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Spectral-element simulations of turbulent wall-bounded flows including transition and separation
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The spectral-element method (SEM) is used to study wall-bounded turbulent flowsin moderately complex geometries. The first part of the thesis is devoted to simulations of canonical flow cases, such as temporal K-type transitionand turbulent channel flow, to investigate general resolution requirements and computational efficiency of the numerical code nek5000. Large-eddy simulation (LES) is further performed of a plane asymmetric diffuser flow with an opening angle of 8.5 degrees, featuring turbulent flow separation. Good agreement with numerical studies of Herbst (2007) is obtained, and it is concluded that the use of a high-order method is advantageous for flows featuring pressure-induced separation. Moreover, it is shown, both a priori on simpler model problems and a posteriori using the full Navier--Stokes equations, that the numerical instability associated with SEM at high Reynolds numbers is cured either by employing over-integration (dealiasing) or a filter-based stabilisation, thus rendering simulations of moderate to high Reynolds number flows possible.

The second part of the thesis is devoted to the first direct numerical simulation (DNS) of a truly three-dimensional, turbulent and separated diffuser flow at Re = 10 000 (based on bulk velocity and inflow-duct height), experimentally investigated by Cherry et al. (2008). The massively parallel capabilities of the spectral-element method are exploited by running the simulations on up to 32 768 processors. Very good agreement with experimental mean flow data is obtained and it is thus shown that well-resolved simulations of complex turbulent flows with high accuracy are possible at realistic Reynolds numberseven in complicated geometries. An explanation for the discovered asymmetry of the mean separated flow is provided and itis demonstrated that a large-scale quasi-periodic motion is present in the diffuser.

In addition, a new diagnostic measure, based on the maximum vorticity stretching component in every spatial point, is designed and tested in a number of turbulent and transitional flows. Finally, Koopman mode decomposition is performed of a minimal channel flow and compared to classical proper orthogonal decomposition (POD).

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. , ix, 81 p.
Series
Trita-MEK, ISSN 0348-467X ; 2011:15
Keyword [en]
spectral-element method, direct numerical simulation (DNS), large-eddy simulation (LES), turbulence, transition, over-integration, three-dimensional separation, massively parallel simulations, proper orthogonal decomposition (POD), Koopman modes, vorticity stretching, coherence
National Category
Engineering and Technology
Research subject
SRA - E-Science (SeRC)
Identifiers
URN: urn:nbn:se:kth:diva-50294ISBN: 978-91-7501-178-3 (print)OAI: oai:DiVA.org:kth-50294DiVA: diva2:461524
Public defence
2011-12-16, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note
QC 20111206Available from: 2011-12-06 Created: 2011-12-04 Last updated: 2012-05-24Bibliographically approved
List of papers
1. The Spectral-Element and Pseudo-Spectral Methods: A Comparative Study
Open this publication in new window or tab >>The Spectral-Element and Pseudo-Spectral Methods: A Comparative Study
2011 (English)In: Spectral and High Order Methods for Partial Differential Equations: Selected papers from the ICOSAHOM '09 conference, June 22-26, Trondheim, Norway / [ed] Jan S. Hesthaven; Einar M. Rønquist, Springer , 2011, 1, 459-467 p.Chapter in book (Other academic)
Abstract [en]

Turbulent and transitional channel flow simulations have been performed in order to assess the differences concerning speed and accuracy in the pseudo-spectral code simson and the spectral-element code nek5000. The results indicate that the pseudo-spectral code is 4–6 times faster than the spectral-element code in fully turbulent channel flow simulations, and up to 10–20 times faster when taking into account the more severe CFL restriction in the spectral-element code. No particular difference concerning accuracy could be noticed either in the turbulent nor the transitional cases, except for the pressure fluctuations at the wall which converge slower for the spectral-element code.

