Andreas Dillmann

Model-based Control of Vortex Shedding Using Low-dimensional Galerkin Models

A model-based flow control strategy is proposed for the suppression of vortex shedding behind a circular cylinder. The control design is based on a hierarchy of low-dimensional Galerkin models of the cylinder wake. These models are constructed from a Karhunen-Loeve decomposition of a simulation without actuation. The key enablers are an additional physical mode in the Karhunen-Loeve approximation and an energy-based control which respects the regime of model validity. The developed control strategy is successfully tested in direct numerical simulations. Copyright  2003 by J. Gerhard, M. Pastoor, R. King, B.R. Noack, A. Dillmann, M. Morzynski and G. Tadmor. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. ∗Research engineer. Corresponding author: phone: ++49-30-314.79574, x24100; fax: x21129; e-mail: johannes.gerhard@tu-berlin.de †Research engineer ‡Professor §Research engineer ¶Professor ‖Professor ∗∗Associate Professor

Model-based Coherent-structure Control of Turbulent Shear Flows Using Low-dimensional Vortex Models

In this study, a flow control strategy is presented for manipulating coherent shear-flow structures. As a benchmark problem, the transitional flow around a backward-facing step with local acoustic actuation at the upper edge is chosen. The strategy is based on a hierarchy of low-dimensional vortex models and targets the use of control-theory methods for control design. The hierarchy ranges from an one-vortex model which describes the vortex roll-up and shedding to a vortex-blob model which resolves the formation of Kelvin-Helmholtz vortices and the dynamics of the recirculation zone with a few hundred vortices. The higher-dimensional variants predict well the frequency-dependent reduction of the recirculation zone with harmonic actuation. The Lagrangian vortex models incorporate a continuous production, Copyright  2003 by M. Pastoor, R. King, B.R. Noack, A. Dillmann, and G. Tadmor. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Research engineer. Corresponding author: phone: ++49-30-314.79574, x24100; fax: x21129; e-mail: mark.pastoor@tu-berlin.de Professor Research engineer Professor Associate Professor merging, and annihilation of vortices, but this hybrid nature excludes the use of many control-theory methods. Hence, oneand two-dimensional Eulerian vortex models employing a remeshing technique are proposed. The dynamics of these Eulerian variants define a continuous evolution in a phase space with fixed dimension and are hence better suited for control-theory and dynamics-systems approaches.

Coherent Structures in a Transitional Flow around a Backward‐Facing Step

The transitional flow around a backward-facing step visualized using illuminated streamlines of a snapshot ~Fig. 1!. The flow separates at the corner of the step. The resu shear layer rolls up in two Kelvin–Helmholtz vortices. In th downstream direction, the streamlines form bundles due secondary streamwise vorticity. The fluid experiences a sm backward flow in the upstream region below the shear la The flow field is obtained from a large-eddy simulation Kaltenbach and Janke at a Reynolds number of Re H53000 based on oncoming velocity and on step height. The co sponding boundary conditions are described in Ref. 1. The streamlines are illuminated in order to enhance

Reduction of Flap Side-Edge Noise: Passive and Active Flow Control

Microphone array and particle image velocimetry measurements have been performed to investigate the potential of passive and active flow control methods for flap noise reduction. The extended wing flap of the swept constant chord half-model was equipped with either a blowing facility as an active flow control device or with other flap side-edge modifications such as wing tip fences, microtabs and winglets. The flap side edge noise is reduced with the blowing configuration between 2 kHz and 5 kHz. The maximum noise reduction of 15:9 dB is achieved at 2:9 kHz. Varying the diameter of the blowing orifices shows that the noise reduction is governed by the momentum rather than the flow rate of the blowing. The winglets and the suction side fence are most effective in reducing the flap side-edge noise. The reduced level with these configurations is even lower than with the active blowing. The vortex generators and the pressure side fence turn out to be the least effective flow control devices. PIV-measurements at an isolated unswept flap model show that the main vortex on the suction side exhibits a very inhomogeneous vorticity distribution which can be attributed to the unstable shear layer that separates at the lower corner of the flap side-edge and to the negative vorticity production on the suction surface. With blowing the vorticity of the shear layer is concentrated in several small vortices. The distance between those vortices and the solid surface increases with higher blowing momentum and because of this the negative vorticity production due to recirculation is disappears. These distinct modifications of the side-edge flow field explain the noise reduction shown in the aeroacoustic measurements.

