648 research outputs found
Clustering and collisions of heavy particles in random smooth flows
Finite-size impurities suspended in incompressible flows distribute
inhomogeneously, leading to a drastic enhancement of collisions. A description
of the dynamics in the full position-velocity phase space is essential to
understand the underlying mechanisms, especially for polydisperse suspensions.
These issues are here studied for particles much heavier than the fluid by
means of a Lagrangian approach. It is shown that inertia enhances collision
rates through two effects: correlation among particle positions induced by the
carrier flow and uncorrelation between velocities due to their finite size. A
phenomenological model yields an estimate of collision rates for particle pairs
with different sizes. This approach is supported by numerical simulations in
random flows.Comment: 12 pages, 9 Figures (revTeX 4) final published versio
Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks
Planetesimals in gaseous protoplanetary disks may grow by collecting dust
particles. Hydrodynamical studies show that small particles generally avoid
collisions with the planetesimals because they are entrained by the flow around
them. This occurs when , the Stokes number, defined as the ratio of the
dust stopping time to the planetesimal crossing time, becomes much smaller than
unity. However, these studies have been limited to the laminar case, whereas
these disks are believed to be turbulent. We want to estimate the influence of
gas turbulence on the dust-planetesimal collision rate and on the impact
speeds. We used three-dimensional direct numerical simulations of a fixed
sphere (planetesimal) facing a laminar and turbulent flow seeded with small
inertial particles (dust) subject to a Stokes drag. A no-slip boundary
condition on the planetesimal surface is modeled via a penalty method. We find
that turbulence can significantly increase the collision rate of dust particles
with planetesimals. For a high turbulence case (when the amplitude of turbulent
fluctuations is similar to the headwind velocity), we find that the collision
probability remains equal to the geometrical rate or even higher for , i.e., for dust sizes an order of magnitude smaller than in the laminar
case. We derive expressions to calculate impact probabilities as a function of
dust and planetesimal size and turbulent intensity
Inertial particles driven by a telegraph noise
We present a model for the Lagrangian dynamics of inertial particles in a
compressible flow, where fluid velocity gradients are modelled by a telegraph
noise. The model allows for an analytic investigation of the role of time
correlation of the flow in the aggregation-disorder transition of inertial
particle. The dependence on Stokes and Kubo numbers of the Lyapunov exponent of
particle trajectories reveals the presence of a region in parameter space (St,
Ku) where the leading Lyapunov exponent changes sign, thus signaling the
transition. The asymptotics of short and long-correlated flows are discussed,
as well as the fluid-tracer limit.Comment: 8 pages, 6 figure
Universality of Velocity Gradients in Forced Burgers Turbulence
It is demonstrated that Burgers turbulence subject to large-scale
white-noise-in-time random forcing has a universal power-law tail with exponent
-7/2 in the probability density function of negative velocity gradients, as
predicted by E, Khanin, Mazel and Sinai (1997, Phys. Rev. Lett. 78, 1904). A
particle and shock tracking numerical method gives about five decades of
scaling. Using a Lagrangian approach, the -7/2 law is related to the shape of
the unstable manifold associated to the global minimizer.Comment: 4 pages, 2 figures, RevTex4, published versio
Lyapunov exponents of heavy particles in turbulence
Lyapunov exponents of heavy particles and tracers advected by homogeneous and
isotropic turbulent flows are investigated by means of direct numerical
simulations. For large values of the Stokes number, the main effect of inertia
is to reduce the chaoticity with respect to fluid tracers. Conversely, for
small inertia, a counter-intuitive increase of the first Lyapunov exponent is
observed. The flow intermittency is found to induce a Reynolds number
dependency for the statistics of the finite time Lyapunov exponents of tracers.
