scholarly journals From primary instabilities to secondary instabilities in Görtler vortex flows

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Xi Chen ◽  
Jianqiang Chen ◽  
Xianxu Yuan ◽  
Guohua Tu ◽  
Yifeng Zhang
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Transformation Process ◽  
Secondary Instability ◽  
Direct Numerical Simulations ◽  
Boundary Layer Transition ◽  
Layer Transition ◽  
Mode Synchronization ◽  
Secondary Instabilities ◽  
Primary Instability

Abstract We have studied the transformation process from primary instabilities to secondary instabilities with direct numerical simulations and stability theories (Spatial Biglobal and plane-marching parabolized stability equations) in detail. First Mack mode and second Mack mode are shown to be able to evolve into the sinuous mode and the varicose mode of secondary instability, respectively. Although the characteristics of second Mack mode eventually lose in the downstream due to the synchronization with the continuous spectrum, second Mack mode is found to be able to trigger a sequence of mode resonations which in turn give birth to highly unstable secondary instabilities. In contrast, first Mack mode does not involve in any mode synchronization. Nevertheless, it can still “jump" to a sinuous mode of secondary instability with a much larger growth rate than that of the first Mack mode. Therefore, secondary instabilities of Görtler vortices are highly receptive to the primary instabilities in the upstream, so that one should consider the primary instability in the upstream and the secondary instability in the downstream as a whole in order to get an accurate prediction of the boundary layer transition.

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.

Boundary-layer transition by interaction of discrete and continuous modes

2008 ◽  
Vol 604 ◽  
pp. 199-233 ◽  
Author(s):  
YANG LIU ◽  
TAMER A. ZAKI ◽  
PAUL A. DURBIN
Keyword(s):  
Boundary Layer ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Boundary Layer Transition ◽  
Length Scale ◽  
Bypass Transition ◽  
Continuous Mode ◽  
Layer Transition ◽  
Boundary Layer Turbulence ◽  
Tollmien Schlichting

The natural and bypass routes to boundary-layer turbulence have traditionally been studied independently. In certain flow regimes, both transition mechanisms might coexist, and, if so, can interact. A nonlinear interaction of discrete and continuous Orr-Sommerfeld modes, which are at the origin of orderly and bypass transition, respectively, is found. It causes breakdown to turbulence, even though neither mode alone is sufficient. Direct numerical simulations of the interaction shows that breakdown occurs through a pattern of Λ-structures, similar to the secondary instability of Tollmien–Schlichting waves. However, the streaks produced by the Orr-Sommerfeld continuous mode set the spanwise length scale, which is much smaller than that of the secondary instability of Tollmien–Schlichting waves. Floquet analysis explains some of the features seen in the simulations as a competition between destabilizing and stabilizing interactions between finite-amplitude distortions.

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