2,830 research outputs found
A non-hybrid method for the PDF equations of turbulent flows on unstructured grids
In probability density function (PDF) methods of turbulent flows, the joint
PDF of several flow variables is computed by numerically integrating a system
of stochastic differential equations for Lagrangian particles. A set of
parallel algorithms is proposed to provide an efficient solution of the PDF
transport equation, modeling the joint PDF of turbulent velocity, frequency and
concentration of a passive scalar in geometrically complex configurations. An
unstructured Eulerian grid is employed to extract Eulerian statistics, to solve
for quantities represented at fixed locations of the domain (e.g. the mean
pressure) and to track particles. All three aspects regarding the grid make use
of the finite element method (FEM) employing the simplest linear FEM shape
functions. To model the small-scale mixing of the transported scalar, the
interaction by exchange with the conditional mean model is adopted. An adaptive
algorithm that computes the velocity-conditioned scalar mean is proposed that
homogenizes the statistical error over the sample space with no assumption on
the shape of the underlying velocity PDF. Compared to other hybrid
particle-in-cell approaches for the PDF equations, the current methodology is
consistent without the need for consistency conditions. The algorithm is tested
by computing the dispersion of passive scalars released from concentrated
sources in two different turbulent flows: the fully developed turbulent channel
flow and a street canyon (or cavity) flow. Algorithmic details on estimating
conditional and unconditional statistics, particle tracking and particle-number
control are presented in detail. Relevant aspects of performance and
parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200
Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one
of the most promising and viable numerical tools to study turbulent dispersed
flows when the computational cost of Direct Numerical Simulation (DNS) becomes
too expensive. The applicability of this approach is however limited if the
effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are
neglected. In this paper, we propose to take these effects into account by
means of a Lagrangian stochastic SGS model for the equations of particle
motion. The model extends to particle-laden flows the velocity-filtered density
function method originally developed for reactive flows. The underlying
filtered density function is simulated through a Lagrangian Monte Carlo
procedure that solves for a set of Stochastic Differential Equations (SDEs)
along individual particle trajectories. The resulting model is tested for the
reference case of turbulent channel flow, using a hybrid algorithm in which the
fluid velocity field is provided by LES and then used to advance the SDEs in
time. The model consistency is assessed in the limit of particles with zero
inertia, when "duplicate fields" are available from both the Eulerian LES and
the Lagrangian tracking. Tests with inertial particles were performed to
examine the capability of the model to capture particle preferential
concentration and near-wall segregation. Upon comparison with DNS-based
statistics, our results show improved accuracy and considerably reduced errors
with respect to the case in which no SGS model is used in the equations of
particle motion
Some relations between Lagrangian models and synthetic random velocity fields
We propose an alternative interpretation of Markovian transport models based
on the well-mixedness condition, in terms of the properties of a random
velocity field with second order structure functions scaling linearly in the
space time increments. This interpretation allows direct association of the
drift and noise terms entering the model, with the geometry of the turbulent
fluctuations. In particular, the well known non-uniqueness problem in the
well-mixedness approach is solved in terms of the antisymmetric part of the
velocity correlations; its relation with the presence of non-zero mean helicity
and other geometrical properties of the flow is elucidated. The well-mixedness
condition appears to be a special case of the relation between conditional
velocity increments of the random field and the one-point Eulerian velocity
distribution, allowing generalization of the approach to the transport of
non-tracer quantities. Application to solid particle transport leads to a model
satisfying, in the homogeneous isotropic turbulence case, all the conditions on
the behaviour of the correlation times for the fluid velocity sampled by the
particles. In particular, correlation times in the gravity and in the inertia
dominated case, respectively, longer and shorter than in the passive tracer
case; in the gravity dominated case, correlation times longer for velocity
components along gravity, than for the perpendicular ones. The model produces,
in channel flow geometry, particle deposition rates in agreement with
experiments.Comment: 54 pages, 8 eps figures included; contains additional material on
SO(3) and on turbulent channel flows. Few typos correcte
Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches
In large-eddy simulation (LES) of turbulent dispersed flows, modelling and numerical inaccuracies are incurred because LES provides only an approximation of the filtered velocity. Interpolation errors can also occur (on coarse-grained domains, for instance). These inaccuracies affect the estimation of the forces acting on particles, obtained when the filtered fluid velocity is supplied to the Lagrangian equation of particle motion, and accumulate in time. As a result, particle trajectories in LES fields progressively diverge from particle trajectories in DNS fields, which can be considered as the exact numerical reference: the flow fields seen by the particles become less and less correlated, and the forces acting on particles are evaluated at increasingly different locations. In this paper, we review models and strategies that have been proposed in the Eulerian\u2013Lagrangian framework to correct the above-mentioned sources of inaccuracy on particle dynamics and to improve the prediction of particle dispersion in turbulent dispersed flows
The instanton method and its numerical implementation in fluid mechanics
A precise characterization of structures occurring in turbulent fluid flows
at high Reynolds numbers is one of the last open problems of classical physics.
In this review we discuss recent developments related to the application of
instanton methods to turbulence. Instantons are saddle point configurations of
the underlying path integrals. They are equivalent to minimizers of the related
Freidlin-Wentzell action and known to be able to characterize rare events in
such systems. While there is an impressive body of work concerning their
analytical description, this review focuses on the question on how to compute
these minimizers numerically. In a short introduction we present the relevant
mathematical and physical background before we discuss the stochastic Burgers
equation in detail. We present algorithms to compute instantons numerically by
an efficient solution of the corresponding Euler-Lagrange equations. A second
focus is the discussion of a recently developed numerical filtering technique
that allows to extract instantons from direct numerical simulations. In the
following we present modifications of the algorithms to make them efficient
when applied to two- or three-dimensional fluid dynamical problems. We
illustrate these ideas using the two-dimensional Burgers equation and the
three-dimensional Navier-Stokes equations
Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows
Breakup of small aggregates in fully developed turbulence is studied by means
of direct numerical simulations in a series of typical bounded and unbounded
flow configurations, such as a turbulent channel flow, a developing boundary
layer and homogeneous isotropic turbulence. The simplest criterion for breakup
is adopted, whereas aggregate breakup occurs when the local hydrodynamic stress
, with being the energy dissipation
at the position of the aggregate, overcomes a given threshold
, which is characteristic for a given type of aggregates.
Results show that the breakup rate decreases with increasing threshold. For
small thresholds, it develops a universal scaling among the different flows.
For high thresholds, the breakup rates show strong differences between the
different flow configurations, highlighting the importance of non-universal
mean-flow properties. To further assess the effects of flow inhomogeneity and
turbulent fluctuations, theresults are compared with those obtained in a smooth
stochastic flow. Furthermore, we discuss the limitations and applicability of a
set of independent proxies.Comment: 15 pages, 12 figures, Refinded discussion in Section 2.1, results
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