Shervin Bagheri

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KTH Mechanics
100 44 Stockholm
Sweden
shervin (at) mech.kth.se
+46(0)8-790 6770

visiting adress
Room: 2718
Osquars Backe 18
Stockholm

journal publications

 

A computational continuum model of poroelastic beds

Lacis, Zampogna, & Bagheri
Proc. R. Soc. A Vol. 473:20160932, 2017

[Abstract] [Open Access]

 

Abstract. Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to describe such configurations by deriving and validating a continuum model for the poroelastic bed and its interface with the above free fluid. We show that, using stress continuity condition and slip velocity condition at the interface, the effective model captures the effects of small changes in the microstructure anisotropy correctly and predicts the overall behaviour in a physically consistent and controllable manner. Moreover, we show that the performance of the effective model is accurate by validating with fully microscopic resolved simulations. The proposed computational tool can be used in investigations in a wide range of fields, including mechanical engineering, bio-engineering and geophysics.

 

Passive control of a falling sphere by elliptic-shaped appendages

Lacis, Olivieri, Mazzino & Bagheri
Phys. Rev. Fluids Vol. 2, 033901, 2017

[Abstract] [ArXiv]

 

Abstract. The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies -- being either as surface imperfections or appendages that serve a function -- are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, in a similar way that an inverted pendulum is unstable under gravity. Due to this instability, non-trivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow.

 

A framework for computing effective boundary conditions at the interface between free fluid and a porous medium

Lacis & Bagheri
J. Fluid Mech. Vol. 812, 2017

[Abstract] [Open Access] [Github]

 

Abstract. Interfacial boundary conditions determined from empirical or ad-hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical and accurate method to compute the effective boundary conditions at the interface between a porous surface and an overlying flow. Using multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (1967). The components of the tensors determining the effective slip velocity at the interface are obtained by solving a set of Stokes equations in a small computational domain near the interface containing both free flow and porous medium. Using the lid-driven cavity flow with a porous bed, we demonstrate that the derived boundary condition is accurate and robust by comparing an effective model to direct numerical simulations. Finally, we provide an open source code that solves the microscale problems and computes the velocity boundary condition without free parameters over any porous bed.

 

Energy efficiency and performance limitations of linear adaptive control for transition delay

Fabbiane, Bagheri & Henningson
J. Fluid Mech Vol 810, 2017

[Abstract] [Open Access]

 

Abstract. This manuscript demonstrates the first successful application of the delayed-x-LMS (dxLMS) control algorithm for TS-wave cancelation. Active wave cancelation of two-dimensional broadband Tollmien–Schlichting (TS) disturbances is performed with a single DBD plasma actuator. The experiments are conducted in flight on the pressure side of a laminar flow wing glove, mounted on a manned glider. The stability properties of the controller are investigated in detail with experimental flight data, DNS and stability anal-ysis of the boundary layer. Finally, a model-free approach for dxLMS operation is introduced to operate the control-ler as a ‘black-box’ system, which automatically adjusts the controller settings based on a group speed measurement of the disturbance wave packets. The modified dxLMS control-ler is operated without a model and is able to adapt to vary-ing conditions that may occur during flight in atmosphere.

 

In‑flight active wave cancelation with delayed‑x‑LMS control algorithm in a laminar boundary layer

Simon, Fabbiane, Nemitz, Bagheri, Henningson & Grundmann
Exp. Fluids Vol 57:160, 2016

[Abstract] [Online PDF]

 

Abstract. This manuscript demonstrates the first successful application of the delayed-x-LMS (dxLMS) control algorithm for TS-wave cancelation. Active wave cancelation of two-dimensional broadband Tollmien–Schlichting (TS) disturbances is performed with a single DBD plasma actuator. The experiments are conducted in flight on the pressure side of a laminar flow wing glove, mounted on a manned glider. The stability properties of the controller are investigated in detail with experimental flight data, DNS and stability anal-ysis of the boundary layer. Finally, a model-free approach for dxLMS operation is introduced to operate the control-ler as a ‘black-box’ system, which automatically adjusts the controller settings based on a group speed measurement of the disturbance wave packets. The modified dxLMS control-ler is operated without a model and is able to adapt to vary-ing conditions that may occur during flight in atmosphere.

