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Brynjell-Rahkola, MattiasORCID iD iconorcid.org/0000-0001-9446-7477
Publications (8 of 8) Show all publications
Brynjell-Rahkola, M., Tuckerman, L. S., Schlatter, P. & Henningson, D. S. (2017). Computing Optimal Forcing Using Laplace Preconditioning. Communications in Computational Physics, 22(5), 1508-1532
Open this publication in new window or tab >>Computing Optimal Forcing Using Laplace Preconditioning
2017 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 22, no 5, p. 1508-1532Article in journal (Refereed) Published
Abstract [en]

For problems governed by a non-normal operator, the leading eigenvalue of the operator is of limited interest and a more relevant measure of the stability is obtained by considering the harmonic forcing causing the largest system response. Various methods for determining this so-called optimal forcing exist, but they all suffer from great computational expense and are hence not practical for large-scale problems. In the present paper a new method is presented, which is applicable to problems of arbitrary size. The method does not rely on timestepping, but on the solution of linear systems, in which the inverse Laplacian acts as a preconditioner. By formulating the search for the optimal forcing as an eigenvalue problem based on the resolvent operator, repeated system solves amount to power iterations, in which the dominant eigenvalue is seen to correspond to the energy amplification in a system for a given frequency, and the eigenfunction to the corresponding forcing function. Implementation of the method requires only minor modifications of an existing timestepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss the method, first, in the context of the linear Ginzburg-Landau equation and then, the two-dimensional lid-driven cavity flow governed by the Navier-Stokes equations. Most importantly, we demonstrate that for the lid-driven cavity, the optimal forcing can be computed using a factor of up to 500 times fewer operator evaluations than the standard method based on exponential timestepping.

Place, publisher, year, edition, pages
Cambridge University Press, 2017
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-214476 (URN)10.4208/cicp.OA-2016-0070 (DOI)000408436300012 ()2-s2.0-85046660943 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20171011

Available from: 2017-10-11 Created: 2017-10-11 Last updated: 2018-06-19Bibliographically approved
Brynjell-Rahkola, M., Shahriari, N., Schlatter, P., Hanifi, A. & Henningson, D. S. (2017). Stability and sensitivity of a cross-flow-dominated Falkner-Skan-Cooke boundary layer with discrete surface roughness. Journal of Fluid Mechanics, 826, 830-850
Open this publication in new window or tab >>Stability and sensitivity of a cross-flow-dominated Falkner-Skan-Cooke boundary layer with discrete surface roughness
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2017 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 826, p. 830-850Article in journal (Refereed) Published
Abstract [en]

With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner-Skan-Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the cross-flow (CF) vortices instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the epsilon-pseudospectrum, and the dependency on the domain is analysed through an impulse response, structural sensitivity analysis and an energy budget. It is shown that while the frequencies remain relatively unchanged, the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if sufficiently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than can be resolved using finite-precision arithmetic.

Place, publisher, year, edition, pages
Cambridge University Press, 2017
Keywords
absolute/convective instability, boundary layer stability, transition to turbulence
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-214322 (URN)10.1017/jfm.2017.466 (DOI)000407571200038 ()2-s2.0-85029412275 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20170914

Available from: 2017-09-14 Created: 2017-09-14 Last updated: 2017-11-23Bibliographically approved
Brynjell-Rahkola, M., Schlatter, P., Hanifi, A. & Henningson, D. S. (2015). Global Stability Analysis of a Roughness Wake in a Falkner-Skan-Cooke Boundary Layer. In: Procedia IUTAM: . Paper presented at 8th IUTAM-ABCM Symposium on Laminar Turbulent Transition, LTT 2014, 8 September - 12 September 2014 (pp. 192-200). Elsevier
Open this publication in new window or tab >>Global Stability Analysis of a Roughness Wake in a Falkner-Skan-Cooke Boundary Layer
2015 (English)In: Procedia IUTAM, Elsevier, 2015, p. 192-200Conference paper, Published paper (Refereed)
Abstract [en]

A global stability analysis of a Falkner-Skan-Cooke boundary layer with distributed three-dimensional surface roughness is per- formed using high-order direct numerical simulations. Computations have been performed for different sizes of the roughness elements, and a time-stepping method has been used to find the instability modes. The study shows that a critical roughness height beyond which a global instability is excited does exist. Furthermore, the origins of this instability is examined by means of an energy analysis, which reveals the production and dissipation terms responsible for the instability, as well as the region in space where the instability originates.

