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Numerical studies of transtion in wall-bounded flows
KTH, School of Engineering Sciences (SCI), Mechanics.
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Disturbances introduced in wall-bounded flows can grow and lead to transition from laminar to turbulent flow. In order to reduce losses or enhance mixing in energy systems, a fundamental understanding of the flow stability and transition mechanism is important. In the present thesis, the stability, transition mechanism and early turbulent evolution of wall-bounded flows are studied. The stability is investigated by means of linear stability equations and the transition mechanism and turbulence are studied using direct numerical simulations. Three base flows are considered, the Falkner-Skan boundary layer, boundary layers subjected to wall suction and the Blasius wall jet. The stability with respect to the exponential growth of waves and the algebraic growth of optimal streaks is studied for the Falkner-Skan boundary layer. For the algebraic growth, the optimal initial location, where the optimal disturbance is introduced in the boundary layer, is found to move downstream with decreased pressure gradient. A unified transition prediction method incorporating the influences of pressure gradient and free-stream turbulence is suggested. The algebraic growth of streaks in boundary layers subjected to wall suction is calculated. It is found that the spatial analysis gives larger optimal growth than temporal theory. Furthermore, it is found that the optimal growth is larger if the suction begins a distance downstream of the leading edge. Thresholds for transition of periodic and localized disturbances as well as the spreading of turbulent spots in the asymptotic suction boundary layer are investigated for Reynolds number Re=500, 800 and 1200 based on the displacement thickness and the free-stream velocity. It is found that the threshold amplitude scales like Re^-1.05 for transition initiated by streamwise vortices and random noise, like Re^-1.3 for oblique transition and like Re^-1.5 for the localized disturbance. The turbulent spot is found to take a bullet-shaped form that becomes more distinct and increases its spreading rate for higher Reynolds number. The Blasius wall jet is matched to the measured flow in an experimental wall-jet facility. Both the linear and nonlinear regime of introduced waves and streaks are investigated and compared to measurements. It is demonstrated that the streaks play an important role in the breakdown process where they suppress pairing and enhance breakdown to turbulence. Furthermore, statistics from the early turbulent regime are analyzed and reveal a reasonable self-similar behavior, which is most pronounced with inner scaling in the near-wall region.

Place, publisher, year, edition, pages
Stockholm: KTH , 2005. , viii, 48 p.
Series
Trita-MEK, ISSN 0348-467X ; 2005:17
Keyword [en]
boundary layer, suction, wall jet, streaks, waves, periodic disturbance, localized disturbance, turbulent spot, algebraic growth, exponential growth, stability, transition thresholds, transition prediction, PSE, DNS
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-546OAI: oai:DiVA.org:kth-546DiVA: diva2:14386
Public defence
2005-12-16, F3, F-huset, Lindstedsvägen 26, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20101025Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2010-10-25Bibliographically approved
List of papers
1. Exponential vs algebraic growth and transition prediction in boundary layer flow
Open this publication in new window or tab >>Exponential vs algebraic growth and transition prediction in boundary layer flow
2003 (English)In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 70, 183-210 p.Article in journal (Refereed) Published
Abstract [en]

For applications regarding transition prediction, wing design and control of boundary layers, the fundamental understanding of disturbance growth in the flat-plate boundary layer is an important issue. In the present work we investigate the energy growth of eigenmodes and non-modal optimal disturbances. We present a set of linear governing equations for the parabolic evolution of wavelike disturbances valid both for the exponential and algebraic growth scenario. The base flow is taken as the Falkner-Skan similarity solution with favorable, adverse and zero pressure gradients. The optimization is carried out over the initial streamwise position as well as the spanwise wave number and frequency. The exponential growth is maximized in the sense that the envelope of the most amplified eigenmode is calculated. In the case of algebraic growth, an adjoint-based optimization technique is used. We find that the optimal algebraic disturbance introduced at a certain downstream position gives rise to a larger growth than for the optimal disturbance introduced at the leading edge. The exponential and algebraic growth is compared and a unified transition-prediction method based on available experimental data is suggested.