 

Stabilizing effect of porosity on a flapping filament

Natali, Pralits, Mazzino & Bagheri
J. Fluids and Structures. Vol 61, 2016

[Abstract] [doi] [PDF]

 

Abstract. A new way of handling, simultaneously, porosity and bending resistance of a massive filament is proposed. Our strategy extends the previous methods where porosity was taken into account in the absence of bending resistance of the structure and overcomes related numerical issues. The new strategy has been exploited to investigate how porosity affects the stability of slender elastic objects exposed to a uniform stream. To understand under which conditions porosity becomes important, we propose a simple resonance mechanism between a properly defined characteristic porous time-scale and the standard characteristic hydrodynamic time-scale. The resonance condition results in a critical value for the porosity above which porosity is important for the resulting filament flapping regime, otherwise its role can be considered of little importance. Our estimation for the critical value of the porosity is in fairly good agreement with our DNS results. The computations also allow us to quantitatively establish the stabilizing role of porosity in the flapping regimes

 

A stable fluid-structure-interaction solver for low-density rigid bodies using the immersed boundary projection method

Lacis, Taira & Bagheri
J. Comp. Phys. vol. 305, 2015

[Abstract] [arXiv] [doi]

 

Abstract. Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Similar to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We show that our method achieves second-order accuracy in space and first-order in time (third-order for practical settings), only with a small additional computational cost to the original method. Our implicit coupling yields stable solution for density ratios as low as $10^{-4}$. We also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method.

 

Experimental study of a three dimensional cylinder-filament system

Brosse, Finmo, Lundell & Bagheri
Exp. Fluids 56:130 2015

[Abstract] [PDF (Pre-print)] [doi]

 

Abstract. This experimental study reports on the behavior of a filament attached to the rear of a three-dimensional cylinder. The axis of the cylinder is placed normal to a uniform incoming flow and the filament is free to move in the cylinder wake. The mean position of the filament is studied as a function of the filament length L. It is found that for long (L/D > 6.5, where D is the cylinder diameter) and short (L/D < 2) filaments the mean position of the filament tends to align with the incoming flow, whereas for intermediate filament lengths (2 < L/D < 6.5) the filament lies down on the cylinder and tends to align with the cylinder axis. The underlying mechanism of the bifurcations are discussed and related to buckling and inverted-pendulum-like instabilities.

 

On the role of adaptivity for robust laminar flow control

Fabbiane, Simon, Fischer, Grundmann, Bagheri & Henningson
J. Fluid Mech. vol. 767, pp. 094104, 2015

[Abstract] [PDF] [doi]

 

Abstract. In boundary-layer flows, one may reduce skin-friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien–Schlichting (TS) waves. In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for. However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based LQG controller in wind-tunnel experiments. In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

 

Passive appendages generate drift through symmetry breaking

Lācis, Brosse, Ingremeau, Mazzino, Lundell, Kellay & Bagheri
Nature Comm. vol. 5, pp. 5310, 2014

[Abstract] [doi (Open Access)]

 

Abstract.

Plants and animals use plumes, barbs, tails, feathers, hairs and fins to aid locomotion. Many of these appendages are not actively controlled, instead they have to interact passively with the surrounding fluid to generate motion. We use theory, experiments, and numerical simulations to show that an object with a protrusion in a separated flow drifts sideways by exploiting a symmetry-breaking instability similar to the instability of an inverted pendulum. Our model explains why the straight position of an appendage in a fluid flow is unstable and how it stabilizes either to the left or right of the incoming flow direction. It is plausible that organisms with appendages in a separated flow use this newly discovered mechanism for locomotion; examples include the drift of plumed seeds without wind and the passive reorientation of motile animals.

 

Effects of weak noise on oscillating flows: Linking quality factor, Floquet modes and Koopman spectrum

Bagheri
Phys. Fluids vol. 26, pp. 094104, 2014

[Abstract] [PDF] [doi]

 

Abstract. Many fluid flows, such as bluff body wakes, exhibit stable self-sustained oscillations for a wide range of parameters. Here we study the effect of weak noise on such flows. In the presence of noise, a flow with self-sustained oscillations is characterized not only by its period, but also by the so-called quality factor. This measure gives an estimation of the number of oscillations over which periodicity is maintained. Using a recent theory (Gaspard, J. Stat. Phys., 106, p.57-96, 2002), we report on two observations that provide insight into effects of noise on fluid flows with self-sustained oscillations. First, the quality factor is composed of the Floquet vectors of the linearized deterministic system and its size depends on the inner-product between first direct and adjoint Floquet vectors. Second, the quality factor can readily be observed from the spectrum of evolution operators. This has consequences for Koopman/Dynamic Mode Decomposition (DMD) analyzes, which have quickly become popular tools for extracting coherent structures associated with different frequencies from both (nonlinear) numerical and experimental flows. In particular, the presence of noise induces a damping on the eigenvalues, which increases quadratically with the frequency.

 

Adaptive and model-based control theory applied to convectively unstable flows

Fabbiane, Semeraro, Bagheri & Henningson
App. Mech. Rev. vol. 66, pp. 060801, 2014

[Abstract] [PDF] [doi]

 

Abstract. Research on active control for the delay of laminar-turbulent transition in boundary layers has made a significant progress in the last two decades, but the employed strategies have been many and dispersed. Using one framework, we review model-based techniques, such as linear-quadratic regulators, and model-free adaptive methods, such as least-mean square filters. The former are supported by a elegant and powerful theoretical basis, whereas the latter may provide a more practical approach in the presence of complex disturbance environments, that are difficult to model. We compare the meth- ods with a particular focus on efficiency, practicability and robustness to uncertainties. Each step is exemplified on the one-dimensional linearized Kuramoto-Sivashinsky equation, that shows many similarities with the initial linear stages of the transition process of the flow over a flat plate. Also, the source code for the examples are provided.

