2,451 research outputs found
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
We present an estimator-based control design procedure for flow control,
using reduced-order models of the governing equations, linearized about a
possibly unstable steady state. The reduced models are obtained using an
approximate balanced truncation method that retains the most controllable and
observable modes of the system. The original method is valid only for stable
linear systems, and we present an extension to unstable linear systems. The
dynamics on the unstable subspace are represented by projecting the original
equations onto the global unstable eigenmodes, assumed to be small in number. A
snapshot-based algorithm is developed, using approximate balanced truncation,
for obtaining a reduced-order model of the dynamics on the stable subspace. The
proposed algorithm is used to study feedback control of 2-D flow over a flat
plate at a low Reynolds number and at large angles of attack, where the natural
flow is vortex shedding, though there also exists an unstable steady state. For
control design, we derive reduced-order models valid in the neighborhood of
this unstable steady state. The actuation is modeled as a localized body force
near the leading edge of the flat plate, and the sensors are two velocity
measurements in the near-wake of the plate. A reduced-order Kalman filter is
developed based on these models and is shown to accurately reconstruct the flow
field from the sensor measurements, and the resulting estimator-based control
is shown to stabilize the unstable steady state. For small perturbations of the
steady state, the model accurately predicts the response of the full
simulation. Furthermore, the resulting controller is even able to suppress the
stable periodic vortex shedding, where the nonlinear effects are strong, thus
implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure
Hydrogen solubility in zirconium intermetallic second phase particles
The enthalpies of solution of H in Zr binary intermetallic compounds formed
with Cu, Cr, Fe, Mo, Ni, Nb, Sn and V were calculated by means of density
functional theory simulations and compared to that of H in {\alpha}-Zr. It is
predicted that all Zr-rich phases (formed with Cu, Fe, Ni and Sn), and those
phases formed with Nb and V, offer lower energy, more stable sites for H than
{\alpha}-Zr. Conversely, Mo and Cr containing phases do not provide
preferential solution sites for H. In all cases the most stable site for H are
those that offer the highest coordination fraction of Zr atoms. Often these are
four Zr tetrahedra but not always. Implications with respect to H-trapping
properties of commonly observed ternary phases such as Zr(Cr,Fe)2, Zr2(Fe,Ni)
and Zr(Nb,Fe)2 are also discussed.Comment: manuscript accepted for publication in Journal of Nuclear Materials
(2013
Single polymer dynamics: coil-stretch transition in a random flow
By quantitative studies of statistics of polymer stretching in a random flow
and of a flow field we demonstrate that the stretching of polymer molecules in
a 3D random flow occurs rather sharply via the coil-stretch transition at the
value of the criterion close to theoretically predicted.Comment: 4 pages, 5 figure
Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows
Nontrivial steady flows have recently been found that capture the main
structures of the turbulent buffer layer. We study the effects of polymer
addition on these "exact coherent states" (ECS) in plane Couette flow. Despite
the simplicity of the ECS flows, these effects closely mirror those observed
experimentally: Structures shift to larger length scales, wall-normal
fluctuations are suppressed while streamwise ones are enhanced, and drag is
reduced. The mechanism underlying these effects is elucidated. These results
suggest that the ECS are closely related to buffer layer turbulence.Comment: 5 pages, 3 figures, published version, Phys. Rev. Lett. 89, 208301
(2002
Small scale statistics of viscoelastic turbulence
The small scale statistics of homogeneous isotropic turbulence of dilute
polymer solutions is investigated by means of direct numerical simulations of a
simplified viscoelastic fluid model. It is found that polymers only partially
suppress the turbulent cascade below the Lumley scale, leaving a remnant energy
flux even for large elasticity. As a consequence, fluid acceleration in
viscoelastic flows is reduced with respect to Newtonian turbulence, whereas its
rescaled probability density is left unchanged. At large scales the velocity
field is found to be unaffected by the presence of polymers.Comment: 7 pages, 4 figure
Second-order closures for compressible turbulence
This viewgraph presentation discusses project description, turbulence models, and computational engine and results for second-order closures for compressible turbulence
The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer
