2,168 research outputs found
Exact regularized point particle method for multi-phase flows in the two-way coupling regime
Particulate flows have been largely studied under the simplifying assumptions
of one-way coupling regime where the disperse phase do not react-back on the
carrier fluid. In the context of turbulent flows, many non trivial phenomena
such as small scales particles clustering or preferential spatial accumulation
have been explained and understood. A more complete view of multiphase flows
can be gained calling into play two-way coupling effects, i.e. by accounting
for the inter-phase momentum exchange between the carrier and the suspended
phase, certainly relevant at increasing mass loading. In such regime, partially
investigated in the past by the so-called Particle In Cell (PIC) method, much
is still to be learned about the dynamics of the disperse phase and the ensuing
alteration of the carrier flow.
In this paper we present a new methodology rigorously designed to capture the
inter-phase momentum exchange for particles smaller than the smallest
hydrodynamical scale, e.g. the Kolmogorov scale in a turbulent flow. In fact,
the momentum coupling mechanism exploits the unsteady Stokes flow around a
small rigid sphere where the transient disturbance produced by each particle is
evaluated in a closed form. The particles are described as lumped, point masses
which would lead to the appearance of singularities. A rigorous regularization
procedure is conceived to extract the physically relevant interactions between
particles and fluid which avoids any "ah hoc" assumption. The approach is
suited for high efficiency implementation on massively parallel machines since
the transient disturbance produced by the particles is strongly localized in
space around the actual particle position. As will be shown, hundred thousands
particles can therefore be handled at an affordable computational cost as
demonstrated by a preliminary application to a particle laden turbulent shear
flow.Comment: Submitted to Journal of Fluid Mechanics, 56 pages, 15 figure
A high accuracy Leray-deconvolution model of turbulence and its limiting behavior
In 1934 J. Leray proposed a regularization of the Navier-Stokes equations
whose limits were weak solutions of the NSE. Recently, a modification of the
Leray model, called the Leray-alpha model, has atracted study for turbulent
flow simulation. One common drawback of Leray type regularizations is their low
accuracy. Increasing the accuracy of a simulation based on a Leray
regularization requires cutting the averaging radius, i.e., remeshing and
resolving on finer meshes. This report analyzes a family of Leray type models
of arbitrarily high orders of accuracy for fixed averaging radius. We establish
the basic theory of the entire family including limiting behavior as the
averaging radius decreases to zero, (a simple extension of results known for
the Leray model). We also give a more technically interesting result on the
limit as the order of the models increases with fixed averaging radius. Because
of this property, increasing accuracy of the model is potentially cheaper than
decreasing the averaging radius (or meshwidth) and high order models are doubly
interesting
Poloidal-toroidal decomposition in a finite cylinder. II. Discretization, regularization and validation
The Navier-Stokes equations in a finite cylinder are written in terms of
poloidal and toroidal potentials in order to impose incompressibility.
Regularity of the solutions is ensured in several ways: First, the potentials
are represented using a spectral basis which is analytic at the cylindrical
axis. Second, the non-physical discontinuous boundary conditions at the
cylindrical corners are smoothed using a polynomial approximation to a steep
exponential profile. Third, the nonlinear term is evaluated in such a way as to
eliminate singularities. The resulting pseudo-spectral code is tested using
exact polynomial solutions and the spectral convergence of the coefficients is
demonstrated. Our solutions are shown to agree with exact polynomial solutions
and with previous axisymmetric calculations of vortex breakdown and of
nonaxisymmetric calculations of onset of helical spirals. Parallelization by
azimuthal wavenumber is shown to be highly effective
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