Session RB: Turbulence Simulations VI

Geometric nature of particle trajectory in isotropic turbulence

The geometric nature of particle trajectory is investigated for understanding the Lagrangian nature of turbulence using direct numerical simulation of isotropic turbulence. Probability density functions and autocorrelations along a fluid particle trajectory associated with geometric quantities such as curvature and torsion of the Lagrangian trajectory are provided. We propose the ratio of torsion to curvature as an important parameter to identify the particle trajectory, and it is found to play a crucial role in understanding the geometric shape of particle trajectory. The relationship between Lagrangian helicity and the ratio of torsion to curvature is investigated where Lagrangian helicity is defined as a dot product of velocity and vorticity vectors at the point of a fluid particle. We also found that probability density functions of torsion and torsion normalized by curvature clearly show well-established slope in log--log plots. Lagrangian helicity is intermittently distributed and high Lagrangian helicity is always found, where high acceleration is observed. Regarding the relationship between coherent structure and acceleration, coherent structure can be understood in terms of Lagrangian helicity, curvature, and torsion. Geometric characteristics for solid particles are also investigated and its behavior differs depending on the Stokes number.   

Turbulence computations on a 4096$^3$ periodic domain: passive scalars at high Schmidt number and Lagrangian statistics conditioned on local flow structure

Rapid advances in Cyberinfrastructure, with more to come on the horizon, are presenting many opportunities for extending simulations of turbulence towards previously inaccessible parameter regimes and improved results in problems with greater complexity. In our group we have performed $4096^3$ simulations of isotropic turbulence on three massively parallel machines to study turbulence at higher Reynolds number, higher Schmidt number, or better resolution than usually practiced. One topic studied is Batchelor scaling and small-scale intermittency of passive scalar fields in turbulent mixing at high Schmidt number with a demonstrable viscous-convective range. Another is the behavior of Lagrangian structure functions at high Reynolds number ($R_\lambda\approx 1000$), with conditional sampling used to distinguish between the characteristics of strain-dominated versus rotation-dominated regions of the flow. We shall discuss both problems briefly, and conclude with an overview of current and future challenges involved in striving towards the next level, involving Petascale computing and beyond.   

Behavior of Heavy Particles in Turbulent Channel Flow

The motion of heavy particles in turbulent channel flow was investigated by using direct numerical simulation. We assumed that Stokes drag, Saffman lift and Magnus lift act on the motion of heavy spherical particles in turbulence. In this study, Stokes number is defined as the particle response time normalized by the wall units. The range of the Stokes number is 0.1$\sim $50 and the diameter of a particle is 0.06$\sim $0.3 in wall unit. Collision of particles with the wall is modelled by an elastic collision. Relevant velocity and acceleration statistics of heavy particles for the given range of Stokes number were investigated to interpret the particle accumulation near the wall. Particle accumulation at the wall is maximized when the Stokes number is around 15. And we found that Saffman lift force has a great effect on particle acceleration in the wall-normal direction near the wall. Detailed statistics including probability density function and autocorrelation of particle velocity and acceleration will be presented in the meeting.   

Maximum Drag Reduction Asymptote in Turbulent Channel Flow of Polymer Solutions

It is well known that the addition of a small amount of soluble high molecular weight polymers to wall bounded turbulent flows can lead to dramatic drag reduction (DR). Salient features of this phenomenon include: (1) existence of threshold for the onset of DR, and (2) an upper bound referred to as the maximum drag reduction (MDR) or the Virk asymptote. Computational studies including DNS and viscoelastic exact coherent structures have provided significant insight into the mechanism by which polymers alter turbulence and give rise to DR. Despite the significant progress in understanding polymer induced drag reduction in the low (DR$<$40$\%$) and high (40$\%$$<$DR$<$60$\% $) DR regimes, fundamental understanding of existence of a universal upper limit of drag reduction and the nature of the flow at this limit is still lacking. In this study, we have developed new mechanistic insight at MDR both in terms of the existence of a universal upper limit and the nature of the flow in this regime by analyzing extensive hi-fidelity direct numerical simulation data of turbulent channel flows of dilute polymeric solutions.   