The statistical objects characterizing turbulence in real turbulent flows
differ from those of the ideal homogeneous isotropic model.They
containcontributions from various 2d and 3d aspects, and from the superposition
ofinhomogeneous and anisotropic contributions. We employ the recently
introduceddecomposition of statistical tensor objects into irreducible
representations of theSO(3) symmetry group (characterized by and
indices), to disentangle someof these contributions, separating the universal
and the asymptotic from the specific aspects of the flow. The different
contributions transform differently under rotations and so form a complete
basis in which to represent the tensor objects under study. The experimental
data arerecorded with hot-wire probes placed at various heights in the
atmospheric surfacelayer. Time series data from single probes and from pairs of
probes are analyzed to compute the amplitudes and exponents of different
contributions to the second order statistical objects characterized by ,
and . The analysis shows the need to make a careful distinction
between long-lived quasi 2d turbulent motions (close to the ground) and
relatively short-lived 3d motions. We demonstrate that the leading scaling
exponents in the three leading sectors () appear to be different
butuniversal, independent of the positions of the probe, and the large
scaleproperties. The measured values of the exponent are , and .
We present theoretical arguments for the values of these exponents usingthe
Clebsch representation of the Euler equations; neglecting anomalous
corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML)
version of this paper is avaliable at http://lvov.weizmann.ac.il
Laminarisation of flow at low Reynolds number due to streamwise body force
It is well established that when a turbulent flow is subjected to a non-uniform body force, the turbulence may be significantly suppressed in comparison with that of the flow of the same flow rate and hence the flow is said to be laminarised. This is the situation in buoyancy-aided mixed convection when severe heat transfer deterioration may occur. Here we report results of direct numerical simulations of flow with a linear or a step-change profile of body force. In contrast to the conventional view, we show that applying a body force to a turbulent flow while keeping the pressure force unchanged causes little changes to the key characteristics of the turbulence. In particular, the mixing characteristics of the turbulence represented by the turbulent viscosity remain largely unaffected. The so-called flow laminarisation due to a body force is in effect a reduction in the apparent Reynolds number of the flow, based on an apparent friction velocity associated with only the pressure force of the flow (i.e. excluding the contribution of the body force). The new understanding allows the level of the flow ‘laminarisation’ and when the full laminarisation occurs to be readily predicted. In terms of the near-wall turbulence structure, the numbers of ejections and sweeps are little influenced by the imposition of the body force, whereas the strength of each event may be enhanced if the coverage of the body force extends significantly away from the wall. The streamwise turbulent stress is usually increased in accordance with the observation of more and stronger elongated streaks, but the wall-normal and the circumferential turbulent stresses are largely unchanged
Dynamics of threads and polymers in turbulence: power-law distributions and synchronization
We study the behavior of threads and polymers in a turbulent flow. These
objects have finite spatial extension, so the flow along them differs slightly.
The corresponding drag forces produce a finite average stretching and the
thread is stretched most of the time. Nevertheless, the probability of
shrinking fluctuations is significant and is known to decay only as a
power-law. We show that the exponent of the power law is a universal number
independent of the statistics of the flow. For polymers the coil-stretch
transition exists: the flow must have a sufficiently large Lyapunov exponent to
overcome the elastic resistance and stretch the polymer from the coiled state
it takes otherwise. The probability of shrinking from the stretched state above
the transition again obeys a power law but with a non-universal exponent. We
show that well above the transition the exponent becomes universal and derive
the corresponding expression. Furthermore, we demonstrate synchronization: the
end-to-end distances of threads or polymers above the transition are
synchronized by the flow and become identical. Thus, the transition from
Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as
an ordering transition.Comment: 13 pages, version accepted to Journal of Statistical Mechanic
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