Keyword
boundary layer, optimal disturbance, stability, transition prediction
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-8899 (URN)10.1023/B:APPL.0000004918.05683.46 (DOI)000186733100008 ()
Note
QC 20101021Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2017-12-14Bibliographically approved
2. Optimal disturbances in suction boundary layers.
Open this publication in new window or tab >>Optimal disturbances in suction boundary layers.
2007 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 26, no 3, 330-343 p.Article in journal (Refereed) Published
Abstract [en]

A well-known optimization procedure is used to find the optimal disturbances in two different suction boundary layers within the spatial framework. The maximum algebraic growth in the asymptotic suction boundary layer is presented and compared to previous temporal results. Furthermore, the spatial approach allows a study of a developing boundary layer in which a region at the leading edge is left free from suction. This new flow, which emulates the base flow of a recent wind-tunnel experiment, is herein denoted a semi-suction boundary layer. It is found that the optimal disturbances for these two suction boundary layers consist of streamwise vortices that develop into streamwise streaks, as previously found for a number of shear flows. It is shown that the maximum energy growth in the semi-suction boundary layer is obtained over the upstream region where no suction is applied. The result indicates that the spanwise scale of the streaks is set in this region, which is in agreement with previous experimental findings.

Keyword
Suction boundary layer, Optimal disturbance, Algebraic growth, Streamwise streaks, Free-stream turbulence
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-8900 (URN)10.1016/j.euromechflu.2006.07.003 (DOI)000245207500002 ()2-s2.0-33847247341 (Scopus ID)
Note
Uppdaterad från "In press" till published: 20101021. QC 20101021Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2017-12-14Bibliographically approved
3. A study of the Blasius wall jet
Open this publication in new window or tab >>A study of the Blasius wall jet
2005 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 539, 313-347 p.Article in journal (Refereed) Published
Abstract [en]

A plane wall-jet flow is numerically investigated and compared to experiments. The measured base flow is matched to a boundary-layer solution developing from a coupled Blasius boundary layer and Blasius shear layer. Linear stability analysis is performed, revealing high instability of two-dimensional eigenmodes and non-modal streaks. The nonlinear stage of laminar-flow breakdown is studied with three-dimensional direct numerical simulations and experimentally visualized. In the direct numerical simulation, an investigation of the nonlinear interaction between two-dimensional waves and streaks is made. The role of subharmonic waves and pairing of vortex rollers is also investigated. It is demonstrated that the streaks play an important role in the breakdown process, where their growth is transformed from algebraic to exponential as they become part of the secondary instability of the two-dimensional waves. In the presence of streaks, pairing is suppressed and breakdown to turbulence is enhanced.

Keyword
direct numerical-simulation, boundary-layer-flow, plane mixing layers, turbulent transition, instability, stability, suction, disturbances, receptivity, mechanism
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-8901 (URN)10.1017/S0022112005005628 (DOI)000232413800013 ()2-s2.0-33644596059 (Scopus ID)
Note
QC 20101021Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2017-12-14Bibliographically approved
4. Transition thresholds in the asymptotic suction boundary layer
Open this publication in new window or tab >>Transition thresholds in the asymptotic suction boundary layer
2005 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 17, no 12Article in journal (Refereed) Published
Abstract [en]

Energy thresholds for transition to turbulence in an asymptotic suction boundary layer is calculated by means of temporal direct numerical simulations. The temporal assumption limits the analysis to periodic disturbances with horizontal wave numbers determined by the computational box size. Three well known transition scenarios are investigated: oblique transition, the growth and breakdown of streaks triggered by streamwise vortices, and the development of random noise. Linear disturbance simulations and stability diagnostics are also performed for a base flow consisting of the suction boundary layer and a streak. The scenarios are found to trigger transition by similar mechanisms as obtained for other flows. Transition at the lowest initial energy is provided by the oblique wave scenario for the considered Reynolds numbers 500, 800, and 1200. The Reynolds number dependence on the energy thresholds are determined for each scenario. The threshold scales like Re-2.6 for oblique transition and like Re-2.1 for transition initiated by streamwise vortices and random noise, indicating that oblique transition has the lowest energy threshold also for larger Reynolds numbers.