Such intermittency effects are found to persist at increasing inertia.Comment: 4 pages, 4 figure
Dynamics and statistics of heavy particles in turbulent flows
We present the results of Direct Numerical Simulations (DNS) of turbulent
flows seeded with millions of passive inertial particles. The maximum Taylor's
Reynolds number is around 200. We consider particles much heavier than the
carrier flow in the limit when the Stokes drag force dominates their dynamical
evolution. We discuss both the transient and the stationary regimes. In the
transient regime, we study the growt of inhomogeneities in the particle spatial
distribution driven by the preferential concentration out of intense vortex
filaments. In the stationary regime, we study the acceleration fluctuations as
a function of the Stokes number in the range [0.16:3.3]. We also compare our
results with those of pure fluid tracers (St=0) and we find a critical behavior
of inertia for small Stokes values. Starting from the pure monodisperse
statistics we also characterize polydisperse suspensions with a given mean
Stokes.Comment: 13 pages, 10 figures, 2 table
Acceleration statistics of heavy particles in turbulence
We present the results of direct numerical simulations of heavy particle
transport in homogeneous, isotropic, fully developed turbulence, up to
resolution (). Following the trajectories of up
to 120 million particles with Stokes numbers, , in the range from 0.16 to
3.5 we are able to characterize in full detail the statistics of particle
acceleration. We show that: ({\it i}) The root-mean-squared acceleration
sharply falls off from the fluid tracer value already at quite
small Stokes numbers; ({\it ii}) At a given the normalised acceleration
increases with consistently
with the trend observed for fluid tracers; ({\it iii}) The tails of the
probability density function of the normalised acceleration
decrease with . Two concurrent mechanisms lead to the above results:
preferential concentration of particles, very effective at small , and
filtering induced by the particle response time, that takes over at larger
.Comment: 10 pages, 3 figs, 2 tables. A section with new results has been
added. Revised version accepted for pubblication on Journal of Fluid
Mechanic
Heavy particle concentration in turbulence at dissipative and inertial scales
Spatial distributions of heavy particles suspended in an incompressible
isotropic and homogeneous turbulent flow are investigated by means of high
resolution direct numerical simulations. In the dissipative range, it is shown
that particles form fractal clusters with properties independent of the
Reynolds number. Clustering is there optimal when the particle response time is
of the order of the Kolmogorov time scale . In the inertial range,
the particle distribution is no longer scale-invariant. It is however shown
that deviations from uniformity depend on a rescaled contraction rate, which is
different from the local Stokes number given by dimensional analysis. Particle
distribution is characterized by voids spanning all scales of the turbulent
flow; their signature in the coarse-grained mass probability distribution is an
algebraic behavior at small densities.Comment: 4 RevTeX pgs + 4 color Figures included, 1 figure eliminated second
part of the paper completely revise
Acceleration disturbances due to local gravity gradients in ASTROD I
The Astrodynamical Space Test of Relativity using Optical Devices (ASTROD)
mission consists of three spacecraft in separate solar orbits and carries out
laser interferometric ranging. ASTROD aims at testing relativistic gravity,
measuring the solar system and detecting gravitational waves. Because of the
larger arm length, the sensitivity of ASTROD to gravitational waves is
estimated to be about 30 times better than Laser Interferometer Space Antenna
(LISA) in the frequency range lower than about 0.1 mHz. ASTROD I is a simple
version of ASTROD, employing one spacecraft in a solar orbit. It is the first
step for ASTROD and serves as a technology demonstration mission for ASTROD. In
addition, several scientific results are expected in the ASTROD I experiment.
The required acceleration noise level of ASTROD I is 10^-13 m s^-2 Hz^{-1/2} at
the frequency of 0.1 mHz. In this paper, we focus on local gravity gradient
noise that could be one of the largest acceleration disturbances in the ASTROD
I experiment. We have carried out gravitational modelling for the current
test-mass design and simplified configurations of ASTROD I by using an
analytical method and the Monte Carlo method. Our analyses can be applied to
figure out the optimal designs of the test mass and the constructing materials
of the spacecraft, and the configuration of compensation mass to reduce local
gravity gradients.Comment: 6 pages, presented at the 6th Edoardo Amaldi Conference (Okinawa
Japan, June 2005); to be published in Journal of Physics: Conference Serie
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