) is used to extract the dominant modes, in an effort to explain low-frequency switching of sides inside the pipe. A number of additional interesting features are explored, which include sub-straight and sub-laminar drag for specific choices of curvature and Reynolds number: In particular the case with sub-laminar drag is investigated further, and our analysis shows the existence of a spanwise wave in the bent pipe, which in fact leads to lower overall pressure drop.   

Enstrophy along particle trajectories through vortex clusters in DNS of turbulent channel flow

We augment the traditional study of wall-bounded turbulence from the Eulerian point of view by analyzing the Lagrangian trajectories of fluid tracers tracked in a DNS of a turbulent channel at $Re_{\tau}=2000$. After storing consecutive fields for 50 wall units in time, ensembles of $O(10^6)$ particles seeded on short detached vortex clusters centered at both $y^+\approx 200$ and the core of the channel are tracked backward ($T^+_b=-50$) in time, then restarted forward. Velocity gradients are interpolated along trajectories for these particles for a total duration of 100 units ($T^+_{forward}=50$ past the seeding instant), providing representative histories of enstrophy acquisition and loss by fluid particles throughout the expected lifetime of intense vortical structures. The statistics of initial position $X(T^+_b=-50)$, along with joint and conditional statistics of temporal increments of velocity and vorticity throughout the complete simulation (from $T^+=-50$ to 50), describe how the structures above the buffer layer, typically educed from Eulerian variables, act on fluid, clarifying our understanding. The corresponding results for particles initialized in the core are compared to the particles initialized around vortices centered at $y^+=200$.