| 1. |
- Bagheri, Shervin, et al.
(författare)
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Input-output analysis and control design of spatially developing shear flows
- 2008
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Ingår i: 5th AIAA Theoretical Fluid Mechanics Conference. - 9781563479427
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Konferensbidrag (refereegranskat)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.
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| 2. |
- Bagheri, Shervin, et al.
(författare)
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Matrix-free methods for the stability and control of boundary layers
- 2009
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Ingår i: AIAA Journal. - : American Institute of Aeronautics and Astronautics (AIAA). - 0001-1452 .- 1533-385X. ; 47:5, s. 1057-1068
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Tidskriftsartikel (refereegranskat)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.
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| 3. |
- Chevalier, Mattias, et al.
(författare)
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Linear feedback control and estimation applied to instabilities in spatially developing boundary layers
- 2007
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Ingår i: Journal of Fluid Mechanics. - 0022-1120 .- 1469-7645. ; 588, s. 163-187
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Hogberg & Henningson (J. Fluid Mech. vol. 470, 2002, p. 151), where exact knowledge of the entire flow state was assumed for the control. We apply recent developments in stochastic models for the external sources of disturbances that allow the efficient use of several wall measurements for estimation of the flow evolution: the two components of the skin friction and the pressure fluctuation at the wall. Perturbations to base flow profiles of the family of Falkner-Skan-Cooke boundary layers are estimated by use of wall measurements. The estimated state is in turn fed back for control in order to reduce the kinetic energy of the perturbations. The control actuation is achieved by means of unsteady blowing and suction at the wall. Flow perturbations are generated in the upstream region in the computational box and propagate in the boundary layer. Measurements are extracted downstream over a thin strip, followed by a second thin strip where the actuation is performed. It is shown that flow disturbances can be efficiently estimated and controlled in spatially evolving boundary layers for a wide range of base flows and disturbances.
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| 4. |
- Chevalier, Mattias P., et al.
(författare)
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Feedback control in spatially growing boundary layers
- 2006
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Konferensbidrag (refereegranskat)abstract
- Linear feedback control has been applied to transitional boundary layer flows. Information from wall-mounted sensors is used to estimate the flow state. The estimated state is then used to compute the optimal feedback control which is applied as blowing and suction with zero net mass-flux through the wall. The performance of the controller is tested in direct numerical simulations of a spatially growing Falkner-Skan- Cooke boundary layer where an inflectional instability is triggered. The extension to spatial boundary layer flows is an important step towards real applications.
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| 5. |
- Henningson, Dan S., et al.
(författare)
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The use of global modes to understand transition and perform flow control
- 2008
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Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 20:3
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Tidskriftsartikel (refereegranskat)abstract
- The stability of nonparallel flows is considered using superposition of global modes. When perturbed by the worst case initial condition, these flows often exhibit a large transient growth associated with the development of wave packets. The global modes of the systems also provide a good starting point for the design of reduced order models used to control the growing disturbances. Three recent investigations are reviewed. The first example is the growth of a wave packet on a falling liquid sheet. The optimal perturbation analysis shows that the worst case initial condition is a localized disturbance that creates a propagating wave packet that hits the downstream end, regenerating a wave packet upstream through a global pressure pulse. Second, we consider two-dimensional disturbances in the Blasius boundary layer. It is found that a wave packet is optimally excited by an initial condition consisting of localized backward leaning Orr structures. Finally, the control of a globally unstable boundary-layer flow along a shallow cavity is considered. The disturbance propagation is associated with the development of a wave packet along the cavity shear layer, unstable to the Kelvin-Helmholtz mechanism, followed by a global cycle related to the two unstable global modes. Direct numerical simulations of this flow are coupled to a measurement feedback controller, which senses the wall shear stress at the downstream lip of the cavity and provides the actuation at the upstream lip. A reduced order model for the control is obtained by a projection on the least stable global eigenmodes. The linear-quadratic-Gaussian controller is run in parallel to the Navier-Stokes time integration and it is shown to damp out the global oscillations.
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| 6. |
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| 7. |
- Kierkegaard, Axel, et al.
(författare)
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Flow field eigenmode decompositions in aeroacoustics
- 2010
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Ingår i: Computers & Fluids. - : Elsevier BV. - 0045-7930 .- 1879-0747. ; 39:2, s. 338-344
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Tidskriftsartikel (refereegranskat)abstract
- In this paper an efficient method to study sound generation processes in low Mach number flows is presented. We apply the methodology on a two-dimensional flow over a cavity with smoothed corners. Instead of the full flow field obtained from, for example a Direct Numerical Simulation (DNS), we use a reduced model based on global modes to obtain the aeroacoustic sources. Global modes are eigenmodes to the Navier-Stokes equations, linearized about a steady base flow. In a reduced model the perturbations from a steady state are approximated by a linear combination of the eigenmodes. The time dependence is determined by the corresponding eigenvalues. Curie's equation is used to calculate the acoustic field, and by studying the source terms in Curie's equation, mechanisms for sources of sound are identified. Results of acoustic pressure in the far-field and source strengths for different superpositions of eigenmodes are presented.
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| 8. |
- Kierkegaard, Axel, et al.
(författare)
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Identifications of sources of sound in low Mach number flows by the use of flow field eigenmodes
- 2006
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Ingår i: 13th International Congress on Sound and Vibration 2006. - 9781627481502 ; , s. 2967-2974
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Konferensbidrag (refereegranskat)abstract
- We present a method to study sound generation processes in low Mach Number flows. Instead of the full flow field obtained from e.g a DNS, we consider a base flow together with a time-dependent perturbation ,where the perturbation satisfy the Navier-Stokes equations linearized around the base-flow. In a reduced model the perturbation is approximated by a linear combination of the cigenmodes of a corresponding eigenvalue problem. The behavior in time is determined by the corresponding eigenvalues. Curie's equation is used to calculate the acoustic field. By studying the source terms in Curie's equation, it is possible to identify mechanisms for sources of sound. This makes it possible to study how the different sources of sound depend on different structures of the flow field. We apply the methodology on a two- dimensional flow over a cavity with smoothed corners. Results of acoustic pressure in the far field and source strengths for different superpositions of eigenmodes are presented.
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| 9. |
- Monokrousos, Antonios, et al.
(författare)
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Global optimal disturbances in the Blasius flow using time-steppers
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The stability of the Blasius flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of optimisation methods at relatively high Reynolds numbers. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimisation problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearised Navier-Stokes equations. In both cases the evolution equations for the Lagrange multiplier are the adjoint Navier-Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. The optimal initial condition for spanwise wavelengths of the order of the boundary layer thickness are streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths it is the Orr mechanism combined with oblique wave packet propagation that dominates. It is found that the latter mechanism is dominant for the relatively high Reynolds number and the long computational domain considered here. The spatial structure of the optimal forcing is similar to the that of the optimal initial condition, and the response to forcing is also dominated by the Orr/oblique wave mechanism, however less so than in the former case. The lift-up mechanism is, as in the local approach using the Orr-Sommerfeld squire equations, most efficient at zero frequency and degrades slowly for increasing frequencies.
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| 10. |
- Monokrousos, Antonios, et al.
(författare)
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Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers
- 2010
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Ingår i: Journal of Fluid Mechanics. - 0022-1120 .- 1469-7645. ; 650, s. 181-214
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Tidskriftsartikel (refereegranskat)abstract
- The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier-Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien-Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed.
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