 

Centralised versus Decentralised Active Control of Boundary Layer Instabilities

Dadfar, Fabbiane, Bagheri & Henningson
Flow Turbulence Combust July, 2014

[Abstract] [PDF] [doi]

 

Abstract. We use linear control theory to construct an output feedback controller for the attenuation of small-amplitude three-dimensional Tollmien-Schlichting (TS) wavepackets in a flat-plate boundary layer. A three-dimensional viscous, incompressible flow developing on a zero-pressure gradient boundary layer in a low Reynolds number environment is analyzed using direct numerical simulations. In this configuration, we distribute evenly in the spanwise direction up to 72 localized objects near the wall (18 disturbances sources, 18 actuators, 18 estimation sensors and 18 objective sensors). In a fully three-dimensional configuration, the interconnection between inputs and outputs becomes quickly unfeasible when the number of actuators and sensors increases in the spanwise direction. The objective of this work is to understand how an efficient controller may be designed by connecting only a subset of the actuators to sensors, thereby reducing the complexity of the controller, without comprising the efficiency. If n and m are the number of sensor-actuator pairs for the whole system and for a single control unit, respectively, then in a decentralised strategy, the number of interconnections decreases mn compared to a centralized strategy, which has n2 interconnections. We find that using a semi-decentralized approach – where small control units consisting of 3 estimation sensors connected to 3 actuators are replicated 6 times along the spanwise direction – results only in a 11% reduction of control performance. We explain how “wide” in the spanwise direction a control unit should be for a sat- isfactory control performance. Moreover, the control unit should be designed to account for the perturbations that are coming from the lateral sides (crosstalk) of the estimation sensors. We have also found that the influence of crosstalk is not as essential as the spreading effect.

 

Transition delay in a boundary layer flow using active control

Semeraro, Bagheri, Brandt & Henningson
J. Fluid Mech. vol. 731, pp 288-311, 2013

[Abstract] [PDF] [doi]

 

Abstract. Active linear control is applied to delay the onset of laminar-turbulent transition in the boundary layer over a flat plate. The analysis is carried out by numerical simulations of the nonlinear, transitional regime. A three-dimensional, localised initial condition triggering Tollmien-Schlichting (TS) waves of finite amplitude is used to numerically simulate the transition to turbulence. Linear quadratic Gaussian (LQG) controllers based on reduced-order models of the linearised Navier-Stokes equations are designed, where the wall sensors the actuators are localised in space. An extensive parametric analysis is carried out in the nonlinear regime, for different disturbance amplitudes, by investigating the effects of the actuation on the flow due to different distributions of the localised actuators along the spanwise direction, different sizes of the actuator and the effort of the controllers. We identify the range of parameters where the controllers are effective and highlight the limits of the device for high amplitudes and strong control action. Despite the fully linear control approach, it is shown that the device is effective in delaying the onset of laminar-turbulent transition in the presence of packets characterised by amplitudes a ≈ 1% of the free-stream velocity at the actuator location. Up to these amplitudes, it is found that a proper choice of the actuators positively effects the perfor- mance of the controller. For a transitional case, a ≈ 0.20%, we show a transition delay of ∆Rex = 3.0 × 10^5.

 

Koopman-mode decomposition of the cylinder wake

Bagheri
J. Fluid Mech. vol. 726, pp 596-623, 2013

[Abstract] [PDF] [doi]

 

Abstract. The Koopman operator provides a powerful way of analyzing nonlinear flow dynamics using linear techniques. The operator defines how observables evolve in time along a non-linear flow trajectory. In this paper, we perform a Koopman analysis of the first Hopf bifurcation of the flow past a circular cylinder. First, we decompose the flow into a sequence of Koopman modes, where each mode evolves in time with one single frequency/growth rate and amplitude/phase, corresponding to the complex eigenvalues and eigenfunctions of the Koopman operator, respectively. The analytical construction of these modes shows how the amplitudes and phases of nonlinear global modes oscillating with the vortex shedding frequency or its harmonics evolve as the flow develops and later sustains self- excited oscillations. Second, we compute the dynamic modes using the dynamic mode decomposition (DMD) algorithm, which fits a linear combination of exponential terms to a sequence of snapshots spaced equally in time. It is shown that under certain conditions the DMD algorithm approximates Koopman modes, and hence provides a viable method to decompose the flow into saturated and transient oscillatory modes. Finally, the relevance of the analysis to frequency selection, global modes and shift modes is discussed.

