31 research outputs found
Turbulent pair dispersion as a ballistic cascade phenomenology
Since the pioneering work of Richardson in 1926, later refined by Batchelor
and Obukhov in 1950, it is predicted that the rate of separation of pairs of
fluid elements in turbulent flows with initial separation at inertial scales,
grows ballistically first (Batchelor regime), before undergoing a transition
towards a super-diffusive regime where the mean-square separation grows as t^3
(Richardson regime). Richardson empirically interpreted this super-diffusive
regime in terms of a non-Fickian process with a scale dependent diffusion
coefficient (the celebrated Richardson's "4/3rd" law). However, the actual
physical mechanism at the origin of such a scale dependent diffusion
coefficient remains unclear. The present article proposes a simple physical
phenomenology for the time evolution of the mean square relative separation in
turbulent flows, based on a scale dependent ballistic scenario rather than a
scale dependent diffusive. This phenomenology accurately retrieves most of the
known features of relative dispersion ; among others : (i) it is quantitatively
consistent with recent numerical simulations and experiments (both for the
short term Batchelor regime and the long term Richardson regime, and for all
initial separations at inertial scales), (ii) it gives a simple physical
explanation of the origin of the super diffusive t^3 Richardson regime which
naturally builts itself as an iterative process of elementary
short-term-scale-dependent ballistic steps, (iii) it shows that the Richardson
constant is directly related to the Kolmogorov constant (and eventually to a
ballistic persistence parameter) and (iv) in a further extension of the
phenomenology, taking into account third order corrections, it robustly
describes the temporal asymmetry between forward and backward dispersion, with
an explicit connection to the cascade of energy flux across scales
Preferential concentration of inertial sub-kolmogorov particles. The roles of mass loading of particles, Stokes and Reynolds numbers
Turbulent flows laden with inertial particles present multiple open questions
and are a subject of great interest in current research. Due to their higher
density compared to the carrier fluid, inertial particles tend to form high
concentration regions, i.e. clusters, and low concentration regions, i.e.
voids, due to the interaction with the turbulence. In this work, we present an
experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov
particles in homogeneous isotropic turbulent flows. Three control parameters
have been varied over significant ranges: ,
and volume fraction . The scaling of clustering characteristics, such as the distribution
of Vorono\"i areas and the dimensions of cluster and void regions, with the
three parameters are discussed. In particular, for the polydispersed size
distributions considered here, clustering is found to be enhanced strongly
(quasi-linearly) by and noticeably (with a square-root
dependency) with , while the cluster and void sizes, scaled with the
Kolmogorov lengthscale , are driven primarily by . Cluster
length scales up to , measured
at the highest , while void length
scaled also with is typically two times larger ().
The lack of sensitivity of the above characteristics to the Stokes number lends
support to the "sweep-stick" particle accumulation scenario. The non-negligible
influence of the volume fraction, however, is not considered by that model and
can be connected with collective effects
Do finite size neutrally buoyant particles cluster?
We investigate the preferential concentration of particles which are
neutrally buoyant but with a diameter significantly larger than the dissipation
scale of the carrier flow. Such particles are known not to behave as flow
tracers (Qureshi et al., Phys. Re. Lett. 2007) but whether they do cluster or
not remains an open question. For this purpose, we take advantage of a new
turbulence generating apparatus, the Lagrangian Exploration Module which
produces homogeneous and isotropic turbulence in a closed water flow. The flow
is seeded with neutrally buoyant particles with diameter 700\mum, corresponding
to 4.4 to 17 times the turbulent dissipation scale when the rotation frequency
of the impellers driving the flow goes from 2 Hz to 12 Hz, and spanning a range
of Stokes numbers from 1.6 to 24.2. The spatial structuration of these
inclusions is then investigated by a Voronoi tesselation analysis, as recently
proposed by Monchaux et al. (Phys. Fluids 2010), from images of particle
concentration field taken in a laser sheet at the center of the flow. No matter
the rotating frequency and subsequently the Reynolds and Stokes numbers, the
particles are found not to cluster. The Stokes number by itself is therefore
shown to be an insufficient indicator of the clustering trend in particles
laden flows
Large spheres motion in a non homogeneous turbulent flow
We investigate the dynamics of very large particles freely advected in a
turbulent von Karman flow. Contrary to other experiments for which the particle
dynamics is generally studied near the geometrical center of the flow, we track
the particles in the whole experiment volume. We observe a strong influence of
the mean structure of the flow that generates an unexpected large-scale
sampling effect for the larger particles studied; contrary to neutrally buoyant
particles of smaller yet finite sizes that exhibit no preferential
concentration in homogeneous and isotropic turbulence (Fiabane et al., Phys.
Rev. E 86(3), 2012). We find that particles whose diameter approaches the flow
integral length scale explore the von Karman flow non-uniformly, with a higher
probability to move in the vicinity of two tori situated near the poloidal
neutral lines. This preferential sampling is quite robust with respect to
changes of any varied parameters: Reynolds number, particle density and
particle surface roughness
Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxen forces
The dynamics of particles in turbulence when the particle-size is larger than
the dissipative scale of the carrier flow is studied. Recent experiments have
highlighted signatures of particles finiteness on their statistical properties,
namely a decrease of their acceleration variance, an increase of correlation
times -at increasing the particles size- and an independence of the probability
density function of the acceleration once normalized to their variance. These
effects are not captured by point particle models. By means of a detailed
comparison between numerical simulations and experimental data, we show that a
more accurate model is obtained once Faxen corrections are included.Comment: 10 pages, 4 figure
Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow
We study the 6-dimensional dynamics -- position and orientation -- of a large
sphere advected by a turbulent flow. The movement of the sphere is recorded
with 2 high-speed cameras. Its orientation is tracked using a novel, efficient
algorithm; it is based on the identification of possible orientation
`candidates' at each time step, with the dynamics later obtained from
maximization of a likelihood function. Analysis of the resulting linear and
angular velocities and accelerations reveal a surprising intermittency for an
object whose size lies in the integral range, close to the integral scale of
the underlying turbulent flow
Rotational intermittency and turbulence induced lift experienced by large particles in a turbulent flow
The motion of a large, neutrally buoyant, particle, freely advected by a
turbulent flow is determined experimentally. We demonstrate that both the
translational and angular accelerations exhibit very wide probability
distributions, a manifestation of intermittency. The orientation of the angular
velocity with respect to the trajectory, as well as the translational
acceleration conditioned on the spinning velocity provide evidence of a lift
force acting on the particle.Comment: 4 page, 4 figure