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## PDF modeling of turbulent flows on unstructured grids

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/06/2010
Português

Relevância na Pesquisa

467.6964%

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 mathematically
exact treatment of advection, viscous effects and arbitrarily complex chemical
reactions is possible; these processes are treated without closure assumptions.
A set of 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 and to track
particles. All three aspects regarding the grid make use of the finite element
method. Compared to hybrid methods, the current methodology is stand-alone,
therefore it is consistent both numerically and at the level of turbulence
closure without the use of consistency conditions. Several newly developed
algorithms are described that facilitate the numerical solution in complex flow
geometries, including a stabilized mean-pressure projection scheme, the
estimation of conditional and unconditional Eulerian statistics and their
derivatives from stochastic particle fields...

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## Extending the Langevin model to variable-density pressure-gradient-driven turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/01/2011
Português

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467.6964%

We extend the generalized Langevin model, originally developed for the
Lagrangian fluid particle velocity in constant-density shear-driven turbulence,
to variable-density (VD) pressure-gradient-driven flows. VD effects due to
non-uniform mass concentrations (e.g. mixing of different species) are
considered. In the extended model large density fluctuations leading to large
differential fluid accelerations are accounted for. This is an essential
ingredient to represent the strong coupling between the density and velocity
fields in VD hydrodynamics driven by active scalar mixing. The small scale
anisotropy, a fundamentally "non-Kolmogorovian" feature of
pressure-gradient-driven flows, is captured by a tensorial stochastic diffusion
term. The extension is so constructed that it reduces to the original Langevin
model in the limit of constant density. We show that coupling a Lagrangian
mass-density particle model to the proposed extended velocity equation results
in a statistical representation of VD turbulence that has important benefits.
Namely, the effects of the mass flux and the specific volume, both essential in
the prediction of VD flows, are retained in closed form and require no explicit
closure assumptions. The paper seeks to describe a theoretical framework
necessary for subsequent applications. We derive the rigorous mathematical
consequences of assuming a particular functional form of the stochastic
momentum equation coupled to the stochastic density field in VD flows. A
previous article discussed VD mixing and developed a stochastic Lagrangian
model equation for the mass-density. Second in the series...

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## A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/06/2010
Português

Relevância na Pesquisa

467.6964%

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...

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## Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/03/2010
Português

Relevância na Pesquisa

467.6964%

Dispersion of a passive scalar from concentrated sources in fully developed
turbulent channel flow is studied with the probability density function (PDF)
method. The joint PDF of velocity, turbulent frequency and scalar concentration
is represented by a large number of Lagrangian particles. A stochastic
near-wall PDF model combines the generalized Langevin model of Haworth & Pope
with Durbin's method of elliptic relaxation to provide a mathematically exact
treatment of convective and viscous transport with a non-local representation
of the near-wall Reynolds stress anisotropy. The presence of walls is
incorporated through the imposition of no-slip and impermeability conditions on
particles without the use of damping or wall-functions. Information on the
turbulent timescale is supplied by the gamma-distribution model of van Slooten
et al. Two different micromixing models are compared that incorporate the
effect of small scale mixing on the transported scalar: the widely used
interaction by exchange with the mean (IEM) and the interaction by exchange
with the conditional mean (IECM) model. Single-point velocity and concentration
statistics are compared to direct numerical simulation and experimental data at
Re_\tau=1080 based on the friction velocity and the channel half width. The
joint model accurately reproduces a wide variety of conditional and
unconditional statistics in both physical and composition space.; Comment: Accepted in Physics of Fluids...

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## Joint PDF modelling of turbulent flow and dispersion in an urban street canyon

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/03/2010
Português

Relevância na Pesquisa

467.6964%

#Physics - Geophysics#Physics - Computational Physics#Physics - Fluid Dynamics#85A10, 76F25, 76F55, 76M35, 37N10

The joint probability density function (PDF) of turbulent velocity and
concentration of a passive scalar in an urban street canyon is computed using a
newly developed particle-in-cell Monte Carlo method. Compared to moment
closures, the PDF methodology provides the full one-point one-time PDF of the
underlying fields containing all higher moments and correlations. The
small-scale mixing of the scalar released from a concentrated source at the
street level is modelled by the interaction by exchange with the conditional
mean (IECM) model, with a micro-mixing time scale designed for geometrically
complex settings. The boundary layer along no-slip walls (building sides and
tops) is fully resolved using an elliptic relaxation technique, which captures
the high anisotropy and inhomogeneity of the Reynolds stress tensor in these
regions. A less computationally intensive technique based on wall functions to
represent boundary layers and its effect on the solution are also explored. The
calculated statistics are compared to experimental data and large-eddy
simulation. The present work can be considered as the first example of
computation of the full joint PDF of velocity and a transported passive scalar
in an urban setting. The methodology proves successful in providing high level
statistical information on the turbulence and pollutant concentration fields in
complex urban scenarios.; Comment: Accepted in Boundary-Layer Meteorology...

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## Exploring the beta distribution in variable-density turbulent mixing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

467.6964%

In assumed probability density function (pdf) methods of turbulent
combustion, the shape of the scalar pdf is assumed a priori and the pdf is
parametrized by its moments for which model equations are solved. In
non-premixed flows the beta distribution has been a convenient choice to
represent the mixture fraction in binary mixtures or a progress variable in
combustion. Here the beta-pdf approach is extended to variable-density mixing:
mixing between materials that have very large density differences and thus the
scalar fields are active. As a consequence, new mixing phenomena arise due to
1) cubic non-linearities in the Navier-Stokes equation, 2) additional
non-linearities in the molecular diffusion terms and 3) the appearance of the
specific volume as a dynamical variable. The assumed beta-pdf approach is
extended to transported pdf methods by giving the associated stochastic
differential equation (SDE). The beta distribution is shown to be a realizable,
consistent and sufficiently general representation of the marginal pdf of the
fluid density, an active scalar, in non-premixed variable-density turbulent
mixing. The moment equations derived from mass conservation are compared to the
moment equations derived from the governing SDE. This yields a series of
relations between the non-stationary coefficients of the SDE and the mixing
physics. Our treatment of this problem is general: the mixing is mathematically
represented by the divergence of the velocity field which can only be specified
once the problem is defined. In this paper we seek to describe a theoretical
framework to subsequent applications. We report and document several rigorous
mathematical results...

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