Lorenz Pyta

Model Reduction and Control of a Compressible Channel Flow with Combustion

Abstract A model reduction for a compressible flow with combustion is performed using the POD-Galerkin procedure. The model parameters are determined by an optimization. The obtained reduced-order model is incorporated in a model predictive controller and results are shown from a closed-loop CFD-simulation. The controller influences the fuel mass-flow boundary condition to control the temperature at a certain point within the computational domain.

Model based control of the incompressible Navier-Stokes-Equations using interpolatory model reduction

In the present paper a model reduction of the 2D incompressible Navier-Stokes-Equations is performed for different operating points using the POD-Galerkin technique. The arising nonlinear models are interpolated with a combination of a basis-interpolation on the Grassmann manifold and a subsequent Galerkin projection. These interpolatory models are not only validated, but also incorporated in a model predictive controller, whose performance is compared to two different controllers of the same type but without interpolatory models.

Nonlinear model reduction of the Navier-Stokes-Equations

In this paper three different methods for nonlinear dimensionality reduction are examined: Sammon mapping, Laplacian eigenmaps and autoencoder. These are extended such that they fit in the framework of snapshot based model reduction of flow problems and can be effectively combined with the Galerkin projection. All three methods are compared to the Proper Orthogonal Decomposition as standard benchmark of model reduction. For the Navier-Stokes-Equations especially the Laplacian Eigenmaps can increase the quality of the reduced order model significantly.

Optimal feedback control of the incompressible Navier-Stokes-Equations using reduced order models

A novel scheme for an optimal feedback-control of distributed parameter systems is proposed. Therefore, the optimal control problem for the two-dimensional incompressible Navier-Stokes-Equations with an actuation via boundary-conditions is set up. Afterwards the Navier-Stokes-Equations and their adjoint equations are solved numerically. A model reduction is performed for both solutions using the POD-Galerkin procedure. The optimal feedback control is computed online from the reduced order models in each time step without need of further optimization. Results are shown for closed-loop simulations with the Navier-Stokes-Equations.

Parameter space approach for large scale systems

The computational costs of the parameter space approach, which is used to calculate the stability boundaries for linear time-invariant systems (LTI), increase fast with the dimension of the investigated system. In this paper, the authors present a successive approximation of the stability boundaries for large scale systems. The approximation provides a fast and accurate estimation of the stability boundaries. Furthermore, the approximation converges to the stability boundaries of the large scale system and points, that are not stable, are never classified as stable during approximation. Thus, the new method enables the applicability of the parameter space approach to large scale systems by greatly reducing the computational costs.

Verteiltparametrische Modellierung und Regelung eines thermischen Festbettspeichers

Zusammenfassung Im Falle variabler Strompreise für solarthermische Kraftwerke ist es notwendig, die Beladungszustände der thermischen Speicher zur regeln. Hierfür wird eine auf den Solarturm Jülich angepasste verteiltparametrische Modellierung thermischer Festbettspeicher vorgenommen und diese an realen Messdaten validiert. Auf Basis dieser Modelle findet ein verteiltparametrischer Reglerentwurf statt, der den optimalen Stelleingriff durch die Lösung reduzierter Modelle des zugehörigen Optimierungsproblems bestimmt. Zur Durchführung der Modellreduktion werden zwei Methoden zur Bestimmung der Basisfunktionen untereinander verglichen. Ergebnisse der Modellreduktion werden an Messdaten validiert und der Regler in der Simulation mit dem nicht reduzierten Modell getestet.

Space-selective nonlinear reduced-order models for turbulent boundary layer drag reduction

Reduced-Order Models (ROMs) for 3D-turbulent flows based on Galerkin projection usually suffer from a large number of necessary basis functions to capture the relevant system dynamics. In this paper a new method to build a ROM for turbulent boundary layers is presented. Therefore the authors combine the Laplacian Eigenmaps as nonlinear dimensionality reduction method with the Galerkin projection. The neighborhood appearing in the Laplacian Eigenmaps is defined by a space-selective weighting approach, which moves the focus to the wall-near structures and thus enables to catch the control-relevant dynamics. As example turbulent boundary layer drag reduction by spanwise traveling waves is investigated using high-resolved CFD simulations.