Place, publisher, year, edition, pages
Elsevier, 2015
Keywords
energy analysis, Falkner-Skan-Cooke (FSC), global instability, surface roughness, Atmospheric thermodynamics, Boundary layers, Energy management, Stability, Falkner-Skan, Falkner-Skan-Cooke boundary layers, Global stability analysis, Roughness elements, Three-dimensional surface, Time stepping method
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-176117 (URN)10.1016/j.piutam.2015.03.040 (DOI)000380499200023 ()2-s2.0-84940645851 (Scopus ID)
External cooperation:
Conference
8th IUTAM-ABCM Symposium on Laminar Turbulent Transition, LTT 2014, 8 September - 12 September 2014
Note

QC 20151127

Available from: 2015-11-27 Created: 2015-11-02 Last updated: 2016-08-30Bibliographically approved
Brynjell-Rahkola, M. (2015). Global stability analysis of three-dimensional boundary layer flows. (Licentiate dissertation). KTH Royal Institute of Technology
Open this publication in new window or tab >>Global stability analysis of three-dimensional boundary layer flows
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis considers the stability and transition of incompressible boundary layers. In particular, the Falkner–Skan–Cooke boundary layer subject to a cylindrical surface roughness, and the Blasius boundary layer with applied localized suction are investigated. These flows are of great importance within the aviation industry, feature complex transition scenarios, and are strongly three-dimensional in nature. Consequently, no assumptions regarding homogeneity in any of the spatial directions are possible, and the stability of the flow is governed by an extensive three-dimensional eigenvalue problem.

The stability of these flows is addressed by high-order direct numerical simulations using the spectral element method, in combination with a Krylov subspace projection method. Such techniques target the long-term behavior of the flow and can provide lower limits beyond which transition is unavoidable. The origin of the instabilities, as well as the mechanisms leading to transition in the aforementioned cases are studied and the findings are reported.

Additionally, a novel method for computing the optimal forcing of a dynamical system is developed. This type of analysis provides valuable information about the frequencies and structures that cause the largest energy amplification in the system. The method is based on the inverse power method, and is discussed in the context of the one-dimensional Ginzburg–Landau equation and a two-dimensional flow case governed by the Navier–Stokes equations.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2015. p. x, 30
Series
TRITA-MEK, ISSN 0348-467X ; 2015:07
Keywords
Hydrodynamic stability, transition to turbulence, global analysis, boundary layers, roughness, laminar flow control, Stokes/Laplace preconditioner, optimal forcing, crossflow vortices, Ginzburg-Landau, Falkner-Skan-Cooke, Blasius, lid-driven cavity
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-175353 (URN)978-91-7595-725-8 (ISBN)
Presentation
2015-10-30, D3, Lindstedtsvägen 5, KTH, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20151015

Available from: 2015-10-15 Created: 2015-10-12 Last updated: 2015-10-15Bibliographically approved
Brynjell-Rahkola, M., Barman, E., Peplinski, A., Hanifi, A. & Henningson, D. S. (2015). On the stability of flat plate boundary layers subject to localized suction.
Open this publication in new window or tab >>On the stability of flat plate boundary layers subject to localized suction
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2015 (English)Report (Other academic)
Abstract [en]

The stability of the Blasius boundary layer subject to localized suction is revisited. Using tools of global stability analysis, the leading direct and adjoint eigenpairs are determined, and novel insight into the sensitivity and receptivity of the flow is obtained. The problem is addressed through high-order spectral element simulations, which enables the inclusion of a suction pipe into the domain. Due to this, a detailed investigation of the connection between the pipe flow and the boundary layer flow is possible. For all cases investigated, the former always turns out to transition for a lower Reynolds number and suction rate than the latter, and the transition scenario is found to be due to a global instability originating inside a separation bubble at the pipe inlet. Identification of such regions, provides information that is valuable in further development of algorithms for laminar flow control.

