Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability

1994 ◽  
Vol 268 ◽  
pp. 1-36 ◽  
Author(s):  
M. R. Malik ◽  
F. Li ◽  
C.-L. Chang
Keyword(s):  
Boundary Layer ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Secondary Instability ◽  
Initial Amplitude ◽  
Swept Wing ◽  
Dimensional Boundary ◽  
Stationary Vortex ◽  
Downstream Development

Nonlinear stability of a model swept-wing boundary layer, subject to crossflow instability, is investigated by numerically solving the governing partial differential equations. The three-dimensional boundary layer is unstable to both stationary and travelling crossflow disturbances. Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble quite well the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in these calculations. Nonlinear interaction of the stationary and travelling waves is also studied. When initial amplitude of the stationary vortex is larger than the travelling mode, the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the travelling mode dominates the downstream development owing to its higher growth rate. It is also found that, prior to laminar/turbulent transition, the three-dimensional boundary layer is subject to a high-frequency secondary instability, which is in agreement with the experiments of Poll (1985) and Kohama, Saric & Hoos (1991). The frequency of this secondary instability, which resides on top of the stationary crossflow vortex, is an order of magnitude higher than the frequency of the most-amplified travelling crossflow mode.

Secondary instability of crossflow vortices and swept-wing boundary-layer transition

1999 ◽  
Vol 399 ◽  
pp. 85-115 ◽  
Author(s):  
MUJEEB R. MALIK ◽  
FEI LI ◽  
MEELAN M. CHOUDHARI ◽  
CHAU-LYAN CHANG
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Boundary Layer Transition ◽  
Swept Wing ◽  
Layer Transition ◽  
Transition Prediction ◽  
Dimensional Boundary

Crossflow instability of a three-dimensional boundary layer is a common cause of transition in swept-wing flows. The boundary-layer flow modified by the presence of finite-amplitude crossflow modes is susceptible to high-frequency secondary instabilities, which are believed to harbinger the onset of transition. The role of secondary instability in transition prediction is theoretically examined for the recent swept-wing experimental data by Reibert et al. (1996). Exploiting the experimental observation that the underlying three-dimensional boundary layer is convectively unstable, non-linear parabolized stability equations are used to compute a new basic state for the secondary instability analysis based on a two-dimensional eigenvalue approach. The predicted evolution of stationary crossflow vortices is in close agreement with the experimental data. The suppression of naturally dominant crossflow modes by artificial roughness distribution at a subcritical spacing is also confirmed. The analysis reveals a number of secondary instability modes belonging to two basic families which, in some sense, are akin to the ‘horseshoe’ and ‘sinuous’ modes of the Görtler vortex problem. The frequency range of the secondary instability is consistent with that measured in earlier experiments by Kohama et al. (1991), as is the overall growth of the secondary instability mode prior to the onset of transition (e.g. Kohama et al. 1996). Results indicate that the N-factor correlation based on secondary instability growth rates may yield a more robust criterion for transition onset prediction in comparison with an absolute amplitude criterion that is based on primary instability alone.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer

2002 ◽  
Vol 456 ◽  
pp. 49-84 ◽  
Author(s):  
PETER WASSERMANN ◽  
MARKUS KLOKER
Keyword(s):  
Boundary Layer ◽  
Passive Control ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Secondary Instability ◽  
Base Flow ◽  
Transition Control ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Underlying Mechanisms

Crossflow-vortex-induced laminar breakdown in a three-dimensional flat-plate boundary-layer flow is investigated in detail by means of spatial direct numerical simulations. The base flow is generic for an infinite swept wing, with decreasing favourable chordwise pressure gradient. First, the downstream growth and nonlinear saturation states initiated by a crossflow-vortex-mode packet as well as by single crossflow-vortex modes with various spanwise wavenumbers are simulated. Second, the secondary instability of the flow induced by the saturated crossflow vortices is scrutinized, clearly indicating the convective nature of the secondary instability and strengthening knowledge of the conditions for its onset. Emphasis is on the effect of crossflow-vortex-mode packets and of the spanwise vortex spacing on the secondary stability properties of the saturation states. Saturated uniform crossflow vortices initiated by single crossflow-vortex modes turn out to be less unstable than vortices initiated by a packet of vortex modes, and closely spaced saturated vortices are even stable. Third, we investigate the transition control strategy of upstream flow deformation by appropriate steady nonlinear vortex modes as applied in wind tunnel experiments at the Arizona State University. A significant transition delay is shown in the base flow considered here, and the underlying mechanisms are specified.

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