Oliver Lehmann

Mean field representation of the natural and actuated cylinder wake

The necessity to include dynamic mean field representations in low order Galerkin models, and the role and form of such representations, are explored along natural and forced transients of the cylinder wake flow. The shift mode was introduced by Noack et al. [J. Fluid Mech. 497, 335 (2003)] as a least-order Galerkin representation of mean flow variations. The need to include the shift mode was argued in that paper in terms of the dynamic properties of a low order Galerkin model. The present study revisits and elucidates this issue with a direct focus on the Navier–Stokes equations (NSEs) and on the bilateral coupling between variations in the fluctuation growth rate and mean flow variations in the NSE. A detailed transient modal energy flow analysis is introduced as a new tool to quantitatively demonstrate the indispensable role of mean field variations, as well as the capacity of the shift mode to represent that contribution. Four variants of local and global shift mode derivations are examined and compa...

Spatiotemporal Characterization of a Conical Swirler Flow Field Under Strong Forcing

In this study, a spatiotemporal characterization of forced and unforced flows of a conical swirler is performed based on particle image velocimetry (PIV) and laser Doppler anemometry (LDA). The measurements are performed at a Reynolds number of 33,000 and a swirl number of 0.71. Axisymmetric forcing is applied to approximate the effects of thermoacoustic instabilities on the flow field at the burner inlet and outlet. The actuation frequencies are set at the natural flow frequency (Strouhal number St f ≈0.92) and two higher frequencies (St f ≈1.3 and 1.55) that are not harmonically related to the natural frequency. Phase-averaged measurement are used as a first step to visualize the coherent flow structures. Second, proper orthogonal decomposition (POD) is applied to the PIV data to characterize the effect of the actuation on the fluctuating flow. Measurements indicate a typical natural flow instability of helical nature in the unforced case. The associated induced pressure and flow oscillations travel upstream to the swirler inlet where generally fuel is injected. This observation is of critical importance with respect to the stability of the combustion. Harmonic actuation at different frequencies and amplitudes does not affect the mean velocity profile at the outlet, while the coherent velocity fluctuations are strongly influenced at both the inlet and outlet. On one hand, the dominant helical mode is replaced by an axisymmetric vortex ring if the flow is forced at the natural flow frequency. On the other hand, the natural flow frequency prevails at the outlet under forcing at higher frequencies and POD analysis indicates that the helical structure is still present. The presented results give new insight into the flow dynamics of a swirling flow burner under strong forcing.

Reduced-order models for closed-loop wake control

We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and stochastic fluctuations. Secondly, their range of validity is restricted by ignoring mode deformations during natural and actuated transients. We address the first challenge by including shift mode(s) and nonlinear turbulence models. The resulting robust least-order model lives on an inertial manifold, which links slow variations in the base flow and coherent and stochastic fluctuation amplitudes. The second challenge, the deformation of coherent structures, is addressed by parameter-dependent modes, allowing smooth transitions between operating conditions. Now, the Galerkin model lives on a refined manifold incorporating mode deformations. Control design is a simple corollary of the distilled model structure. We illustrate the modelling path for actuated wake flows.

Tuned POD Galerkin models for transient feedback regulation of the cylinder wake

Proper orthogonal decomposition (POD) Galerkin models are typically obtained from a single reference, such as an attractor. The POD model provides a very efficient representation of the reference but is often incapable to handle transient dynamics and other changes in flow conditions. These shortcomings are detrimental in feedback flow control applications. A novel concept of tuned Galerkin models is suggested, by which the global model interpolates a succession of similar-structure local models. The tuned model covers a controlled transient manifold, compensating for the gradual deformation of dominant flow structures, along such transients. The model is an enabler for both improved tracking performance, as well as for optimized control hardware placement, taking into account the entire dynamic range of interest. These concepts are demonstrated in the benchmark of stabilization of the wake flow behind a circular cylinder.

Shift Modes and Transient Dynamics in Low Order, Design Oriented Galerkin Models

The shift mode has been introduced in Ref. [1] as a critical enabler for transient representation of very low dimensional empirical Galerkin models in fluid flow systems. As introduced and used in a number of flow control studies since, the shift mode is a simple representation of a missing dynamic mean-field correction, pointing from an unstable steady solution to a stable natural attractor. In this study we explore alternative local definitions of the shift mode, their interdependence and consistency. In particular, we investigate short term proper orthogonal decomposition of natural and controlled transients. In addition, the mean-field directions are estimated from short term analysis of simulations, and from the corresponding Reynolds stress equation.

From the Lab to the Real World: Re-identification in an Airport Camera Network

Over the past ten years, human re-identification has received increased attention from the computer vision research community. However, for the most part, these research papers are divorced from the context of how such algorithms would be used in a real-world system. This paper describes the unique opportunity our group of academic researchers had to design and deploy a human re-identification system in a demanding real-world environment: a busy airport. The system had to be designed from the ground up, including robust modules for real-time human detection and tracking, a distributed, low-latency software architecture, and a front-end user interface designed for a specific scenario. None of these issues are typically addressed in re-identification research papers, but all are critical to an effective system that end users would actually be willing to adopt. We detail the challenges of the real-world airport environment, the computer vision algorithms underlying our human detection and re-identification algorithms, our robust software architecture, and the ground-truthing system required to provide the training and validation data for the algorithms. Our initial results show that despite the challenges and constraints of the airport environment, the proposed system achieves very good performance while operating in real time.

Galerkin Models Enhancements for Flow Control

Low order Galerkin models were originally introduced as an effective tool for stability analysis of fixed points and, later, of attractors, in nonlinear distributed systems. An evolving interest in their use as low complexity dynamical models, goes well beyond that original intent. It exposes often severe weaknesses of low order Galerkin models as dynamic predictors and has motivated efforts, spanning nearly three decades, to alleviate these shortcomings. Transients across natural and enforced variations in the operating point, unsteady inflow, boundary actuation and both aeroelastic and actuated boundary motion, are hallmarks of current and envisioned needs in feedback flow control applications, bringing these shortcomings to even higher prominence. Building on the discussion in our previous chapters, we shall now review changes in the Galerkin paradigm that aim to create a mathematically and physically consistent modeling framework, that remove what are otherwise intractable roadblocks. We shall then highlight some guiding design principles that are especially important in the context of these models. We shall continue to use the simple example of wake flow instabilities to illustrate the various issues, ideas and methods that will be discussed in this chapter.

Low Order Galerkin Models for the Actuated Flow Around 2-D Airfoils

The objective of this paper is twofold. One is to explore extensions of the generalized mean-field empirical Galerkin model, previously developed for wake instabilities 1 to singularly actuated 2D airfoils, including a high lift configuration and a single airfoil at a high angle of attack. We present a minimum order mean field model, explore the role of the mean field as a mediator between actuation and dominant instabilities, and illustrate the need for richer mode-sets, as operating conditions change and during sharp transients. The second objective is to develop computational tools for effective extraction of empirical modes, for such models. We present two such tools. The first is the utilization of temporal harmonic analysis to separate the empirical reference into sub-reference, each representing a single (time varying) coherent flow structures’ category. The second is a two-step approximate POD procedure, intended to drastically reduce the computational cost of POD approximations of very long / rich reference ensembles. It is based on a first step reference partitioning and a second step global analysis, with an a priori guaranteed resolution level.