Keyword
free-stream turbulence, plane poiseuille flow, localized disturbances, subcritical transition, oblique transition, bypass transition, pressure-gradient, algebraic growth, channel flows, shear flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-8902 (URN)10.1063/1.2136900 (DOI)000233603000019 ()2-s2.0-30044443822 (Scopus ID)
Note
Uppdaterad från "In press" till published: 20101021. QC 20101021Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2017-12-14Bibliographically approved
5. Turbulent spots in the asymptotic suction boundary layer
Open this publication in new window or tab >>Turbulent spots in the asymptotic suction boundary layer
2007 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 584, 397-413 p.Article in journal (Refereed) Published
Abstract [en]

Amplitude thresholds for transition of localized disturbances, their breakdown to turbulence and the development of turbulent spots in the asymptotic suction boundary layer are studied using direct numerical simulations. A parametric study of the horizontal scales of the initial disturbance is performed and the disturbances that lead to the highest growth under the conditions investigated are used in the simulations. The Reynolds-number dependence of the threshold amplitude of a localized disturbance is investigated for 500 <= Re <= 1200, based on the free-stream velocity and the displacement thickness. It is found that the threshold amplitude scales as Re-1.5 for the considered Reynolds numbers. For Re <= 367, the localized disturbance does not lead to a turbulent spot and this provides an estimate of the critical Reynolds number for the onset of turbulence. When the localized disturbance breaks down to a turbulent spot, it happens through the development of hairpin and spiral vortices. The shape and spreading rate of the turbulent spot are determined for Re = 500, 800 and 1200. Flow visualizations reveal that the turbulent spot takes a bullet-shaped form that becomes more distinct for higher Reynolds numbers. Long streaks extend in front of the spot and in its wake a calm region exists. The spreading rate of the turbulent spot is found to increase with increasing Reynolds number.

Keyword
plane poiseuille flow, adverse pressure-gradient, free-stream turbulence, couette-flow, localized disturbances, subcritical transition, numerical simulations, bypass transition, channel flows, shear flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-8903 (URN)10.1017/S0022112007006544 (DOI)000249137500018 ()2-s2.0-34547787137 (Scopus ID)
Note
Uppdaterad från manuskript till artikel: 20101025. QC 20101025Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2017-12-14Bibliographically approved
6. Early turbulent evolution of the Blasius wall jet
Open this publication in new window or tab >>Early turbulent evolution of the Blasius wall jet
2006 (English)In: Journal of turbulence, ISSN 1468-5248, E-ISSN 1468-5248, Vol. 7, 1-17 p.Article in journal (Refereed) Published
Abstract [en]

The first direct numerical simulation that is sufficiently large to study the self-similar behaviour of a turbulent wall jet is performed. The investigation is an extension of the simulation performed by Levin et al. (2005, A study of the Blasius wall jet. Journal of Fluid Mechanics, 539, 313-347). The same numerical method is used, but a significantly larger computational domain enables us to follow the development of the flow throughout the transition into its early turbulent evolution. Two-dimensional waves and streamwise elongated streaks, matched to measured disturbances, are introduced in the flow to trigger a natural transition mechanism. The Reynolds number is 3090 based on the inlet velocity and the nozzle height. The simulation provides detailed visualisations of the flow structures and statistics of mean flow and turbulent stresses. A weak subharmonic behaviour in the transition region is revealed by animations of the flow. The averaged data are presented in both inner and outer scalings in order to identify self-similar behaviour. Despite the low Reynolds number and the short computational domain, the turbulent flow exhibits a reasonable self-similar behaviour, which is most pronounced with inner scaling in the near-wall region

Keyword
Direct numerical simulation, Streaks, Transition; Turbulence, Wall jet
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-8904 (URN)10.1080/14685240600854884 (DOI)000242548700001 ()2-s2.0-33845970201 (Scopus ID)
Note
QC 20100830Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2017-12-14Bibliographically approved

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Citation style
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Output format
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