Dirk M. Luchtenburg

Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition

For the systematic development of feedback flow controllers, a numerical model that captures the dynamic behaviour of the flow field to be controlled is required. This poses a particular challenge for flow fields where the dynamic behaviour is nonlinear, and the governing equations cannot easily be solved in closed form. This has led to many versions of low-dimensional modelling techniques, which we extend in this work to represent better the impact of actuation on the flow. For the benchmark problem of a circular cylinder wake in the laminar regime, we introduce a novel extension to the proper orthogonal decomposition (POD) procedure that facilitates mode construction from transient data sets. We demonstrate the performance of this new decomposition by applying it to a data set from the development of the limit cycle oscillation of a circular cylinder wake simulation as well as an ensemble of transient forced simulation results. The modes obtained from this decomposition, which we refer to as the double POD (DPOD) method, correctly track the changes of the spatial modes both during the evolution of the limit cycle and when forcing is applied by transverse translation of the cylinder. The mode amplitudes, which are obtained by projecting the original data sets onto the truncated DPOD modes, can be used to construct a dynamic mathematical model of the wake that accurately predicts the wake flow dynamics within the lock-in region at low forcing amplitudes. This low-dimensional model, derived using nonlinear artificial neural network based system identification methods, is robust and accurate and can be used to simulate the dynamic behaviour of the wake flow. We demonstrate this ability not just for unforced and open-loop forced data, but also for a feedback-controlled simulation that leads to a 90 % reduction in lift fluctuations. This indicates the possibility of constructing accurate dynamic low-dimensional models for feedback control by using unforced and transient forced data only.

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier-Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

Spatio-Temporal Characterization of a Conical Swirler Flow Field Under Strong Forcing

In this study, a spatio-temporal characterization of forced and unforced flows of a conical swirler is done 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 Stf ≈ 0.92) and two higher frequencies (Stf ≈ 1.3 and 1.55) that are not harmonically related. Phase locked and phase averaged measurement are used as a first step to visualize the coherent flow structures. Secondly, 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 affects the mean-field profile most at the outlet, while the coherent velocity fluctuations are strongly influenced at both 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.Copyright

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 Modelling of Turbulent Jets for Noise Control

A reduced-ordermodelling (ROM) strategy is pursued to achieve a mechanistic understanding of jet flow mechanisms targeting jet noise control. Coherent flow structures of the jet are identified by the proper orthogonal decomposition (POD) and wavelet analysis. These techniques are applied to an LES data ensemble with velocity snapshots of a three-dimensional, incompressible jet at a Reynolds number of Re=3600. A low-dimensionalGalerkin model of a three-dimensional jet is extracted and calibrated to the physical dynamics. To obtain the desired mechanistic understanding of jet noise generation, the loudest flow structures are distilled by a goal-oriented generalisation of the POD approach we term ’most observable decomposition’ (MOD). Thus, a reduction of the number of dynamically most important degrees of freedom by one order of magnitude is achieved. Capability of the presented ROM strategy for jet noise control is demonstrated by suppression of loud flow structures.

Turbulence Control Based on Reduced-Order Models and Nonlinear Control Design

We present a closed-loop flow control strategy for experiments and simulations. This strategy is based on low-order Galerkin models and nonlinear control. One key enabler is a partitioning of the flow in low-, dominant- and high-frequency components, i.e. a base flow, coherent structures and stochastic fluctuations. Another enabler is a control design exploiting the nonlinearities distilled by the model. Examples are presented for the actuated flow around a high-lift configuration and the controlled bluff body wake.

Combination of Image Postprocessing Tools to Identify Coherent Structures of Premixed Flames

A combination of postprocessing tools of OH*-chemiluminescence snapshots is used to characterize the coherent structures of two types of premixed burners: a bluff body and an industrial swirl burner. Two methods are combined to extract the structures: a phase-averaging algorithm and the proper orthogonal decomposition. The first method is based on the estimation of the instantaneous phase of the snapshots relative to a (local) time-resolved signal. A phase-sorting-phase-averaging algorithm then reconstructs the evolution of the flame at a chosen frequency over one cycle. The proper orthogonal decomposition method is used as a filter to smoothen the snapshots. Both methods provide insight into the physical mechanisms of coherent structures in the two premixed flames under consideration. The snapshots of the bluff-body combustion exhibit a symmetric structure. This indicates that the von Karman vortex street in the cold flow is suppressed by the addition of heat in the shear layer. Three coexisting flame structures of the swirl burner in the combustion chamber could be identified: a natural helical structure of the burner and two axisymmetric modes. Increasing the amplitude of acoustic forcing at the natural flow frequency changes the helical structure to an axisymmetric one.

Large-scale dynamics in the flow around a finite cylinder with a ground plate

To date, physically meaningful representations of the nonstationarity in complex 3D flows with converged turbulent statistics are scarce and shed little light on the nonlinear processes in turbulent motion. This study attempts to address part of this deficit by concentrating on the kinematics of larger scales of motion. Two methods are utilized to describe the kinematics of large-scale unsteady motion in the flow around a wall-mounted finite circular cylinder at Reynolds number ReD = 200?000. The first, Proper Orthogonal Decomposition (POD), is a global method resulting in spatial modes defined over the whole domain and their corresponding temporal coefficients. The second, Coherent Structure Tracking (CST), belongs to a class of local methods that extracts connected domains in the flow data. Modes specific for distinct harmonics are extracted by temporal harmonic filtering. Based on time coefficients of the dominant mode pairs provided by POD or harmonic filtering, phase-averaging has been performed. A scalar-field version of CST is proposed, yielding an intuitively more accessible description of the flow. The extent to which POD and CST are complementary is discussed, as well as the extent to which they partially overlap. The combination of POD, filtering, phase-averaging and CST allowed for identification and quantification of important flow patterns in a complex turbulent flow field.

Numerical Simulation and Analysis of the Flow Around a Wall-Mounted Finite Cylinder

Numerical studies employing LES and DES are presented for the flow around a wall-mounted finite cylinder at a Reynolds number of Re D = 200,000. Very good agreement between the numerical and experimental results is achieved for the steady mean motion, turbulence quantities and the motion of large coherent structures. The synergy between the joint studies within the research unit “Imaging Measurement Methods for Flow Analysis” and the application of POD, particle and structure tracking algorithms allow for a more complete description of the unsteady flow investigated. New insight to the coherent turbulent motion is obtained.

Modeling the Fuel/Air Mixing to Control the Pressure Pulsations and NO x Emissions in a Lean Premixed Combustor

This paper presents an overviewof the methodology developed to predict, control and optimize the NOx emissions and stability of lean premixed combustors. Investigations are performed firstly in cold flow and are validated with reacting flow measurements. A new cold flow mixing model describes the relevant characteristics of the fuel/airmixing, i.e. themixing quality and convective time delays, for different operating points of the system.Measurements in the combustor are performed to correct the flame position effect or calibrate the cold flowresults.The model is for the first time implemented in an extremum seeking controller to optimize the emissions and pressure pulsations of the combustor by adjusting the fuel mixing profile. A further increase of the fuel/air mixing, necessary for further NOx reductions, with pulsating fuel injection, is demonstrated. At the end, the developed adaptive control strategies demonstrate opportunities for future efficiency increases in industrial combustors.