18,175 research outputs found
Reduced-order modeling of transonic flows around an airfoil submitted to small deformations
A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier–Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations
Sum-of-Squares approach to feedback control of laminar wake flows
A novel nonlinear feedback control design methodology for incompressible
fluid flows aiming at the optimisation of long-time averages of flow quantities
is presented. It applies to reduced-order finite-dimensional models of fluid
flows, expressed as a set of first-order nonlinear ordinary differential
equations with the right-hand side being a polynomial function in the state
variables and in the controls. The key idea, first discussed in Chernyshenko et
al. 2014, Philos. T. Roy. Soc. 372(2020), is that the difficulties of treating
and optimising long-time averages of a cost are relaxed by using the
upper/lower bounds of such averages as the objective function. In this setting,
control design reduces to finding a feedback controller that optimises the
bound, subject to a polynomial inequality constraint involving the cost
function, the nonlinear system, the controller itself and a tunable polynomial
function. A numerically tractable approach to the solution of such optimisation
problems, based on Sum-of-Squares techniques and semidefinite programming, is
proposed.
To showcase the methodology, the mitigation of the fluctuation kinetic energy
in the unsteady wake behind a circular cylinder in the laminar regime at
Re=100, via controlled angular motions of the surface, is numerically
investigated. A compact reduced-order model that resolves the long-term
behaviour of the fluid flow and the effects of actuation, is derived using
Proper Orthogonal Decomposition and Galerkin projection. In a full-information
setting, feedback controllers are then designed to reduce the long-time average
of the kinetic energy associated with the limit cycle. These controllers are
then implemented in direct numerical simulations of the actuated flow. Control
performance, energy efficiency, and physical control mechanisms identified are
analysed. Key elements, implications and future work are discussed
Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows
We propose a variational approach to identification of an optimal nonlinear
eddy viscosity as a subscale turbulence representation for POD models. The
ansatz for the eddy viscosity is given in terms of an arbitrary function of the
resolved fluctuation energy. This function is found as a minimizer of a cost
functional measuring the difference between the target data coming from a
resolved direct or large-eddy simulation of the flow and its reconstruction
based on the POD model. The optimization is performed with a data-assimilation
approach generalizing the 4D-VAR method. POD models with optimal eddy
viscosities are presented for a 2D incompressible mixing layer at
(based on the initial vorticity thickness and the velocity of the high-speed
stream) and a 3D Ahmed body wake at (based on the body height and
the free-stream velocity). The variational optimization formulation elucidates
a number of interesting physical insights concerning the eddy-viscosity ansatz
used. The 20-dimensional model of the mixing-layer reveals a negative
eddy-viscosity regime at low fluctuation levels which improves the transient
times towards the attractor. The 100-dimensional wake model yields more
accurate energy distributions as compared to the nonlinear modal eddy-viscosity
benchmark {proposed recently} by \"Osth et al. (2014). Our methodology can be
applied to construct quite arbitrary closure relations and, more generally,
constitutive relations optimizing statistical properties of a broad class of
reduced-order models.Comment: 41 pages, 16 figures; accepted for publication in Journal of Fluid
Mechanic
Quantum control and measurement of atomic spins in polarization spectroscopy
Quantum control and measurement are two sides of the same coin. To affect a
dynamical map, well-designed time-dependent control fields must be applied to
the system of interest. To read out the quantum state, information about the
system must be transferred to a probe field. We study a particular example of
this dual action in the context of quantum control and measurement of atomic
spins through the light-shift interaction with an off-resonant optical probe.
By introducing an irreducible tensor decomposition, we identify the coupling of
the Stokes vector of the light field with moments of the atomic spin state.
This shows how polarization spectroscopy can be used for continuous weak
measurement of atomic observables that evolve as a function of time.
Simultaneously, the state-dependent light shift induced by the probe field can
drive nonlinear dynamics of the spin, and can be used to generate arbitrary
unitary transformations on the atoms. We revisit the derivation of the master
equation in order to give a unified description of spin dynamics in the
presence of both nonlinear dynamics and photon scattering. Based on this
formalism, we review applications to quantum control, including the design of
state-to-state mappings, and quantum-state reconstruction via continuous weak
measurement on a dynamically controlled ensemble
Cluster-based reduced-order modelling of a mixing layer
We propose a novel cluster-based reduced-order modelling (CROM) strategy of
unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's
group (Burkardt et al. 2006) and and transition matrix models introduced in
fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a
potential alternative to POD models and generalises the Ulam-Galerkin method
classically used in dynamical systems to determine a finite-rank approximation
of the Perron-Frobenius operator. The proposed strategy processes a
time-resolved sequence of flow snapshots in two steps. First, the snapshot data
are clustered into a small number of representative states, called centroids,
in the state space. These centroids partition the state space in complementary
non-overlapping regions (centroidal Voronoi cells). Departing from the standard
algorithm, the probabilities of the clusters are determined, and the states are
sorted by analysis of the transition matrix. Secondly, the transitions between
the states are dynamically modelled using a Markov process. Physical mechanisms
are then distilled by a refined analysis of the Markov process, e.g. using
finite-time Lyapunov exponent and entropic methods. This CROM framework is
applied to the Lorenz attractor (as illustrative example), to velocity fields
of the spatially evolving incompressible mixing layer and the three-dimensional
turbulent wake of a bluff body. For these examples, CROM is shown to identify
non-trivial quasi-attractors and transition processes in an unsupervised
manner. CROM has numerous potential applications for the systematic
identification of physical mechanisms of complex dynamics, for comparison of
flow evolution models, for the identification of precursors to desirable and
undesirable events, and for flow control applications exploiting nonlinear
actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material.
Accepted for publication in Journal of Fluid Mechanic
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