6,405 research outputs found
Controller design for the Navier-Stokes system. Part I: Concept & numerical results
We present a widely applicable construction recipe for closed-loop feedback controllers of nonlinear dynamical systems. Its basic idea consists in approximately solving certain instantaneous optimization problems for the discrete-in-time dynamical system. Easy incorporation of control constraints is one key feature of the recipe. The instationary Navier-Stokes equations serve as model application. In the first part of the work, we introduce the basic construction recipes and present numerical results for several closed-loop feedback control laws derived with the recipe. The stability analysis is contained in the second part of the work
Relaminarisation of Re_{\tau} = 100 channel flow with globally stabilising linear feedback control
The problems of nonlinearity and high dimension have so far prevented a
complete solution of the control of turbulent flow. Addressing the problem of
nonlinearity, we propose a flow control strategy which ensures that the energy
of any perturbation to the target profile decays monotonically. The
controller's estimate of the flow state is similarly guaranteed to converge to
the true value. We present a one-time off-line synthesis procedure, which
generalises to accommodate more restrictive actuation and sensing arrangements,
with conditions for existence for the controller given in this case. The
control is tested in turbulent channel flow () using full-domain
sensing and actuation on the wall-normal velocity. Concentrated at the point of
maximum inflection in the mean profile, the control directly counters the
supply of turbulence energy arising from the interaction of the wall-normal
perturbations with the flow shear. It is found that the control is only
required for the larger-scale motions, specifically those above the scale of
the mean streak spacing. Minimal control effort is required once laminar flow
is achieved. The response of the near-wall flow is examined in detail, with
particular emphasis on the pressure and wall-normal velocity fields, in the
context of Landahl's theory of sheared turbulence
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to
account for a large fraction of unresolved fluctuation energy. These Galerkin
methods are applied to Large Eddy Simulation data for a flow around the
vehicle-like bluff body call Ahmed body. This flow has three challenges for any
reduced-order model: a high Reynolds number, coherent structures with broadband
frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin
models are found to be most accurate with modal eddy viscosities as proposed by
Rempfer & Fasel (1994). Robustness of the model solution with respect to
initial conditions, eddy viscosity values and model order is only achieved for
state-dependent eddy viscosities as proposed by Noack, Morzynski & Tadmor
(2011). Only the POD system with state-dependent modal eddy viscosities can
address all challenges of the flow characteristics. All parameters are
analytically derived from the Navier-Stokes based balance equations with the
available data. We arrive at simple general guidelines for robust and accurate
POD models which can be expected to hold for a large class of turbulent flows.Comment: Submitted to the Journal of Fluid Mechanic
Relaminarisation of Re_τ=100 channel flow with globally stabilising linear feedback control
The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller’s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl’s theory of sheared turbulence
Electro-magnetic control of cylinder wake
The objective of this dissertation is to develop open and closed-loop control algorithms for manipulating wake flows past a solid cylinder in an electrically low-conducting fluid (e.g. seawater). The intent is to avoid both vortex shedding and flow separation from the body. It is desired to reduce the mean drag significantly and prevent the lift from becoming non-zero at all times. This is achieved through the introduction of a Lorentz force in the azimuthal direction generated by an array of permanent magnets and electrodes located on the solid structure. The array of actuators offers the advantage of making the Lorentz force time and space dependent. More specifically, a closed-loop control algorithm has been derived from the equations of motion capable of determining at all times the intensity of the Lorentz force in order to control the flow. This is achieved first, independently of the flow (open loop algorithm) and second, based on some partial flow information measured on the surface of the solid body (closed-loop algorithm). The latter offers the advantage of requiring a significantly reduced amount of control power. After considering the flow past a fixed solid structure, there is control of the more complex flowstructure interaction that occurs when the body is free to move. Thus it is possible to prevent any flow induced vibration from occurring
A minimization principle for the description of time-dependent modes associated with transient instabilities
We introduce a minimization formulation for the determination of a
finite-dimensional, time-dependent, orthonormal basis that captures directions
of the phase space associated with transient instabilities. While these
instabilities have finite lifetime they can play a crucial role by either
altering the system dynamics through the activation of other instabilities, or
by creating sudden nonlinear energy transfers that lead to extreme responses.
However, their essentially transient character makes their description a
particularly challenging task. We develop a minimization framework that focuses
on the optimal approximation of the system dynamics in the neighborhood of the
system state. This minimization formulation results in differential equations
that evolve a time-dependent basis so that it optimally approximates the most
unstable directions. We demonstrate the capability of the method for two
families of problems: i) linear systems including the advection-diffusion
operator in a strongly non-normal regime as well as the Orr-Sommerfeld/Squire
operator, and ii) nonlinear problems including a low-dimensional system with
transient instabilities and the vertical jet in crossflow. We demonstrate that
the time-dependent subspace captures the strongly transient non-normal energy
growth (in the short time regime), while for longer times the modes capture the
expected asymptotic behavior
Metric for attractor overlap
We present the first general metric for attractor overlap (MAO) facilitating
an unsupervised comparison of flow data sets. The starting point is two or more
attractors, i.e., ensembles of states representing different operating
conditions. The proposed metric generalizes the standard Hilbert-space distance
between two snapshots to snapshot ensembles of two attractors. A reduced-order
analysis for big data and many attractors is enabled by coarse-graining the
snapshots into representative clusters with corresponding centroids and
population probabilities. For a large number of attractors, MAO is augmented by
proximity maps for the snapshots, the centroids, and the attractors, giving
scientifically interpretable visual access to the closeness of the states. The
coherent structures belonging to the overlap and disjoint states between these
attractors are distilled by few representative centroids. We employ MAO for two
quite different actuated flow configurations: (1) a two-dimensional wake of the
fluidic pinball with vortices in a narrow frequency range and (2)
three-dimensional wall turbulence with broadband frequency spectrum manipulated
by spanwise traveling transversal surface waves. MAO compares and classifies
these actuated flows in agreement with physical intuition. For instance, the
first feature coordinate of the attractor proximity map correlates with drag
for the fluidic pinball and for the turbulent boundary layer. MAO has a large
spectrum of potential applications ranging from a quantitative comparison
between numerical simulations and experimental particle-image velocimetry data
to the analysis of simulations representing a myriad of different operating
conditions.Comment: 33 pages, 20 figure
- …