99 research outputs found
Propagation velocity and space-time correlation of perturbations in turbulent channel flow
A database obtained from direct numerical simulation of a turbulent channel flow is analyzed to extract the propagation velocity V of velocity, vorticity, and pressure fluctuations from their space-time correlations. A surprising result is that V is approximately the same as the local mean velocity for most of the channel, except for the near-wall region. For y(+) is less than or equal to 15, V is virtually constant, implying that perturbations of all flow variables propagate like waves near the wall. In this region V is 55 percent of the centerline velocity U(sub c) for velocity and vorticity perturbations and 75 percent of U(sub c) for pressure perturbations. Scale-dependence of V is also examined by analyzing the bandpass filtered flow fields. Comprehensive documentation of the propagation velocities and space-time correlation data, which should prove useful in the evaluation of Taylor's hypothesis is presented. An attempt was made to explain some of the data in terms of our current understanding of organized structures, although not all of the data can be explained this way
Elliptic jets, part 2. Dynamics of coherent structures: Pairing
The dynamics of the jet column mode of vortex pairing in the near field of an elliptic jet was investigated. Hot-wire measurements and flow visualization were used to examine the details of the pairing mechanism of nonplanar vortical elliptic structures and its effect on such turbulence measures as coherent velocities, incoherent turbulence intensities, incoherent and coherent Reynolds, stresses, turbulence production, and mass entrainment. It was found that pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane. In the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently, producing considerably greater entrainment and mixing than in circular or plane jets
Cut-and-connect of two antiparallel vortex tubes
Motivated by an early conjecture that vortex cut-and-connect plays a key role in mixing and production of turbulence, helicity and aerodynamic noise, the cross-linking of two antiparallel viscous vortex tubes via direct numerical simulation is studied. The Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 64 cubed grid points in a periodic domain for initial Reynolds numbers Re up to 1000. The vortex tubes are given an initial sinusoidal perturbation to induce a collision and keep the two tubes pressed against each other as annihilation continues. Cross-sectional and wire plots of various properties depict three stages of evolution: (1) Inviscid induction causing vortex cores to first approach and form a contact zone with a dipole cross-section, and then to flatten and stretch; (2) Vorticity annihilation in the contact zone accompanied by bridging between the two vortices at both ends of the contact zone due to a collection of cross-linked vortex lines, now orthogonal to the initial vortex tubes. The direction of dipole advection in the contact zone reverses; and (3) Threading of the remnants of the original vortices in between the bridges as they pull apart. The crucial stage 2 is shown to be a simple consequence of vorticity annihilation in the contact zone, link-up of the un-annihilated parts of vortex lines, and stretching and advection by the vortex tube swirl of the cross-linked lines, which accumulate at stagnation points in front of the annihilating vortex dipole. It is claimed that bridging is the essence of any vorticity cross-linking and that annihilation is sustained by stretching of the dipole by the bridges. Vortex reconnection details are found to be insensitive to asymmetry. Modeling of the reconnection process is briefly examined. The 3D spatial details of scalar transport (at unity Schmidt number), enstrophy production, dissipation and helicity are also examined
Length-scale cascade and spread rate of atomizing planar liquid jets
The primary breakup of a planar liquid jet is explored via direct numerical
simulation (DNS) of the incompressible Navier-Stokes equation with level-set
and volume-of-fluid interface capturing methods. PDFs of the local radius of
curvature and the local cross-flow displacement of the liquid-gas interface are
evaluated over wide ranges of the Reynolds number (), Weber number (),
density ratio and viscosity ratio. The temporal cascade of liquid-structure
length scales and the spread rate of the liquid jet during primary atomization
are analyzed. The formation rate of different surface structures, e.g. lobes,
ligaments and droplets, are compared for different flow conditions and are
explained in terms of the vortex dynamics in each atomization domain that we
identified recently. With increasing , the average radius of curvature of
the surface decreases, the number of small droplets increases, and the cascade
and the surface area growth occur at faster rates. The spray angle is mainly
affected by and density ratio, and is larger at higher , at higher
density ratios, and also at lower . The change in the spray spread rate
versus is attributed to the angle of ligaments stretching from the jet
core, which increases as decreases. Gas viscosity has negligible effect on
both the droplet-size distribution and the spray angle. Increasing the
wavelength-to-sheet-thickness ratio, however, increases the spray angle and the
structure cascade rate, while decreasing the droplet size. The smallest length
scale is determined more by surface tension and liquid inertia than by the
liquid viscosity, while gas inertia and liquid surface tension are the key
parameters in determining the spray angle.Comment: Submitted for publication to International Journal of Multiphase
Flow. 37 pages; 33 figure
Understanding liquid-jet atomization cascades via vortex dynamics
Temporal instabilities of a planar liquid jet are studied using direct
numerical simulation (DNS) of the incompressible Navier-Stokes equations with
level-set (LS) and volume-of-fluid (VoF) surface tracking methods.