 

Spontaneous symmetry breaking of a hinged flapping filament generates lift

Bagheri, Mazzino & Bottaro
Phys. Rev. Lett. 109, 154502, 2012

[Abstract] [PDF] [doi] [Animations] [Media Coverage]

 

Flapping filament

 

Abstract. Elastic filamentous structures found on swimming and flying organisms are versatile in function, rendering their precise contribution to locomotion difficult to assess. We show in this Letter that a single passive filament hinged on the rear of a bluff body placed in a stream can generate a net lift force without increasing the mean drag force on the body. This is a consequence of spontaneous symmetry breaking in the filament’s flapping dynamics. The phenomenon is related to a resonance between the frequency associated to the von-K ́arman vortex street developing behind the bluff body and the natural frequency of the free bending vibrations of the filament.

 

PhysOrg by Lisa Zyga (English)

Science Nordic by Ingrid Spilde (English)

Videnskab dk by Jeppe Wojcik (Danish)

NRK by Ingrid Spilde (Norwegian)

KTH by Peter Larsson (Swedish)

 

Computational hydrodynamic stability and flow control based on spectral analysis of linear operators

Bagheri
Arch. Comput. Methods Eng. Vol. 19 (3), 341-379I 2012

[Abstract][PDF][doi]

 

Abstract. This paper considers the analysis and control of fluid flows using tools from dynamical systems and control theory. The employed tools are derived from the spectral analysis of various linear operators associated with the Navier–Stokes equations. Spectral decomposition of the linearized Navier-Stokes operator, the Koopman operator, the spatial correlation operator and the Hankel operator provide a means to gain physical insight into the dynamics of complex flows and enables the construction of low-dimensional models suitable for control design. Since the discretization of the Navier-Stokes equations often leads to very large-scale dynamical systems, matrix-free and in some cases iter- ative techniques have to be employed to solve the eigenvalue problem. The common theme of the numerical algorithms is the use of direct numerical simulations. The theory and the algorithms are exemplified on flow over a flat plate and a jet in crossflow, as prototypes for the laminar-turbulent transition and three-dimensional vortex shedding.

 

Bifurcation and stability analysis of a jet in crossflow: Onset of global instability at a low velocity ratio

Ilak, Schlatter, Bagheri & Henningson
J. Fluid Mech. vol. 696, pp 94-121, 2012

[Abstract] [PDF] [doi] [JFM cover]

 

Abstract. We study direct numerical simulations (DNS) of a jet in crossflow at low values of the jet- to-crossflow velocity ratio R. We observe that, as the ratio R increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behavior, before finally becoming turbulent, as seen in the simulation of Bagheri et al. (2009b). The first bifurcation is found to occur at R = 0.675, and the observed shedding of hairpin vortices is linked to a possible existence of a local absolute instability connected to the region of reversed flow immediately downstream of the jet. We focus on this first bifurcation, and find that a global linear stability analysis predicts well the frequency and initial growth rate of the nonlinear DNS simulation at R = 0.675, and that good qualitative predictions about the dynamics can still be made at slightly higher values of R where multiple unstable eigenmodes are present. In addition, we compute the adjoint global eigenmodes, and find that the overlap of the direct and the adjoint eigenmode, also known as a ‘wavemaker’, provides additional evidence that the source of the first instability indeed lies in the shear layer just downstream of the jet.

 

Stability of a jet in crossflow

Ilak, Schlatter, Bagheri, Chevalier & Henningson
Phys. Fluids vol. 23 (091113), 2011

[Abstract][PDF] [doi]

 

Abstract. We have produced a fluid dynamics video with data from Direct Numerical Simulation (DNS) of a jet in crossflow at several low values of the velocity inflow ratio R. We show that, as the velocity ratio R increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi periodic behavior, before finally exhibiting asymmetric chaotic motion. We also perform a stability analysis just above the first bifurcation, where R is the bifurcation parameter. Using the overlap of the direct and the adjoint eigenmodes, we confirm that the first instability arises in the shear layer downstream of the jet orifice on the boundary of the backflow region just behind the jet.

 

Secondary threshold amplitudes for sinuous streak breakdown

Cossu, Brandt, Bagheri & Henningson
Phys. Fluids vol. 21(074103), 2011

[Abstract] [PDF][doi]

 

Abstract. The nonlinear stability of laminar sinuously bent streaks is studied for the plane Couette flow at Re = 500 in a nearly-minimal box and for the Blasius boundary layer at Reδ∗ = 700. The initial perturbations are nonlinearly saturated streamwise streaks of amplitude AU perturbed with sinuous perturbations of amplitude AW. The local boundary of the basin of attraction of the linearly stable laminar flow is computed by bisection in the AU − AW plane. When the streamwise uniform streaks (AW = 0) are locally unstable, typically for AU > 25−27% for the considered flows, sinuous perturbations of amplitude below AW ≈ 1−2% are sufficient to induce breakdown and counteract the streak viscous dissipation. The critical amplitude of the sinuous perturbations increases when the streamwise streak amplitude is decreased. With secondary perturbations amplitude AW ≈ 4%, breakdown is induced on stable streamwise streaks with AU ≈ 13%, following the secondary transient growth scenario first examined by Schoppa & Hussain (J. Fluid Mech. 453, 2002). A cross-over, where the critical amplitude of the sinuous perturbation become larger than the amplitude of streamwise streaks, is observed for streaks of small amplitude AU < 5 − 6%. In this case the transition is induced by an initial transient amplification of streamwise vortices, forced by the decaying sinuous mode. This is followed by the growth of the streaks and final breakdown. Our results show that the stability of streamwise streaks should always be assessed in terms of both the streak amplitude and the amplitude of spanwise velocity perturbations.