Place, publisher, year, edition, pages
Springer, 2011 Edition: 1
Series
Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 76
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-25929 (URN)10.1007/978-3-642-15337-2_44 (DOI)2-s2.0-78651552857 (Scopus ID)978-3-642-15336-5 (ISBN)
Note
QC 20101105Available from: 2010-11-05 Created: 2010-11-05 Last updated: 2011-12-06Bibliographically approved
2. Stabilization of the Spectral-Element Method in Turbulent Flow Simulations
Open this publication in new window or tab >>Stabilization of the Spectral-Element Method in Turbulent Flow Simulations
2011 (English)In: Spectral and High Order Methods for Partial Differential Equations: Selected papers from the ICOSAHOM '09 conference, June 22-26, Trondheim, Norway, Springer , 2011, 1, 449-458 p.Conference paper, Published paper (Refereed)
Abstract [en]

The effect of over-integration and filter-based stabilization in the spectral-element method is investigated. There is a need to stabilize the SEM for flow problems involving non-smooth solutions, e.g., turbulent flow simulations. In model problems such as the Burgers’ equation (similar to Kirby and Karniadakis, J. Comput. Phys. 191:249–264, 2003) and the scalar transport equation together with full Navier–Stokes simulations it is noticed that over-integration with the full 3/2-rule is not required for stability. The first additional over-integration nodes are the most efficient to remove aliasing errors. Alternatively, filter-based stabilization can in many cases alone help to stabilize the computation.

Place, publisher, year, edition, pages
Springer, 2011 Edition: 1
Series
Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 76
Keyword
Aliasing error, Burgers' equations, Filter-based, Flow problems, Model problems, Navier Stokes simulation, Non-smooth, Scalar transport equation, SEM, Spectral element method
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-25931 (URN)10.1007/978-3-642-15337-2_43 (DOI)2-s2.0-78651526122 (Scopus ID)978-3-642-15336-5 (ISBN)
Conference
8th International Conference on Spectral and High Order Methods, ICOSAHOM'09; Trondheim; Norway; 22 June 2009 through 26 June 2009
Note

QC 20101105

Available from: 2010-11-05 Created: 2010-11-05 Last updated: 2013-11-06Bibliographically approved
3. Large-Eddy Simulation of Turbulent Flow in a Plane Asymmetric Diffuser by the Spectral-Element Method
Open this publication in new window or tab >>Large-Eddy Simulation of Turbulent Flow in a Plane Asymmetric Diffuser by the Spectral-Element Method
2010 (English)In: Direct and Large-Eddy Simulation VII: Proceedings of the Seventh International ERCOFTAC Workshop on Direct and Large-Eddy Simulation, held at the University of Trieste, September 8-10, 2008 / [ed] Vincenzo Armenio, Bernard Geurts; Jochen Fröhlich, Springer , 2010, 1, 193-199 p.Chapter in book (Other academic)
Abstract [en]

LES and no-model LES (coarse-grid DNS) have been performed of turbulent flow in a plane asymmetric diffuser by the Spectral-Element Method (SEM). Mean profile and turbulent stresses compare well to LES results from Herbst e, however the SEM generally predicts a later (i.e. further downstream) separation. It can be concluded that the use of a high-order method is advantageous for flows featuring pressure-induced separation.

Place, publisher, year, edition, pages
Springer, 2010 Edition: 1
Series
ERCOFTAC Series, ISSN 1382-4309 ; Vol 13, Part 2
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-25932 (URN)10.1007/978-90-481-3652-0_29 (DOI)000306194300029 ()978-90-481-3651-3 (ISBN)
Note

QC 20101105

Available from: 2010-11-05 Created: 2010-11-05 Last updated: 2013-05-06Bibliographically approved
4. Koopman mode decomposition of a minimal channel flow
Open this publication in new window or tab >>Koopman mode decomposition of a minimal channel flow
2010 (English)Report (Other academic)
National Category
Engineering and Technology
Research subject
SRA - E-Science (SeRC)
Identifiers
urn:nbn:se:kth:diva-50293 (URN)
Funder
Swedish e‐Science Research Center
Note
QC 20111206Available from: 2011-12-04 Created: 2011-12-04 Last updated: 2011-12-06Bibliographically approved
5. A vorticity stretching diagnostic for turbulent and transitional flows
Open this publication in new window or tab >>A vorticity stretching diagnostic for turbulent and transitional flows
2012 (English)In: Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, E-ISSN 1432-2250, Vol. 26, no 6, 485-499 p.Article in journal (Refereed) Published
Abstract [en]