contours are used to relate the vortex dynamics to the surface dynamics at
different stages of the jet breakup, namely, lobe formation, lobe perforation,
ligament formation, stretching, and tearing. Three distinct breakup mechanisms
are identified in the primary breakup, which are well categorized on the
parameter space of gas Weber number () versus liquid Reynolds number
(). These mechanisms are analyzed here from a vortex dynamics
perspective. Vortex dynamics explains the hairpin formation, and the
interaction between the hairpins and the Kelvin-Helmholtz (KH) roller explains
the perforation of the lobes, which is attributed to the streamwise overlapping
of two oppositely-oriented hairpin vortices on top and bottom of the lobe. The
formation of corrugations on the lobe front edge at high is also related
to the location and structure of the hairpins with respect to the KH vortex.
The lobe perforation and corrugation formation are inhibited at low and
low due to the high surface tension and viscous forces, which damp the
small scale corrugations and resist hole formation. Streamwise vorticity
generation - resulting in three-dimensional instabilities - is mainly caused by
vortex stretching and baroclinic torque at high and low density ratios,
respectively. Generation of streamwise vortices and their interaction with
spanwise vortices produce the liquid structures seen at various flow
conditions. Understanding the liquid sheet breakup and the related vortex
dynamics are crucial for controlling the droplet size distribution in primary
atomization.Comment: Submitted for publication in Journal of Fluid Mechanics. 56 pages; 52
figure
Head-on collision of viscous vortex rings
The head-on collision of two identical axisymmetric viscous vortex rings is studied through direct simulations of the incompressible Navier-Stokes equations. The initial vorticity distributions considered are those of Hill's spherical vortex and of rings with circular Gaussian cores, each at Reynolds numbers of about 350 and 1000. The Reynolds number is defined by Gamma/Nu, the ratio of circulation to viscosity. As the vortices approach each other by self-induction, the radii increase by mutual induction, and vorticy cancels through viscous cross-diffusion across the collision plane. Following contact, the vorticity distribution in the core forms a head-tail structure (for the cases considered). The characteristic time of vorticity annihilation is compared with that of a 3D collision experiment and 3D numerical simulations. It is found that the annihilation time is somewhat longer in the axisymmetric case than it is in the symmetry plane of the experiment and 3D numerical simulation. By comparing the annihilatiom time with a viscous timescale and a circulation timescale, it is deduced that both the strain rate due to local effects and to 3D vorticity realignment are important
Bulk flow scaling for turbulent channel and pipe flows
We report a theory deriving bulk flow scaling for canonical wall-bounded
flows. The theory accounts for the symmetries of boundary geometry (flat plate
channel versus circular pipe) by a variational calculation for a large-scale
energy length, which characterizes its bulk flow scaling by a simple exponent,
i.e. for channel and 5 for pipe. The predicted mean velocity shows
excellent agreement with several dozen sets of quality empirical data for a
wide range of the Reynolds number (Re), with a universal bulk flow constant
. Predictions for dissipation and turbulent transport in the
bulk flow are also given, awaiting data verification.Comment: 4 pages, 4 figure
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