10,236 research outputs found
Fluid flow dynamics under location uncertainty
We present a derivation of a stochastic model of Navier Stokes equations that
relies on a decomposition of the velocity fields into a differentiable drift
component and a time uncorrelated uncertainty random term. This type of
decomposition is reminiscent in spirit to the classical Reynolds decomposition.
However, the random velocity fluctuations considered here are not
differentiable with respect to time, and they must be handled through
stochastic calculus. The dynamics associated with the differentiable drift
component is derived from a stochastic version of the Reynolds transport
theorem. It includes in its general form an uncertainty dependent "subgrid"
bulk formula that cannot be immediately related to the usual Boussinesq eddy
viscosity assumption constructed from thermal molecular agitation analogy. This
formulation, emerging from uncertainties on the fluid parcels location,
explains with another viewpoint some subgrid eddy diffusion models currently
used in computational fluid dynamics or in geophysical sciences and paves the
way for new large-scales flow modelling. We finally describe an applications of
our formalism to the derivation of stochastic versions of the Shallow water
equations or to the definition of reduced order dynamical systems
Wind Energy and the Turbulent Nature of the Atmospheric Boundary Layer
Wind turbines operate in the atmospheric boundary layer, where they are
exposed to the turbulent atmospheric flows. As the response time of wind
turbine is typically in the range of seconds, they are affected by the small
scale intermittent properties of the turbulent wind. Consequently, basic
features which are known for small-scale homogeneous isotropic turbulence, and
in particular the well-known intermittency problem, have an important impact on
the wind energy conversion process. We report on basic research results
concerning the small-scale intermittent properties of atmospheric flows and
their impact on the wind energy conversion process. The analysis of wind data
shows strongly intermittent statistics of wind fluctuations. To achieve
numerical modeling a data-driven superposition model is proposed. For the
experimental reproduction and adjustment of intermittent flows a so-called
active grid setup is presented. Its ability is shown to generate reproducible
properties of atmospheric flows on the smaller scales of the laboratory
conditions of a wind tunnel. As an application example the response dynamics of
different anemometer types are tested. To achieve a proper understanding of the
impact of intermittent turbulent inflow properties on wind turbines we present
methods of numerical and stochastic modeling, and compare the results to
measurement data. As a summarizing result we find that atmospheric turbulence
imposes its intermittent features on the complete wind energy conversion
process. Intermittent turbulence features are not only present in atmospheric
wind, but are also dominant in the loads on the turbine, i.e. rotor torque and
thrust, and in the electrical power output signal. We conclude that profound
knowledge of turbulent statistics and the application of suitable numerical as
well as experimental methods are necessary to grasp these unique features (...)Comment: Accepted by the Journal of Turbulence on May 17, 201
A LES-Langevin model for turbulence
We propose a new model of turbulence for use in large-eddy simulations (LES).
The turbulent force, represented here by the turbulent Lamb vector, is divided
in two contributions. The contribution including only subfilter fields is
deterministically modeled through a classical eddy-viscosity. The other
contribution including both filtered and subfilter scales is dynamically
computed as solution of a generalized (stochastic) Langevin equation. This
equation is derived using Rapid Distortion Theory (RDT) applied to the
subfilter scales. The general friction operator therefore includes both
advection and stretching by the resolved scale. The stochastic noise is derived
as the sum of a contribution from the energy cascade and a contribution from
the pressure. The LES model is thus made of an equation for the resolved scale,
including the turbulent force, and a generalized Langevin equation integrated
on a twice-finer grid. The model is validated by comparison to DNS and is
tested against classical LES models for isotropic homogeneous turbulence, based
on eddy viscosity. We show that even in this situation, where no walls are
present, our inclusion of backscatter through the Langevin equation results in
a better description of the flow.Comment: 18 pages, 14 figures, to appear in Eur. Phys. J.
- …