272 research outputs found
Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms
As a generalization of the mass-flux based classical stream-tube, the concept
of momentum and energy transport tubes is discussed as a flow visualization
tool. These transport tubes have the property, respectively, that no fluxes of
momentum or energy exist over their respective tube mantles. As an example
application using data from large-eddy simulation, such tubes are visualized
for the mean-flow structure of turbulent flow in large wind farms, in fully
developed wind-turbine-array boundary layers. The three-dimensional
organization of energy transport tubes changes considerably when turbine
spacings are varied, enabling the visualization of the path taken by the
kinetic energy flux that is ultimately available at any given turbine within
the array.Comment: Accepted for publication in Journal of Fluid Mechanic
On the decay of dispersive motions in the outer region of rough-wall boundary layers
In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow
solutions exist that lead to so-called dispersive velocity components and
dispersive stresses. They play a significant role in the mean-flow momentum
balance near the wall, but typically disappear in the outer layer. A
theoretical framework is presented to study the decay of dispersive motions in
the outer layer. To this end, the problem is formulated in Fourier space, and a
set of governing ordinary differential equations per mode in wavenumber space
is derived by linearizing the Reynolds-averaged Navier-Stokes equations around
a constant background velocity. With further simplifications, analytically
tractable solutions are found consisting of linear combinations of
and , with the wall distance, the magnitude of the
horizontal wavevector , and where is a
function of and the Reynolds number . Moreover, for
or , is found, in
which case solutions consist of a linear combination of and
, and are Reynolds number independent. These analytical relations
are verified in the limit of using the rough boundary layer experiments
by Vanderwel and Ganapathisubramani (J. Fluid Mech. 774, R2, 2015) and are in
good agreement for , with the boundary-layer
thickness and
A new wake-merging method for wind-farm power prediction in presence of heterogeneous background velocity fields
Many wind farms are placed near coastal regions or in proximity of orographic
obstacles. The meso-scale gradients that develop in these zones make wind farms
operating in velocity fields that are rarely uniform. However, all existing
wake-merging methods in engineering wind-farm wake models assume a homogeneous
background velocity field in and around the farm, relying on a single
wind-speed value usually measured several hundreds of meters upstream of the
first row of turbines. In this study, we derive a new momentum-conserving
wake-merging method capable of superimposing the waked flow on a heterogeneous
background velocity field. We couple the proposed wake-merging method with four
different wake models, i.e. the Gaussian, super-Gaussian, double-Gaussian and
Ishihara model, and we test its performance against LES data, dual-Doppler
radar measurements and SCADA data from the Horns Rev, London Array, and
Westermost Rough farm. Next to this, as an additional point of reference, the
standard Jensen model with quadratic superposition is also included. Results
show that the new method performs similarly to linear superposition of velocity
deficits in homogeneous conditions but it shows better performance when a
spatially varying background velocity is used. The most accurate estimates are
obtained when the wake-merging method is coupled with the double-Gaussian and
Gaussian single-wake model. The Ishihara model also shows good agreements with
observations. In contrast to this, the Jensen and super-Gaussian wake model
underestimate the farm power output for all wind speeds, wind directions and
wind farms considered in our analysis
Periodic Shadowing Sensitivity Analysis of Chaotic Systems
The sensitivity of long-time averages of a hyperbolic chaotic system to
parameter perturbations can be determined using the shadowing direction, the
uniformly-bounded-in-time solution of the sensitivity equations. Although its
existence is formally guaranteed for certain systems, methods to determine it
are hardly available. One practical approach is the Least-Squares Shadowing
(LSS) algorithm (Q Wang, SIAM J Numer Anal 52, 156, 2014), whereby the
shadowing direction is approximated by the solution of the sensitivity
equations with the least square average norm. Here, we present an alternative,
potentially simpler shadowing-based algorithm, termed periodic shadowing. The
key idea is to obtain a bounded solution of the sensitivity equations by
complementing it with periodic boundary conditions in time. We show that this
is not only justifiable when the reference trajectory is itself periodic, but
also possible and effective for chaotic trajectories. Our error analysis shows
that periodic shadowing has the same convergence rates as LSS when the time
span is increased: the sensitivity error first decays as and then,
asymptotically as . We demonstrate the approach on the Lorenz
equations, and also show that, as tends to infinity, periodic shadowing
sensitivities converge to the same value obtained from long unstable periodic
orbits (D Lasagna, SIAM J Appl Dyn Syst 17, 1, 2018) for which there is no
shadowing error. Finally, finite-difference approximations of the sensitivity
are also examined, and we show that subtle non-hyperbolicity features of the
Lorenz system introduce a small, yet systematic, bias
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