Günter Bärwolff

The manipulated transitional backward-facing step flow: an experimental and direct numerical simulation investigation

Abstract Results from a joint experimental and direct numerical simulation (DNS) investigation are presented for the flow over a backward-facing step manipulated by low-amplitude time-periodic (harmonic) blowing/suction excitation through a narrow slot at the edge of the step. For a Reynolds number of Reh=3000 (based on step height, h, and inflow velocity, Uo) and for laminar inflow, a 33% reduction of the mean recirculation length (in comparison to the non-manipulated reference case) could be obtained with a forcing amplitude of the order of one per cent of Uo. Based on the momentum thickness, θ, of the incoming laminar boundary layer (at the edge of the step), the corresponding optimum Strouhal number is Stθ=foptθ/Uo=0.012. From the experimental data it can be concluded that, in our flow case, the optimum frequency, fopt=50 Hz , was the most amplified frequency in the transition-to-turbulence process of the separated laminar shear layer. Detailed comparison of the experimental data with data from the numerical simulation shows that DNS and experimental data agree up to second-order statistics. The joint experimental and numerical investigations exhibit a complementary nature in the sense that, on the one hand, the main advantage of the experiment was the relative ease with which a wide range of forcing parameters could be tested and, on the other hand, DNS could provide spatio-temporal details of the flow which could not be so easily obtained in the experiment.

Direct Numerical Simulation of Transitional Backward-Facing Step Flow Manipulated by Oscillating Blowing/Suction

The backward-facing step flow with laminar inflow is of particular interest because of the fact that the shear layer separating from the edge of the step undergoes transition to turbulence (at appropriate Reynolds number). There are experimental investigations carried out on the controlled manipulation of this flow case (Re=3000) by the research group of Prof. H. Fernholz (TU Berlin, Germany). Related experimental work has been accomplished by Hasan (1992). For turbulent boundary layer inflow, and Re=5100, there are DNS results available from Le, Moin and Kim (1993), and LES results from Akselvoll and Moin (1993).

Boundary control of a Boussinesq equation for a crystal growth problem: aspects of numerical solution

Abstract An optimization problem for a Boussinesq equation system will be formulated. We are looking for a temperature profile or an appropriate velocity on the boundary of the considered region of the thermal coupled flow problem to induce a forced convection, which implies a velocity field close to a prescribed one. For such tracking type optimization problems with tracking type minimization functionals, the evaluation of the first-order necessary optimality condition leads to an optimality system consisting of the forward (primal) and adjoint (dual) mathematical model. Besides the derivation of the optimality system we discuss aspects of numerical solution, e.g. the spatial and time discretization and the iteration method for the solution of the resulting coupled nonlinear primal and dual problem in this paper. The optimization concept will be applied to a crystal growth flow and results of two-dimensional and three-dimensional model problems will be presented.

Numerical Modelling of Two- and Three- Dimensional External and Internal Unsteady Incompressible Flow Problems

In this paper we will discuss numerical methods that solve the full two- and three-dimensional time dependent Navier-Stokes equations and the possibility of coupling the heat conduction equation by the Boussinesq approximation. The solution methods will be applied i) to the investigation of a crystal melt flow caused by free and forced convection as an internal flow problem, and ii) to the full 3d flow around a circular cylinder as a base for LES and as an external flow problem. During the consideration of the two fluid dynamical problem classes the formulation of suitable conservative boundary conditions, especially in the case of ‘open’ boundaries will be discussed.

On the Convergence and Stability of a Pressure–Velocity Iteration of Chorin Type with Natural Boundary Conditions

Because of the implementation of numerical solution algorithms for the nonstationary Navier–Stokes equations of an incompressible fluid on massively parallel computers iterative methods are of special interest. A red–black pressure–velocity iteration that allows an efficient parallelization based on a domain decomposition [3] will be analyzed in this paper. We prove the equivalence of the pressure–velocity iteration (PUI) by Chorin/Hirt/Cook [1, 2] with a SOR iteration to solve a Poisson equation for the pressure. We show this on a 2D rectangle with some special outflow boundary conditions and Dirichlet data for the velocity elsewhere. This equivalence allows us to prove the convergence of that iteration scheme. We also discuss the stability of the occurring discrete Laplacian in discrete Sobolev spaces.

Modeling of Pedestrian Flows Using Hybrid Models of Euler Equations and Dynamical Systems

In the last years various systems have been developed for controlling, planning and predicting the traffic of persons and vehicles, in particular under security aspects. Going beyond pure counting and statistical models, approaches were found to be very adequate and accurate which are based on well‐known concepts originally developed in very different research areas, namely continuum mechanics and computer science. In the present paper, we outline a continuum mechanical approach for the description of pedestrain flow.

Application of Higher Order BDF Discretization of the Boussinesq Equation and the Heat Transport Equation

During the growth of crystals there were observed crystal defects under some conditions of the growth device. As a result of experiments a transition from the twodimensional flow regime of a crystal melt in axisymmetric zone melting devices to an unsteady threedimensional behavior of the velocity and temperature field was found. This behavior leads to striations as undesirable crystal defects. For the investigation of this symmetry break a mathematical model of the crystal melt was formulated for

Vektoranalysis und Kurvenintegrale

Wir bewegen uns im Schwerefeld der Erde. Im taglichen Leben haben wir durch die Nutzung elektrischer Gerate mit elektrischen Feldern und Magnetfeldern zu tun. Die Bewegung von Flussigkeiten und Gasen wird durch Geschwindigkeitsfelder beschrieben. In den genannten Fallen kann man die Felder durch Abbildungen aus dem ( {mathbb{R}}^{3} ) (dem dreidimensionalen physikalischen Raum, wo z.B. die Flussigkeit stromt) in den ( {mathbb{R}}^{3} ) (den Raum der Geschwindigkeitsvektoren) auffassen.

Flächenintegrale, Volumenintegrale und Integralsätze

Nachdem wir im Kapitel 2 Integrale von Funktionen einer Veranderlichen betrachtet haben und im Kapitel 7 uber Kurven integriert haben, ist ein Ziel des vorliegenden Kapitels die Berechnung von Integralen uber Flachen und Volumina. Dabei ist die Berechnung von Flacheninhalten und die Volumenberechnung mit eingeschlossen. Neben der konkreten Berechnung von Flachen- und Volumenintegralen wird im Folgenden mit den Integralsatzen von STOKES, GAUSS und GREEN die Verbindung zwischen Kurven- und Flachenintegralen bzw. Flachen- und Volumenintegralen hergestellt.

Analysis von Funktionen einer Veränderlichen

Hauptgegenstand der Analysis sind Funktionen und deren Eigenschaften. Funktionen werden in Physik, Mechanik und Ingenieurwissenschaften zur Beschreibung von Gesetzmasigkeiten verwendet. Mittels Differentiation von Funktionen bestimmt man in der Mechanik Geschwindigkeiten und Beschleunigungen, die Integration ermoglicht z.B. die Berechnung von Tragheitsmomenten und die Bestimmung von Kurvenlangen.