 

Feedback control of three-dimensional optimal disturbances using reduced-order models

Semeraro, Bagheri, Brandt & Henningson
J. Fluid Mech., vol. 677, 2011

[Abstract] [PDF][doi]

 

Abstract. The attenuation of three-dimensional wavepackets of streaks and Tollmien-Schlichting (TS) waves in a transitional boundary layer using feedback control is investigated numerically. Arrays of localized sensors and actuators (about 10–20) with compact spatial support are distributed near the rigid wall equidistantly along the spanwise direction and connected to a low-dimensional (r = 60) LQG controller. The control objective is to minimize the disturbance energy in a domain spanned by a number of proper orthogonal decomposition (POD) modes. The feedback controller is based on a reduced-order model of the linearized Navier-Stokes equations including the inputs and outputs, computed using a snapshot-based balanced truncation method. To account for the different temporal and spatial behaviour of the two main instabilities of boundary layer flows, we design two controllers. We demonstrate that the two controller reduce the energy growth of both TS wavepackets and streak-packets substantially and efficiently, using relatively few sensors and actuators. The robustness of the controller is investigated by varying the number of actuators and sensors, the Reynolds number and the pressure gradient. This work constitutes the first experimentally feasible simulation-based control design using localized sensing and acting devices in conjunction with linear control theory in a three-dimensional setting.

 

Transition delay using control theory

Bagheri & Henningson
Phil. Trans. R. Soc. A vol. 369(1940), 2011

[Abstract] [PDF][doi]

 

Abstract. This review gives an account of recent research efforts to use feedback control for the delay of laminar-turbulent transition in wall-bounded shear flows. The emphasis is on reducing the growth of small-amplitude disturbances in the boundary layer using numerical simulations and a linear control approach. Starting with the application of classical control theory to two-dimensional perturbations developing in spatially invariant flows, flow control based on control theory has progressed toward more realistic three-dimensional, spatially inhomogeneous flow configurations with localized sensing/actuation. The development of low-dimensional models of the Navier–Stokes equations has played a key role in this progress. Moreover, shortcomings and future challenges as well as recent experimental advances in this multidisciplinary field are discussed.

 

Self-sustained global oscillations in a jet in crossflow

Schlatter, Bagheri & Henningson
Theor. Comp. Fluid. Mech.,vol. 25, 2011

[Abstract] [PDF] [doi]

 

Abstract. A jet-in-crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. Various computational methods are employed: full non-linear direct numerical simulation (DNS), steady-state calculation, as well as a modal decomposition into linear global eigenmodes and proper orthogonal decomposition (POD) modes. The steady-state solution of the governing the Navier–Stokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the freestream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair. The steady state further shows the appearance of a vortex sheet shielding the jet from the incoming crossflow. This sheet develops further downstream into a secondary vortex pair, whereas the main counter-rotating vortex pair is directly related to the inflowing jet. From non-linear DNS, the characteristics of the various unsteady vortical structures (shear-layer vortices, upright vortices, and the wall-vortex system) are analyzed. The analysis of time frequencies at various locations in the flow and the modal decomposition into global eigenmodes and POD modes clearly shows the emergence of two dominant frequencies; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the wall region downstream of the jet orifice Both of these different frequencies could be related to different modes with species characteristics. The origin of these two frequencies could be traced back to the region of reversed flow downstream of the jet orifice This region is seen to oscillate in the wall-normal direction with the high frequency and in the spanwise direction with the low frequency. The high frequency oscillation is then amplified by the shear layer, generating the characteristic half-ring shear-layer vortices and the corresponding upright vortices. The slow spanwise oscillation, similar to vortex shedding around a fixed cylinder, is in turn responsible for low-frequency wiggling of the whole jet configuration.

