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Exponential vs algebraic growth and transition prediction in boundary layer flow
KTH, Superseded Departments, Mechanics.
KTH, Superseded Departments, Mechanics.ORCID iD: 0000-0001-7864-3071
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.

Place, publisher, year, edition, pages
2003. Vol. 70, 183-210 p.
Keyword [en]
boundary layer, optimal disturbance, stability, transition prediction
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-8899DOI: 10.1023/B:APPL.0000004918.05683.46ISI: 000186733100008OAI: oai:DiVA.org:kth-8899DiVA: diva2:14380
Note
QC 20101021Available from: 2005-12-08 Created: 2005-12-08 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Numerical studies of transtion in wall-bounded flows
Open this publication in new window or tab >>Numerical studies of transtion in wall-bounded flows
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
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:nbn:se:kth:diva-546 (URN)
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

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