Control, observation and energy regulation of wake flow instabilities

A three-dimensional Galerkin model is used in feedback design to regulate the perturbation kinetic energy in the flow around a cylinder. The objective may vary from stabilization in order to reduce drag to mixing enhancement. The Landau model [H.K. Khalil, 2002] includes an oscillatory state pair and a shift mode, exchanging energy with the mean flow. Given the models simplicity, it is essential to maintain closed-loop dynamics close to the systems natural dynamic range which is represented by an invariant manifold and a natural frequency, adding a design constraint addressed in this note.

REDUCTION OF FLAP SIDE EDGE NOISE BY ACTIVE FLOW CONTROL

One dominant airframe noise source is situated at the side edge of the extended wing flap. The objective of the present study is to reduce this noise by blowing air into the flap side-edge vortex to displace or destroy the vortical structure and thus reduce the emission of sound. PIV measurements without blowing yield a rather complicated unsteady vortical structure at the flap side-edge which confirms the assumption of a noise source. This is verified by microphone array measurements. They show that the flap side-edge noise, besides other noise sources, is present over a broad frequency range. The flight parameters such as angle of incidence and slat and flap angles, however, determine which noise source is dominant. PIV measurements with blowing show that the vortical structure can be almost completely dispersed and that the maximum vorticity in the vortex core is reduced. Consequently, a reduction of the flap side‐edge noise can be seen in the microphone array measurement. In addition, the sound pressure level in the acoustic far field is reduced by 3 to 4 dB above 1.25 kHz.

Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 2. Free jet flow

By extending the methods of Part 1, the general problem of steady cylindrical supersonic free jet flow is treated in a similar manner to the flow in quasi-cylindrical ducts. It is shown that the presence of a finite pressure jump at the nozzle lip gives rise to a periodic singularity pattern in the flow field. Basic examples of free jet flows are discussed, and for the case of a nearly ideally expanded axisymmetric jet, theoretical Mach—Zehnder interferograms are calculated by analytical integration of the density field. Excellent agreement with experiment proves the validity of linear theory even close to the singularities and far downstream of the nozzle orifice. Furthermore, it is shown that Packs formula for the wavelength of the shock cell structure is inconsistent; the correct formula is derived and excellent agreement with Emdens empirical fit is found.

Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 1. Flow in ducts

Based on linear potential theory, the general three-dimensional problem of steady supersonic flow inside quasi-cylindrical ducts is formulated as an initial-boundary-value problem for the wave equation, whose general solution arises as an infinite double series of the Fourier-Bessel type. For a broad class of solutions including the general axisymmetric case, it is shown that the presence of a discontinuity in wall slope leads to a periodic singularity pattern associated with non-uniform convergence of the corresponding series solutions, which thus are unsuitable for direct numerical computation. This practical difficulty is overcome by extending a classical analytical method, viz. Kummers series transformation

A Simplified Model of the Wave Generation Due to Train-Tunnel Entry

The compression wave generated when a high-speed train enters a tunnel at Mach numbers smaller than 0.4 can be described in good approximation by a linear theory of an inviscid fluid. The wave equation for the acoustic potential becomes the governing equation. It is solved by a three dimensional boundary element method in time domain which forces a vanishing normal component of the velocity at the tunnel wall. It is assumed that the elements are compact in time. This leads to a linear equation in which a special matrix-vector multiplication has to be evaluated for every time-step. The aim is to create a fast method which sets as few constraints on the geometry as possible but nevertheless gives an accurate description of the wave propagation. In a first step the elements are assumed to be rectangles and an infinitely thin cylindric tube of finite length is taken as the geometry of the tunnel. The train is modeled by a single moving mass source of monopole type. It defines a semi-infinite body whose shape slightly changes when entering the tunnel. The results of this simple model along with the comparison with analytical solutions and experimental data are shown and discussed.

Aerodynamic Loads Induced by Passing Trains on Track Side Objects

The aerodynamic loads on a sphere induced by the head pressure pulse of a passing train are calculated using potential flow theory. The results are compared with experimental data which were measured in a moving model rig. The loads were calculated using two different theoretical approaches. They show good agreement with the experimentally obtained results even though in the theoretical model the geometry of the train and the embankment is simplified.