41,427 research outputs found
PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,
The aim of the paper is to discuss the main characteristics of a complete
theoretical and numerical model for turbulent polydispersed two-phase flows,
pointing out some specific issues. The theoretical details of the model have
already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001
]. Consequently, the present work is mainly focused on complementary aspects,
that are often overlooked and that require particular attention. In particular,
the following points are analysed : the necessity to add an extra term in the
equation for the velocity of the fluid seen in the case of twoway coupling, the
theoretical and numerical evaluations of particle averages and the fulfilment
of the particle mass-continuity constraint. The theoretical model is developed
within the PDF formalism. The important-physical choice of the state vector
variables is first discussed and the model is then expressed as a stochastic
differential equation (SDE) written in continuous time (Langevin equations) for
the velocity of the fluid seen. The interests and limitations of Langevin
equations, compared to the single-phase case, are reviewed. From the numerical
point of view, the model corresponds to an hybrid Eulerian/Lagrangian approach
where the fluid and particle phases are simulated by different methods.
Important aspects of the Monte Carlo particle/mesh numerical method are
emphasised. Finally, the complete model is validated and its performance is
assessed by simulating a bluff-body case with an important recirculation zone
and in which two-way coupling is noticeable.Comment: 23 pages, 10 figure
Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection
We investigate the utility of the convex hull of many Lagrangian tracers to
analyze transport properties of turbulent flows with different anisotropy. In
direct numerical simulations of statistically homogeneous and stationary
Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD
Boussinesq convection a comparison with Lagrangian pair dispersion shows that
convex hull statistics capture the asymptotic dispersive behavior of a large
group of passive tracer particles. Moreover, convex hull analysis provides
additional information on the sub-ensemble of tracers that on average disperse
most efficiently in the form of extreme value statistics and flow anisotropy
via the geometric properties of the convex hulls. We use the convex hull
surface geometry to examine the anisotropy that occurs in turbulent convection.
Applying extreme value theory, we show that the maximal square extensions of
convex hull vertices are well described by a classic extreme value
distribution, the Gumbel distribution. During turbulent convection,
intermittent convective plumes grow and accelerate the dispersion of Lagrangian
tracers. Convex hull analysis yields information that supplements standard
Lagrangian analysis of coherent turbulent structures and their influence on the
global statistics of the flow.Comment: 18 pages, 10 figures, preprin
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
Progress in mixed Eulerian-Lagrangian finite element simulation of forming processes
A review is given of a mixed Eulerian-Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may occur when the updated Lagrange method is applied, can be avoided. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities and numerical diffusion. Prediction of contact phenomena such as gap openning and/or closing and sliding with friction is accomplished by a special contact element. The method is demonstrated by simulations of an upsetting process and a wire drawing process
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Numerical and Experimental Investigation of the Morphology Development of Expansion Clouds by a Powder Jet Flow
Explosion suppression is often the preferred method of explosion attenuation in industry. The morphology development of suppression clouds is important for the design of necessary coverage of the product. This paper presents a numerical and experimental investigation of the growth of powder dispersion as it expands from a discharge nozzle. A Lagrangian stochastic particle-tracking approach and the RNG k-e turbulence model are adopted in the flow field solver for the dispersed and continuous phases. The flow fields coupled with the particle interactions are predicted. The dispersion characteristics of the expansion of the powder cloud through a pipe for short intervals of time are investigated. This was compared with (1) captured images from experiments, (2) experimental data, and (3) results of previous simulations. Particle positions along the jet are presented. The effects of flow rate on the development of the cloud and a comparison with experimental results are also presented. It is noted that the coverage of the powder cloud can be controlled by the flow rate of the jet, and the developing length of the cloud is more influenced by the flow rate of jet flow than the developing width. The good qualitative agreements achieved are useful for further optimisation of product design
Langevin PDF simulation of particle deposition in a turbulent pipe flow
The paper deals with the description of particle deposition on walls from a
turbulent flow over a large range of particle diameter, using a Langevin PDF
model. The first aim of the work is to test how the present Langevin model is
able to describe this phenomenon and to outline the physical as- pects which
play a major role in particle deposition. The general features and
characteristics of the present stochastic model are first recalled. Then,
results obtained with the standard form of the model are presented along with
an analysis which has been carried out to check the sensitivity of the
predictions on different mean fluid quantities. These results show that the
physical repre- sentation of the near-wall physics has to be improved and that,
in particular, one possible route is to introduce specific features related to
the near-wall coherent structures. In the following, we propose a simple
phenomenological model that introduces some of the effects due to the presence
of turbulent coherent structures on particles in a thin layer close to the
wall. The results obtained with this phenomenological model are in good
agreement with experimental evidence and this suggests to pursue in that
direction, towards the development of more general and rigorous stochastic
models that provide a link between a geometrical description of turbulent flow
and a statistical one.Comment: 40 pages, 8 figure
Persistent accelerations disentangle Lagrangian turbulence
Particles in turbulence frequently encounter extreme accelerations between
extended periods of quiescence. The occurrence of extreme events is closely
related to the intermittent spatial distribution of intense flow structures
such as vorticity filaments. This mixed history of flow conditions leads to
very complex particle statistics with a pronounced scale dependence, which
presents one of the major challenges on the way to a non-equilibrium
statistical mechanics of turbulence. Here, we introduce the notion of
persistent Lagrangian acceleration, quantified by the squared particle
acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian
particle data from simulations on this coarse-grained acceleration, we find
remarkably simple, close-to-Gaussian statistics for a range of Reynolds
numbers. This opens the possibility to decompose the complex particle
statistics into much simpler sub-ensembles. Based on this observation, we
develop a comprehensive theoretical framework for Lagrangian single-particle
statistics that captures the acceleration, velocity increments as well as
single-particle dispersion
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