Vorticity stretching in wall-bounded turbulent and transitional flows has been investigated by means of a new diagnostic measure, denoted by , designed to pick up regions with large amounts of vorticity stretching. It is based on the maximum vorticity stretching component in every spatial point, thus yielding athree-dimensional scalar field. The measure was applied in four different flows with increasing complexity: (a) the near-wall cycle in an asymptotic suction boundary layer (ASBL), (b) K-type transition in a plane channelflow, (c) fully turbulent channel flow at Reτ = 180 and (d) a complex turbulent three-dimensional separated flow. Instantaneous data show that the coherent structures associated with intense vorticity stretching in all four cases have the shape of flat ‘pancake’ structures in the vicinity of high-speed streaks, here denoted ‘h-type’events. The other event found is of ‘l-type’, present on top of an unstable low-speed streak. These events (l-type) are further thought to be associated with the exponential growth of streamwise vorticity in the turbulent near-wall cycle. It was found that the largest occurrence of vorticity stretching in the fully turbulent wall-bounded flows is present at a wall-normal distance of y + = 6.5, i.e. in the transition between the viscous sublayer and buffer layer. The associated structures have a streamwise length of ∼200–300 wall units. In K-type transition, the -measure accurately locates the regions of interest, in particular the formation of high-speed streaks nearthe wall (h-type) and the appearance of the hairpin vortex (l-type). In the turbulent separated flow, the structures containing large amounts of vorticity stretching increase in size and magnitude in the shear layer upstreamof the separation bubble but vanish in the backflow region itself. Overall, the measure proved to be useful inshowing growing instabilities before they develop into structures, highlighting the mechanisms creating high shear region on a wall and showing turbulence creation associated with instantaneous separations.

Keyword
Laminar-turbulent transition, vorticity stretching, turbulent flows
National Category
Engineering and Technology
Research subject
SRA - E-Science (SeRC)
Identifiers
urn:nbn:se:kth:diva-50287 (URN)10.1007/s00162-011-0245-7 (DOI)000310538000001 ()2-s2.0-84869080518 (Scopus ID)
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20121113

Available from: 2011-12-04 Created: 2011-12-04 Last updated: 2017-12-08Bibliographically approved
6. Direct numerical simulation of separated flow in a three-dimensional diffuser
Open this publication in new window or tab >>Direct numerical simulation of separated flow in a three-dimensional diffuser
2010 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 650, 307-318 p.Article in journal (Refereed) Published
Abstract [en]

A direct numerical simulation (DNS) of turbulent flow in a three-dimensional diffuser at Re = 10 000 (based on bulk velocity and inflow-duct height) was performed with a massively parallel high-order spectral element method running on up to 32 768 processors. Accurate inflow condition is ensured through unsteady trip forcing and a long development section. Mean flow results are in good agreement with experimental data by Cherry et al. (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803-811), in particular the separated region starting from one corner and gradually spreading to the top expanding diffuser wall. It is found that the corner vortices induced by the secondary flow in the duct persist into the diffuser, where they give rise to a dominant low-speed streak, due to a similar mechanism as the 'lift-up effect' in transitional shear flows, thus governing the separation behaviour. Well-resolved simulations of complex turbulent flows are thus possible even at realistic Reynolds numbers, providing accurate and detailed information about the flow physics. The available Reynolds stress budgets provide valuable references for future development of turbulence models.

Keyword
Bulk velocity, Complex turbulent flows, Experimental data, Flow physics, Heat fluid flow, High-order, Inflow conditions, Mean flow, Reynolds stress, Separated flows, Separated region, Separation behaviour, Spectral element method
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-25925 (URN)10.1017/S0022112010000558 (DOI)000278212500011 ()2-s2.0-77952428627 (Scopus ID)
Note
QC 20101105Available from: 2010-11-05 Created: 2010-11-05 Last updated: 2017-12-12Bibliographically approved
7. Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser
Open this publication in new window or tab >>Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 699, 320-351 p.Article in journal (Refereed) Published
Keyword
jets, separated flows, turbulence simulation
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-50288 (URN)10.1017/jfm.2012.107 (DOI)000303833300012 ()2-s2.0-84864262099 (Scopus ID)
Funder
Knut and Alice Wallenberg FoundationSwedish e‐Science Research Center
Note

Updated from submitted to published. QC 20120605

Available from: 2011-12-04 Created: 2011-12-04 Last updated: 2017-12-08Bibliographically approved

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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