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This work is devoted to the numerical comparison of four active control techniques in order to increase the pressure recovery generated by the deceleration of a slightly compressible viscous flow over a dihedral plane. It is performed by the use of vortex generator jets and intrusive sensors. The governing equations, the two-dimensional direct numerical simulation code and the flow configuration are first briefly recalled. Then, the objective of the control is carefully displayed, and the uncontrolled...
This work is devoted to the numerical comparison of four active control
techniques in order to increase the pressure recovery generated by the
deceleration of a slightly compressible viscous flow over a dihedral plane.
It is performed by the
use of vortex generator jets and intrusive sensors. The governing equations,
the two-dimensional direct numerical simulation code and the
flow configuration are first briefly recalled. Then, the objective of the
control is carefully displayed, and the uncontrolled...
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
We wish to show how the shock position in a nozzle could be
controlled. Optimal control theory and algorithm is applied to the
transonic equation. The difficulty is that the derivative with
respect to the shock position involves a Dirac mass. The one
dimensional case is solved, the two dimensional one is analyzed .
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
We consider the flow of gas through pipelines controlled by a compressor
station. Under a subsonic flow assumption we prove the existence
of classical solutions for a given finite time interval.
The existence result is used to construct Riemannian feedback laws and
to prove a stabilization result for a coupled system of gas pipes with a compressor
station. We introduce a Lyapunov function and prove exponential decay
with respect to the L2-norm.
An exploratory study is performed to investigate the use of a time-dependent discrete
adjoint methodology for design optimization of a high-lift wing configuration augmented
with an active flow control system. The location and blowing parameters associated with a
series of jet actuation orifices are used as design variables. In addition, a geometric
parameterization scheme is developed to provide a compact set of design variables
describing the wing...
This paper is divided into two parts and focuses on the linear independence of boundary traces of eigenfunctions of boundary value problems. Part I deals with second-order elliptic operators, and Part II with Stokes (and Oseen) operators.
Part I: Let be an eigenvalue of a second-order elliptic operator defined on an open, sufficiently smooth, bounded domain Ω in ℝⁿ, with Neumann homogeneous boundary conditions on Γ = tial Ω. Let be the corresponding linearly independent (normalized) eigenfunctions...
In this talk, I will present a recent result obtained in [6] with O. Glass, S. Guerrero and J.-P. Puel on the local exact controllability of the -d compressible Navier-Stokes equations. The goal of these notes is to give an informal presentation of this article and we refer the reader to it for extensive details.
In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given , the system can be driven at rest and the structure to its reference configuration at time . To show this result, we first consider a linearized system....
In this paper, we prove a controllability
result for a fluid-structure interaction problem. In dimension two,
a rigid structure moves into an incompressible fluid governed by
Navier-Stokes equations. The control acts on a fixed subset of the
fluid domain. We prove that, for small initial data, this system is
null controllable, that is, for a given T > 0, the system can be
driven at rest and the structure to its reference configuration at
time T. To show this result, we first consider a linearized
system....
In this paper we present an analysis of the partial differential equations that
describe the Chemical Vapor Infiltration (CVI) processes. The mathematical model
requires at least two partial differential equations, one describing the
gas phase and one corresponding to the solid phase.
A key difficulty in the process is the long processing times that are typically
required. We address here the issue of optimization and show that we can choose
appropriate pressure and temperature to minimize these...
We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over...
An optimal control problem for a model for stationary, low Mach
number, highly nonisothermal, viscous flows is considered.
The control problem involves the minimization of a measure of
the distance between the velocity field and a given target
velocity field. The existence of solutions of a boundary value
problem for the model equations is established as is the
existence of solutions of the optimal control problem. Then, a
derivation of an optimality system, i.e., a boundary value
problem from...
In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization
problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
A Lagrange–Newton–SQP method is analyzed for the optimal control of the
Burgers equation. Distributed controls are given, which are restricted by
pointwise lower and upper bounds. The convergence of the method is proved in
appropriate Banach spaces. This proof is based on a weak second-order
sufficient optimality condition and the theory of Newton methods for
generalized equations in Banach spaces. For the numerical realization a
primal-dual active set strategy is applied. Numerical examples are...
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