Publisher
p. 20
National Category
Fluid Mechanics and Acoustics Aerospace Engineering
Research subject
Aerospace Engineering; Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-175350 (URN)
Note

QC 20151015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2017-08-15Bibliographically approved
Brynjell-Rahkola, M., Shahriari, N., Schlatter, P., Hanifi, A. & Henningson, D. S. (2015). Onset of global instability behind distributed surface roughness in a Falkner–Skan–Cooke boundary layer.
Open this publication in new window or tab >>Onset of global instability behind distributed surface roughness in a Falkner–Skan–Cooke boundary layer
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2015 (English)Report (Other academic)
Abstract [en]

A three-dimensional linear global stability analysis of a Falkner–Skan–Cooke boundary layer with distributed three-dimensional surface roughness is performed. The Falkner–Skan–Cooke boundary layer models the flow over swept airplane wings, and investigation of the critical roughness size for which a global instability emerges is thus of great importance within aeronautical applications. The study considers high-order direct numerical simulations and shows that such a critical roughness height exists for the Falkner–Skan–Cooke boundary layer. The roughness Reynolds number and roughness element aspect ratio for which this happens is comparable to the transition data reported in the literature for two-dimensional boundary layers. This demonstrates the importance of the local flow conditions in the vicinity of the roughness for triggering a global instability, although the resulting breakdown scenario is completely different from that of two-dimensional boundary layers. This breakdown scenario is studied in detail, and a global energy analysis is used to reveal the structures and mechanisms responsible for production and dissipation of perturbation energy.

Publisher
p. 33
National Category
Fluid Mechanics and Acoustics Aerospace Engineering
Research subject
Engineering Mechanics; Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-175347 (URN)
Note

QC 20151015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-15Bibliographically approved
Brynjell-Rahkola, M., Schlatter, P., Hanifi, A. & Henningson, D. S. (2013). Modal analysis of roughness-induced crossflow vortices in a Falkner-Skan-Cooke boundary layer. In: International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2013: . Paper presented at 8th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2013, 28 August 2013 through 30 August 2013. TSFP-8
Open this publication in new window or tab >>Modal analysis of roughness-induced crossflow vortices in a Falkner-Skan-Cooke boundary layer
2013 (English)In: International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2013, TSFP-8 , 2013Conference paper, Published paper (Refereed)
Abstract [en]

A three-dimensional global stability analysis using high-order direct numerical simulations is performed to investigate the effect of surface roughness with Reynolds number (based on roughness height) Rek above and below the critical value for transition, on the eigenmodes of a Falkner-Skan-Cooke boundary layer. The surface roughness is introduced with the immersed boundary method and the eigenvalues and eigenfunctions are solved using an iterative time-stepper method. The study reveals a global instability for the case with higher Reynolds number that causes the flow in the non-linear simulations to break down to turbulence shortly downstream of the roughness. Examination of the unstable linear global modes show that these are the same modes that are observed in experiments immediately before breakdown due to secondary instability, which emphasizes the importance of these modes in transition.

Place, publisher, year, edition, pages
TSFP-8, 2013
Keywords
Atmospheric thermodynamics, Boundary layers, Computational fluid dynamics, Eigenvalues and eigenfunctions, Iterative methods, Modal analysis, Reynolds equation, Reynolds number, Surface roughness, Turbulence, Turbulent flow, Vortex flow, Crossflow vortices, Falkner-Skan-Cooke boundary layers, Global instability, Global stability analysis, Immersed boundary methods, Nonlinear simulations, Roughness height, Secondary instability, Shear flow
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-222982 (URN)2-s2.0-85034229223 (Scopus ID)9780000000002 (ISBN)
Conference
8th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2013, 28 August 2013 through 30 August 2013
Note

QC 20180326

Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2018-03-26Bibliographically approved
Brynjell-Rahkola, M., Tuckerman, L., Schlatter, P. & Henningson, D. S.A method for computing optimal forcing of convectively unstable flows using Laplace preconditioning.
Open this publication in new window or tab >>A method for computing optimal forcing of convectively unstable flows using Laplace preconditioning
(English)Manuscript (preprint) (Other academic)
Abstract [en]

For problems governed by a non-normal operator, the leading eigenvalue of the operator is of limited interest and a more relevant measure of the stability is obtained by considering the harmonic forcing causing the largest system response. Various methods for determining this so-called optimal forcing exist, but they all suffer from great computational expense and are hence not practical for large-scale problems. In the present paper a new method is presented, which is applicable to problems of arbitrary size. The method does not rely on timestepping, but on the solution of linear systems, in which the inverse Laplacian acts as a preconditioner. By formulating the problem of finding the optimal forcing as an eigenvalue problem based on the resolvent operator, repeated system solves amount to power iterations, in which the dominant eigenvalue is seen to correspond to the energy amplification in a system for a given frequency, and the eigenfunction to the optimal forcing function. Implementation of the method requires only minor modifications of an existing time-stepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss it in the context of the linear Ginzburg-Landau equation.

National Category
Fluid Mechanics and Acoustics Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-175352 (URN)
Note

QS 2015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-15Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9446-7477

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