 

Model reduction of the nonlinear complex Ginzburg-Landau equation

Ilak, Bagheri, Brandt, Rowley & Henningson
SIAM J. App. Dyn. Sys., vol. 9(4), 2010

[Abstract] [PDF][doi]

 

Abstract. Reduced-order models of the nonlinear Complex Ginzburg-Landau (CGL) equation are computed using a nonlinear generalization of balanced truncation. The method involves Galerkin projection of the nonlinear dynamics onto modes determined by balanced truncation of a linearized system, and is compared to a standard method using projection onto Proper Orthogonal Decomposition (POD) modes computed from snapshots of nonlinear simulations. It is found that the nonlinear reduced-order models obtained using modes from linear balanced truncation capture very well the transient dynamics of the CGL equation, and outperform POD models, i.e. a higher number of POD modes than linear balancing modes is typically necessary in order to capture the dynamics of the original system correctly. In addition, we find that the performance of POD models compares well to that of balanced truncation models when the degree of non-normality in the system, in this case determined by the streamwise extent of a disturbance amplification region, is lower. Our findings therefore indicate that the superior performance of balanced truncation compared to POD/Galerkin models in capturing the input/output dynamics of linear systems extends to the case of a nonlinear system, both for the case of significant transient growth, which represents a basic model of boundary layer instabilities, and for a limit cycle case that represents a basic model of vortex shedding past a cylinder.

 

Spectral analysis of nonlinear flows

Rowley, Mezic, Bagheri, Schlatter & Henningson
J. Fluid Mech., vol 641, 2009

[Abstract] [PDF] [doi]

 

Abstract. We present a technique for describing the global behavior of complex, nonlinear flows, by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a standard Arnoldi algorithm. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to Proper Orthogonal Decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.

 

Global stability of a jet in crossflow

Bagheri, Schlatter, Schmid & Henningson
J. Fluid Mech., vol 624, 2009

[Abstract] [PDF] [doi]

 

Abstract. A linear stability analysis shows that the jet in cross-flow is characterized by self-sustained global oscillations for a jet-to-cross-flow velocity ratio of three. A fully three-dimensional unstable steady-state solution and its associated global eigenmodes are computed by direct numerical simulations and iterative eigenvalue routines. The steady flow, obtained by means of selective frequency damping, consists mainly of a (steady) counter-rotating vortex pair (CVP) in the far field and horseshoe-shaped vortices close to the wall. High- frequency unstable global eigenmodes associated with shear layer instabilities on the CVP and low-frequency modes associated with shedding vortices in the wake of the jet are identified. Furthermore, different spanwise symmetries of the global modes are discussed. This work constitutes the first simulation-based global stability analysis of a fully three-dimensional base flow.

 

Matrix-free methods for the stability and control of boundary layers

Bagheri, Åkervik, Brandt & Henningson
AIAA J., vol 47, 2009

[Abstract] [PDF][doi]

 

Abstract. This paper presents matrix-free methods for the stability analysis and control design of high-dimensional systems arising from the discretized linearized Navier-Stokes equations. The methods are applied to the two-dimensional spatially developing Blasius boundary-layer. A critical step in the process of systematically investigating stability properties and designing feedback controllers is solving very large eigenvalue problems by storing only velocity fields at different times instead of large matrices. For stability analysis, where the entire dynamics of perturbations in space and time is of interest, iterative and adjoint-based optimization techniques are employed to compute the global eigenmodes and the optimal initial conditions. The latter are the initial conditions yielding the largest possible energy growth over a finite time interval. The leading global eigenmodes take the shape of Tollmien-Schlichting wavepackets located far downstream in streamwise direction, whereas the leading optimal disturbances are tilted structures located far upstream in the boundary layer. For control design on the other hand, the input-output behavior of the system is of interest and the snapshot-method is employed to compute balanced modes that correctly capture this behavior. The inputs are external disturbances and wall actuation and the outputs are sensors that extract wall shear stress. A low-dimensional model that capture the input-output behavior is constructed by projection onto balanced modes. The reduced-order model is then used to design a feedback control strategy such that the growth of disturbances are damped as they propagate downstream.

 

Input-output analysis and control design applied to a linear model of spatially developing flows

Bagheri, Hoepffner, Schmid & Henningson
App. Mech. Rev., vol 62(2), 2009

[Abstract] [PDF] [doi] [Matlab codes]

 

Abstract. This review presents a framework for the input-output analysis and control design for fluid dynamical systems using examples applied to the linear complex Ginzburg-Landau equation. Input-output analysis generalizes hydrodynamic stability analysis by considering a finite-time horizon over which energy amplification, driven by a specific input (actuator) and measured at a specific output (sensor), is observed. In the control design the loop is closed between the output and the input through a feedback gain. Methods from control theory are reviewed and applied to the Ginzburg-Landau equation in a manner that is readily generalized to fluid mechanics problems, thus giving a fluid mechanics audience an accessible introduction to the subject.