Normal stress difference and drag reduction mechanism in Johnson-Segalman viscoelastic turbulence

The mechanism of turbulent drag reduction in the polymer- diluted flow is studied using the DNS data for homogeneous isotropic turbulence and pipe flow. The polymer stress $\tau$ is obtained by solving the non-affine Johnson-Segalman constitutive equation. The drag reduction is maximal when non- affinity is either minimum or maximum, but the largest reduction is achieved when non-affinity is maximum. The pressure force due to $\tau$, $\nabla p_\tau$, tends to oppose to that due to the solvent $\nabla p_s$, e.g., in the core of the vortex tube in which $p_s$ is minimal, $p_\tau$ bulges out. The normal-stress difference (NSD) is obtained on the basis of new eigenvectors which span the isosurfaces of vortex tube and sheet. It is shown in both flows that the first NSD is predominantly positive and the second is negative along the sheets and tubes. Thus, an extra tension is exerted on the sheet and tube. With an increase of effective viscosity by an addition of elongation viscosity, resistance of the sheet and tube to their stretching is enhanced. When non-affinity is maximum, the transformation of the sheet into the tube is restrained because the sheet tends to snap back to the original flat form due to viscoelastic effect. When non-affinity is minimum, the tubes are created but its stretching is suppressed. In both cases, cascade of the energy into the small scales is restricted leading to the reduction of drag.   

Statistics of polymer extensions in turbulent channel flow

We carry out direct numerical simulations of three dimensional channel flow with passive polymer additives. We also calculate, for the first time, the PDF of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Wi less than 1) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at Wi approximately 1. For the Oldroyd-B model we find that the PDF of polymer extensions shows power-law behavior irrespective of the wall-normal coordinate of the polymer molecule, but the range of scaling does depend on the wall-normal coordinate. The exponent of this power-law matches with the earlier theoretical results within error bars. In addition we also find the dependence of the PDF of polymer extension on the wall-normal coordinate, v.i.z, the polymer are more stretched near the wall than at the center of the flow. We further study the orientation of the polymers with respect the channel geometry. Our results show that the polymers close to the wall have a very high probability of being oriented along the stream-wise direction of the flow.   

Effect of inter-particle collision in particle-laden homogeneous isotropic turbulence

It has been known that Inter-particle collision of small spherical particles in particle laden homogeneous isotropic turbulence modifies the statistical characteristics of particle behaviour. For example, the dispersion of heavy particles is decreased by this collision effect (Lavieville 1997). Still, the mechanism of interaction between particle's collision and turbulence is not clear. Direct numerical simulations are performed for particle-laden isotropic turbulence by adopting a spectral method, and the 4th-order Hermite interpolation is used for tracking particles. Inter-particle collision is considered as a complete energy conserved elastic process. Because the collision-induced particle acceleration is not quite related with the particle's current-state properties and this irrelevance becomes dominant as the Stokes number increases, there are some significant statistical modifications observed in the behaviour of high Stokes number particles. We found that the particle velocity integral time scale decreases as the Stokes number becomes larger due to enhanced interference due to collision. Furthermore, the particle dispersion is suppressed for the same reason. The particle concentration tendency is also slightly mitigated due to the presence of particle volume and by collision. But there is no clear evidence about the variation of particle velocity variance. More detailed results will be presented in the meeting.   

Direct numerical simulation of strained turbulence and particles within

We present results from direct numerical simulations of strained turbulent flows. Our focus is on the influence of the straining on the motions of passive and inertial particles of varied Stokes numbers. The results are compared with existing numerical and experimental data, and we seek to emphasize the effects of the strain geometry and strain rate on the particle behavior. Eulerian flow field results, and the Lagrangian particle velocity and acceleration statistics are presented. The Rogallo algorithm is applied for simulating the flow field in a non-cubical domain.