The structure of the vorticity field in turbulent channel flow. Part 1: Analysis of instantaneous fields and statistical correlations

An investigation into the existence of hairpin vortices in turbulent channel flow is conducted using a database generated by the large eddy simulation technique. It is shown that away from the wall the distribution of the inclination angle of vorticity vector attains its maximum at about 45 deg to the wall. Two point correlations of velocity and vorticity fluctuations strongly support a flow model consisting of vortical structures inclined at 45 deg to the wall. The instantaneous vorticity vectors plotted in planes inclined at 45 deg show that the flow contains an appreciable number of hairpins. Vortex lines are used to display the three dimensional structure of hairpins, which are shown to be generated from deformation of transverse vortex filaments

Geometric study of Lagrangian and Eulerian structures in turbulent channel flow

We report the detailed multi-scale and multi-directional geometric study of both evolving Lagrangian and instantaneous Eulerian structures in turbulent channel flow at low and moderate Reynolds numbers. The Lagrangian structures (material surfaces) are obtained by tracking the Lagrangian scalar field, and Eulerian structures are extracted from the swirling strength field at a time instant. The multi-scale and multi-directional geometric analysis, based on the mirror-extended curvelet transform, is developed to quantify the geometry, including the averaged inclination and sweep angles, of both structures at up to eight scales ranging from the half-height δ of the channel to several viscous length scales δ_ν. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of streamwise and spanwise directions. The results show that coherent quasi-streamwise structures in the near-wall region are composed of inclined objects with averaged inclination angle 35°–45°, averaged sweep angle 30°–40° and characteristic scale 20δ_ν, and 'curved legs' with averaged inclination angle 20°–30°, averaged sweep angle 15°–30° and length scale 5δ_ν–10δ_ν. The temporal evolution of Lagrangian structures shows increasing inclination and sweep angles with time, which may correspond to the lifting process of near-wall quasi-streamwise vortices. The large-scale structures that appear to be composed of a number of individual small-scale objects are detected using cross-correlations between Eulerian structures with large and small scales. These packets are located at the near-wall region with the typical height 0.25δ and may extend over 10δ in the streamwise direction in moderate-Reynolds-number, long channel flows. In addition, the effects of the Reynolds number and comparisons between Lagrangian and Eulerian structures are discussed

A review of quasi-coherent structures in a numerically simulated turbulent boundary layer

Preliminary results of a comprehensive study of the structural aspects of a numerically simulated number turbulent boundary layer are presented. A direct Navier-Stokes simulation of a flat-plate, zero pressure gradient boundary layer at Re0 = 670 was used. Most of the known nonrandom, coherent features of turbulent boundary layers are confirmed in the simulation, and several new aspects of their spatial character are reported. The spatial relationships between many of the various structures are described, forming the basis for a more complete kinematical picture of boundary layer physics than has been previously known. In particular, the importance of vortex structures of various forms to the generation of Reynolds shear stress is investigated

The structure of the vorticity field in turbulent channel flow. Part 2: Study of ensemble-averaged fields

Several conditional sampling techniques are applied to a data base generated by large-eddy simulation of turbulent channel flow. It is shown that the bursting process is associated with well-organized horseshoe vortices inclined at about 45 deg. to the wall. These vortical structures are identified by examining the vortex lines of three-dimensional, ensemble averaged vorticity fields. Two distinct horseshoe-shaped vortices corresponding to the sweep and ejection events are detected. These vortices are associated with high Reynolds shear stress and hence make a significant contribution to turbulent energy production. The dependency of the ensemble averaged vortical structures on the detection criteria, and the question of whether this ensemble-averaged structure is an artifact of the ensemble averaging process are examined. The ensemble-averaged pattern of these vortical structures that emerge from the analysis could provide the basis for a hypothetical model of the organized structures of wall-bounded shear flows

Three-dimensional flow in cavity with elevated helicity driven by parallel walls

The proposed flow in a 3-D cubic cavity is driven by its parallel walls moving in perpendicular directions to create a genuinely three-dimensional highly separated vortical flow yet having simple single-block cubical geometry of computational domain. The elevated level of helicity is caused by motion of a wall in the direction of axis of primary vortex created by a parallel wall. The velocity vector field is obtained numerically by using second-order upwind scheme and 200^3 grid. Helicity, magnitude of normalized helicity and kinematic vorticity number are evaluated for Reynolds numbers ranging from 100 to 1000. Formation of two primary vortices with their axis oriented perpendicularly and patterns of secondary vortices are discussed. Computational results are compared to the well-known 3-D recirculating cavity flow case where the lid moves in the direction parallel to the cavity side walls. Also results are compared to the diagonally top-driven cavity and to cavity flow driven by moving top and side walls. The streamlines for the proposed flow show that the particles emerging from top and bottom of cavity do mix well. Quantitative evaluation of mixing of two fluids in the proposed cavity flow confirms that the mixing occurs faster than in the benchmark case.Comment: 38 pages, 13 figures The revised includes quantification of mixing rate; numerical modeling of the transient version.The revised version has four substantially improved figures and three new figures; number of literature references increased from 26 to 4

Contributions of numerical simulation data bases to the physics, modeling and measurement of turbulence

The use of simulation data bases for the examination of turbulent flows is an effective research tool. Studies of the structure of turbulence have been hampered by the limited number of probes and the impossibility of measuring all desired quantities. Also, flow visualization is confined to the observation of passive markers with limited field of view and contamination caused by time-history effects. Computer flow fields are a new resource for turbulence research, providing all the instantaneous flow variables in three-dimensional space. Simulation data bases also provide much-needed information for phenomenological turbulence modeling. Three dimensional velocity and pressure fields from direct simulations can be used to compute all the terms in the transport equations for the Reynolds stresses and the dissipation rate. However, only a few, geometrically simple flows have been computed by direct numerical simulation, and the inventory of simulation does not fully address the current modeling needs in complex turbulent flows. The availability of three-dimensional flow fields also poses challenges in developing new techniques for their analysis, techniques based on experimental methods, some of which are used here for the analysis of direct-simulation data bases in studies of the mechanics of turbulent flows