 

Input-output analysis, model reduction and control of the flat-plate boundary layer

Bagheri, Brandt & Henningson

J. Fluid. Mech, vol 620, 2009

[Abstract] [PDF][doi]

 

Abstract. The dynamics and control of two-dimensional disturbances in the spatially evolving boundary layer on a flat-plate are investigated from an input-output viewpoint. From the linearized Navier–Stokes equations with inputs (disturbances and actuators) and outputs (objective function and sensor) controllable, observable and balanced modes are extracted using the snapshot-method and a matrix-free time-stepper approach. A balanced reduced-order model is constructed and shown to capture the input-output behavior of linearized Navier–Stokes equations. This model is finally used to design a H2-feedback controller to suppress the growth of two-dimensional perturbations inside the boundary-layer.

 

The stabilizing effect of streaks on Tollmien-Schlichting waves and oblique waves: A parametric study

Bagheri &. Hanifi
Phys. of Fluids, vol 6, 2007

[Abstract] [PDF][doi]

 

Abstract: The stabilizing effect of finite amplitude streaks on the linear growth of unstable perturbations (TS and oblique waves) is numerically investigated by means of the nonlinear Parabolized Stability Equations. We have found that for stabilization of a TS-wave, there exists an ``optimal' spanwise spacing of the streaks. These streaks reach their maximum amplitudes close to the first neutral point of the TS-wave and induce the largest distortion of the mean flow in the unstable region of the TS-wave. For a such distribution, the required streak amplitude for complete stabilization of a given TS-wave is considerably lower than for $\beta=0.45$, which is the optimal for streak growth and used in previous studies. We have also observed a damping effect of streaks on the growth rate of oblique waves in Blasius boundary layer and for TS- waves in Falkner-Skan boundary layers.

 

proceedings

Reduced-order models for flow control: balanced modes and Koopman modes

Rowley, Mezic, Bagheri, Schlatter & Henningson
7th IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 2009

[Abstract] [PDF][doi]

 

Abstract. This paper addresses recent developments in model-reduction techniques applicable to fluid flows. The main goal is to obtain low-order models tractable enough to be used for analysis and design of feedback laws for flow control, while retaining the essential physics. We first give a brief overview of several model reduction techniques, including Proper Orthogonal Decomposition, balanced truncation, and the related Eigensystem Realization Algorithm, and discuss strengths and weaknesses of each approach. We then describe a new method for analyzing nonlinear flows based on spectral analysis of the Koopman operator, a linear operator defined for any nonlinear dynamical system. We show that, for an example of a jet in crossflow, the resulting Koopman modes decouple the dynamics at different time scales more effectively than POD modes, and capture the relevant frequencies more accurately than linear stability analysis.

 

Linear control of 3D disturbance on a flat-plate
Semeraro, Bagheri, Brandt & Henningson

7th IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 2009

[Abstract] [PDF][doi]

 

Abstract. Using a number of localized sensors and actuators, a feedback controller is designed in order to reduce the growth of three-dimensional disturbances in the flat- plate boundary layer. A reduced-order model of the input-output system (composed of the linearized Navier–Stokes equations including inputs and outputs) is computed by projection onto a number of balanced truncation modes. It is shown that a model with 50 degrees of freedom captures the input-output behavior of the high-dimensional system. The controller is based on a classical LQG scheme with a row of three sensors in the spanwise direction connected to a row of three actuators further downstream. The controller minimizes the perturbation energy in a spatial region defined by a number of (objective) functions.

 

Input-output analysis and control of spatially developing flows

Bagheri, Åkervik, Brandt & Henningson
AIAA paper 2008-4099, 5th AIAA Theoretical Fluid Mechanics Conference, Seattle, Washington, USA, June, 2008

[Abstract] [PDF]

 

Abstract. A framework for the input-output analysis, model reduction and control design of spatially developing shear flows is presented using the Blasius boundary-layer flow as an example. An input-output formulation of the governing equations yields a flexible formulation for treating stability problems and for developing control strategies that optimize given objectives. Model reduction plays an important role in this process since the dynamical systems that describe most flows are discretized partial differential equations with a very large number of degrees of freedom. Moreover, as system theoretical tools,such as controllability, observability and balancing has become computationally tractable for large-scale systems, a systematic approach to model reduction is presented.


theses

Analysis and control of transitional shear flows using global modes

Phd thesis, February, 2010

[Abstract] [PDF]

 

Abstract: In this thesis direct numerical simulations are used to investigate two phenomena in shear flows: laminar-turbulent transition over a flat plate and periodic vortex shedding induced by a jet in crossflow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is described and low-dimensional models suitable for control design are developed; this is done by decomposing the flow into global modes determined from spectral analysis of various linear operators associated with the Navier–Stokes equations.

 

Two distinct self-sustained global oscillations, associated with the shedding of vortices, are identified from direct numerical simulations of the jet in crossflow. The investigation is split into a linear stability analysis of the steady Flow and a nonlinear analysis of the unsteady Flow The eigenmodes of the Navier–Stokes equations, linearized about an unstable steady solution reveal the presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities. The unsteady nonlinear dynamics is decomposed into a sequence of Koopman modes, determined from the spectral analysis of the Koopman operator. These modes represent spatial structures with periodic behavior in time. A shear-layer mode and a wall mode are identified, corresponding to high-frequency and low-frequency self-sustained oscillations in the jet in crossflow, respectively.

 

The knowledge of global modes is also useful for transition control, where the objective is to reduce the growth of small-amplitude disturbances to delay the transition to turbulence. Using a particular basis of global modes, known as balanced modes, low-dimensional models that capture the behavior between actuator and sensor signals in a flat-plate boundary layer are constructed and used to design optimal feedback controllers. It is shown that by using control theory in combination with sensing/actuation in small, localized, regions near the rigid wall, the energy of disturbances may be reduced by an order of magnitude.

 

Stability analysis and control design of spatially developing flows

Licentiate thesis, May, 2008

[Abstract] [PDF]

 

Abstract. Methods in hydrodynamic stability, systems and control theory are applied to spatially developing flows, where the flow is not required to vary slowly in the streamwise direction. A substantial part of the thesis presents a theoretical framework for the stability analysis, input-output behavior, model reduction and control design for fluid dynamical systems using examples on the linear complex Ginzburg-Landau equation. The framework is then applied to high dimensional systems arising from the discretized Navier–Stokes equations. In particular, global stability analysis of the three-dimensional jet in cross flow and control design of two-dimensional disturbances in the flat-plate boundary layer are performed. Finally, a parametric study of the passive control of two-dimensional disturbances in a flat-plate boundary layer using streamwise streaks is presented.

 

Nonlinear interaction of optimal streaks and Tollmien-Schlichting waves

Master thesis, January, 2006

[Abstract] [PDF]

 

Abstract. The Parabolized Stability Equations have been modified to account for the algebraic growth of streaks. Using these equations, the nonlinear interaction of TS waves and steady streamwise streaks, and the stabilizing effect of the streaks on the mean flow has been verified with previous DNS results [6]. The spatial growth rates and energies of TS waves have been calculated in the presence of a set of streaks with maximum amplitudes between 0–25% of U∞. It was found that the stabilizing effect of the streak is considerably increased for higher amplitudes. This can be attributed to the fast increase of the mean flow excess close to the boundary wall with the streak amplitude. Furthermore, the amplification (N-factors) and energies of the TS waves was calculated in the presence of a set of streaks with varying spanwise wave numbers and fixed maximum streak amplitudes. In this case, it was found that the optimal stabilization effect is obtained for streaks with the location of the maximum amplitude close to Branch I of the TS wave. These streaks generate the largest total mean flow excess in the unstable streamwise region of the TS waves.

 

reports

Model reduction using the AISIAD method

Chandler, Mack & Bagheri
Internal report, 2008

[Abstract] [PDF]

 

Abstract. Many powerful linear systems and control theory tools have been out of the reach of the fluids community due to the complexity of the Navier-Stokes equations. Flow control based on systematic methods adopted from control theory is becoming a fairly mature field, with both computational and experimental advances. In this sense, model reduction plays an important role in developing effective control strategies for practical applications, since the dynamical systems which describe most flows are discretized partial differential equations with many degrees of freedom. Currently, balanced truncation represents the standard method of model reduction in systems and control theory which preserves the main input-output characteristics of the system. In this article we investigate an approximate balanced truncation by applying a modified version of the AISIAD algorithm [4]. The method is demonstrated on the Ginzburg-Landau equation and the linearized flow in a plane channel.

 

Research on the interaction between streamwise streaks and Tollmien--Schlichting waves at KTH

Bagheri, Fransson & Schlatter
Ercoftac Bulletin, vol 74, 2007

[Abstract] [PDF]

 

Abstract. This paper summarises the experimental and numerical investigations on how two different types of disturbances may, in a positive way, interact in a flat plate boundary-layer flow. The project, which mainly has been centered at KTH, has been performed in collaboration with colleagues from University of Bologna and LadHyX CNRS Ecole Polytechnique, during the last years. The main phenomena — the stabilising effect of streamwise boundary-layer streaks on Tollmien-Schlichting waves (and other exponential disturbances) — have been captured both in experiments [1, 2] and with different numerical approaches such as direct numerical simulations [3], parabolic stability equation calculations [5] and large-eddy simulations [6]. We will here briefly review the methods and the main results of these studies, and discuss how they correlate with each other. For related references outside KTH the interested reader is referred to the journal publications in the reference list.

 

Control of the Linearized Channel Flow via Adjoint-Based Iterative Optimization

Castano, Bagheri & Schulze
Ercoftac Bulletin, vol 73, 2007

[Abstract] [PDF]

 

Abstract. This project focuses on the adjoint-based optimal control of small disturbances in a channel flow. The linear evolution of these disturbances is governed by the Orr-Sommerfeld/Squire equations. The control is applied by means of a time dependent blowing and suction a(t) at the lower wall (y = −1), cf. fig. 1. The objective of the controller is to minimize the disturbance energy in the domain at some time t = T.